TSTP Solution File: DAT071_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT071_1 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 14:36:36 EDT 2022
% Result : Theorem 0.14s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : DAT071_1 : TPTP v8.1.0. Released v6.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n017.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 31 01:11:21 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.14/0.40 % SZS status Theorem
% 0.14/0.40 % SZS output start Proof
% 0.14/0.40 tff(read_type, type, (
% 0.14/0.40 read: ( array * $int ) > $int)).
% 0.14/0.40 tff(tptp_fun_I_13_type, type, (
% 0.14/0.40 tptp_fun_I_13: $int)).
% 0.14/0.40 tff(tptp_fun_A_11_type, type, (
% 0.14/0.40 tptp_fun_A_11: array)).
% 0.14/0.40 tff(tptp_fun_W2_8_type, type, (
% 0.14/0.40 tptp_fun_W2_8: $int)).
% 0.14/0.40 tff(tptp_fun_W1_9_type, type, (
% 0.14/0.40 tptp_fun_W1_9: $int)).
% 0.14/0.40 tff(tptp_fun_N_10_type, type, (
% 0.14/0.40 tptp_fun_N_10: $int)).
% 0.14/0.40 tff(tptp_fun_I_12_type, type, (
% 0.14/0.40 tptp_fun_I_12: $int)).
% 0.14/0.40 tff(1,plain,
% 0.14/0.40 (((![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0)) & (~$lesseq($sum(N!10, $product(-1, I!12)), 0)) & $greatereq(I!12, 0) & ($sum(W1!9, $product(-1, read(A!11, I!12))) = 0) & ![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0)) & (~$lesseq($sum(N!10, $product(-1, I!13)), 0)) & $greatereq(I!13, 0) & ($sum(W2!8, $product(-1, read(A!11, I!13))) = 0)) & (~($sum(W2!8, $product(-1, W1!9)) = 0))) <=> (![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0)) & (~$lesseq($sum(N!10, $product(-1, I!12)), 0)) & $greatereq(I!12, 0) & ($sum(W1!9, $product(-1, read(A!11, I!12))) = 0) & ![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0)) & (~$lesseq($sum(N!10, $product(-1, I!13)), 0)) & $greatereq(I!13, 0) & ($sum(W2!8, $product(-1, read(A!11, I!13))) = 0) & (~($sum(W2!8, $product(-1, W1!9)) = 0)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(2,plain,
% 0.14/0.40 ((~($sum(W1!9, $product(-1, W2!8)) = 0)) <=> (~($sum(W2!8, $product(-1, W1!9)) = 0))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(3,plain,
% 0.14/0.40 ((![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0)) & ((~$lesseq($sum(N!10, $product(-1, I!12)), 0)) & $greatereq(I!12, 0) & ($sum(W1!9, $product(-1, read(A!11, I!12))) = 0)) & ![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0)) & ((~$lesseq($sum(N!10, $product(-1, I!13)), 0)) & $greatereq(I!13, 0) & ($sum(W2!8, $product(-1, read(A!11, I!13))) = 0))) <=> (![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0)) & (~$lesseq($sum(N!10, $product(-1, I!12)), 0)) & $greatereq(I!12, 0) & ($sum(W1!9, $product(-1, read(A!11, I!12))) = 0) & ![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0)) & (~$lesseq($sum(N!10, $product(-1, I!13)), 0)) & $greatereq(I!13, 0) & ($sum(W2!8, $product(-1, read(A!11, I!13))) = 0))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(4,plain,
% 0.14/0.40 (((~$greatereq($sum(I!13, $product(-1, N!10)), 0)) & $greatereq(I!13, 0) & ($sum(W2!8, $product(-1, read(A!11, I!13))) = 0)) <=> ((~$lesseq($sum(N!10, $product(-1, I!13)), 0)) & $greatereq(I!13, 0) & ($sum(W2!8, $product(-1, read(A!11, I!13))) = 0))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(5,plain,
% 0.14/0.40 (((~$greatereq($sum(I!12, $product(-1, N!10)), 0)) & $greatereq(I!12, 0) & ($sum(W1!9, $product(-1, read(A!11, I!12))) = 0)) <=> ((~$lesseq($sum(N!10, $product(-1, I!12)), 0)) & $greatereq(I!12, 0) & ($sum(W1!9, $product(-1, read(A!11, I!12))) = 0))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(6,plain,
% 0.14/0.40 ((![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0)) & ((~$greatereq($sum(I!12, $product(-1, N!10)), 0)) & $greatereq(I!12, 0) & ($sum(W1!9, $product(-1, read(A!11, I!12))) = 0)) & ![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0)) & ((~$greatereq($sum(I!13, $product(-1, N!10)), 0)) & $greatereq(I!13, 0) & ($sum(W2!8, $product(-1, read(A!11, I!13))) = 0))) <=> (![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0)) & ((~$lesseq($sum(N!10, $product(-1, I!12)), 0)) & $greatereq(I!12, 0) & ($sum(W1!9, $product(-1, read(A!11, I!12))) = 0)) & ![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0)) & ((~$lesseq($sum(N!10, $product(-1, I!13)), 0)) & $greatereq(I!13, 0) & ($sum(W2!8, $product(-1, read(A!11, I!13))) = 0)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[5, 4])).
% 0.20/0.41 tff(7,plain,
% 0.20/0.41 ((![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0)) & ((~$greatereq($sum(I!12, $product(-1, N!10)), 0)) & $greatereq(I!12, 0) & ($sum(W1!9, $product(-1, read(A!11, I!12))) = 0)) & ![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0)) & ((~$greatereq($sum(I!13, $product(-1, N!10)), 0)) & $greatereq(I!13, 0) & ($sum(W2!8, $product(-1, read(A!11, I!13))) = 0))) <=> (![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0)) & (~$lesseq($sum(N!10, $product(-1, I!12)), 0)) & $greatereq(I!12, 0) & ($sum(W1!9, $product(-1, read(A!11, I!12))) = 0) & ![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0)) & (~$lesseq($sum(N!10, $product(-1, I!13)), 0)) & $greatereq(I!13, 0) & ($sum(W2!8, $product(-1, read(A!11, I!13))) = 0))),
% 0.20/0.41 inference(transitivity,[status(thm)],[6, 3])).
% 0.20/0.41 tff(8,plain,
% 0.20/0.41 (((![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0)) & ((~$greatereq($sum(I!12, $product(-1, N!10)), 0)) & $greatereq(I!12, 0) & ($sum(W1!9, $product(-1, read(A!11, I!12))) = 0)) & ![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0)) & ((~$greatereq($sum(I!13, $product(-1, N!10)), 0)) & $greatereq(I!13, 0) & ($sum(W2!8, $product(-1, read(A!11, I!13))) = 0))) & (~($sum(W1!9, $product(-1, W2!8)) = 0))) <=> ((![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0)) & (~$lesseq($sum(N!10, $product(-1, I!12)), 0)) & $greatereq(I!12, 0) & ($sum(W1!9, $product(-1, read(A!11, I!12))) = 0) & ![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0)) & (~$lesseq($sum(N!10, $product(-1, I!13)), 0)) & $greatereq(I!13, 0) & ($sum(W2!8, $product(-1, read(A!11, I!13))) = 0)) & (~($sum(W2!8, $product(-1, W1!9)) = 0)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[7, 2])).
% 0.20/0.41 tff(9,plain,
% 0.20/0.41 (((![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0)) & ((~$greatereq($sum(I!12, $product(-1, N!10)), 0)) & $greatereq(I!12, 0) & ($sum(W1!9, $product(-1, read(A!11, I!12))) = 0)) & ![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0)) & ((~$greatereq($sum(I!13, $product(-1, N!10)), 0)) & $greatereq(I!13, 0) & ($sum(W2!8, $product(-1, read(A!11, I!13))) = 0))) & (~($sum(W1!9, $product(-1, W2!8)) = 0))) <=> (![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0)) & (~$lesseq($sum(N!10, $product(-1, I!12)), 0)) & $greatereq(I!12, 0) & ($sum(W1!9, $product(-1, read(A!11, I!12))) = 0) & ![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0)) & (~$lesseq($sum(N!10, $product(-1, I!13)), 0)) & $greatereq(I!13, 0) & ($sum(W2!8, $product(-1, read(A!11, I!13))) = 0) & (~($sum(W2!8, $product(-1, W1!9)) = 0)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[8, 1])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 ((~![A: array, N: $int, W1: $int, W2: $int] : ((~(![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W1, $product(-1, read(A, I))), 0)) & ?[I: $int] : ((~$greatereq($sum(I, $product(-1, N)), 0)) & $greatereq(I, 0) & ($sum(W1, $product(-1, read(A, I))) = 0)) & ![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W2, $product(-1, read(A, I))), 0)) & ?[I: $int] : ((~$greatereq($sum(I, $product(-1, N)), 0)) & $greatereq(I, 0) & ($sum(W2, $product(-1, read(A, I))) = 0)))) | ($sum(W1, $product(-1, W2)) = 0))) <=> (~![A: array, N: $int, W1: $int, W2: $int] : ((~(![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W1, $product(-1, read(A, I))), 0)) & ?[I: $int] : ((~$greatereq($sum(I, $product(-1, N)), 0)) & $greatereq(I, 0) & ($sum(W1, $product(-1, read(A, I))) = 0)) & ![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W2, $product(-1, read(A, I))), 0)) & ?[I: $int] : ((~$greatereq($sum(I, $product(-1, N)), 0)) & $greatereq(I, 0) & ($sum(W2, $product(-1, read(A, I))) = 0)))) | ($sum(W1, $product(-1, W2)) = 0)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(11,plain,
% 0.20/0.41 ((~![A: array, N: $int, W1: $int, W2: $int] : ((~(![I: $int] : ((~((~$lesseq($sum(N, $product(-1, I)), 0)) & $greatereq(I, 0))) | $lesseq($sum(read(A, I), $product(-1, W1)), 0)) & ?[I: $int] : ((~$lesseq($sum(N, $product(-1, I)), 0)) & $greatereq(I, 0) & ($sum(read(A, I), $product(-1, W1)) = 0)) & ![I: $int] : ((~((~$lesseq($sum(N, $product(-1, I)), 0)) & $greatereq(I, 0))) | $lesseq($sum(read(A, I), $product(-1, W2)), 0)) & ?[I: $int] : ((~$lesseq($sum(N, $product(-1, I)), 0)) & $greatereq(I, 0) & ($sum(read(A, I), $product(-1, W2)) = 0)))) | ($sum(W1, $product(-1, W2)) = 0))) <=> (~![A: array, N: $int, W1: $int, W2: $int] : ((~(![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W1, $product(-1, read(A, I))), 0)) & ?[I: $int] : ((~$greatereq($sum(I, $product(-1, N)), 0)) & $greatereq(I, 0) & ($sum(W1, $product(-1, read(A, I))) = 0)) & ![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W2, $product(-1, read(A, I))), 0)) & ?[I: $int] : ((~$greatereq($sum(I, $product(-1, N)), 0)) & $greatereq(I, 0) & ($sum(W2, $product(-1, read(A, I))) = 0)))) | ($sum(W1, $product(-1, W2)) = 0)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(12,plain,
% 0.20/0.41 ((~![A: array, N: $int, W1: $int, W2: $int] : ((~(![I: $int] : ((~((~$lesseq(N, I)) & $greatereq(I, 0))) | $lesseq(read(A, I), W1)) & ?[I: $int] : ((~$lesseq(N, I)) & $greatereq(I, 0) & (read(A, I) = W1)) & ![I: $int] : ((~((~$lesseq(N, I)) & $greatereq(I, 0))) | $lesseq(read(A, I), W2)) & ?[I: $int] : ((~$lesseq(N, I)) & $greatereq(I, 0) & (read(A, I) = W2)))) | (W1 = W2))) <=> (~![A: array, N: $int, W1: $int, W2: $int] : ((~(![I: $int] : ((~((~$lesseq($sum(N, $product(-1, I)), 0)) & $greatereq(I, 0))) | $lesseq($sum(read(A, I), $product(-1, W1)), 0)) & ?[I: $int] : ((~$lesseq($sum(N, $product(-1, I)), 0)) & $greatereq(I, 0) & ($sum(read(A, I), $product(-1, W1)) = 0)) & ![I: $int] : ((~((~$lesseq($sum(N, $product(-1, I)), 0)) & $greatereq(I, 0))) | $lesseq($sum(read(A, I), $product(-1, W2)), 0)) & ?[I: $int] : ((~$lesseq($sum(N, $product(-1, I)), 0)) & $greatereq(I, 0) & ($sum(read(A, I), $product(-1, W2)) = 0)))) | ($sum(W1, $product(-1, W2)) = 0)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(13,plain,
% 0.20/0.41 ((~![A: array, N: $int, W1: $int, W2: $int] : ((~(![I: $int] : ((~((~$lesseq(N, I)) & $greatereq(I, 0))) | $lesseq(read(A, I), W1)) & ?[I: $int] : ((~$lesseq(N, I)) & $greatereq(I, 0) & (read(A, I) = W1)) & ![I: $int] : ((~((~$lesseq(N, I)) & $greatereq(I, 0))) | $lesseq(read(A, I), W2)) & ?[I: $int] : ((~$lesseq(N, I)) & $greatereq(I, 0) & (read(A, I) = W2)))) | (W1 = W2))) <=> (~![A: array, N: $int, W1: $int, W2: $int] : ((~(![I: $int] : ((~((~$lesseq(N, I)) & $greatereq(I, 0))) | $lesseq(read(A, I), W1)) & ?[I: $int] : ((~$lesseq(N, I)) & $greatereq(I, 0) & (read(A, I) = W1)) & ![I: $int] : ((~((~$lesseq(N, I)) & $greatereq(I, 0))) | $lesseq(read(A, I), W2)) & ?[I: $int] : ((~$lesseq(N, I)) & $greatereq(I, 0) & (read(A, I) = W2)))) | (W1 = W2)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 ((~![A: array, N: $int, W1: $int, W2: $int] : ((((![I: $int] : (($greater(N, I) & $greatereq(I, 0)) => $lesseq(read(A, I), W1)) & ?[I: $int] : (($greater(N, I) & $greatereq(I, 0)) & (read(A, I) = W1))) & ![I: $int] : (($greater(N, I) & $greatereq(I, 0)) => $lesseq(read(A, I), W2))) & ?[I: $int] : (($greater(N, I) & $greatereq(I, 0)) & (read(A, I) = W2))) => (W1 = W2))) <=> (~![A: array, N: $int, W1: $int, W2: $int] : ((~(![I: $int] : ((~((~$lesseq(N, I)) & $greatereq(I, 0))) | $lesseq(read(A, I), W1)) & ?[I: $int] : ((~$lesseq(N, I)) & $greatereq(I, 0) & (read(A, I) = W1)) & ![I: $int] : ((~((~$lesseq(N, I)) & $greatereq(I, 0))) | $lesseq(read(A, I), W2)) & ?[I: $int] : ((~$lesseq(N, I)) & $greatereq(I, 0) & (read(A, I) = W2)))) | (W1 = W2)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(15,axiom,(~![A: array, N: $int, W1: $int, W2: $int] : ((((![I: $int] : (($greater(N, I) & $greatereq(I, 0)) => $lesseq(read(A, I), W1)) & ?[I: $int] : (($greater(N, I) & $greatereq(I, 0)) & (read(A, I) = W1))) & ![I: $int] : (($greater(N, I) & $greatereq(I, 0)) => $lesseq(read(A, I), W2))) & ?[I: $int] : (($greater(N, I) & $greatereq(I, 0)) & (read(A, I) = W2))) => (W1 = W2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c')).
% 0.20/0.41 tff(16,plain,
% 0.20/0.41 (~![A: array, N: $int, W1: $int, W2: $int] : ((~(![I: $int] : ((~((~$lesseq(N, I)) & $greatereq(I, 0))) | $lesseq(read(A, I), W1)) & ?[I: $int] : ((~$lesseq(N, I)) & $greatereq(I, 0) & (read(A, I) = W1)) & ![I: $int] : ((~((~$lesseq(N, I)) & $greatereq(I, 0))) | $lesseq(read(A, I), W2)) & ?[I: $int] : ((~$lesseq(N, I)) & $greatereq(I, 0) & (read(A, I) = W2)))) | (W1 = W2))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.41 tff(17,plain,
% 0.20/0.41 (~![A: array, N: $int, W1: $int, W2: $int] : ((~(![I: $int] : ((~((~$lesseq(N, I)) & $greatereq(I, 0))) | $lesseq(read(A, I), W1)) & ?[I: $int] : ((~$lesseq(N, I)) & $greatereq(I, 0) & (read(A, I) = W1)) & ![I: $int] : ((~((~$lesseq(N, I)) & $greatereq(I, 0))) | $lesseq(read(A, I), W2)) & ?[I: $int] : ((~$lesseq(N, I)) & $greatereq(I, 0) & (read(A, I) = W2)))) | (W1 = W2))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.20/0.41 tff(18,plain,
% 0.20/0.41 (~![A: array, N: $int, W1: $int, W2: $int] : ((~(![I: $int] : ((~((~$lesseq(N, I)) & $greatereq(I, 0))) | $lesseq(read(A, I), W1)) & ?[I: $int] : ((~$lesseq(N, I)) & $greatereq(I, 0) & (read(A, I) = W1)) & ![I: $int] : ((~((~$lesseq(N, I)) & $greatereq(I, 0))) | $lesseq(read(A, I), W2)) & ?[I: $int] : ((~$lesseq(N, I)) & $greatereq(I, 0) & (read(A, I) = W2)))) | (W1 = W2))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 (~![A: array, N: $int, W1: $int, W2: $int] : ((~(![I: $int] : ((~((~$lesseq(N, I)) & $greatereq(I, 0))) | $lesseq(read(A, I), W1)) & ?[I: $int] : ((~$lesseq(N, I)) & $greatereq(I, 0) & (read(A, I) = W1)) & ![I: $int] : ((~((~$lesseq(N, I)) & $greatereq(I, 0))) | $lesseq(read(A, I), W2)) & ?[I: $int] : ((~$lesseq(N, I)) & $greatereq(I, 0) & (read(A, I) = W2)))) | (W1 = W2))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.20/0.41 tff(20,plain,
% 0.20/0.41 (~![A: array, N: $int, W1: $int, W2: $int] : ((~(![I: $int] : ((~((~$lesseq($sum(N, $product(-1, I)), 0)) & $greatereq(I, 0))) | $lesseq($sum(read(A, I), $product(-1, W1)), 0)) & ?[I: $int] : ((~$lesseq($sum(N, $product(-1, I)), 0)) & $greatereq(I, 0) & ($sum(read(A, I), $product(-1, W1)) = 0)) & ![I: $int] : ((~((~$lesseq($sum(N, $product(-1, I)), 0)) & $greatereq(I, 0))) | $lesseq($sum(read(A, I), $product(-1, W2)), 0)) & ?[I: $int] : ((~$lesseq($sum(N, $product(-1, I)), 0)) & $greatereq(I, 0) & ($sum(read(A, I), $product(-1, W2)) = 0)))) | ($sum(W1, $product(-1, W2)) = 0))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.20/0.41 tff(21,plain,
% 0.20/0.41 (~![A: array, N: $int, W1: $int, W2: $int] : ((~(![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W1, $product(-1, read(A, I))), 0)) & ?[I: $int] : ((~$greatereq($sum(I, $product(-1, N)), 0)) & $greatereq(I, 0) & ($sum(W1, $product(-1, read(A, I))) = 0)) & ![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W2, $product(-1, read(A, I))), 0)) & ?[I: $int] : ((~$greatereq($sum(I, $product(-1, N)), 0)) & $greatereq(I, 0) & ($sum(W2, $product(-1, read(A, I))) = 0)))) | ($sum(W1, $product(-1, W2)) = 0))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[20, 11])).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 (~![A: array, N: $int, W1: $int, W2: $int] : ((~(![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W1, $product(-1, read(A, I))), 0)) & ?[I: $int] : ((~$greatereq($sum(I, $product(-1, N)), 0)) & $greatereq(I, 0) & ($sum(W1, $product(-1, read(A, I))) = 0)) & ![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W2, $product(-1, read(A, I))), 0)) & ?[I: $int] : ((~$greatereq($sum(I, $product(-1, N)), 0)) & $greatereq(I, 0) & ($sum(W2, $product(-1, read(A, I))) = 0)))) | ($sum(W1, $product(-1, W2)) = 0))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[21, 10])).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 (~![A: array, N: $int, W1: $int, W2: $int] : ((~(![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W1, $product(-1, read(A, I))), 0)) & ?[I: $int] : ((~$greatereq($sum(I, $product(-1, N)), 0)) & $greatereq(I, 0) & ($sum(W1, $product(-1, read(A, I))) = 0)) & ![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W2, $product(-1, read(A, I))), 0)) & ?[I: $int] : ((~$greatereq($sum(I, $product(-1, N)), 0)) & $greatereq(I, 0) & ($sum(W2, $product(-1, read(A, I))) = 0)))) | ($sum(W1, $product(-1, W2)) = 0))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[22, 10])).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 (![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0)) & (~$lesseq($sum(N!10, $product(-1, I!12)), 0)) & $greatereq(I!12, 0) & ($sum(W1!9, $product(-1, read(A!11, I!12))) = 0) & ![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0)) & (~$lesseq($sum(N!10, $product(-1, I!13)), 0)) & $greatereq(I!13, 0) & ($sum(W2!8, $product(-1, read(A!11, I!13))) = 0) & (~($sum(W2!8, $product(-1, W1!9)) = 0))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[23, 9])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 ($sum(W2!8, $product(-1, read(A!11, I!13))) = 0),
% 0.20/0.41 inference(and_elim,[status(thm)],[24])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 ((~($sum(W2!8, $product(-1, read(A!11, I!13))) = 0)) | $lesseq($sum(W2!8, $product(-1, read(A!11, I!13))), 0)),
% 0.20/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 ($lesseq($sum(W2!8, $product(-1, read(A!11, I!13))), 0)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 (^[I: $int] : refl(((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0)) <=> ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0)) <=> ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 (^[I: $int] : trans(monotonicity(trans(monotonicity(rewrite(((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0)) <=> (~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0)))), ((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) <=> (~(~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0)))))), rewrite((~(~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0)))) <=> ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0))), ((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) <=> ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0)))), (((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0)) <=> (((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0)) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0)))), rewrite((((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0)) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0)) <=> ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0))), (((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0)) <=> ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 (![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0)) <=> ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[30])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 (![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0))),
% 0.20/0.41 inference(and_elim,[status(thm)],[24])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 (![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 (![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 ($greatereq(I!12, 0)),
% 0.20/0.41 inference(and_elim,[status(thm)],[24])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 (~$lesseq($sum(N!10, $product(-1, I!12)), 0)),
% 0.20/0.41 inference(and_elim,[status(thm)],[24])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 (((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0))) | ((~$greatereq(I!12, 0)) | $lesseq($sum(N!10, $product(-1, I!12)), 0) | $greatereq($sum(W2!8, $product(-1, read(A!11, I!12))), 0))) <=> ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0))) | (~$greatereq(I!12, 0)) | $lesseq($sum(N!10, $product(-1, I!12)), 0) | $greatereq($sum(W2!8, $product(-1, read(A!11, I!12))), 0))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 (((~$greatereq(I!12, 0)) | $greatereq($sum(I!12, $product(-1, N!10)), 0) | $greatereq($sum(W2!8, $product(-1, read(A!11, I!12))), 0)) <=> ((~$greatereq(I!12, 0)) | $lesseq($sum(N!10, $product(-1, I!12)), 0) | $greatereq($sum(W2!8, $product(-1, read(A!11, I!12))), 0))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0))) | ((~$greatereq(I!12, 0)) | $greatereq($sum(I!12, $product(-1, N!10)), 0) | $greatereq($sum(W2!8, $product(-1, read(A!11, I!12))), 0))) <=> ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0))) | ((~$greatereq(I!12, 0)) | $lesseq($sum(N!10, $product(-1, I!12)), 0) | $greatereq($sum(W2!8, $product(-1, read(A!11, I!12))), 0)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[38])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 (((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0))) | ((~$greatereq(I!12, 0)) | $greatereq($sum(I!12, $product(-1, N!10)), 0) | $greatereq($sum(W2!8, $product(-1, read(A!11, I!12))), 0))) <=> ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0))) | (~$greatereq(I!12, 0)) | $lesseq($sum(N!10, $product(-1, I!12)), 0) | $greatereq($sum(W2!8, $product(-1, read(A!11, I!12))), 0))),
% 0.20/0.42 inference(transitivity,[status(thm)],[39, 37])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0))) | ((~$greatereq(I!12, 0)) | $greatereq($sum(I!12, $product(-1, N!10)), 0) | $greatereq($sum(W2!8, $product(-1, read(A!11, I!12))), 0))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0) | $greatereq($sum(W2!8, $product(-1, read(A!11, I))), 0))) | (~$greatereq(I!12, 0)) | $lesseq($sum(N!10, $product(-1, I!12)), 0) | $greatereq($sum(W2!8, $product(-1, read(A!11, I!12))), 0)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 ($greatereq($sum(W2!8, $product(-1, read(A!11, I!12))), 0)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[42, 36, 35, 34])).
% 0.20/0.42 tff(44,assumption,(~$greatereq($sum(W2!8, $product(-1, W1!9)), 0)), introduced(assumption)).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 ($sum(W1!9, $product(-1, read(A!11, I!12))) = 0),
% 0.20/0.42 inference(and_elim,[status(thm)],[24])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 ((~($sum(W1!9, $product(-1, read(A!11, I!12))) = 0)) | $lesseq($sum(W1!9, $product(-1, read(A!11, I!12))), 0)),
% 0.20/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.42 tff(47,plain,
% 0.20/0.42 ($lesseq($sum(W1!9, $product(-1, read(A!11, I!12))), 0)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(theory_lemma,[status(thm)],[47, 44, 43])).
% 0.20/0.42 tff(49,plain,($greatereq($sum(W2!8, $product(-1, W1!9)), 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(50,plain,
% 0.20/0.42 (~($sum(W2!8, $product(-1, W1!9)) = 0)),
% 0.20/0.42 inference(and_elim,[status(thm)],[24])).
% 0.20/0.42 tff(51,plain,
% 0.20/0.42 (($sum(W2!8, $product(-1, W1!9)) = 0) | (~$lesseq($sum(W2!8, $product(-1, W1!9)), 0)) | (~$greatereq($sum(W2!8, $product(-1, W1!9)), 0))),
% 0.20/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.42 tff(52,plain,
% 0.20/0.42 ((~$lesseq($sum(W2!8, $product(-1, W1!9)), 0)) | (~$greatereq($sum(W2!8, $product(-1, W1!9)), 0))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.20/0.42 tff(53,plain,
% 0.20/0.42 (~$lesseq($sum(W2!8, $product(-1, W1!9)), 0)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[52, 49])).
% 0.20/0.42 tff(54,plain,
% 0.20/0.42 ($greatereq(I!13, 0)),
% 0.20/0.42 inference(and_elim,[status(thm)],[24])).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 (~$lesseq($sum(N!10, $product(-1, I!13)), 0)),
% 0.20/0.42 inference(and_elim,[status(thm)],[24])).
% 0.20/0.42 tff(56,plain,
% 0.20/0.42 (^[I: $int] : refl(((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0)) <=> ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(57,plain,
% 0.20/0.42 (![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0)) <=> ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[56])).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 (^[I: $int] : trans(monotonicity(trans(monotonicity(rewrite(((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0)) <=> (~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0)))), ((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) <=> (~(~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0)))))), rewrite((~(~((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0)))) <=> ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0))), ((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) <=> ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0)))), (((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0)) <=> (((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0)) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0)))), rewrite((((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0)) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0)) <=> ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0))), (((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0)) <=> ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(59,plain,
% 0.20/0.42 (![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0)) <=> ![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[58])).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 (![I: $int] : ((~((~$greatereq($sum(I, $product(-1, N!10)), 0)) & $greatereq(I, 0))) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0))),
% 0.20/0.42 inference(and_elim,[status(thm)],[24])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 (![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.42 tff(62,plain,
% 0.20/0.42 (![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 (((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0))) | ((~$greatereq(I!13, 0)) | $lesseq($sum(N!10, $product(-1, I!13)), 0) | $greatereq($sum(W1!9, $product(-1, read(A!11, I!13))), 0))) <=> ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0))) | (~$greatereq(I!13, 0)) | $lesseq($sum(N!10, $product(-1, I!13)), 0) | $greatereq($sum(W1!9, $product(-1, read(A!11, I!13))), 0))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 (((~$greatereq(I!13, 0)) | $greatereq($sum(I!13, $product(-1, N!10)), 0) | $greatereq($sum(W1!9, $product(-1, read(A!11, I!13))), 0)) <=> ((~$greatereq(I!13, 0)) | $lesseq($sum(N!10, $product(-1, I!13)), 0) | $greatereq($sum(W1!9, $product(-1, read(A!11, I!13))), 0))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(65,plain,
% 0.20/0.42 (((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0))) | ((~$greatereq(I!13, 0)) | $greatereq($sum(I!13, $product(-1, N!10)), 0) | $greatereq($sum(W1!9, $product(-1, read(A!11, I!13))), 0))) <=> ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0))) | ((~$greatereq(I!13, 0)) | $lesseq($sum(N!10, $product(-1, I!13)), 0) | $greatereq($sum(W1!9, $product(-1, read(A!11, I!13))), 0)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[64])).
% 0.20/0.42 tff(66,plain,
% 0.20/0.42 (((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0))) | ((~$greatereq(I!13, 0)) | $greatereq($sum(I!13, $product(-1, N!10)), 0) | $greatereq($sum(W1!9, $product(-1, read(A!11, I!13))), 0))) <=> ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0))) | (~$greatereq(I!13, 0)) | $lesseq($sum(N!10, $product(-1, I!13)), 0) | $greatereq($sum(W1!9, $product(-1, read(A!11, I!13))), 0))),
% 0.20/0.42 inference(transitivity,[status(thm)],[65, 63])).
% 0.20/0.42 tff(67,plain,
% 0.20/0.42 ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0))) | ((~$greatereq(I!13, 0)) | $greatereq($sum(I!13, $product(-1, N!10)), 0) | $greatereq($sum(W1!9, $product(-1, read(A!11, I!13))), 0))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(68,plain,
% 0.20/0.42 ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, N!10)), 0) | $greatereq($sum(W1!9, $product(-1, read(A!11, I))), 0))) | (~$greatereq(I!13, 0)) | $lesseq($sum(N!10, $product(-1, I!13)), 0) | $greatereq($sum(W1!9, $product(-1, read(A!11, I!13))), 0)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.20/0.42 tff(69,plain,
% 0.20/0.42 ($greatereq($sum(W1!9, $product(-1, read(A!11, I!13))), 0)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[68, 62, 55, 54])).
% 0.20/0.42 tff(70,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(theory_lemma,[status(thm)],[69, 53, 27])).
% 0.20/0.42 % SZS output end Proof
%------------------------------------------------------------------------------