TSTP Solution File: DAT073_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT073_1 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 28.14s 18.35s
% Output : Proof 28.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : DAT073_1 : TPTP v8.1.0. Released v6.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 01:45:41 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.
% 28.14/18.35 % SZS status Theorem
% 28.14/18.35 % SZS output start Proof
% 28.14/18.35 tff(inRange_type, type, (
% 28.14/18.35 inRange: ( array * $int * $int ) > $o)).
% 28.14/18.35 tff(max_type, type, (
% 28.14/18.35 max: ( array * $int ) > $int)).
% 28.14/18.35 tff(write_type, type, (
% 28.14/18.35 write: ( array * $int * $int ) > array)).
% 28.14/18.35 tff(elem_8_type, type, (
% 28.14/18.35 elem_8: array)).
% 28.14/18.35 tff(read_type, type, (
% 28.14/18.35 read: ( array * $int ) > $int)).
% 28.14/18.35 tff(tptp_fun_I_4_type, type, (
% 28.14/18.35 tptp_fun_I_4: ( $int * $int * array ) > $int)).
% 28.14/18.35 tff(1,assumption,((~((~inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq(I, 2439) | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), I), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), I), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0))))))) | (~(inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439) | (~((~$greatereq(tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1)), 0)) | (~((~$greatereq($sum(max(write(write(elem!8, 0, 0), 0, -1), 2439), $product(-1, read(write(write(elem!8, 0, 0), 0, -1), tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1))))), 0)) | (~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1))), 0)))) | $greatereq(tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1)), 2439)))))), introduced(assumption)).
% 28.14/18.35 tff(2,plain,
% 28.14/18.35 (^[A: array, R: $int, N: $int] : refl((~((~((~inRange(A, R, N)) | ![I: $int] : ($lesseq($sum(N, $product(-1, I)), 0) | (~$greatereq(I, 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, I))), 0)) | (~$greatereq(read(A, I), 0))))))) | (~(inRange(A, R, N) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0) | (~$greatereq(tptp_fun_I_4(N, R, A), 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0)) | (~$greatereq(read(A, tptp_fun_I_4(N, R, A)), 0)))))))))) <=> (~((~((~inRange(A, R, N)) | ![I: $int] : ($lesseq($sum(N, $product(-1, I)), 0) | (~$greatereq(I, 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, I))), 0)) | (~$greatereq(read(A, I), 0))))))) | (~(inRange(A, R, N) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0) | (~$greatereq(tptp_fun_I_4(N, R, A), 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0)) | (~$greatereq(read(A, tptp_fun_I_4(N, R, A)), 0)))))))))))),
% 28.14/18.35 inference(bind,[status(th)],[])).
% 28.14/18.35 tff(3,plain,
% 28.14/18.35 (![A: array, R: $int, N: $int] : (~((~((~inRange(A, R, N)) | ![I: $int] : ($lesseq($sum(N, $product(-1, I)), 0) | (~$greatereq(I, 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, I))), 0)) | (~$greatereq(read(A, I), 0))))))) | (~(inRange(A, R, N) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0) | (~$greatereq(tptp_fun_I_4(N, R, A), 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0)) | (~$greatereq(read(A, tptp_fun_I_4(N, R, A)), 0)))))))))) <=> ![A: array, R: $int, N: $int] : (~((~((~inRange(A, R, N)) | ![I: $int] : ($lesseq($sum(N, $product(-1, I)), 0) | (~$greatereq(I, 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, I))), 0)) | (~$greatereq(read(A, I), 0))))))) | (~(inRange(A, R, N) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0) | (~$greatereq(tptp_fun_I_4(N, R, A), 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0)) | (~$greatereq(read(A, tptp_fun_I_4(N, R, A)), 0))))))))))),
% 28.14/18.35 inference(quant_intro,[status(thm)],[2])).
% 28.14/18.35 tff(4,plain,
% 28.14/18.35 (^[A: array, R: $int, N: $int] : rewrite((~((~((~inRange(A, R, N)) | ![I: $int] : ($lesseq($sum(N, $product(-1, I)), 0) | (~$greatereq(I, 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, I))), 0)) | (~$greatereq(read(A, I), 0))))))) | (~(inRange(A, R, N) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0) | (~$greatereq(tptp_fun_I_4(N, R, A), 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0)) | (~$greatereq(read(A, tptp_fun_I_4(N, R, A)), 0)))))))))) <=> (~((~((~inRange(A, R, N)) | ![I: $int] : ($lesseq($sum(N, $product(-1, I)), 0) | (~$greatereq(I, 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, I))), 0)) | (~$greatereq(read(A, I), 0))))))) | (~(inRange(A, R, N) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0) | (~$greatereq(tptp_fun_I_4(N, R, A), 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0)) | (~$greatereq(read(A, tptp_fun_I_4(N, R, A)), 0)))))))))))),
% 28.14/18.35 inference(bind,[status(th)],[])).
% 28.14/18.35 tff(5,plain,
% 28.14/18.35 (![A: array, R: $int, N: $int] : (~((~((~inRange(A, R, N)) | ![I: $int] : ($lesseq($sum(N, $product(-1, I)), 0) | (~$greatereq(I, 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, I))), 0)) | (~$greatereq(read(A, I), 0))))))) | (~(inRange(A, R, N) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0) | (~$greatereq(tptp_fun_I_4(N, R, A), 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0)) | (~$greatereq(read(A, tptp_fun_I_4(N, R, A)), 0)))))))))) <=> ![A: array, R: $int, N: $int] : (~((~((~inRange(A, R, N)) | ![I: $int] : ($lesseq($sum(N, $product(-1, I)), 0) | (~$greatereq(I, 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, I))), 0)) | (~$greatereq(read(A, I), 0))))))) | (~(inRange(A, R, N) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0) | (~$greatereq(tptp_fun_I_4(N, R, A), 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0)) | (~$greatereq(read(A, tptp_fun_I_4(N, R, A)), 0))))))))))),
% 28.14/18.35 inference(quant_intro,[status(thm)],[4])).
% 28.14/18.35 tff(6,plain,
% 28.14/18.35 (![A: array, R: $int, N: $int] : (~((~((~inRange(A, R, N)) | ![I: $int] : ($lesseq($sum(N, $product(-1, I)), 0) | (~$greatereq(I, 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, I))), 0)) | (~$greatereq(read(A, I), 0))))))) | (~(inRange(A, R, N) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0) | (~$greatereq(tptp_fun_I_4(N, R, A), 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0)) | (~$greatereq(read(A, tptp_fun_I_4(N, R, A)), 0)))))))))) <=> ![A: array, R: $int, N: $int] : (~((~((~inRange(A, R, N)) | ![I: $int] : ($lesseq($sum(N, $product(-1, I)), 0) | (~$greatereq(I, 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, I))), 0)) | (~$greatereq(read(A, I), 0))))))) | (~(inRange(A, R, N) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0) | (~$greatereq(tptp_fun_I_4(N, R, A), 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0)) | (~$greatereq(read(A, tptp_fun_I_4(N, R, A)), 0))))))))))),
% 28.14/18.35 inference(transitivity,[status(thm)],[5, 3])).
% 28.14/18.35 tff(7,plain,
% 28.14/18.35 (^[A: array, R: $int, N: $int] : trans(monotonicity(rewrite(((~inRange(A, R, N)) | ![I: $int] : ((~((~$lesseq($sum(N, $product(-1, I)), 0)) & $greatereq(I, 0))) | ($greatereq($sum(R, $product(-1, read(A, I))), 0) & $greatereq(read(A, I), 0)))) <=> ((~inRange(A, R, N)) | ![I: $int] : ($lesseq($sum(N, $product(-1, I)), 0) | (~$greatereq(I, 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, I))), 0)) | (~$greatereq(read(A, I), 0))))))), trans(monotonicity(rewrite((~((~((~$lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0)) & $greatereq(tptp_fun_I_4(N, R, A), 0))) | ($greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0) & $greatereq(read(A, tptp_fun_I_4(N, R, A)), 0)))) <=> (~($lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0) | (~$greatereq(tptp_fun_I_4(N, R, A), 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0)) | (~$greatereq(read(A, tptp_fun_I_4(N, R, A)), 0))))))), ((inRange(A, R, N) | (~((~((~$lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0)) & $greatereq(tptp_fun_I_4(N, R, A), 0))) | ($greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0) & $greatereq(read(A, tptp_fun_I_4(N, R, A)), 0))))) <=> (inRange(A, R, N) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0) | (~$greatereq(tptp_fun_I_4(N, R, A), 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0)) | (~$greatereq(read(A, tptp_fun_I_4(N, R, A)), 0))))))))), rewrite((inRange(A, R, N) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0) | (~$greatereq(tptp_fun_I_4(N, R, A), 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0)) | (~$greatereq(read(A, tptp_fun_I_4(N, R, A)), 0))))))) <=> (inRange(A, R, N) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0) | (~$greatereq(tptp_fun_I_4(N, R, A), 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0)) | (~$greatereq(read(A, tptp_fun_I_4(N, R, A)), 0)))))))), ((inRange(A, R, N) | (~((~((~$lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0)) & $greatereq(tptp_fun_I_4(N, R, A), 0))) | ($greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0) & $greatereq(read(A, tptp_fun_I_4(N, R, A)), 0))))) <=> (inRange(A, R, N) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0) | (~$greatereq(tptp_fun_I_4(N, R, A), 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0)) | (~$greatereq(read(A, tptp_fun_I_4(N, R, A)), 0))))))))), ((((~inRange(A, R, N)) | ![I: $int] : ((~((~$lesseq($sum(N, $product(-1, I)), 0)) & $greatereq(I, 0))) | ($greatereq($sum(R, $product(-1, read(A, I))), 0) & $greatereq(read(A, I), 0)))) & (inRange(A, R, N) | (~((~((~$lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0)) & $greatereq(tptp_fun_I_4(N, R, A), 0))) | ($greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0) & $greatereq(read(A, tptp_fun_I_4(N, R, A)), 0)))))) <=> (((~inRange(A, R, N)) | ![I: $int] : ($lesseq($sum(N, $product(-1, I)), 0) | (~$greatereq(I, 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, I))), 0)) | (~$greatereq(read(A, I), 0)))))) & (inRange(A, R, N) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0) | (~$greatereq(tptp_fun_I_4(N, R, A), 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0)) | (~$greatereq(read(A, tptp_fun_I_4(N, R, A)), 0)))))))))), rewrite((((~inRange(A, R, N)) | ![I: $int] : ($lesseq($sum(N, $product(-1, I)), 0) | (~$greatereq(I, 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, I))), 0)) | (~$greatereq(read(A, I), 0)))))) & (inRange(A, R, N) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0) | (~$greatereq(tptp_fun_I_4(N, R, A), 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0)) | (~$greatereq(read(A, tptp_fun_I_4(N, R, A)), 0)))))))) <=> (~((~((~inRange(A, R, N)) | ![I: $int] : ($lesseq($sum(N, $product(-1, I)), 0) | (~$greatereq(I, 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, I))), 0)) | (~$greatereq(read(A, I), 0))))))) | (~(inRange(A, R, N) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0) | (~$greatereq(tptp_fun_I_4(N, R, A), 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0)) | (~$greatereq(read(A, tptp_fun_I_4(N, R, A)), 0))))))))))), ((((~inRange(A, R, N)) | ![I: $int] : ((~((~$lesseq($sum(N, $product(-1, I)), 0)) & $greatereq(I, 0))) | ($greatereq($sum(R, $product(-1, read(A, I))), 0) & $greatereq(read(A, I), 0)))) & (inRange(A, R, N) | (~((~((~$lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0)) & $greatereq(tptp_fun_I_4(N, R, A), 0))) | ($greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0) & $greatereq(read(A, tptp_fun_I_4(N, R, A)), 0)))))) <=> (~((~((~inRange(A, R, N)) | ![I: $int] : ($lesseq($sum(N, $product(-1, I)), 0) | (~$greatereq(I, 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, I))), 0)) | (~$greatereq(read(A, I), 0))))))) | (~(inRange(A, R, N) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0) | (~$greatereq(tptp_fun_I_4(N, R, A), 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0)) | (~$greatereq(read(A, tptp_fun_I_4(N, R, A)), 0))))))))))))),
% 28.14/18.35 inference(bind,[status(th)],[])).
% 28.14/18.35 tff(8,plain,
% 28.14/18.35 (![A: array, R: $int, N: $int] : (((~inRange(A, R, N)) | ![I: $int] : ((~((~$lesseq($sum(N, $product(-1, I)), 0)) & $greatereq(I, 0))) | ($greatereq($sum(R, $product(-1, read(A, I))), 0) & $greatereq(read(A, I), 0)))) & (inRange(A, R, N) | (~((~((~$lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0)) & $greatereq(tptp_fun_I_4(N, R, A), 0))) | ($greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0) & $greatereq(read(A, tptp_fun_I_4(N, R, A)), 0)))))) <=> ![A: array, R: $int, N: $int] : (~((~((~inRange(A, R, N)) | ![I: $int] : ($lesseq($sum(N, $product(-1, I)), 0) | (~$greatereq(I, 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, I))), 0)) | (~$greatereq(read(A, I), 0))))))) | (~(inRange(A, R, N) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0) | (~$greatereq(tptp_fun_I_4(N, R, A), 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0)) | (~$greatereq(read(A, tptp_fun_I_4(N, R, A)), 0))))))))))),
% 28.14/18.35 inference(quant_intro,[status(thm)],[7])).
% 28.14/18.35 tff(9,plain,
% 28.14/18.35 (^[A: array, R: $int, N: $int] : rewrite((inRange(A, R, N) <=> ![I: $int] : ((~((~$lesseq(N, I)) & $greatereq(I, 0))) | ($greatereq(R, read(A, I)) & $greatereq(read(A, I), 0)))) <=> (inRange(A, R, N) <=> ![I: $int] : ((~((~$lesseq($sum(N, $product(-1, I)), 0)) & $greatereq(I, 0))) | ($greatereq($sum(R, $product(-1, read(A, I))), 0) & $greatereq(read(A, I), 0)))))),
% 28.14/18.35 inference(bind,[status(th)],[])).
% 28.14/18.35 tff(10,plain,
% 28.14/18.35 (![A: array, R: $int, N: $int] : (inRange(A, R, N) <=> ![I: $int] : ((~((~$lesseq(N, I)) & $greatereq(I, 0))) | ($greatereq(R, read(A, I)) & $greatereq(read(A, I), 0)))) <=> ![A: array, R: $int, N: $int] : (inRange(A, R, N) <=> ![I: $int] : ((~((~$lesseq($sum(N, $product(-1, I)), 0)) & $greatereq(I, 0))) | ($greatereq($sum(R, $product(-1, read(A, I))), 0) & $greatereq(read(A, I), 0))))),
% 28.14/18.35 inference(quant_intro,[status(thm)],[9])).
% 28.14/18.35 tff(11,plain,
% 28.14/18.35 (![A: array, R: $int, N: $int] : (inRange(A, R, N) <=> ![I: $int] : ((~((~$lesseq(N, I)) & $greatereq(I, 0))) | ($greatereq(R, read(A, I)) & $greatereq(read(A, I), 0)))) <=> ![A: array, R: $int, N: $int] : (inRange(A, R, N) <=> ![I: $int] : ((~((~$lesseq(N, I)) & $greatereq(I, 0))) | ($greatereq(R, read(A, I)) & $greatereq(read(A, I), 0))))),
% 28.14/18.35 inference(rewrite,[status(thm)],[])).
% 28.14/18.35 tff(12,plain,
% 28.14/18.35 (^[A: array, R: $int, N: $int] : rewrite((inRange(A, R, N) <=> ![I: $int] : (($greater(N, I) & $greatereq(I, 0)) => ($greatereq(R, read(A, I)) & $greatereq(read(A, I), 0)))) <=> (inRange(A, R, N) <=> ![I: $int] : ((~((~$lesseq(N, I)) & $greatereq(I, 0))) | ($greatereq(R, read(A, I)) & $greatereq(read(A, I), 0)))))),
% 28.14/18.35 inference(bind,[status(th)],[])).
% 28.14/18.35 tff(13,plain,
% 28.14/18.35 (![A: array, R: $int, N: $int] : (inRange(A, R, N) <=> ![I: $int] : (($greater(N, I) & $greatereq(I, 0)) => ($greatereq(R, read(A, I)) & $greatereq(read(A, I), 0)))) <=> ![A: array, R: $int, N: $int] : (inRange(A, R, N) <=> ![I: $int] : ((~((~$lesseq(N, I)) & $greatereq(I, 0))) | ($greatereq(R, read(A, I)) & $greatereq(read(A, I), 0))))),
% 28.14/18.35 inference(quant_intro,[status(thm)],[12])).
% 28.14/18.35 tff(14,axiom,(![A: array, R: $int, N: $int] : (inRange(A, R, N) <=> ![I: $int] : (($greater(N, I) & $greatereq(I, 0)) => ($greatereq(R, read(A, I)) & $greatereq(read(A, I), 0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','inRange')).
% 28.14/18.35 tff(15,plain,
% 28.14/18.35 (![A: array, R: $int, N: $int] : (inRange(A, R, N) <=> ![I: $int] : ((~((~$lesseq(N, I)) & $greatereq(I, 0))) | ($greatereq(R, read(A, I)) & $greatereq(read(A, I), 0))))),
% 28.14/18.35 inference(modus_ponens,[status(thm)],[14, 13])).
% 28.14/18.35 tff(16,plain,
% 28.14/18.35 (![A: array, R: $int, N: $int] : (inRange(A, R, N) <=> ![I: $int] : ((~((~$lesseq(N, I)) & $greatereq(I, 0))) | ($greatereq(R, read(A, I)) & $greatereq(read(A, I), 0))))),
% 28.14/18.35 inference(modus_ponens,[status(thm)],[15, 11])).
% 28.14/18.35 tff(17,plain,
% 28.14/18.35 (![A: array, R: $int, N: $int] : (inRange(A, R, N) <=> ![I: $int] : ((~((~$lesseq($sum(N, $product(-1, I)), 0)) & $greatereq(I, 0))) | ($greatereq($sum(R, $product(-1, read(A, I))), 0) & $greatereq(read(A, I), 0))))),
% 28.14/18.35 inference(modus_ponens,[status(thm)],[16, 10])).
% 28.14/18.35 tff(18,plain,(
% 28.14/18.35 ![A: array, R: $int, N: $int] : (((~inRange(A, R, N)) | ![I: $int] : ((~((~$lesseq($sum(N, $product(-1, I)), 0)) & $greatereq(I, 0))) | ($greatereq($sum(R, $product(-1, read(A, I))), 0) & $greatereq(read(A, I), 0)))) & (inRange(A, R, N) | (~((~((~$lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0)) & $greatereq(tptp_fun_I_4(N, R, A), 0))) | ($greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0) & $greatereq(read(A, tptp_fun_I_4(N, R, A)), 0))))))),
% 28.14/18.35 inference(skolemize,[status(sab)],[17])).
% 28.14/18.35 tff(19,plain,
% 28.14/18.35 (![A: array, R: $int, N: $int] : (~((~((~inRange(A, R, N)) | ![I: $int] : ($lesseq($sum(N, $product(-1, I)), 0) | (~$greatereq(I, 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, I))), 0)) | (~$greatereq(read(A, I), 0))))))) | (~(inRange(A, R, N) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0) | (~$greatereq(tptp_fun_I_4(N, R, A), 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0)) | (~$greatereq(read(A, tptp_fun_I_4(N, R, A)), 0))))))))))),
% 28.14/18.35 inference(modus_ponens,[status(thm)],[18, 8])).
% 28.14/18.35 tff(20,plain,
% 28.14/18.35 (![A: array, R: $int, N: $int] : (~((~((~inRange(A, R, N)) | ![I: $int] : ($lesseq($sum(N, $product(-1, I)), 0) | (~$greatereq(I, 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, I))), 0)) | (~$greatereq(read(A, I), 0))))))) | (~(inRange(A, R, N) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0) | (~$greatereq(tptp_fun_I_4(N, R, A), 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0)) | (~$greatereq(read(A, tptp_fun_I_4(N, R, A)), 0))))))))))),
% 28.14/18.35 inference(modus_ponens,[status(thm)],[19, 6])).
% 28.14/18.35 tff(21,plain,
% 28.14/18.35 (((~![A: array, R: $int, N: $int] : (~((~((~inRange(A, R, N)) | ![I: $int] : ($lesseq($sum(N, $product(-1, I)), 0) | (~$greatereq(I, 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, I))), 0)) | (~$greatereq(read(A, I), 0))))))) | (~(inRange(A, R, N) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0) | (~$greatereq(tptp_fun_I_4(N, R, A), 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0)) | (~$greatereq(read(A, tptp_fun_I_4(N, R, A)), 0))))))))))) | (~((~((~inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq(I, 2439) | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), I), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), I), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0))))))) | (~(inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439) | (~((~$greatereq(tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1)), 0)) | (~((~$greatereq($sum(max(write(write(elem!8, 0, 0), 0, -1), 2439), $product(-1, read(write(write(elem!8, 0, 0), 0, -1), tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1))))), 0)) | (~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1))), 0)))) | $greatereq(tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1)), 2439)))))))) <=> ((~![A: array, R: $int, N: $int] : (~((~((~inRange(A, R, N)) | ![I: $int] : ($lesseq($sum(N, $product(-1, I)), 0) | (~$greatereq(I, 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, I))), 0)) | (~$greatereq(read(A, I), 0))))))) | (~(inRange(A, R, N) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0) | (~$greatereq(tptp_fun_I_4(N, R, A), 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0)) | (~$greatereq(read(A, tptp_fun_I_4(N, R, A)), 0))))))))))) | (~((~((~inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq(I, 2439) | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), I), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), I), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0))))))) | (~(inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439) | (~((~$greatereq(tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1)), 0)) | (~((~$greatereq($sum(max(write(write(elem!8, 0, 0), 0, -1), 2439), $product(-1, read(write(write(elem!8, 0, 0), 0, -1), tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1))))), 0)) | (~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1))), 0)))) | $greatereq(tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1)), 2439))))))))),
% 28.14/18.35 inference(rewrite,[status(thm)],[])).
% 28.14/18.35 tff(22,plain,
% 28.14/18.35 ((~((~((~inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439)) | ![I: $int] : ($lesseq($sum(2439, $product(-1, I)), 0) | (~$greatereq(I, 0)) | (~((~$greatereq($sum(max(write(write(elem!8, 0, 0), 0, -1), 2439), $product(-1, read(write(write(elem!8, 0, 0), 0, -1), I))), 0)) | (~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), I), 0))))))) | (~(inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439) | (~($lesseq($sum(2439, $product(-1, tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1)))), 0) | (~$greatereq(tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1)), 0)) | (~((~$greatereq($sum(max(write(write(elem!8, 0, 0), 0, -1), 2439), $product(-1, read(write(write(elem!8, 0, 0), 0, -1), tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1))))), 0)) | (~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1))), 0)))))))))) <=> (~((~((~inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq(I, 2439) | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), I), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), I), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0))))))) | (~(inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439) | (~((~$greatereq(tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1)), 0)) | (~((~$greatereq($sum(max(write(write(elem!8, 0, 0), 0, -1), 2439), $product(-1, read(write(write(elem!8, 0, 0), 0, -1), tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1))))), 0)) | (~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1))), 0)))) | $greatereq(tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1)), 2439)))))))),
% 28.14/18.35 inference(rewrite,[status(thm)],[])).
% 28.14/18.35 tff(23,plain,
% 28.14/18.35 (((~![A: array, R: $int, N: $int] : (~((~((~inRange(A, R, N)) | ![I: $int] : ($lesseq($sum(N, $product(-1, I)), 0) | (~$greatereq(I, 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, I))), 0)) | (~$greatereq(read(A, I), 0))))))) | (~(inRange(A, R, N) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0) | (~$greatereq(tptp_fun_I_4(N, R, A), 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0)) | (~$greatereq(read(A, tptp_fun_I_4(N, R, A)), 0))))))))))) | (~((~((~inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439)) | ![I: $int] : ($lesseq($sum(2439, $product(-1, I)), 0) | (~$greatereq(I, 0)) | (~((~$greatereq($sum(max(write(write(elem!8, 0, 0), 0, -1), 2439), $product(-1, read(write(write(elem!8, 0, 0), 0, -1), I))), 0)) | (~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), I), 0))))))) | (~(inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439) | (~($lesseq($sum(2439, $product(-1, tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1)))), 0) | (~$greatereq(tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1)), 0)) | (~((~$greatereq($sum(max(write(write(elem!8, 0, 0), 0, -1), 2439), $product(-1, read(write(write(elem!8, 0, 0), 0, -1), tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1))))), 0)) | (~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1))), 0))))))))))) <=> ((~![A: array, R: $int, N: $int] : (~((~((~inRange(A, R, N)) | ![I: $int] : ($lesseq($sum(N, $product(-1, I)), 0) | (~$greatereq(I, 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, I))), 0)) | (~$greatereq(read(A, I), 0))))))) | (~(inRange(A, R, N) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0) | (~$greatereq(tptp_fun_I_4(N, R, A), 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0)) | (~$greatereq(read(A, tptp_fun_I_4(N, R, A)), 0))))))))))) | (~((~((~inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq(I, 2439) | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), I), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), I), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0))))))) | (~(inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439) | (~((~$greatereq(tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1)), 0)) | (~((~$greatereq($sum(max(write(write(elem!8, 0, 0), 0, -1), 2439), $product(-1, read(write(write(elem!8, 0, 0), 0, -1), tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1))))), 0)) | (~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1))), 0)))) | $greatereq(tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1)), 2439))))))))),
% 28.14/18.35 inference(monotonicity,[status(thm)],[22])).
% 28.14/18.35 tff(24,plain,
% 28.14/18.35 (((~![A: array, R: $int, N: $int] : (~((~((~inRange(A, R, N)) | ![I: $int] : ($lesseq($sum(N, $product(-1, I)), 0) | (~$greatereq(I, 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, I))), 0)) | (~$greatereq(read(A, I), 0))))))) | (~(inRange(A, R, N) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0) | (~$greatereq(tptp_fun_I_4(N, R, A), 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0)) | (~$greatereq(read(A, tptp_fun_I_4(N, R, A)), 0))))))))))) | (~((~((~inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439)) | ![I: $int] : ($lesseq($sum(2439, $product(-1, I)), 0) | (~$greatereq(I, 0)) | (~((~$greatereq($sum(max(write(write(elem!8, 0, 0), 0, -1), 2439), $product(-1, read(write(write(elem!8, 0, 0), 0, -1), I))), 0)) | (~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), I), 0))))))) | (~(inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439) | (~($lesseq($sum(2439, $product(-1, tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1)))), 0) | (~$greatereq(tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1)), 0)) | (~((~$greatereq($sum(max(write(write(elem!8, 0, 0), 0, -1), 2439), $product(-1, read(write(write(elem!8, 0, 0), 0, -1), tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1))))), 0)) | (~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1))), 0))))))))))) <=> ((~![A: array, R: $int, N: $int] : (~((~((~inRange(A, R, N)) | ![I: $int] : ($lesseq($sum(N, $product(-1, I)), 0) | (~$greatereq(I, 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, I))), 0)) | (~$greatereq(read(A, I), 0))))))) | (~(inRange(A, R, N) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0) | (~$greatereq(tptp_fun_I_4(N, R, A), 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0)) | (~$greatereq(read(A, tptp_fun_I_4(N, R, A)), 0))))))))))) | (~((~((~inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq(I, 2439) | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), I), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), I), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0))))))) | (~(inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439) | (~((~$greatereq(tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1)), 0)) | (~((~$greatereq($sum(max(write(write(elem!8, 0, 0), 0, -1), 2439), $product(-1, read(write(write(elem!8, 0, 0), 0, -1), tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1))))), 0)) | (~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1))), 0)))) | $greatereq(tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1)), 2439))))))))),
% 28.14/18.35 inference(transitivity,[status(thm)],[23, 21])).
% 28.14/18.35 tff(25,plain,
% 28.14/18.35 ((~![A: array, R: $int, N: $int] : (~((~((~inRange(A, R, N)) | ![I: $int] : ($lesseq($sum(N, $product(-1, I)), 0) | (~$greatereq(I, 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, I))), 0)) | (~$greatereq(read(A, I), 0))))))) | (~(inRange(A, R, N) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0) | (~$greatereq(tptp_fun_I_4(N, R, A), 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0)) | (~$greatereq(read(A, tptp_fun_I_4(N, R, A)), 0))))))))))) | (~((~((~inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439)) | ![I: $int] : ($lesseq($sum(2439, $product(-1, I)), 0) | (~$greatereq(I, 0)) | (~((~$greatereq($sum(max(write(write(elem!8, 0, 0), 0, -1), 2439), $product(-1, read(write(write(elem!8, 0, 0), 0, -1), I))), 0)) | (~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), I), 0))))))) | (~(inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439) | (~($lesseq($sum(2439, $product(-1, tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1)))), 0) | (~$greatereq(tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1)), 0)) | (~((~$greatereq($sum(max(write(write(elem!8, 0, 0), 0, -1), 2439), $product(-1, read(write(write(elem!8, 0, 0), 0, -1), tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1))))), 0)) | (~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1))), 0))))))))))),
% 28.14/18.35 inference(quant_inst,[status(thm)],[])).
% 28.14/18.35 tff(26,plain,
% 28.14/18.35 ((~![A: array, R: $int, N: $int] : (~((~((~inRange(A, R, N)) | ![I: $int] : ($lesseq($sum(N, $product(-1, I)), 0) | (~$greatereq(I, 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, I))), 0)) | (~$greatereq(read(A, I), 0))))))) | (~(inRange(A, R, N) | (~($lesseq($sum(N, $product(-1, tptp_fun_I_4(N, R, A))), 0) | (~$greatereq(tptp_fun_I_4(N, R, A), 0)) | (~((~$greatereq($sum(R, $product(-1, read(A, tptp_fun_I_4(N, R, A)))), 0)) | (~$greatereq(read(A, tptp_fun_I_4(N, R, A)), 0))))))))))) | (~((~((~inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq(I, 2439) | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), I), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), I), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0))))))) | (~(inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439) | (~((~$greatereq(tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1)), 0)) | (~((~$greatereq($sum(max(write(write(elem!8, 0, 0), 0, -1), 2439), $product(-1, read(write(write(elem!8, 0, 0), 0, -1), tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1))))), 0)) | (~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1))), 0)))) | $greatereq(tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1)), 2439)))))))),
% 28.14/18.35 inference(modus_ponens,[status(thm)],[25, 24])).
% 28.14/18.35 tff(27,plain,
% 28.14/18.35 ($false),
% 28.14/18.35 inference(unit_resolution,[status(thm)],[26, 20, 1])).
% 28.14/18.35 tff(28,plain,(~((~((~inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq(I, 2439) | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), I), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), I), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0))))))) | (~(inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439) | (~((~$greatereq(tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1)), 0)) | (~((~$greatereq($sum(max(write(write(elem!8, 0, 0), 0, -1), 2439), $product(-1, read(write(write(elem!8, 0, 0), 0, -1), tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1))))), 0)) | (~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1))), 0)))) | $greatereq(tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1)), 2439))))))), inference(lemma,lemma(discharge,[]))).
% 28.14/18.35 tff(29,plain,
% 28.14/18.35 (((~((~inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq(I, 2439) | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), I), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), I), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0))))))) | (~(inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439) | (~((~$greatereq(tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1)), 0)) | (~((~$greatereq($sum(max(write(write(elem!8, 0, 0), 0, -1), 2439), $product(-1, read(write(write(elem!8, 0, 0), 0, -1), tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1))))), 0)) | (~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1))), 0)))) | $greatereq(tptp_fun_I_4(2439, max(write(write(elem!8, 0, 0), 0, -1), 2439), write(write(elem!8, 0, 0), 0, -1)), 2439)))))) | ((~inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq(I, 2439) | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), I), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), I), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0))))))),
% 28.14/18.35 inference(tautology,[status(thm)],[])).
% 28.14/18.35 tff(30,plain,
% 28.14/18.35 ((~inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq(I, 2439) | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), I), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), I), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0)))))),
% 28.14/18.35 inference(unit_resolution,[status(thm)],[29, 28])).
% 28.14/18.35 tff(31,plain,
% 28.14/18.35 (^[A: array, I: $int, V: $int] : refl(($sum(V, $product(-1, read(write(A, I, V), I))) = 0) <=> ($sum(V, $product(-1, read(write(A, I, V), I))) = 0))),
% 28.14/18.35 inference(bind,[status(th)],[])).
% 28.14/18.35 tff(32,plain,
% 28.14/18.35 (![A: array, I: $int, V: $int] : ($sum(V, $product(-1, read(write(A, I, V), I))) = 0) <=> ![A: array, I: $int, V: $int] : ($sum(V, $product(-1, read(write(A, I, V), I))) = 0)),
% 28.14/18.35 inference(quant_intro,[status(thm)],[31])).
% 28.14/18.35 tff(33,plain,
% 28.14/18.35 (^[A: array, I: $int, V: $int] : trans(monotonicity(rewrite($sum(read(write(A, I, V), I), $product(-1, V)) = $sum($product(-1, V), read(write(A, I, V), I))), (($sum(read(write(A, I, V), I), $product(-1, V)) = 0) <=> ($sum($product(-1, V), read(write(A, I, V), I)) = 0))), rewrite(($sum($product(-1, V), read(write(A, I, V), I)) = 0) <=> ($sum(V, $product(-1, read(write(A, I, V), I))) = 0)), (($sum(read(write(A, I, V), I), $product(-1, V)) = 0) <=> ($sum(V, $product(-1, read(write(A, I, V), I))) = 0)))),
% 28.14/18.35 inference(bind,[status(th)],[])).
% 28.14/18.35 tff(34,plain,
% 28.14/18.35 (![A: array, I: $int, V: $int] : ($sum(read(write(A, I, V), I), $product(-1, V)) = 0) <=> ![A: array, I: $int, V: $int] : ($sum(V, $product(-1, read(write(A, I, V), I))) = 0)),
% 28.14/18.35 inference(quant_intro,[status(thm)],[33])).
% 28.14/18.35 tff(35,plain,
% 28.14/18.35 (^[A: array, I: $int, V: $int] : rewrite((read(write(A, I, V), I) = V) <=> ($sum(read(write(A, I, V), I), $product(-1, V)) = 0))),
% 28.14/18.35 inference(bind,[status(th)],[])).
% 28.14/18.35 tff(36,plain,
% 28.14/18.35 (![A: array, I: $int, V: $int] : (read(write(A, I, V), I) = V) <=> ![A: array, I: $int, V: $int] : ($sum(read(write(A, I, V), I), $product(-1, V)) = 0)),
% 28.14/18.35 inference(quant_intro,[status(thm)],[35])).
% 28.14/18.35 tff(37,plain,
% 28.14/18.35 (![A: array, I: $int, V: $int] : (read(write(A, I, V), I) = V) <=> ![A: array, I: $int, V: $int] : (read(write(A, I, V), I) = V)),
% 28.14/18.35 inference(rewrite,[status(thm)],[])).
% 28.14/18.35 tff(38,axiom,(![A: array, I: $int, V: $int] : (read(write(A, I, V), I) = V)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax1')).
% 28.14/18.35 tff(39,plain,
% 28.14/18.35 (![A: array, I: $int, V: $int] : (read(write(A, I, V), I) = V)),
% 28.14/18.35 inference(modus_ponens,[status(thm)],[38, 37])).
% 28.14/18.35 tff(40,plain,
% 28.14/18.35 (![A: array, I: $int, V: $int] : ($sum(read(write(A, I, V), I), $product(-1, V)) = 0)),
% 28.14/18.35 inference(modus_ponens,[status(thm)],[39, 36])).
% 28.14/18.35 tff(41,plain,
% 28.14/18.35 (![A: array, I: $int, V: $int] : ($sum(V, $product(-1, read(write(A, I, V), I))) = 0)),
% 28.14/18.35 inference(modus_ponens,[status(thm)],[40, 34])).
% 28.14/18.35 tff(42,plain,(
% 28.14/18.35 ![A: array, I: $int, V: $int] : ($sum(V, $product(-1, read(write(A, I, V), I))) = 0)),
% 28.14/18.35 inference(skolemize,[status(sab)],[41])).
% 28.14/18.35 tff(43,plain,
% 28.14/18.35 (![A: array, I: $int, V: $int] : ($sum(V, $product(-1, read(write(A, I, V), I))) = 0)),
% 28.14/18.35 inference(modus_ponens,[status(thm)],[42, 32])).
% 28.14/18.35 tff(44,plain,
% 28.14/18.35 (((~![A: array, I: $int, V: $int] : ($sum(V, $product(-1, read(write(A, I, V), I))) = 0)) | (read(write(write(elem!8, 0, 0), 0, -1), 0) = -1)) <=> ((~![A: array, I: $int, V: $int] : ($sum(V, $product(-1, read(write(A, I, V), I))) = 0)) | (read(write(write(elem!8, 0, 0), 0, -1), 0) = -1))),
% 28.14/18.35 inference(rewrite,[status(thm)],[])).
% 28.14/18.35 tff(45,plain,
% 28.14/18.35 (($sum(-1, $product(-1, read(write(write(elem!8, 0, 0), 0, -1), 0))) = 0) <=> (read(write(write(elem!8, 0, 0), 0, -1), 0) = -1)),
% 28.14/18.35 inference(rewrite,[status(thm)],[])).
% 28.14/18.35 tff(46,plain,
% 28.14/18.35 (((~![A: array, I: $int, V: $int] : ($sum(V, $product(-1, read(write(A, I, V), I))) = 0)) | ($sum(-1, $product(-1, read(write(write(elem!8, 0, 0), 0, -1), 0))) = 0)) <=> ((~![A: array, I: $int, V: $int] : ($sum(V, $product(-1, read(write(A, I, V), I))) = 0)) | (read(write(write(elem!8, 0, 0), 0, -1), 0) = -1))),
% 28.14/18.35 inference(monotonicity,[status(thm)],[45])).
% 28.14/18.35 tff(47,plain,
% 28.14/18.35 (((~![A: array, I: $int, V: $int] : ($sum(V, $product(-1, read(write(A, I, V), I))) = 0)) | ($sum(-1, $product(-1, read(write(write(elem!8, 0, 0), 0, -1), 0))) = 0)) <=> ((~![A: array, I: $int, V: $int] : ($sum(V, $product(-1, read(write(A, I, V), I))) = 0)) | (read(write(write(elem!8, 0, 0), 0, -1), 0) = -1))),
% 28.14/18.35 inference(transitivity,[status(thm)],[46, 44])).
% 28.14/18.35 tff(48,plain,
% 28.14/18.35 ((~![A: array, I: $int, V: $int] : ($sum(V, $product(-1, read(write(A, I, V), I))) = 0)) | ($sum(-1, $product(-1, read(write(write(elem!8, 0, 0), 0, -1), 0))) = 0)),
% 28.14/18.35 inference(quant_inst,[status(thm)],[])).
% 28.14/18.35 tff(49,plain,
% 28.14/18.35 ((~![A: array, I: $int, V: $int] : ($sum(V, $product(-1, read(write(A, I, V), I))) = 0)) | (read(write(write(elem!8, 0, 0), 0, -1), 0) = -1)),
% 28.14/18.36 inference(modus_ponens,[status(thm)],[48, 47])).
% 28.14/18.36 tff(50,plain,
% 28.14/18.36 (read(write(write(elem!8, 0, 0), 0, -1), 0) = -1),
% 28.14/18.36 inference(unit_resolution,[status(thm)],[49, 43])).
% 28.14/18.36 tff(51,plain,
% 28.14/18.36 ((~(read(write(write(elem!8, 0, 0), 0, -1), 0) = -1)) | $lesseq(read(write(write(elem!8, 0, 0), 0, -1), 0), -1)),
% 28.14/18.36 inference(theory_lemma,[status(thm)],[])).
% 28.14/18.36 tff(52,plain,
% 28.14/18.36 ($lesseq(read(write(write(elem!8, 0, 0), 0, -1), 0), -1)),
% 28.14/18.36 inference(unit_resolution,[status(thm)],[51, 50])).
% 28.14/18.36 tff(53,plain,
% 28.14/18.36 ((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), 0), 0)) | (~$lesseq(read(write(write(elem!8, 0, 0), 0, -1), 0), -1))),
% 28.14/18.36 inference(theory_lemma,[status(thm)],[])).
% 28.14/18.36 tff(54,plain,
% 28.14/18.36 (~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), 0), 0)),
% 28.14/18.36 inference(unit_resolution,[status(thm)],[53, 52])).
% 28.14/18.36 tff(55,plain,
% 28.14/18.36 (((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), 0), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), 0), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0))) | $greatereq(read(write(write(elem!8, 0, 0), 0, -1), 0), 0)),
% 28.14/18.36 inference(tautology,[status(thm)],[])).
% 28.14/18.36 tff(56,plain,
% 28.14/18.36 ((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), 0), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), 0), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0))),
% 28.14/18.36 inference(unit_resolution,[status(thm)],[55, 54])).
% 28.14/18.36 tff(57,assumption,(![I: $int] : ((~$greatereq(I, 0)) | $greatereq(I, 2439) | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), I), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), I), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0)))))), introduced(assumption)).
% 28.14/18.36 tff(58,plain,
% 28.14/18.36 (((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq(I, 2439) | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), I), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), I), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0)))))) | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), 0), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), 0), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0))))) <=> ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq(I, 2439) | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), I), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), I), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0)))))) | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), 0), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), 0), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0)))))),
% 28.14/18.36 inference(rewrite,[status(thm)],[])).
% 28.14/18.36 tff(59,plain,
% 28.14/18.36 (($false | $false | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), 0), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), 0), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0))))) <=> (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), 0), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), 0), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0))))),
% 28.14/18.36 inference(rewrite,[status(thm)],[])).
% 28.14/18.36 tff(60,plain,
% 28.14/18.36 ($greatereq(0, 2439) <=> $false),
% 28.14/18.36 inference(rewrite,[status(thm)],[])).
% 28.14/18.36 tff(61,plain,
% 28.14/18.36 ((~$true) <=> $false),
% 28.14/18.36 inference(rewrite,[status(thm)],[])).
% 28.14/18.36 tff(62,plain,
% 28.14/18.36 ($greatereq(0, 0) <=> $true),
% 28.14/18.36 inference(rewrite,[status(thm)],[])).
% 28.14/18.36 tff(63,plain,
% 28.14/18.36 ((~$greatereq(0, 0)) <=> (~$true)),
% 28.14/18.36 inference(monotonicity,[status(thm)],[62])).
% 28.14/18.36 tff(64,plain,
% 28.14/18.36 ((~$greatereq(0, 0)) <=> $false),
% 28.14/18.36 inference(transitivity,[status(thm)],[63, 61])).
% 28.14/18.36 tff(65,plain,
% 28.14/18.36 (((~$greatereq(0, 0)) | $greatereq(0, 2439) | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), 0), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), 0), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0))))) <=> ($false | $false | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), 0), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), 0), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0)))))),
% 28.14/18.36 inference(monotonicity,[status(thm)],[64, 60])).
% 28.14/18.36 tff(66,plain,
% 28.14/18.36 (((~$greatereq(0, 0)) | $greatereq(0, 2439) | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), 0), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), 0), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0))))) <=> (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), 0), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), 0), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0))))),
% 28.14/18.36 inference(transitivity,[status(thm)],[65, 59])).
% 28.14/18.36 tff(67,plain,
% 28.14/18.36 (((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq(I, 2439) | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), I), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), I), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0)))))) | ((~$greatereq(0, 0)) | $greatereq(0, 2439) | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), 0), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), 0), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0)))))) <=> ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq(I, 2439) | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), I), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), I), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0)))))) | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), 0), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), 0), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0)))))),
% 28.14/18.36 inference(monotonicity,[status(thm)],[66])).
% 28.14/18.36 tff(68,plain,
% 28.14/18.36 (((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq(I, 2439) | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), I), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), I), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0)))))) | ((~$greatereq(0, 0)) | $greatereq(0, 2439) | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), 0), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), 0), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0)))))) <=> ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq(I, 2439) | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), I), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), I), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0)))))) | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), 0), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), 0), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0)))))),
% 28.14/18.36 inference(transitivity,[status(thm)],[67, 58])).
% 28.14/18.36 tff(69,plain,
% 28.14/18.36 ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq(I, 2439) | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), I), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), I), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0)))))) | ((~$greatereq(0, 0)) | $greatereq(0, 2439) | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), 0), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), 0), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0)))))),
% 28.14/18.36 inference(quant_inst,[status(thm)],[])).
% 28.14/18.36 tff(70,plain,
% 28.14/18.36 ((~![I: $int] : ((~$greatereq(I, 0)) | $greatereq(I, 2439) | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), I), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), I), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0)))))) | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), 0), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), 0), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0))))),
% 28.14/18.36 inference(modus_ponens,[status(thm)],[69, 68])).
% 28.14/18.36 tff(71,plain,
% 28.14/18.36 ($false),
% 28.14/18.36 inference(unit_resolution,[status(thm)],[70, 57, 56])).
% 28.14/18.36 tff(72,plain,(~![I: $int] : ((~$greatereq(I, 0)) | $greatereq(I, 2439) | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), I), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), I), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0)))))), inference(lemma,lemma(discharge,[]))).
% 28.14/18.36 tff(73,plain,
% 28.14/18.36 ((~((~inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq(I, 2439) | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), I), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), I), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0))))))) | (~inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq(I, 2439) | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), I), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), I), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0)))))),
% 28.14/18.36 inference(tautology,[status(thm)],[])).
% 28.14/18.36 tff(74,plain,
% 28.14/18.36 ((~((~inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439)) | ![I: $int] : ((~$greatereq(I, 0)) | $greatereq(I, 2439) | (~((~$greatereq(read(write(write(elem!8, 0, 0), 0, -1), I), 0)) | (~$lesseq($sum(read(write(write(elem!8, 0, 0), 0, -1), I), $product(-1, max(write(write(elem!8, 0, 0), 0, -1), 2439))), 0))))))) | (~inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439))),
% 28.14/18.36 inference(unit_resolution,[status(thm)],[73, 72])).
% 28.14/18.36 tff(75,plain,
% 28.14/18.36 (~inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439)),
% 28.14/18.36 inference(unit_resolution,[status(thm)],[74, 30])).
% 28.14/18.36 tff(76,plain,
% 28.14/18.36 (^[A: array, N: $int] : refl(((~$greatereq(N, 0)) | inRange(A, max(A, N), N)) <=> ((~$greatereq(N, 0)) | inRange(A, max(A, N), N)))),
% 28.14/18.36 inference(bind,[status(th)],[])).
% 28.14/18.36 tff(77,plain,
% 28.14/18.36 (![A: array, N: $int] : ((~$greatereq(N, 0)) | inRange(A, max(A, N), N)) <=> ![A: array, N: $int] : ((~$greatereq(N, 0)) | inRange(A, max(A, N), N))),
% 28.14/18.36 inference(quant_intro,[status(thm)],[76])).
% 28.14/18.36 tff(78,plain,
% 28.14/18.36 (![A: array, N: $int] : ((~$greatereq(N, 0)) | inRange(A, max(A, N), N)) <=> ![A: array, N: $int] : ((~$greatereq(N, 0)) | inRange(A, max(A, N), N))),
% 28.14/18.36 inference(rewrite,[status(thm)],[])).
% 28.14/18.36 tff(79,plain,
% 28.14/18.36 ((~(~![A: array, N: $int] : ((~$greatereq(N, 0)) | inRange(A, max(A, N), N)))) <=> ![A: array, N: $int] : ((~$greatereq(N, 0)) | inRange(A, max(A, N), N))),
% 28.14/18.36 inference(rewrite,[status(thm)],[])).
% 28.14/18.36 tff(80,plain,
% 28.14/18.36 ((~![A: array, N: $int] : ($greatereq(N, 0) => inRange(A, max(A, N), N))) <=> (~![A: array, N: $int] : ((~$greatereq(N, 0)) | inRange(A, max(A, N), N)))),
% 28.14/18.36 inference(rewrite,[status(thm)],[])).
% 28.14/18.36 tff(81,plain,
% 28.14/18.36 ((~(~![A: array, N: $int] : ($greatereq(N, 0) => inRange(A, max(A, N), N)))) <=> (~(~![A: array, N: $int] : ((~$greatereq(N, 0)) | inRange(A, max(A, N), N))))),
% 28.14/18.36 inference(monotonicity,[status(thm)],[80])).
% 28.14/18.36 tff(82,plain,
% 28.14/18.36 ((~(~![A: array, N: $int] : ($greatereq(N, 0) => inRange(A, max(A, N), N)))) <=> ![A: array, N: $int] : ((~$greatereq(N, 0)) | inRange(A, max(A, N), N))),
% 28.14/18.36 inference(transitivity,[status(thm)],[81, 79])).
% 28.14/18.36 tff(83,axiom,(~(~![A: array, N: $int] : ($greatereq(N, 0) => inRange(A, max(A, N), N)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c1')).
% 28.14/18.36 tff(84,plain,
% 28.14/18.36 (![A: array, N: $int] : ((~$greatereq(N, 0)) | inRange(A, max(A, N), N))),
% 28.14/18.36 inference(modus_ponens,[status(thm)],[83, 82])).
% 28.14/18.36 tff(85,plain,
% 28.14/18.36 (![A: array, N: $int] : ((~$greatereq(N, 0)) | inRange(A, max(A, N), N))),
% 28.14/18.36 inference(modus_ponens,[status(thm)],[84, 78])).
% 28.14/18.36 tff(86,plain,(
% 28.14/18.36 ![A: array, N: $int] : ((~$greatereq(N, 0)) | inRange(A, max(A, N), N))),
% 28.14/18.36 inference(skolemize,[status(sab)],[85])).
% 28.14/18.36 tff(87,plain,
% 28.14/18.36 (![A: array, N: $int] : ((~$greatereq(N, 0)) | inRange(A, max(A, N), N))),
% 28.14/18.36 inference(modus_ponens,[status(thm)],[86, 77])).
% 28.14/18.36 tff(88,plain,
% 28.14/18.36 (((~![A: array, N: $int] : ((~$greatereq(N, 0)) | inRange(A, max(A, N), N))) | inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439)) <=> ((~![A: array, N: $int] : ((~$greatereq(N, 0)) | inRange(A, max(A, N), N))) | inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439))),
% 28.14/18.36 inference(rewrite,[status(thm)],[])).
% 28.14/18.37 tff(89,plain,
% 28.14/18.37 (($false | inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439)) <=> inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439)),
% 28.14/18.37 inference(rewrite,[status(thm)],[])).
% 28.14/18.37 tff(90,plain,
% 28.14/18.37 ($greatereq(2439, 0) <=> $true),
% 28.14/18.37 inference(rewrite,[status(thm)],[])).
% 28.14/18.37 tff(91,plain,
% 28.14/18.37 ((~$greatereq(2439, 0)) <=> (~$true)),
% 28.14/18.37 inference(monotonicity,[status(thm)],[90])).
% 28.14/18.37 tff(92,plain,
% 28.14/18.37 ((~$greatereq(2439, 0)) <=> $false),
% 28.14/18.37 inference(transitivity,[status(thm)],[91, 61])).
% 28.14/18.37 tff(93,plain,
% 28.14/18.37 (((~$greatereq(2439, 0)) | inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439)) <=> ($false | inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439))),
% 28.14/18.37 inference(monotonicity,[status(thm)],[92])).
% 28.14/18.37 tff(94,plain,
% 28.14/18.37 (((~$greatereq(2439, 0)) | inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439)) <=> inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439)),
% 28.14/18.37 inference(transitivity,[status(thm)],[93, 89])).
% 28.14/18.37 tff(95,plain,
% 28.14/18.37 (((~![A: array, N: $int] : ((~$greatereq(N, 0)) | inRange(A, max(A, N), N))) | ((~$greatereq(2439, 0)) | inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439))) <=> ((~![A: array, N: $int] : ((~$greatereq(N, 0)) | inRange(A, max(A, N), N))) | inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439))),
% 28.14/18.37 inference(monotonicity,[status(thm)],[94])).
% 28.14/18.37 tff(96,plain,
% 28.14/18.37 (((~![A: array, N: $int] : ((~$greatereq(N, 0)) | inRange(A, max(A, N), N))) | ((~$greatereq(2439, 0)) | inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439))) <=> ((~![A: array, N: $int] : ((~$greatereq(N, 0)) | inRange(A, max(A, N), N))) | inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439))),
% 28.14/18.37 inference(transitivity,[status(thm)],[95, 88])).
% 28.14/18.37 tff(97,plain,
% 28.14/18.37 ((~![A: array, N: $int] : ((~$greatereq(N, 0)) | inRange(A, max(A, N), N))) | ((~$greatereq(2439, 0)) | inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439))),
% 28.14/18.37 inference(quant_inst,[status(thm)],[])).
% 28.14/18.37 tff(98,plain,
% 28.14/18.37 ((~![A: array, N: $int] : ((~$greatereq(N, 0)) | inRange(A, max(A, N), N))) | inRange(write(write(elem!8, 0, 0), 0, -1), max(write(write(elem!8, 0, 0), 0, -1), 2439), 2439)),
% 28.14/18.37 inference(modus_ponens,[status(thm)],[97, 96])).
% 28.14/18.37 tff(99,plain,
% 28.14/18.37 ($false),
% 28.14/18.37 inference(unit_resolution,[status(thm)],[98, 87, 75])).
% 28.14/18.37 % SZS output end Proof
%------------------------------------------------------------------------------