TSTP Solution File: DAT072_1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT072_1 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 14:36:37 EDT 2022
% Result : Theorem 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : DAT072_1 : TPTP v8.1.0. Released v6.1.0.
% 0.05/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 31 01:50:34 EDT 2022
% 0.13/0.35 % 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.
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 tff(read_type, type, (
% 0.20/0.42 read: ( array * $int ) > $int)).
% 0.20/0.42 tff(tptp_fun_I_0_type, type, (
% 0.20/0.42 tptp_fun_I_0: ( array * array ) > $int)).
% 0.20/0.42 tff(tptp_fun_B1_10_type, type, (
% 0.20/0.42 tptp_fun_B1_10: array)).
% 0.20/0.42 tff(tptp_fun_B2_9_type, type, (
% 0.20/0.42 tptp_fun_B2_9: array)).
% 0.20/0.42 tff(tptp_fun_N_8_type, type, (
% 0.20/0.42 tptp_fun_N_8: $int)).
% 0.20/0.42 tff(tptp_fun_A_11_type, type, (
% 0.20/0.42 tptp_fun_A_11: array)).
% 0.20/0.42 tff(1,assumption,(~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0)))), introduced(assumption)).
% 0.20/0.42 tff(2,plain,
% 0.20/0.42 (((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0))) | ((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(3,plain,
% 0.20/0.42 ((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.20/0.42 tff(4,assumption,((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0)), introduced(assumption)).
% 0.20/0.42 tff(5,assumption,(~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0)))), introduced(assumption)).
% 0.20/0.42 tff(6,plain,
% 0.20/0.42 (((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0))) | $greatereq(tptp_fun_I_0(B2!9, B1!10), 0)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(7,plain,
% 0.20/0.42 ($greatereq(tptp_fun_I_0(B2!9, B1!10), 0)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[6, 5])).
% 0.20/0.42 tff(8,plain,
% 0.20/0.42 (((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0))) | (~$lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(9,plain,
% 0.20/0.42 (~$lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[8, 5])).
% 0.20/0.42 tff(10,plain,
% 0.20/0.42 ((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))) | (~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(11,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[10, 9, 7, 4])).
% 0.20/0.42 tff(12,plain,(((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0))) | (~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 ((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[12, 3])).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 (^[I: $int] : refl(((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B2!9, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(A!11, I), $product(-1, read(B2!9, I))) = 0))))) <=> ((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B2!9, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(A!11, I), $product(-1, read(B2!9, I))) = 0))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 (![I: $int] : ((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B2!9, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(A!11, I), $product(-1, read(B2!9, I))) = 0))))) <=> ![I: $int] : ((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B2!9, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(A!11, I), $product(-1, read(B2!9, I))) = 0)))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 (^[I: $int] : trans(monotonicity(rewrite(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(B2!9, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)) <=> (~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B2!9, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0))))), rewrite((((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(A!11, I), $product(-1, read(B2!9, I))) = 0)) <=> (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(A!11, I), $product(-1, read(B2!9, I))) = 0))))), ((($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(B2!9, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)) | (((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(A!11, I), $product(-1, read(B2!9, I))) = 0))) <=> ((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B2!9, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(A!11, I), $product(-1, read(B2!9, I))) = 0))))))), rewrite(((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B2!9, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(A!11, I), $product(-1, read(B2!9, I))) = 0))))) <=> ((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B2!9, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(A!11, I), $product(-1, read(B2!9, I))) = 0)))))), ((($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(B2!9, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)) | (((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(A!11, I), $product(-1, read(B2!9, I))) = 0))) <=> ((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B2!9, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(A!11, I), $product(-1, read(B2!9, I))) = 0)))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 (![I: $int] : (($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(B2!9, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)) | (((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(A!11, I), $product(-1, read(B2!9, I))) = 0))) <=> ![I: $int] : ((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B2!9, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(A!11, I), $product(-1, read(B2!9, I))) = 0)))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[16])).
% 0.20/0.43 tff(18,plain,
% 0.20/0.43 (((![I: $int] : (($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(B1!10, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)) | (((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(B1!10, I), $product(-1, read(A!11, I))) = 0))) & ![I: $int] : (($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(B2!9, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)) | (((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(A!11, I), $product(-1, read(B2!9, I))) = 0)))) & (~(B1!10 = B2!9))) <=> (![I: $int] : (($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(B1!10, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)) | (((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(B1!10, I), $product(-1, read(A!11, I))) = 0))) & ![I: $int] : (($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(B2!9, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)) | (((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(A!11, I), $product(-1, read(B2!9, I))) = 0))) & (~(B1!10 = B2!9)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(19,plain,
% 0.20/0.43 ((![I: $int] : (($greatereq(I, 0) & (~$lesseq($sum(N!8, $product(-1, I)), 0)) & ($sum(read(B1!10, I), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, I)))))) = 0)) | (((~$greatereq(I, 0)) | $lesseq($sum(N!8, $product(-1, I)), 0)) & ($sum(read(B1!10, I), $product(-1, read(A!11, I))) = 0))) & ![I: $int] : (($greatereq(I, 0) & (~$lesseq($sum(N!8, $product(-1, I)), 0)) & ($sum(read(B2!9, I), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, I)))))) = 0)) | (((~$greatereq(I, 0)) | $lesseq($sum(N!8, $product(-1, I)), 0)) & ($sum(read(B2!9, I), $product(-1, read(A!11, I))) = 0)))) <=> (![I: $int] : (($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(B1!10, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)) | (((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(B1!10, I), $product(-1, read(A!11, I))) = 0))) & ![I: $int] : (($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(B2!9, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)) | (((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(A!11, I), $product(-1, read(B2!9, I))) = 0))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(20,plain,
% 0.20/0.43 (((![I: $int] : (($greatereq(I, 0) & (~$lesseq($sum(N!8, $product(-1, I)), 0)) & ($sum(read(B1!10, I), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, I)))))) = 0)) | (((~$greatereq(I, 0)) | $lesseq($sum(N!8, $product(-1, I)), 0)) & ($sum(read(B1!10, I), $product(-1, read(A!11, I))) = 0))) & ![I: $int] : (($greatereq(I, 0) & (~$lesseq($sum(N!8, $product(-1, I)), 0)) & ($sum(read(B2!9, I), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, I)))))) = 0)) | (((~$greatereq(I, 0)) | $lesseq($sum(N!8, $product(-1, I)), 0)) & ($sum(read(B2!9, I), $product(-1, read(A!11, I))) = 0)))) & (~(B1!10 = B2!9))) <=> ((![I: $int] : (($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(B1!10, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)) | (((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(B1!10, I), $product(-1, read(A!11, I))) = 0))) & ![I: $int] : (($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(B2!9, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)) | (((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(A!11, I), $product(-1, read(B2!9, I))) = 0)))) & (~(B1!10 = B2!9)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[19])).
% 0.20/0.43 tff(21,plain,
% 0.20/0.43 (((![I: $int] : (($greatereq(I, 0) & (~$lesseq($sum(N!8, $product(-1, I)), 0)) & ($sum(read(B1!10, I), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, I)))))) = 0)) | (((~$greatereq(I, 0)) | $lesseq($sum(N!8, $product(-1, I)), 0)) & ($sum(read(B1!10, I), $product(-1, read(A!11, I))) = 0))) & ![I: $int] : (($greatereq(I, 0) & (~$lesseq($sum(N!8, $product(-1, I)), 0)) & ($sum(read(B2!9, I), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, I)))))) = 0)) | (((~$greatereq(I, 0)) | $lesseq($sum(N!8, $product(-1, I)), 0)) & ($sum(read(B2!9, I), $product(-1, read(A!11, I))) = 0)))) & (~(B1!10 = B2!9))) <=> (![I: $int] : (($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(B1!10, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)) | (((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(B1!10, I), $product(-1, read(A!11, I))) = 0))) & ![I: $int] : (($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(B2!9, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)) | (((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(A!11, I), $product(-1, read(B2!9, I))) = 0))) & (~(B1!10 = B2!9)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[20, 18])).
% 0.20/0.43 tff(22,plain,
% 0.20/0.43 ((~![A: array, B1: array, B2: array, N: $int] : ((~(![I: $int] : (($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B1, I), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, I)))))) = 0)) | (((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B1, I), $product(-1, read(A, I))) = 0))) & ![I: $int] : (($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B2, I), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, I)))))) = 0)) | (((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B2, I), $product(-1, read(A, I))) = 0))))) | (B1 = B2))) <=> (~![A: array, B1: array, B2: array, N: $int] : ((~(![I: $int] : (($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B1, I), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, I)))))) = 0)) | (((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B1, I), $product(-1, read(A, I))) = 0))) & ![I: $int] : (($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B2, I), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, I)))))) = 0)) | (((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B2, I), $product(-1, read(A, I))) = 0))))) | (B1 = B2)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(23,plain,
% 0.20/0.43 ((~![A: array, B1: array, B2: array, N: $int] : ((~(![I: $int] : (($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B1, I), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, I)))))) = 0)) | (((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N)), 0)) & ($sum(read(B1, I), $product(-1, read(A, I))) = 0))) & ![I: $int] : (($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B2, I), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, I)))))) = 0)) | (((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N)), 0)) & ($sum(read(B2, I), $product(-1, read(A, I))) = 0))))) | (B1 = B2))) <=> (~![A: array, B1: array, B2: array, N: $int] : ((~(![I: $int] : (($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B1, I), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, I)))))) = 0)) | (((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B1, I), $product(-1, read(A, I))) = 0))) & ![I: $int] : (($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B2, I), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, I)))))) = 0)) | (((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B2, I), $product(-1, read(A, I))) = 0))))) | (B1 = B2)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(24,plain,
% 0.20/0.43 ((~![A: array, B1: array, B2: array, N: $int] : ((~(![I: $int] : (($greatereq(I, 0) & (~$lesseq(N, I)) & (read(B1, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))) | (((~$lesseq(0, I)) | $greatereq(I, N)) & (read(B1, I) = read(A, I)))) & ![I: $int] : (($greatereq(I, 0) & (~$lesseq(N, I)) & (read(B2, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))) | (((~$lesseq(0, I)) | $greatereq(I, N)) & (read(B2, I) = read(A, I)))))) | (B1 = B2))) <=> (~![A: array, B1: array, B2: array, N: $int] : ((~(![I: $int] : (($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B1, I), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, I)))))) = 0)) | (((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N)), 0)) & ($sum(read(B1, I), $product(-1, read(A, I))) = 0))) & ![I: $int] : (($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B2, I), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, I)))))) = 0)) | (((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N)), 0)) & ($sum(read(B2, I), $product(-1, read(A, I))) = 0))))) | (B1 = B2)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(25,plain,
% 0.20/0.43 ((~![A: array, B1: array, B2: array, N: $int] : ((~(![I: $int] : (($greatereq(I, 0) & (~$lesseq(N, I)) & (read(B1, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))) | (((~$lesseq(0, I)) | $greatereq(I, N)) & (read(B1, I) = read(A, I)))) & ![I: $int] : (($greatereq(I, 0) & (~$lesseq(N, I)) & (read(B2, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))) | (((~$lesseq(0, I)) | $greatereq(I, N)) & (read(B2, I) = read(A, I)))))) | (B1 = B2))) <=> (~![A: array, B1: array, B2: array, N: $int] : ((~(![I: $int] : (($greatereq(I, 0) & (~$lesseq(N, I)) & (read(B1, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))) | (((~$lesseq(0, I)) | $greatereq(I, N)) & (read(B1, I) = read(A, I)))) & ![I: $int] : (($greatereq(I, 0) & (~$lesseq(N, I)) & (read(B2, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))) | (((~$lesseq(0, I)) | $greatereq(I, N)) & (read(B2, I) = read(A, I)))))) | (B1 = B2)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(26,plain,
% 0.20/0.43 ((~![A: array, B1: array, B2: array, N: $int] : ((![I: $int] : ((($greatereq(I, 0) & $greater(N, I)) & (read(B1, I) = read(A, $difference(N, $sum(I, 1))))) | (($greater(0, I) | $greatereq(I, N)) & (read(B1, I) = read(A, I)))) & ![I: $int] : ((($greatereq(I, 0) & $greater(N, I)) & (read(B2, I) = read(A, $difference(N, $sum(I, 1))))) | (($greater(0, I) | $greatereq(I, N)) & (read(B2, I) = read(A, I))))) => (B1 = B2))) <=> (~![A: array, B1: array, B2: array, N: $int] : ((~(![I: $int] : (($greatereq(I, 0) & (~$lesseq(N, I)) & (read(B1, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))) | (((~$lesseq(0, I)) | $greatereq(I, N)) & (read(B1, I) = read(A, I)))) & ![I: $int] : (($greatereq(I, 0) & (~$lesseq(N, I)) & (read(B2, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))) | (((~$lesseq(0, I)) | $greatereq(I, N)) & (read(B2, I) = read(A, I)))))) | (B1 = B2)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(27,axiom,(~![A: array, B1: array, B2: array, N: $int] : ((![I: $int] : ((($greatereq(I, 0) & $greater(N, I)) & (read(B1, I) = read(A, $difference(N, $sum(I, 1))))) | (($greater(0, I) | $greatereq(I, N)) & (read(B1, I) = read(A, I)))) & ![I: $int] : ((($greatereq(I, 0) & $greater(N, I)) & (read(B2, I) = read(A, $difference(N, $sum(I, 1))))) | (($greater(0, I) | $greatereq(I, N)) & (read(B2, I) = read(A, I))))) => (B1 = B2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c')).
% 0.20/0.43 tff(28,plain,
% 0.20/0.43 (~![A: array, B1: array, B2: array, N: $int] : ((~(![I: $int] : (($greatereq(I, 0) & (~$lesseq(N, I)) & (read(B1, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))) | (((~$lesseq(0, I)) | $greatereq(I, N)) & (read(B1, I) = read(A, I)))) & ![I: $int] : (($greatereq(I, 0) & (~$lesseq(N, I)) & (read(B2, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))) | (((~$lesseq(0, I)) | $greatereq(I, N)) & (read(B2, I) = read(A, I)))))) | (B1 = B2))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.43 tff(29,plain,
% 0.20/0.43 (~![A: array, B1: array, B2: array, N: $int] : ((~(![I: $int] : (($greatereq(I, 0) & (~$lesseq(N, I)) & (read(B1, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))) | (((~$lesseq(0, I)) | $greatereq(I, N)) & (read(B1, I) = read(A, I)))) & ![I: $int] : (($greatereq(I, 0) & (~$lesseq(N, I)) & (read(B2, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))) | (((~$lesseq(0, I)) | $greatereq(I, N)) & (read(B2, I) = read(A, I)))))) | (B1 = B2))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[28, 25])).
% 0.20/0.43 tff(30,plain,
% 0.20/0.43 (~![A: array, B1: array, B2: array, N: $int] : ((~(![I: $int] : (($greatereq(I, 0) & (~$lesseq(N, I)) & (read(B1, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))) | (((~$lesseq(0, I)) | $greatereq(I, N)) & (read(B1, I) = read(A, I)))) & ![I: $int] : (($greatereq(I, 0) & (~$lesseq(N, I)) & (read(B2, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))) | (((~$lesseq(0, I)) | $greatereq(I, N)) & (read(B2, I) = read(A, I)))))) | (B1 = B2))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.20/0.43 tff(31,plain,
% 0.20/0.43 (~![A: array, B1: array, B2: array, N: $int] : ((~(![I: $int] : (($greatereq(I, 0) & (~$lesseq(N, I)) & (read(B1, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))) | (((~$lesseq(0, I)) | $greatereq(I, N)) & (read(B1, I) = read(A, I)))) & ![I: $int] : (($greatereq(I, 0) & (~$lesseq(N, I)) & (read(B2, I) = read(A, $sum(-1, $sum(N, $product(-1, I)))))) | (((~$lesseq(0, I)) | $greatereq(I, N)) & (read(B2, I) = read(A, I)))))) | (B1 = B2))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[30, 25])).
% 0.20/0.43 tff(32,plain,
% 0.20/0.43 (~![A: array, B1: array, B2: array, N: $int] : ((~(![I: $int] : (($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B1, I), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, I)))))) = 0)) | (((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N)), 0)) & ($sum(read(B1, I), $product(-1, read(A, I))) = 0))) & ![I: $int] : (($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B2, I), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, I)))))) = 0)) | (((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N)), 0)) & ($sum(read(B2, I), $product(-1, read(A, I))) = 0))))) | (B1 = B2))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.20/0.43 tff(33,plain,
% 0.20/0.43 (~![A: array, B1: array, B2: array, N: $int] : ((~(![I: $int] : (($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B1, I), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, I)))))) = 0)) | (((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B1, I), $product(-1, read(A, I))) = 0))) & ![I: $int] : (($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B2, I), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, I)))))) = 0)) | (((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B2, I), $product(-1, read(A, I))) = 0))))) | (B1 = B2))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[32, 23])).
% 0.20/0.43 tff(34,plain,
% 0.20/0.43 (~![A: array, B1: array, B2: array, N: $int] : ((~(![I: $int] : (($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B1, I), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, I)))))) = 0)) | (((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B1, I), $product(-1, read(A, I))) = 0))) & ![I: $int] : (($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B2, I), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, I)))))) = 0)) | (((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B2, I), $product(-1, read(A, I))) = 0))))) | (B1 = B2))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[33, 22])).
% 0.20/0.43 tff(35,plain,
% 0.20/0.43 (~![A: array, B1: array, B2: array, N: $int] : ((~(![I: $int] : (($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B1, I), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, I)))))) = 0)) | (((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B1, I), $product(-1, read(A, I))) = 0))) & ![I: $int] : (($greatereq(I, 0) & (~$lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B2, I), $product(-1, read(A, $sum(-1, $sum(N, $product(-1, I)))))) = 0)) | (((~$greatereq(I, 0)) | $lesseq($sum(N, $product(-1, I)), 0)) & ($sum(read(B2, I), $product(-1, read(A, I))) = 0))))) | (B1 = B2))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[34, 22])).
% 0.20/0.43 tff(36,plain,
% 0.20/0.43 (![I: $int] : (($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(B1!10, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)) | (((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(B1!10, I), $product(-1, read(A!11, I))) = 0))) & ![I: $int] : (($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(B2!9, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)) | (((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(A!11, I), $product(-1, read(B2!9, I))) = 0))) & (~(B1!10 = B2!9))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[35, 21])).
% 0.20/0.43 tff(37,plain,
% 0.20/0.43 (![I: $int] : (($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(B2!9, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)) | (((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(A!11, I), $product(-1, read(B2!9, I))) = 0)))),
% 0.20/0.43 inference(and_elim,[status(thm)],[36])).
% 0.20/0.43 tff(38,plain,
% 0.20/0.43 (![I: $int] : ((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B2!9, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(A!11, I), $product(-1, read(B2!9, I))) = 0)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[37, 17])).
% 0.20/0.43 tff(39,plain,
% 0.20/0.43 (![I: $int] : ((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B2!9, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(A!11, I), $product(-1, read(B2!9, I))) = 0)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[38, 15])).
% 0.20/0.43 tff(40,plain,
% 0.20/0.43 (((~![I: $int] : ((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B2!9, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(A!11, I), $product(-1, read(B2!9, I))) = 0)))))) | ((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0)))))) <=> ((~![I: $int] : ((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B2!9, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(A!11, I), $product(-1, read(B2!9, I))) = 0)))))) | (~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(41,plain,
% 0.20/0.43 (((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0))))) <=> ((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(42,plain,
% 0.20/0.44 ((~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $greatereq($sum(tptp_fun_I_0(B2!9, B1!10), $product(-1, N!8)), 0))) | (~($sum(read(A!11, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(B2!9, tptp_fun_I_0(B2!9, B1!10)))) = 0)))) <=> (~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(43,plain,
% 0.20/0.44 ((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $greatereq($sum(tptp_fun_I_0(B2!9, B1!10), $product(-1, N!8)), 0) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum($product(-1, tptp_fun_I_0(B2!9, B1!10)), N!8))))) = 0)))) <=> (~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(44,plain,
% 0.20/0.44 (((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $greatereq($sum(tptp_fun_I_0(B2!9, B1!10), $product(-1, N!8)), 0) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum($product(-1, tptp_fun_I_0(B2!9, B1!10)), N!8))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $greatereq($sum(tptp_fun_I_0(B2!9, B1!10), $product(-1, N!8)), 0))) | (~($sum(read(A!11, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(B2!9, tptp_fun_I_0(B2!9, B1!10)))) = 0))))) <=> ((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0)))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[43, 42])).
% 0.20/0.44 tff(45,plain,
% 0.20/0.44 (((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $greatereq($sum(tptp_fun_I_0(B2!9, B1!10), $product(-1, N!8)), 0) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum($product(-1, tptp_fun_I_0(B2!9, B1!10)), N!8))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $greatereq($sum(tptp_fun_I_0(B2!9, B1!10), $product(-1, N!8)), 0))) | (~($sum(read(A!11, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(B2!9, tptp_fun_I_0(B2!9, B1!10)))) = 0))))) <=> ((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0)))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[44, 41])).
% 0.20/0.44 tff(46,plain,
% 0.20/0.44 (((~![I: $int] : ((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B2!9, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(A!11, I), $product(-1, read(B2!9, I))) = 0)))))) | ((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $greatereq($sum(tptp_fun_I_0(B2!9, B1!10), $product(-1, N!8)), 0) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum($product(-1, tptp_fun_I_0(B2!9, B1!10)), N!8))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $greatereq($sum(tptp_fun_I_0(B2!9, B1!10), $product(-1, N!8)), 0))) | (~($sum(read(A!11, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(B2!9, tptp_fun_I_0(B2!9, B1!10)))) = 0)))))) <=> ((~![I: $int] : ((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B2!9, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(A!11, I), $product(-1, read(B2!9, I))) = 0)))))) | ((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0))))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[45])).
% 0.20/0.44 tff(47,plain,
% 0.20/0.44 (((~![I: $int] : ((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B2!9, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(A!11, I), $product(-1, read(B2!9, I))) = 0)))))) | ((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $greatereq($sum(tptp_fun_I_0(B2!9, B1!10), $product(-1, N!8)), 0) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum($product(-1, tptp_fun_I_0(B2!9, B1!10)), N!8))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $greatereq($sum(tptp_fun_I_0(B2!9, B1!10), $product(-1, N!8)), 0))) | (~($sum(read(A!11, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(B2!9, tptp_fun_I_0(B2!9, B1!10)))) = 0)))))) <=> ((~![I: $int] : ((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B2!9, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(A!11, I), $product(-1, read(B2!9, I))) = 0)))))) | (~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0)))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[46, 40])).
% 0.20/0.44 tff(48,plain,
% 0.20/0.44 ((~![I: $int] : ((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B2!9, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(A!11, I), $product(-1, read(B2!9, I))) = 0)))))) | ((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $greatereq($sum(tptp_fun_I_0(B2!9, B1!10), $product(-1, N!8)), 0) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum($product(-1, tptp_fun_I_0(B2!9, B1!10)), N!8))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $greatereq($sum(tptp_fun_I_0(B2!9, B1!10), $product(-1, N!8)), 0))) | (~($sum(read(A!11, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(B2!9, tptp_fun_I_0(B2!9, B1!10)))) = 0)))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(49,plain,
% 0.20/0.44 ((~![I: $int] : ((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B2!9, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(A!11, I), $product(-1, read(B2!9, I))) = 0)))))) | (~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.20/0.44 tff(50,plain,
% 0.20/0.44 ((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[49, 39])).
% 0.20/0.44 tff(51,plain,
% 0.20/0.44 (~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[50, 13])).
% 0.20/0.44 tff(52,plain,
% 0.20/0.44 (((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0))) | ($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(53,plain,
% 0.20/0.44 ($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.20/0.44 tff(54,plain,
% 0.20/0.44 ((~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0)) | $lesseq($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))), 0)),
% 0.20/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.44 tff(55,plain,
% 0.20/0.44 ($lesseq($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))), 0)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.20/0.44 tff(56,plain,
% 0.20/0.44 ((~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0)) | $greatereq($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))), 0)),
% 0.20/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.44 tff(57,plain,
% 0.20/0.44 ($greatereq($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))), 0)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[56, 53])).
% 0.20/0.44 tff(58,plain,
% 0.20/0.44 (((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0))) | ($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(59,plain,
% 0.20/0.44 ($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[58, 1])).
% 0.20/0.44 tff(60,plain,
% 0.20/0.44 ((~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0)) | $lesseq($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))), 0)),
% 0.20/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.44 tff(61,plain,
% 0.20/0.44 ($lesseq($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))), 0)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.20/0.45 tff(62,assumption,($greatereq($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))), 0)), introduced(assumption)).
% 0.20/0.45 tff(63,assumption,(~$greatereq($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(B1!10, tptp_fun_I_0(B2!9, B1!10)))), 0)), introduced(assumption)).
% 0.20/0.45 tff(64,assumption,($lesseq($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))), 0)), introduced(assumption)).
% 0.20/0.45 tff(65,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(theory_lemma,[status(thm)],[64, 63, 62])).
% 0.20/0.45 tff(66,plain,($greatereq($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(B1!10, tptp_fun_I_0(B2!9, B1!10)))), 0) | (~$lesseq($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))), 0)) | (~$greatereq($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))), 0))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(67,plain,
% 0.20/0.45 ($greatereq($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(B1!10, tptp_fun_I_0(B2!9, B1!10)))), 0)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[66, 61, 57])).
% 0.20/0.45 tff(68,plain,
% 0.20/0.45 (~(B1!10 = B2!9)),
% 0.20/0.45 inference(and_elim,[status(thm)],[36])).
% 0.20/0.45 tff(69,plain,
% 0.20/0.45 (^[A: array, B: array] : rewrite(((~($sum(read(B, tptp_fun_I_0(B, A)), $product(-1, read(A, tptp_fun_I_0(B, A)))) = 0)) | (A = B)) <=> ((~($sum(read(A, tptp_fun_I_0(B, A)), $product(-1, read(B, tptp_fun_I_0(B, A)))) = 0)) | (A = B)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(70,plain,
% 0.20/0.45 (![A: array, B: array] : ((~($sum(read(B, tptp_fun_I_0(B, A)), $product(-1, read(A, tptp_fun_I_0(B, A)))) = 0)) | (A = B)) <=> ![A: array, B: array] : ((~($sum(read(A, tptp_fun_I_0(B, A)), $product(-1, read(B, tptp_fun_I_0(B, A)))) = 0)) | (A = B))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[69])).
% 0.20/0.45 tff(71,plain,
% 0.20/0.45 (^[A: array, B: array] : rewrite(((~![I: $int] : ($sum(read(A, I), $product(-1, read(B, I))) = 0)) | (A = B)) <=> ((~![I: $int] : ($sum(read(B, I), $product(-1, read(A, I))) = 0)) | (A = B)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(72,plain,
% 0.20/0.45 (![A: array, B: array] : ((~![I: $int] : ($sum(read(A, I), $product(-1, read(B, I))) = 0)) | (A = B)) <=> ![A: array, B: array] : ((~![I: $int] : ($sum(read(B, I), $product(-1, read(A, I))) = 0)) | (A = B))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[71])).
% 0.20/0.45 tff(73,plain,
% 0.20/0.45 (^[A: array, B: array] : rewrite(((~![I: $int] : (read(A, I) = read(B, I))) | (A = B)) <=> ((~![I: $int] : ($sum(read(A, I), $product(-1, read(B, I))) = 0)) | (A = B)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(74,plain,
% 0.20/0.45 (![A: array, B: array] : ((~![I: $int] : (read(A, I) = read(B, I))) | (A = B)) <=> ![A: array, B: array] : ((~![I: $int] : ($sum(read(A, I), $product(-1, read(B, I))) = 0)) | (A = B))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[73])).
% 0.20/0.45 tff(75,plain,
% 0.20/0.45 (![A: array, B: array] : ((~![I: $int] : (read(A, I) = read(B, I))) | (A = B)) <=> ![A: array, B: array] : ((~![I: $int] : (read(A, I) = read(B, I))) | (A = B))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(76,plain,
% 0.20/0.45 (^[A: array, B: array] : rewrite((![I: $int] : (read(A, I) = read(B, I)) => (A = B)) <=> ((~![I: $int] : (read(A, I) = read(B, I))) | (A = B)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(77,plain,
% 0.20/0.45 (![A: array, B: array] : (![I: $int] : (read(A, I) = read(B, I)) => (A = B)) <=> ![A: array, B: array] : ((~![I: $int] : (read(A, I) = read(B, I))) | (A = B))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[76])).
% 0.20/0.45 tff(78,axiom,(![A: array, B: array] : (![I: $int] : (read(A, I) = read(B, I)) => (A = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ext')).
% 0.20/0.45 tff(79,plain,
% 0.20/0.45 (![A: array, B: array] : ((~![I: $int] : (read(A, I) = read(B, I))) | (A = B))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.45 tff(80,plain,
% 0.20/0.45 (![A: array, B: array] : ((~![I: $int] : (read(A, I) = read(B, I))) | (A = B))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.20/0.45 tff(81,plain,
% 0.20/0.45 (![A: array, B: array] : ((~![I: $int] : ($sum(read(A, I), $product(-1, read(B, I))) = 0)) | (A = B))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[80, 74])).
% 0.20/0.45 tff(82,plain,
% 0.20/0.45 (![A: array, B: array] : ((~![I: $int] : ($sum(read(B, I), $product(-1, read(A, I))) = 0)) | (A = B))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[81, 72])).
% 0.20/0.45 tff(83,plain,(
% 0.20/0.45 ![A: array, B: array] : ((~($sum(read(B, tptp_fun_I_0(B, A)), $product(-1, read(A, tptp_fun_I_0(B, A)))) = 0)) | (A = B))),
% 0.20/0.45 inference(skolemize,[status(sab)],[82])).
% 0.20/0.45 tff(84,plain,
% 0.20/0.45 (![A: array, B: array] : ((~($sum(read(A, tptp_fun_I_0(B, A)), $product(-1, read(B, tptp_fun_I_0(B, A)))) = 0)) | (A = B))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[83, 70])).
% 0.20/0.45 tff(85,plain,
% 0.20/0.45 (((~![A: array, B: array] : ((~($sum(read(A, tptp_fun_I_0(B, A)), $product(-1, read(B, tptp_fun_I_0(B, A)))) = 0)) | (A = B))) | ((~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(B1!10, tptp_fun_I_0(B2!9, B1!10)))) = 0)) | (B1!10 = B2!9))) <=> ((~![A: array, B: array] : ((~($sum(read(A, tptp_fun_I_0(B, A)), $product(-1, read(B, tptp_fun_I_0(B, A)))) = 0)) | (A = B))) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(B1!10, tptp_fun_I_0(B2!9, B1!10)))) = 0)) | (B1!10 = B2!9))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(86,plain,
% 0.20/0.45 (((~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(B2!9, tptp_fun_I_0(B2!9, B1!10)))) = 0)) | (B1!10 = B2!9)) <=> ((~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(B1!10, tptp_fun_I_0(B2!9, B1!10)))) = 0)) | (B1!10 = B2!9))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(87,plain,
% 0.20/0.45 (((~![A: array, B: array] : ((~($sum(read(A, tptp_fun_I_0(B, A)), $product(-1, read(B, tptp_fun_I_0(B, A)))) = 0)) | (A = B))) | ((~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(B2!9, tptp_fun_I_0(B2!9, B1!10)))) = 0)) | (B1!10 = B2!9))) <=> ((~![A: array, B: array] : ((~($sum(read(A, tptp_fun_I_0(B, A)), $product(-1, read(B, tptp_fun_I_0(B, A)))) = 0)) | (A = B))) | ((~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(B1!10, tptp_fun_I_0(B2!9, B1!10)))) = 0)) | (B1!10 = B2!9)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[86])).
% 0.20/0.45 tff(88,plain,
% 0.20/0.45 (((~![A: array, B: array] : ((~($sum(read(A, tptp_fun_I_0(B, A)), $product(-1, read(B, tptp_fun_I_0(B, A)))) = 0)) | (A = B))) | ((~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(B2!9, tptp_fun_I_0(B2!9, B1!10)))) = 0)) | (B1!10 = B2!9))) <=> ((~![A: array, B: array] : ((~($sum(read(A, tptp_fun_I_0(B, A)), $product(-1, read(B, tptp_fun_I_0(B, A)))) = 0)) | (A = B))) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(B1!10, tptp_fun_I_0(B2!9, B1!10)))) = 0)) | (B1!10 = B2!9))),
% 0.20/0.45 inference(transitivity,[status(thm)],[87, 85])).
% 0.20/0.45 tff(89,plain,
% 0.20/0.45 ((~![A: array, B: array] : ((~($sum(read(A, tptp_fun_I_0(B, A)), $product(-1, read(B, tptp_fun_I_0(B, A)))) = 0)) | (A = B))) | ((~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(B2!9, tptp_fun_I_0(B2!9, B1!10)))) = 0)) | (B1!10 = B2!9))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(90,plain,
% 0.20/0.45 ((~![A: array, B: array] : ((~($sum(read(A, tptp_fun_I_0(B, A)), $product(-1, read(B, tptp_fun_I_0(B, A)))) = 0)) | (A = B))) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(B1!10, tptp_fun_I_0(B2!9, B1!10)))) = 0)) | (B1!10 = B2!9)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.20/0.45 tff(91,plain,
% 0.20/0.45 (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(B1!10, tptp_fun_I_0(B2!9, B1!10)))) = 0)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[90, 84, 68])).
% 0.20/0.45 tff(92,plain,
% 0.20/0.45 (($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(B1!10, tptp_fun_I_0(B2!9, B1!10)))) = 0) | (~$lesseq($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(B1!10, tptp_fun_I_0(B2!9, B1!10)))), 0)) | (~$greatereq($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(B1!10, tptp_fun_I_0(B2!9, B1!10)))), 0))),
% 0.20/0.45 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.45 tff(93,plain,
% 0.20/0.45 ((~$lesseq($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(B1!10, tptp_fun_I_0(B2!9, B1!10)))), 0)) | (~$greatereq($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(B1!10, tptp_fun_I_0(B2!9, B1!10)))), 0))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.20/0.45 tff(94,plain,
% 0.20/0.45 (~$lesseq($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(B1!10, tptp_fun_I_0(B2!9, B1!10)))), 0)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[93, 67])).
% 0.20/0.45 tff(95,plain,
% 0.20/0.45 ((~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0)) | $greatereq($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))), 0)),
% 0.20/0.45 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.45 tff(96,plain,
% 0.20/0.45 ($greatereq($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))), 0)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[95, 59])).
% 0.20/0.45 tff(97,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(theory_lemma,[status(thm)],[96, 94, 55])).
% 0.20/0.45 tff(98,plain,((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(99,plain,
% 0.20/0.45 (^[I: $int] : refl(((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B1!10, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(B1!10, I), $product(-1, read(A!11, I))) = 0))))) <=> ((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B1!10, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(B1!10, I), $product(-1, read(A!11, I))) = 0))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(100,plain,
% 0.20/0.45 (![I: $int] : ((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B1!10, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(B1!10, I), $product(-1, read(A!11, I))) = 0))))) <=> ![I: $int] : ((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B1!10, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(B1!10, I), $product(-1, read(A!11, I))) = 0)))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[99])).
% 0.20/0.45 tff(101,plain,
% 0.20/0.45 (^[I: $int] : trans(monotonicity(rewrite(($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(B1!10, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)) <=> (~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B1!10, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0))))), rewrite((((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(B1!10, I), $product(-1, read(A!11, I))) = 0)) <=> (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(B1!10, I), $product(-1, read(A!11, I))) = 0))))), ((($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(B1!10, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)) | (((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(B1!10, I), $product(-1, read(A!11, I))) = 0))) <=> ((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B1!10, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(B1!10, I), $product(-1, read(A!11, I))) = 0))))))), rewrite(((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B1!10, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(B1!10, I), $product(-1, read(A!11, I))) = 0))))) <=> ((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B1!10, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(B1!10, I), $product(-1, read(A!11, I))) = 0)))))), ((($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(B1!10, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)) | (((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(B1!10, I), $product(-1, read(A!11, I))) = 0))) <=> ((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B1!10, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(B1!10, I), $product(-1, read(A!11, I))) = 0)))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(102,plain,
% 0.20/0.45 (![I: $int] : (($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(B1!10, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)) | (((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(B1!10, I), $product(-1, read(A!11, I))) = 0))) <=> ![I: $int] : ((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B1!10, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(B1!10, I), $product(-1, read(A!11, I))) = 0)))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[101])).
% 0.20/0.45 tff(103,plain,
% 0.20/0.45 (![I: $int] : (($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(B1!10, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)) | (((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0)) & ($sum(read(B1!10, I), $product(-1, read(A!11, I))) = 0)))),
% 0.20/0.45 inference(and_elim,[status(thm)],[36])).
% 0.20/0.45 tff(104,plain,
% 0.20/0.45 (![I: $int] : ((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B1!10, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(B1!10, I), $product(-1, read(A!11, I))) = 0)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.20/0.45 tff(105,plain,
% 0.20/0.45 (![I: $int] : ((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B1!10, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(B1!10, I), $product(-1, read(A!11, I))) = 0)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.20/0.45 tff(106,plain,
% 0.20/0.45 (((~![I: $int] : ((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B1!10, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(B1!10, I), $product(-1, read(A!11, I))) = 0)))))) | ((~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0)))) | (~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0)))))) <=> ((~![I: $int] : ((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B1!10, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(B1!10, I), $product(-1, read(A!11, I))) = 0)))))) | (~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0)))) | (~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(107,plain,
% 0.20/0.46 (((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0))))) <=> ((~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0)))) | (~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(108,plain,
% 0.20/0.46 ((~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $greatereq($sum(tptp_fun_I_0(B2!9, B1!10), $product(-1, N!8)), 0))) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0)))) <=> (~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(109,plain,
% 0.20/0.46 ((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $greatereq($sum(tptp_fun_I_0(B2!9, B1!10), $product(-1, N!8)), 0) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum($product(-1, tptp_fun_I_0(B2!9, B1!10)), N!8))))) = 0)))) <=> (~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(110,plain,
% 0.20/0.46 (((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $greatereq($sum(tptp_fun_I_0(B2!9, B1!10), $product(-1, N!8)), 0) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum($product(-1, tptp_fun_I_0(B2!9, B1!10)), N!8))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $greatereq($sum(tptp_fun_I_0(B2!9, B1!10), $product(-1, N!8)), 0))) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0))))) <=> ((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0)))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[109, 108])).
% 0.20/0.46 tff(111,plain,
% 0.20/0.46 (((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $greatereq($sum(tptp_fun_I_0(B2!9, B1!10), $product(-1, N!8)), 0) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum($product(-1, tptp_fun_I_0(B2!9, B1!10)), N!8))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $greatereq($sum(tptp_fun_I_0(B2!9, B1!10), $product(-1, N!8)), 0))) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0))))) <=> ((~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0)))) | (~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0)))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[110, 107])).
% 0.20/0.46 tff(112,plain,
% 0.20/0.46 (((~![I: $int] : ((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B1!10, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(B1!10, I), $product(-1, read(A!11, I))) = 0)))))) | ((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $greatereq($sum(tptp_fun_I_0(B2!9, B1!10), $product(-1, N!8)), 0) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum($product(-1, tptp_fun_I_0(B2!9, B1!10)), N!8))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $greatereq($sum(tptp_fun_I_0(B2!9, B1!10), $product(-1, N!8)), 0))) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0)))))) <=> ((~![I: $int] : ((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B1!10, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(B1!10, I), $product(-1, read(A!11, I))) = 0)))))) | ((~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0)))) | (~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0))))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[111])).
% 0.20/0.46 tff(113,plain,
% 0.20/0.46 (((~![I: $int] : ((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B1!10, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(B1!10, I), $product(-1, read(A!11, I))) = 0)))))) | ((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $greatereq($sum(tptp_fun_I_0(B2!9, B1!10), $product(-1, N!8)), 0) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum($product(-1, tptp_fun_I_0(B2!9, B1!10)), N!8))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $greatereq($sum(tptp_fun_I_0(B2!9, B1!10), $product(-1, N!8)), 0))) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0)))))) <=> ((~![I: $int] : ((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B1!10, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(B1!10, I), $product(-1, read(A!11, I))) = 0)))))) | (~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0)))) | (~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0)))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[112, 106])).
% 0.20/0.46 tff(114,plain,
% 0.20/0.46 ((~![I: $int] : ((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B1!10, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(B1!10, I), $product(-1, read(A!11, I))) = 0)))))) | ((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $greatereq($sum(tptp_fun_I_0(B2!9, B1!10), $product(-1, N!8)), 0) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum($product(-1, tptp_fun_I_0(B2!9, B1!10)), N!8))))) = 0)))) | (~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $greatereq($sum(tptp_fun_I_0(B2!9, B1!10), $product(-1, N!8)), 0))) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0)))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(115,plain,
% 0.20/0.46 ((~![I: $int] : ((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0) | (~($sum(read(B1!10, I), $product(-1, read(A!11, $sum(-1, $sum($product(-1, I), N!8))))) = 0)))) | (~((~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!8)), 0))) | (~($sum(read(B1!10, I), $product(-1, read(A!11, I))) = 0)))))) | (~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0)))) | (~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.20/0.46 tff(116,plain,
% 0.20/0.46 ((~((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0)))) | (~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[115, 105])).
% 0.20/0.46 tff(117,plain,
% 0.20/0.46 (~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[116, 98])).
% 0.20/0.46 tff(118,plain,
% 0.20/0.46 (((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0))) | $greatereq(tptp_fun_I_0(B2!9, B1!10), 0)),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(119,plain,
% 0.20/0.46 ($greatereq(tptp_fun_I_0(B2!9, B1!10), 0)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.20/0.46 tff(120,plain,
% 0.20/0.46 (((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0))) | (~$lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(121,plain,
% 0.20/0.46 (~$lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[120, 117])).
% 0.20/0.46 tff(122,plain,
% 0.20/0.46 (~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[10, 121, 119])).
% 0.20/0.46 tff(123,plain,
% 0.20/0.46 (((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0))) | ((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(124,plain,
% 0.20/0.47 ((~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0))) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, tptp_fun_I_0(B2!9, B1!10)))) = 0))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.20/0.47 tff(125,plain,
% 0.20/0.47 (~((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[50, 124])).
% 0.20/0.47 tff(126,plain,
% 0.20/0.47 (((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0) | (~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0))) | ($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(127,plain,
% 0.20/0.47 ($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.20/0.47 tff(128,plain,
% 0.20/0.47 ((~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0)) | $lesseq($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))), 0)),
% 0.20/0.47 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.47 tff(129,plain,
% 0.20/0.47 ($lesseq($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))), 0)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.20/0.47 tff(130,plain,
% 0.20/0.47 ((~($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0)) | $greatereq($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))), 0)),
% 0.20/0.47 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.47 tff(131,plain,
% 0.20/0.47 ($greatereq($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))), 0)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[130, 127])).
% 0.20/0.47 tff(132,plain,
% 0.20/0.47 (((~$greatereq(tptp_fun_I_0(B2!9, B1!10), 0)) | $lesseq($sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))), 0) | (~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0))) | ($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(133,plain,
% 0.20/0.47 ($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[132, 117])).
% 0.20/0.47 tff(134,plain,
% 0.20/0.47 ((~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0)) | $lesseq($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))), 0)),
% 0.20/0.47 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.47 tff(135,plain,
% 0.20/0.47 ($lesseq($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))), 0)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.20/0.47 tff(136,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(theory_lemma,[status(thm)],[135, 63, 131])).
% 0.20/0.47 tff(137,plain,($greatereq($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(B1!10, tptp_fun_I_0(B2!9, B1!10)))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(138,plain,
% 0.20/0.47 (~$lesseq($sum(read(B2!9, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(B1!10, tptp_fun_I_0(B2!9, B1!10)))), 0)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[93, 137])).
% 0.20/0.47 tff(139,plain,
% 0.20/0.47 ((~($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))) = 0)) | $greatereq($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))), 0)),
% 0.20/0.47 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.47 tff(140,plain,
% 0.20/0.47 ($greatereq($sum(read(B1!10, tptp_fun_I_0(B2!9, B1!10)), $product(-1, read(A!11, $sum(-1, $sum(N!8, $product(-1, tptp_fun_I_0(B2!9, B1!10))))))), 0)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[139, 133])).
% 0.20/0.47 tff(141,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(theory_lemma,[status(thm)],[140, 138, 129])).
% 0.20/0.47 % SZS output end Proof
%------------------------------------------------------------------------------