TSTP Solution File: SWW588_2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW588_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 20:59:22 EDT 2022
% Result : Theorem 70.08s 45.36s
% Output : Proof 70.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWW588_2 : TPTP v8.1.0. Released v6.1.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Sep 4 20:09:20 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.
% 70.08/45.36 % SZS status Theorem
% 70.08/45.36 % SZS output start Proof
% 70.08/45.36 tff(tptp_fun_Q_2_type, type, (
% 70.08/45.36 tptp_fun_Q_2: $int)).
% 70.08/45.36 tff(tptp_fun_B_0_type, type, (
% 70.08/45.36 tptp_fun_B_0: $int)).
% 70.08/45.36 tff(tptp_fun_A_1_type, type, (
% 70.08/45.36 tptp_fun_A_1: $int)).
% 70.08/45.36 tff(tptp_fun_R_3_type, type, (
% 70.08/45.36 tptp_fun_R_3: $int)).
% 70.08/45.36 tff(tptp_fun_R1_5_type, type, (
% 70.08/45.36 tptp_fun_R1_5: $int)).
% 70.08/45.36 tff(tptp_fun_Q1_4_type, type, (
% 70.08/45.36 tptp_fun_Q1_4: $int)).
% 70.08/45.36 tff(1,plain,
% 70.08/45.36 ((($greatereq(A!1, 0) & (~$lesseq(B!0, 0))) & ((~$greatereq(A!1, 0)) | (($sum(A!1, $sum($product(-1, R!3), $product(-1, $product(B!0, Q!2)))) = 0) & $greatereq(R!3, 0) & (($lesseq($sum(B!0, $product(-1, R!3)), 0) & ($sum(Q!2, $product(-1, Q1!4)) = -1) & (~((~($sum(B!0, $sum($product(-1, R!3), R1!5)) = 0)) | (($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))) = 0) & $greatereq(R1!5, 0) & $greatereq(R!3, 0) & (~$lesseq($sum(R!3, $product(-1, R1!5)), 0)))))) | ((~$lesseq($sum(B!0, $product(-1, R!3)), 0)) & ![R1: $int] : (~(($sum(R1, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0) & $greatereq(R1, 0) & (~$greatereq($sum(R1, $product(-1, B!0)), 0))))))))) <=> ($greatereq(A!1, 0) & (~$lesseq(B!0, 0)) & ((~$greatereq(A!1, 0)) | (($sum(A!1, $sum($product(-1, R!3), $product(-1, $product(B!0, Q!2)))) = 0) & $greatereq(R!3, 0) & (($lesseq($sum(B!0, $product(-1, R!3)), 0) & ($sum(Q!2, $product(-1, Q1!4)) = -1) & (~((~($sum(B!0, $sum($product(-1, R!3), R1!5)) = 0)) | (($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))) = 0) & $greatereq(R1!5, 0) & $greatereq(R!3, 0) & (~$lesseq($sum(R!3, $product(-1, R1!5)), 0)))))) | ((~$lesseq($sum(B!0, $product(-1, R!3)), 0)) & ![R1: $int] : (~(($sum(R1, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0) & $greatereq(R1, 0) & (~$greatereq($sum(R1, $product(-1, B!0)), 0)))))))))),
% 70.08/45.36 inference(rewrite,[status(thm)],[])).
% 70.08/45.36 tff(2,plain,
% 70.08/45.36 (((~$greatereq(A!1, 0)) | ((~(~(($sum(R!3, $sum($product(B!0, Q!2), $product(-1, A!1))) = 0) & $greatereq(R!3, 0)))) & (((~(~$lesseq($sum(B!0, $product(-1, R!3)), 0))) & ((~(~($sum(Q!2, $product(-1, Q1!4)) = -1))) & (~((~($sum(R1!5, $sum(B!0, $product(-1, R!3))) = 0)) | (($sum(R1!5, $sum($product(Q1!4, B!0), $product(-1, A!1))) = 0) & $greatereq(R1!5, 0) & $greatereq(R!3, 0) & (~$greatereq($sum(R1!5, $product(-1, R!3)), 0))))))) | ((~$lesseq($sum(B!0, $product(-1, R!3)), 0)) & ![R1: $int] : (~(($sum(R1, $sum($product(Q!2, B!0), $product(-1, A!1))) = 0) & $greatereq(R1, 0) & (~$greatereq($sum(R1, $product(-1, B!0)), 0)))))))) <=> ((~$greatereq(A!1, 0)) | (($sum(A!1, $sum($product(-1, R!3), $product(-1, $product(B!0, Q!2)))) = 0) & $greatereq(R!3, 0) & (($lesseq($sum(B!0, $product(-1, R!3)), 0) & ($sum(Q!2, $product(-1, Q1!4)) = -1) & (~((~($sum(B!0, $sum($product(-1, R!3), R1!5)) = 0)) | (($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))) = 0) & $greatereq(R1!5, 0) & $greatereq(R!3, 0) & (~$lesseq($sum(R!3, $product(-1, R1!5)), 0)))))) | ((~$lesseq($sum(B!0, $product(-1, R!3)), 0)) & ![R1: $int] : (~(($sum(R1, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0) & $greatereq(R1, 0) & (~$greatereq($sum(R1, $product(-1, B!0)), 0))))))))),
% 70.08/45.36 inference(rewrite,[status(thm)],[])).
% 70.08/45.36 tff(3,plain,
% 70.08/45.36 ((~(~($greatereq(A!1, 0) & (~$lesseq(B!0, 0))))) <=> ($greatereq(A!1, 0) & (~$lesseq(B!0, 0)))),
% 70.08/45.36 inference(rewrite,[status(thm)],[])).
% 70.08/45.36 tff(4,plain,
% 70.08/45.36 (((~(~($greatereq(A!1, 0) & (~$lesseq(B!0, 0))))) & ((~$greatereq(A!1, 0)) | ((~(~(($sum(R!3, $sum($product(B!0, Q!2), $product(-1, A!1))) = 0) & $greatereq(R!3, 0)))) & (((~(~$lesseq($sum(B!0, $product(-1, R!3)), 0))) & ((~(~($sum(Q!2, $product(-1, Q1!4)) = -1))) & (~((~($sum(R1!5, $sum(B!0, $product(-1, R!3))) = 0)) | (($sum(R1!5, $sum($product(Q1!4, B!0), $product(-1, A!1))) = 0) & $greatereq(R1!5, 0) & $greatereq(R!3, 0) & (~$greatereq($sum(R1!5, $product(-1, R!3)), 0))))))) | ((~$lesseq($sum(B!0, $product(-1, R!3)), 0)) & ![R1: $int] : (~(($sum(R1, $sum($product(Q!2, B!0), $product(-1, A!1))) = 0) & $greatereq(R1, 0) & (~$greatereq($sum(R1, $product(-1, B!0)), 0))))))))) <=> (($greatereq(A!1, 0) & (~$lesseq(B!0, 0))) & ((~$greatereq(A!1, 0)) | (($sum(A!1, $sum($product(-1, R!3), $product(-1, $product(B!0, Q!2)))) = 0) & $greatereq(R!3, 0) & (($lesseq($sum(B!0, $product(-1, R!3)), 0) & ($sum(Q!2, $product(-1, Q1!4)) = -1) & (~((~($sum(B!0, $sum($product(-1, R!3), R1!5)) = 0)) | (($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))) = 0) & $greatereq(R1!5, 0) & $greatereq(R!3, 0) & (~$lesseq($sum(R!3, $product(-1, R1!5)), 0)))))) | ((~$lesseq($sum(B!0, $product(-1, R!3)), 0)) & ![R1: $int] : (~(($sum(R1, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0) & $greatereq(R1, 0) & (~$greatereq($sum(R1, $product(-1, B!0)), 0)))))))))),
% 70.08/45.36 inference(monotonicity,[status(thm)],[3, 2])).
% 70.08/45.36 tff(5,plain,
% 70.08/45.36 (((~(~($greatereq(A!1, 0) & (~$lesseq(B!0, 0))))) & ((~$greatereq(A!1, 0)) | ((~(~(($sum(R!3, $sum($product(B!0, Q!2), $product(-1, A!1))) = 0) & $greatereq(R!3, 0)))) & (((~(~$lesseq($sum(B!0, $product(-1, R!3)), 0))) & ((~(~($sum(Q!2, $product(-1, Q1!4)) = -1))) & (~((~($sum(R1!5, $sum(B!0, $product(-1, R!3))) = 0)) | (($sum(R1!5, $sum($product(Q1!4, B!0), $product(-1, A!1))) = 0) & $greatereq(R1!5, 0) & $greatereq(R!3, 0) & (~$greatereq($sum(R1!5, $product(-1, R!3)), 0))))))) | ((~$lesseq($sum(B!0, $product(-1, R!3)), 0)) & ![R1: $int] : (~(($sum(R1, $sum($product(Q!2, B!0), $product(-1, A!1))) = 0) & $greatereq(R1, 0) & (~$greatereq($sum(R1, $product(-1, B!0)), 0))))))))) <=> ($greatereq(A!1, 0) & (~$lesseq(B!0, 0)) & ((~$greatereq(A!1, 0)) | (($sum(A!1, $sum($product(-1, R!3), $product(-1, $product(B!0, Q!2)))) = 0) & $greatereq(R!3, 0) & (($lesseq($sum(B!0, $product(-1, R!3)), 0) & ($sum(Q!2, $product(-1, Q1!4)) = -1) & (~((~($sum(B!0, $sum($product(-1, R!3), R1!5)) = 0)) | (($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))) = 0) & $greatereq(R1!5, 0) & $greatereq(R!3, 0) & (~$lesseq($sum(R!3, $product(-1, R1!5)), 0)))))) | ((~$lesseq($sum(B!0, $product(-1, R!3)), 0)) & ![R1: $int] : (~(($sum(R1, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0) & $greatereq(R1, 0) & (~$greatereq($sum(R1, $product(-1, B!0)), 0)))))))))),
% 70.08/45.36 inference(transitivity,[status(thm)],[4, 1])).
% 70.08/45.36 tff(6,plain,
% 70.08/45.36 ((~![A: $int, B: $int] : ((~($greatereq(A, 0) & (~$lesseq(B, 0)))) | ($greatereq(A, 0) & ![R: $int, Q: $int] : ((~(($sum(R, $sum($product(B, Q), $product(-1, A))) = 0) & $greatereq(R, 0))) | (((~$lesseq($sum(B, $product(-1, R)), 0)) | ![Q1: $int] : ((~($sum(Q, $product(-1, Q1)) = -1)) | ![R1: $int] : ((~($sum(R1, $sum(B, $product(-1, R))) = 0)) | (($sum(R1, $sum($product(Q1, B), $product(-1, A))) = 0) & $greatereq(R1, 0) & $greatereq(R, 0) & (~$greatereq($sum(R1, $product(-1, R)), 0)))))) & ($lesseq($sum(B, $product(-1, R)), 0) | ?[R1: $int] : (($sum(R1, $sum($product(Q, B), $product(-1, A))) = 0) & $greatereq(R1, 0) & (~$greatereq($sum(R1, $product(-1, B)), 0))))))))) <=> (~![A: $int, B: $int] : ((~($greatereq(A, 0) & (~$lesseq(B, 0)))) | ($greatereq(A, 0) & ![R: $int, Q: $int] : ((~(($sum(R, $sum($product(B, Q), $product(-1, A))) = 0) & $greatereq(R, 0))) | (((~$lesseq($sum(B, $product(-1, R)), 0)) | ![Q1: $int] : ((~($sum(Q, $product(-1, Q1)) = -1)) | ![R1: $int] : ((~($sum(R1, $sum(B, $product(-1, R))) = 0)) | (($sum(R1, $sum($product(Q1, B), $product(-1, A))) = 0) & $greatereq(R1, 0) & $greatereq(R, 0) & (~$greatereq($sum(R1, $product(-1, R)), 0)))))) & ($lesseq($sum(B, $product(-1, R)), 0) | ?[R1: $int] : (($sum(R1, $sum($product(Q, B), $product(-1, A))) = 0) & $greatereq(R1, 0) & (~$greatereq($sum(R1, $product(-1, B)), 0)))))))))),
% 70.08/45.36 inference(rewrite,[status(thm)],[])).
% 70.08/45.36 tff(7,plain,
% 70.08/45.36 ((~![A: $int, B: $int] : ((~($greatereq(A, 0) & (~$lesseq(B, 0)))) | ($greatereq(A, 0) & ![R: $int, Q: $int] : ((~(($sum($product(Q, B), $sum(R, $product(-1, A))) = 0) & $greatereq(R, 0))) | (((~$lesseq($sum(B, $product(-1, R)), 0)) | ![Q1: $int] : ((~($sum(Q1, $product(-1, Q)) = 1)) | ![R1: $int] : ((~($sum(R1, $sum($product(-1, R), B)) = 0)) | (($sum($product(Q1, B), $sum(R1, $product(-1, A))) = 0) & $greatereq(R1, 0) & $greatereq(R, 0) & (~$lesseq($sum(R, $product(-1, R1)), 0)))))) & ($lesseq($sum(B, $product(-1, R)), 0) | ?[R1: $int] : (($sum($product(Q, B), $sum(R1, $product(-1, A))) = 0) & $greatereq(R1, 0) & (~$lesseq($sum(B, $product(-1, R1)), 0))))))))) <=> (~![A: $int, B: $int] : ((~($greatereq(A, 0) & (~$lesseq(B, 0)))) | ($greatereq(A, 0) & ![R: $int, Q: $int] : ((~(($sum(R, $sum($product(B, Q), $product(-1, A))) = 0) & $greatereq(R, 0))) | (((~$lesseq($sum(B, $product(-1, R)), 0)) | ![Q1: $int] : ((~($sum(Q, $product(-1, Q1)) = -1)) | ![R1: $int] : ((~($sum(R1, $sum(B, $product(-1, R))) = 0)) | (($sum(R1, $sum($product(Q1, B), $product(-1, A))) = 0) & $greatereq(R1, 0) & $greatereq(R, 0) & (~$greatereq($sum(R1, $product(-1, R)), 0)))))) & ($lesseq($sum(B, $product(-1, R)), 0) | ?[R1: $int] : (($sum(R1, $sum($product(Q, B), $product(-1, A))) = 0) & $greatereq(R1, 0) & (~$greatereq($sum(R1, $product(-1, B)), 0)))))))))),
% 70.08/45.36 inference(rewrite,[status(thm)],[])).
% 70.08/45.36 tff(8,plain,
% 70.08/45.36 ((~![A: $int, B: $int] : ((~($lesseq(0, A) & (~$lesseq(B, 0)))) | ($lesseq(0, A) & ![R: $int, Q: $int] : ((~(($sum($product(Q, B), R) = A) & $lesseq(0, R))) | (((~$lesseq(B, R)) | ![Q1: $int] : ((~(Q1 = $sum(1, Q))) | ![R1: $int] : ((~(R1 = $sum(R, $product(-1, B)))) | (($sum($product(Q1, B), R1) = A) & $lesseq(0, R1) & $lesseq(0, R) & (~$lesseq(R, R1)))))) & ($lesseq(B, R) | ?[R1: $int] : (($sum($product(Q, B), R1) = A) & $lesseq(0, R1) & (~$lesseq(B, R1))))))))) <=> (~![A: $int, B: $int] : ((~($greatereq(A, 0) & (~$lesseq(B, 0)))) | ($greatereq(A, 0) & ![R: $int, Q: $int] : ((~(($sum($product(Q, B), $sum(R, $product(-1, A))) = 0) & $greatereq(R, 0))) | (((~$lesseq($sum(B, $product(-1, R)), 0)) | ![Q1: $int] : ((~($sum(Q1, $product(-1, Q)) = 1)) | ![R1: $int] : ((~($sum(R1, $sum($product(-1, R), B)) = 0)) | (($sum($product(Q1, B), $sum(R1, $product(-1, A))) = 0) & $greatereq(R1, 0) & $greatereq(R, 0) & (~$lesseq($sum(R, $product(-1, R1)), 0)))))) & ($lesseq($sum(B, $product(-1, R)), 0) | ?[R1: $int] : (($sum($product(Q, B), $sum(R1, $product(-1, A))) = 0) & $greatereq(R1, 0) & (~$lesseq($sum(B, $product(-1, R1)), 0)))))))))),
% 70.08/45.36 inference(rewrite,[status(thm)],[])).
% 70.08/45.36 tff(9,plain,
% 70.08/45.36 ((~![A: $int, B: $int] : ((~($lesseq(0, A) & (~$lesseq(B, 0)))) | ($lesseq(0, A) & ![R: $int, Q: $int] : ((~(($sum($product(Q, B), R) = A) & $lesseq(0, R))) | (((~$lesseq(B, R)) | ![Q1: $int] : ((~(Q1 = $sum(1, Q))) | ![R1: $int] : ((~(R1 = $sum(R, $product(-1, B)))) | (($sum($product(Q1, B), R1) = A) & $lesseq(0, R1) & $lesseq(0, R) & (~$lesseq(R, R1)))))) & ($lesseq(B, R) | ?[R1: $int] : (($sum($product(Q, B), R1) = A) & $lesseq(0, R1) & (~$lesseq(B, R1))))))))) <=> (~![A: $int, B: $int] : ((~($lesseq(0, A) & (~$lesseq(B, 0)))) | ($lesseq(0, A) & ![R: $int, Q: $int] : ((~(($sum($product(Q, B), R) = A) & $lesseq(0, R))) | (((~$lesseq(B, R)) | ![Q1: $int] : ((~(Q1 = $sum(1, Q))) | ![R1: $int] : ((~(R1 = $sum(R, $product(-1, B)))) | (($sum($product(Q1, B), R1) = A) & $lesseq(0, R1) & $lesseq(0, R) & (~$lesseq(R, R1)))))) & ($lesseq(B, R) | ?[R1: $int] : (($sum($product(Q, B), R1) = A) & $lesseq(0, R1) & (~$lesseq(B, R1)))))))))),
% 70.08/45.36 inference(rewrite,[status(thm)],[])).
% 70.08/45.36 tff(10,plain,
% 70.08/45.36 ((~![A: $int, B: $int] : (($lesseq(0, A) & $less(0, B)) => ((($sum($product(0, B), A) = A) & $lesseq(0, A)) & ![R: $int, Q: $int] : ((($sum($product(Q, B), R) = A) & $lesseq(0, R)) => (($lesseq(B, R) => ![Q1: $int] : ((Q1 = $sum(Q, 1)) => ![R1: $int] : ((R1 = $difference(R, B)) => (((($sum($product(Q1, B), R1) = A) & $lesseq(0, R1)) & $lesseq(0, R)) & $less(R1, R))))) & ((~$lesseq(B, R)) => ?[R1: $int] : ((($sum($product(Q, B), R1) = A) & $lesseq(0, R1)) & $less(R1, B)))))))) <=> (~![A: $int, B: $int] : ((~($lesseq(0, A) & (~$lesseq(B, 0)))) | ($lesseq(0, A) & ![R: $int, Q: $int] : ((~(($sum($product(Q, B), R) = A) & $lesseq(0, R))) | (((~$lesseq(B, R)) | ![Q1: $int] : ((~(Q1 = $sum(1, Q))) | ![R1: $int] : ((~(R1 = $sum(R, $product(-1, B)))) | (($sum($product(Q1, B), R1) = A) & $lesseq(0, R1) & $lesseq(0, R) & (~$lesseq(R, R1)))))) & ($lesseq(B, R) | ?[R1: $int] : (($sum($product(Q, B), R1) = A) & $lesseq(0, R1) & (~$lesseq(B, R1)))))))))),
% 70.08/45.36 inference(rewrite,[status(thm)],[])).
% 70.08/45.36 tff(11,axiom,(~![A: $int, B: $int] : (($lesseq(0, A) & $less(0, B)) => ((($sum($product(0, B), A) = A) & $lesseq(0, A)) & ![R: $int, Q: $int] : ((($sum($product(Q, B), R) = A) & $lesseq(0, R)) => (($lesseq(B, R) => ![Q1: $int] : ((Q1 = $sum(Q, 1)) => ![R1: $int] : ((R1 = $difference(R, B)) => (((($sum($product(Q1, B), R1) = A) & $lesseq(0, R1)) & $lesseq(0, R)) & $less(R1, R))))) & ((~$lesseq(B, R)) => ?[R1: $int] : ((($sum($product(Q, B), R1) = A) & $lesseq(0, R1)) & $less(R1, B)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','wP_parameter_division')).
% 70.08/45.36 tff(12,plain,
% 70.08/45.36 (~![A: $int, B: $int] : ((~($lesseq(0, A) & (~$lesseq(B, 0)))) | ($lesseq(0, A) & ![R: $int, Q: $int] : ((~(($sum($product(Q, B), R) = A) & $lesseq(0, R))) | (((~$lesseq(B, R)) | ![Q1: $int] : ((~(Q1 = $sum(1, Q))) | ![R1: $int] : ((~(R1 = $sum(R, $product(-1, B)))) | (($sum($product(Q1, B), R1) = A) & $lesseq(0, R1) & $lesseq(0, R) & (~$lesseq(R, R1)))))) & ($lesseq(B, R) | ?[R1: $int] : (($sum($product(Q, B), R1) = A) & $lesseq(0, R1) & (~$lesseq(B, R1))))))))),
% 70.08/45.36 inference(modus_ponens,[status(thm)],[11, 10])).
% 70.08/45.36 tff(13,plain,
% 70.08/45.36 (~![A: $int, B: $int] : ((~($lesseq(0, A) & (~$lesseq(B, 0)))) | ($lesseq(0, A) & ![R: $int, Q: $int] : ((~(($sum($product(Q, B), R) = A) & $lesseq(0, R))) | (((~$lesseq(B, R)) | ![Q1: $int] : ((~(Q1 = $sum(1, Q))) | ![R1: $int] : ((~(R1 = $sum(R, $product(-1, B)))) | (($sum($product(Q1, B), R1) = A) & $lesseq(0, R1) & $lesseq(0, R) & (~$lesseq(R, R1)))))) & ($lesseq(B, R) | ?[R1: $int] : (($sum($product(Q, B), R1) = A) & $lesseq(0, R1) & (~$lesseq(B, R1))))))))),
% 70.08/45.36 inference(modus_ponens,[status(thm)],[12, 9])).
% 70.08/45.36 tff(14,plain,
% 70.08/45.36 (~![A: $int, B: $int] : ((~($lesseq(0, A) & (~$lesseq(B, 0)))) | ($lesseq(0, A) & ![R: $int, Q: $int] : ((~(($sum($product(Q, B), R) = A) & $lesseq(0, R))) | (((~$lesseq(B, R)) | ![Q1: $int] : ((~(Q1 = $sum(1, Q))) | ![R1: $int] : ((~(R1 = $sum(R, $product(-1, B)))) | (($sum($product(Q1, B), R1) = A) & $lesseq(0, R1) & $lesseq(0, R) & (~$lesseq(R, R1)))))) & ($lesseq(B, R) | ?[R1: $int] : (($sum($product(Q, B), R1) = A) & $lesseq(0, R1) & (~$lesseq(B, R1))))))))),
% 70.08/45.36 inference(modus_ponens,[status(thm)],[13, 9])).
% 70.08/45.36 tff(15,plain,
% 70.08/45.36 (~![A: $int, B: $int] : ((~($lesseq(0, A) & (~$lesseq(B, 0)))) | ($lesseq(0, A) & ![R: $int, Q: $int] : ((~(($sum($product(Q, B), R) = A) & $lesseq(0, R))) | (((~$lesseq(B, R)) | ![Q1: $int] : ((~(Q1 = $sum(1, Q))) | ![R1: $int] : ((~(R1 = $sum(R, $product(-1, B)))) | (($sum($product(Q1, B), R1) = A) & $lesseq(0, R1) & $lesseq(0, R) & (~$lesseq(R, R1)))))) & ($lesseq(B, R) | ?[R1: $int] : (($sum($product(Q, B), R1) = A) & $lesseq(0, R1) & (~$lesseq(B, R1))))))))),
% 70.08/45.36 inference(modus_ponens,[status(thm)],[14, 9])).
% 70.08/45.36 tff(16,plain,
% 70.08/45.36 (~![A: $int, B: $int] : ((~($greatereq(A, 0) & (~$lesseq(B, 0)))) | ($greatereq(A, 0) & ![R: $int, Q: $int] : ((~(($sum($product(Q, B), $sum(R, $product(-1, A))) = 0) & $greatereq(R, 0))) | (((~$lesseq($sum(B, $product(-1, R)), 0)) | ![Q1: $int] : ((~($sum(Q1, $product(-1, Q)) = 1)) | ![R1: $int] : ((~($sum(R1, $sum($product(-1, R), B)) = 0)) | (($sum($product(Q1, B), $sum(R1, $product(-1, A))) = 0) & $greatereq(R1, 0) & $greatereq(R, 0) & (~$lesseq($sum(R, $product(-1, R1)), 0)))))) & ($lesseq($sum(B, $product(-1, R)), 0) | ?[R1: $int] : (($sum($product(Q, B), $sum(R1, $product(-1, A))) = 0) & $greatereq(R1, 0) & (~$lesseq($sum(B, $product(-1, R1)), 0))))))))),
% 70.08/45.36 inference(modus_ponens,[status(thm)],[15, 8])).
% 70.08/45.36 tff(17,plain,
% 70.08/45.36 (~![A: $int, B: $int] : ((~($greatereq(A, 0) & (~$lesseq(B, 0)))) | ($greatereq(A, 0) & ![R: $int, Q: $int] : ((~(($sum(R, $sum($product(B, Q), $product(-1, A))) = 0) & $greatereq(R, 0))) | (((~$lesseq($sum(B, $product(-1, R)), 0)) | ![Q1: $int] : ((~($sum(Q, $product(-1, Q1)) = -1)) | ![R1: $int] : ((~($sum(R1, $sum(B, $product(-1, R))) = 0)) | (($sum(R1, $sum($product(Q1, B), $product(-1, A))) = 0) & $greatereq(R1, 0) & $greatereq(R, 0) & (~$greatereq($sum(R1, $product(-1, R)), 0)))))) & ($lesseq($sum(B, $product(-1, R)), 0) | ?[R1: $int] : (($sum(R1, $sum($product(Q, B), $product(-1, A))) = 0) & $greatereq(R1, 0) & (~$greatereq($sum(R1, $product(-1, B)), 0))))))))),
% 70.08/45.36 inference(modus_ponens,[status(thm)],[16, 7])).
% 70.08/45.36 tff(18,plain,
% 70.08/45.36 (~![A: $int, B: $int] : ((~($greatereq(A, 0) & (~$lesseq(B, 0)))) | ($greatereq(A, 0) & ![R: $int, Q: $int] : ((~(($sum(R, $sum($product(B, Q), $product(-1, A))) = 0) & $greatereq(R, 0))) | (((~$lesseq($sum(B, $product(-1, R)), 0)) | ![Q1: $int] : ((~($sum(Q, $product(-1, Q1)) = -1)) | ![R1: $int] : ((~($sum(R1, $sum(B, $product(-1, R))) = 0)) | (($sum(R1, $sum($product(Q1, B), $product(-1, A))) = 0) & $greatereq(R1, 0) & $greatereq(R, 0) & (~$greatereq($sum(R1, $product(-1, R)), 0)))))) & ($lesseq($sum(B, $product(-1, R)), 0) | ?[R1: $int] : (($sum(R1, $sum($product(Q, B), $product(-1, A))) = 0) & $greatereq(R1, 0) & (~$greatereq($sum(R1, $product(-1, B)), 0))))))))),
% 70.08/45.36 inference(modus_ponens,[status(thm)],[17, 6])).
% 70.08/45.36 tff(19,plain,
% 70.08/45.36 (~![A: $int, B: $int] : ((~($greatereq(A, 0) & (~$lesseq(B, 0)))) | ($greatereq(A, 0) & ![R: $int, Q: $int] : ((~(($sum(R, $sum($product(B, Q), $product(-1, A))) = 0) & $greatereq(R, 0))) | (((~$lesseq($sum(B, $product(-1, R)), 0)) | ![Q1: $int] : ((~($sum(Q, $product(-1, Q1)) = -1)) | ![R1: $int] : ((~($sum(R1, $sum(B, $product(-1, R))) = 0)) | (($sum(R1, $sum($product(Q1, B), $product(-1, A))) = 0) & $greatereq(R1, 0) & $greatereq(R, 0) & (~$greatereq($sum(R1, $product(-1, R)), 0)))))) & ($lesseq($sum(B, $product(-1, R)), 0) | ?[R1: $int] : (($sum(R1, $sum($product(Q, B), $product(-1, A))) = 0) & $greatereq(R1, 0) & (~$greatereq($sum(R1, $product(-1, B)), 0))))))))),
% 70.08/45.36 inference(modus_ponens,[status(thm)],[18, 6])).
% 70.08/45.36 tff(20,plain,
% 70.08/45.36 ($greatereq(A!1, 0) & (~$lesseq(B!0, 0)) & ((~$greatereq(A!1, 0)) | (($sum(A!1, $sum($product(-1, R!3), $product(-1, $product(B!0, Q!2)))) = 0) & $greatereq(R!3, 0) & (($lesseq($sum(B!0, $product(-1, R!3)), 0) & ($sum(Q!2, $product(-1, Q1!4)) = -1) & (~((~($sum(B!0, $sum($product(-1, R!3), R1!5)) = 0)) | (($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))) = 0) & $greatereq(R1!5, 0) & $greatereq(R!3, 0) & (~$lesseq($sum(R!3, $product(-1, R1!5)), 0)))))) | ((~$lesseq($sum(B!0, $product(-1, R!3)), 0)) & ![R1: $int] : (~(($sum(R1, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0) & $greatereq(R1, 0) & (~$greatereq($sum(R1, $product(-1, B!0)), 0))))))))),
% 70.08/45.36 inference(modus_ponens,[status(thm)],[19, 5])).
% 70.08/45.36 tff(21,plain,
% 70.08/45.36 (~$lesseq(B!0, 0)),
% 70.08/45.36 inference(and_elim,[status(thm)],[20])).
% 70.08/45.36 tff(22,assumption,(~((~$lesseq($sum(B!0, $product(-1, R!3)), 0)) | (~($sum(Q!2, $product(-1, Q1!4)) = -1)) | (~($sum(B!0, $sum($product(-1, R!3), R1!5)) = 0)) | (~((~$greatereq(R!3, 0)) | (~$greatereq(R1!5, 0)) | (~($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))) = 0)) | $lesseq($sum(R!3, $product(-1, R1!5)), 0))))), introduced(assumption)).
% 70.08/45.36 tff(23,plain,
% 70.08/45.36 (((~$lesseq($sum(B!0, $product(-1, R!3)), 0)) | (~($sum(Q!2, $product(-1, Q1!4)) = -1)) | (~($sum(B!0, $sum($product(-1, R!3), R1!5)) = 0)) | (~((~$greatereq(R!3, 0)) | (~$greatereq(R1!5, 0)) | (~($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))) = 0)) | $lesseq($sum(R!3, $product(-1, R1!5)), 0)))) | ($sum(B!0, $sum($product(-1, R!3), R1!5)) = 0)),
% 70.08/45.36 inference(tautology,[status(thm)],[])).
% 70.08/45.36 tff(24,plain,
% 70.08/45.36 ($sum(B!0, $sum($product(-1, R!3), R1!5)) = 0),
% 70.08/45.36 inference(unit_resolution,[status(thm)],[23, 22])).
% 70.08/45.36 tff(25,plain,
% 70.08/45.36 ((~($sum(B!0, $sum($product(-1, R!3), R1!5)) = 0)) | $lesseq($sum(B!0, $sum($product(-1, R!3), R1!5)), 0)),
% 70.08/45.36 inference(theory_lemma,[status(thm)],[])).
% 70.08/45.36 tff(26,plain,
% 70.08/45.36 ($lesseq($sum(B!0, $sum($product(-1, R!3), R1!5)), 0)),
% 70.08/45.36 inference(unit_resolution,[status(thm)],[25, 24])).
% 70.08/45.36 tff(27,plain,
% 70.08/45.36 (((~$lesseq($sum(B!0, $product(-1, R!3)), 0)) | (~($sum(Q!2, $product(-1, Q1!4)) = -1)) | (~($sum(B!0, $sum($product(-1, R!3), R1!5)) = 0)) | (~((~$greatereq(R!3, 0)) | (~$greatereq(R1!5, 0)) | (~($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))) = 0)) | $lesseq($sum(R!3, $product(-1, R1!5)), 0)))) | $lesseq($sum(B!0, $product(-1, R!3)), 0)),
% 70.08/45.36 inference(tautology,[status(thm)],[])).
% 70.08/45.36 tff(28,plain,
% 70.08/45.36 ($lesseq($sum(B!0, $product(-1, R!3)), 0)),
% 70.08/45.37 inference(unit_resolution,[status(thm)],[27, 22])).
% 70.08/45.37 tff(29,plain,
% 70.08/45.37 ((~($sum(B!0, $sum($product(-1, R!3), R1!5)) = 0)) | $greatereq($sum(B!0, $sum($product(-1, R!3), R1!5)), 0)),
% 70.08/45.37 inference(theory_lemma,[status(thm)],[])).
% 70.08/45.37 tff(30,plain,
% 70.08/45.37 ($greatereq($sum(B!0, $sum($product(-1, R!3), R1!5)), 0)),
% 70.08/45.37 inference(unit_resolution,[status(thm)],[29, 24])).
% 70.08/45.37 tff(31,plain,
% 70.08/45.37 ($greatereq(R1!5, 0) | (~$greatereq($sum(B!0, $sum($product(-1, R!3), R1!5)), 0)) | (~$lesseq($sum(B!0, $product(-1, R!3)), 0))),
% 70.08/45.37 inference(theory_lemma,[status(thm)],[])).
% 70.08/45.37 tff(32,plain,
% 70.08/45.37 ($greatereq(R1!5, 0)),
% 70.08/45.37 inference(unit_resolution,[status(thm)],[31, 30, 28])).
% 70.08/45.37 tff(33,plain,
% 70.08/45.37 (((~$lesseq($sum(B!0, $product(-1, R!3)), 0)) | (~($sum(Q!2, $product(-1, Q1!4)) = -1)) | (~($sum(B!0, $sum($product(-1, R!3), R1!5)) = 0)) | (~((~$greatereq(R!3, 0)) | (~$greatereq(R1!5, 0)) | (~($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))) = 0)) | $lesseq($sum(R!3, $product(-1, R1!5)), 0)))) | ((~$greatereq(R!3, 0)) | (~$greatereq(R1!5, 0)) | (~($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))) = 0)) | $lesseq($sum(R!3, $product(-1, R1!5)), 0))),
% 70.08/45.37 inference(tautology,[status(thm)],[])).
% 70.08/45.37 tff(34,plain,
% 70.08/45.37 ((~$greatereq(R!3, 0)) | (~$greatereq(R1!5, 0)) | (~($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))) = 0)) | $lesseq($sum(R!3, $product(-1, R1!5)), 0)),
% 70.08/45.37 inference(unit_resolution,[status(thm)],[33, 22])).
% 70.08/45.37 tff(35,plain,
% 70.08/45.37 (((~$lesseq($sum(B!0, $product(-1, R!3)), 0)) | (~($sum(Q!2, $product(-1, Q1!4)) = -1)) | (~($sum(B!0, $sum($product(-1, R!3), R1!5)) = 0)) | (~((~$greatereq(R!3, 0)) | (~$greatereq(R1!5, 0)) | (~($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))) = 0)) | $lesseq($sum(R!3, $product(-1, R1!5)), 0)))) | ($sum(Q!2, $product(-1, Q1!4)) = -1)),
% 70.08/45.37 inference(tautology,[status(thm)],[])).
% 70.08/45.37 tff(36,plain,
% 70.08/45.37 ($sum(Q!2, $product(-1, Q1!4)) = -1),
% 70.08/45.37 inference(unit_resolution,[status(thm)],[35, 22])).
% 70.08/45.37 tff(37,plain,
% 70.08/45.37 ((~($sum(Q!2, $product(-1, Q1!4)) = -1)) | $lesseq($sum(Q!2, $product(-1, Q1!4)), -1)),
% 70.08/45.37 inference(theory_lemma,[status(thm)],[])).
% 70.08/45.37 tff(38,plain,
% 70.08/45.37 ($lesseq($sum(Q!2, $product(-1, Q1!4)), -1)),
% 70.08/45.37 inference(unit_resolution,[status(thm)],[37, 36])).
% 70.08/45.37 tff(39,plain,
% 70.08/45.37 ((~($sum(Q!2, $product(-1, Q1!4)) = -1)) | $greatereq($sum(Q!2, $product(-1, Q1!4)), -1)),
% 70.08/45.37 inference(theory_lemma,[status(thm)],[])).
% 70.08/45.37 tff(40,plain,
% 70.08/45.37 ($greatereq($sum(Q!2, $product(-1, Q1!4)), -1)),
% 70.08/45.37 inference(unit_resolution,[status(thm)],[39, 36])).
% 70.08/45.37 tff(41,assumption,($lesseq($sum(B!0, $sum($product(-1, R!3), R1!5)), 0)), introduced(assumption)).
% 70.08/45.37 tff(42,assumption,($greatereq($sum(B!0, $sum($product(-1, R!3), R1!5)), 0)), introduced(assumption)).
% 70.08/45.37 tff(43,plain,
% 70.08/45.37 ($greatereq(A!1, 0)),
% 70.08/45.37 inference(and_elim,[status(thm)],[20])).
% 70.08/45.37 tff(44,plain,
% 70.08/45.37 (((~$greatereq(A!1, 0)) | (($sum(A!1, $sum($product(-1, R!3), $product(-1, $product(B!0, Q!2)))) = 0) & $greatereq(R!3, 0) & (($lesseq($sum(B!0, $product(-1, R!3)), 0) & ($sum(Q!2, $product(-1, Q1!4)) = -1) & (~((~($sum(B!0, $sum($product(-1, R!3), R1!5)) = 0)) | (($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))) = 0) & $greatereq(R1!5, 0) & $greatereq(R!3, 0) & (~$lesseq($sum(R!3, $product(-1, R1!5)), 0)))))) | ((~$lesseq($sum(B!0, $product(-1, R!3)), 0)) & ![R1: $int] : (~(($sum(R1, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0) & $greatereq(R1, 0) & (~$greatereq($sum(R1, $product(-1, B!0)), 0)))))))) <=> ((~$greatereq(A!1, 0)) | (~((~$greatereq(R!3, 0)) | (~($sum(A!1, $sum($product(-1, R!3), $product(-1, $product(B!0, Q!2)))) = 0)) | (~((~($lesseq($sum(B!0, $product(-1, R!3)), 0) | (~![R1: $int] : ((~$greatereq(R1, 0)) | $greatereq($sum(R1, $product(-1, B!0)), 0) | (~($sum(R1, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0)))))) | (~((~$lesseq($sum(B!0, $product(-1, R!3)), 0)) | (~($sum(Q!2, $product(-1, Q1!4)) = -1)) | (~($sum(B!0, $sum($product(-1, R!3), R1!5)) = 0)) | (~((~$greatereq(R!3, 0)) | (~$greatereq(R1!5, 0)) | (~($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))) = 0)) | $lesseq($sum(R!3, $product(-1, R1!5)), 0))))))))))),
% 70.08/45.37 inference(rewrite,[status(thm)],[])).
% 70.08/45.37 tff(45,plain,
% 70.08/45.37 ((~$greatereq(A!1, 0)) | (($sum(A!1, $sum($product(-1, R!3), $product(-1, $product(B!0, Q!2)))) = 0) & $greatereq(R!3, 0) & (($lesseq($sum(B!0, $product(-1, R!3)), 0) & ($sum(Q!2, $product(-1, Q1!4)) = -1) & (~((~($sum(B!0, $sum($product(-1, R!3), R1!5)) = 0)) | (($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))) = 0) & $greatereq(R1!5, 0) & $greatereq(R!3, 0) & (~$lesseq($sum(R!3, $product(-1, R1!5)), 0)))))) | ((~$lesseq($sum(B!0, $product(-1, R!3)), 0)) & ![R1: $int] : (~(($sum(R1, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0) & $greatereq(R1, 0) & (~$greatereq($sum(R1, $product(-1, B!0)), 0)))))))),
% 70.08/45.37 inference(and_elim,[status(thm)],[20])).
% 70.08/45.37 tff(46,plain,
% 70.08/45.37 ((~$greatereq(A!1, 0)) | (~((~$greatereq(R!3, 0)) | (~($sum(A!1, $sum($product(-1, R!3), $product(-1, $product(B!0, Q!2)))) = 0)) | (~((~($lesseq($sum(B!0, $product(-1, R!3)), 0) | (~![R1: $int] : ((~$greatereq(R1, 0)) | $greatereq($sum(R1, $product(-1, B!0)), 0) | (~($sum(R1, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0)))))) | (~((~$lesseq($sum(B!0, $product(-1, R!3)), 0)) | (~($sum(Q!2, $product(-1, Q1!4)) = -1)) | (~($sum(B!0, $sum($product(-1, R!3), R1!5)) = 0)) | (~((~$greatereq(R!3, 0)) | (~$greatereq(R1!5, 0)) | (~($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))) = 0)) | $lesseq($sum(R!3, $product(-1, R1!5)), 0)))))))))),
% 70.08/45.37 inference(modus_ponens,[status(thm)],[45, 44])).
% 70.08/45.37 tff(47,plain,
% 70.08/45.37 (~((~$greatereq(R!3, 0)) | (~($sum(A!1, $sum($product(-1, R!3), $product(-1, $product(B!0, Q!2)))) = 0)) | (~((~($lesseq($sum(B!0, $product(-1, R!3)), 0) | (~![R1: $int] : ((~$greatereq(R1, 0)) | $greatereq($sum(R1, $product(-1, B!0)), 0) | (~($sum(R1, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0)))))) | (~((~$lesseq($sum(B!0, $product(-1, R!3)), 0)) | (~($sum(Q!2, $product(-1, Q1!4)) = -1)) | (~($sum(B!0, $sum($product(-1, R!3), R1!5)) = 0)) | (~((~$greatereq(R!3, 0)) | (~$greatereq(R1!5, 0)) | (~($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))) = 0)) | $lesseq($sum(R!3, $product(-1, R1!5)), 0))))))))),
% 70.08/45.37 inference(unit_resolution,[status(thm)],[46, 43])).
% 70.08/45.37 tff(48,plain,
% 70.08/45.37 (((~$greatereq(R!3, 0)) | (~($sum(A!1, $sum($product(-1, R!3), $product(-1, $product(B!0, Q!2)))) = 0)) | (~((~($lesseq($sum(B!0, $product(-1, R!3)), 0) | (~![R1: $int] : ((~$greatereq(R1, 0)) | $greatereq($sum(R1, $product(-1, B!0)), 0) | (~($sum(R1, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0)))))) | (~((~$lesseq($sum(B!0, $product(-1, R!3)), 0)) | (~($sum(Q!2, $product(-1, Q1!4)) = -1)) | (~($sum(B!0, $sum($product(-1, R!3), R1!5)) = 0)) | (~((~$greatereq(R!3, 0)) | (~$greatereq(R1!5, 0)) | (~($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))) = 0)) | $lesseq($sum(R!3, $product(-1, R1!5)), 0)))))))) | ($sum(A!1, $sum($product(-1, R!3), $product(-1, $product(B!0, Q!2)))) = 0)),
% 70.08/45.37 inference(tautology,[status(thm)],[])).
% 70.08/45.37 tff(49,plain,
% 70.08/45.37 ($sum(A!1, $sum($product(-1, R!3), $product(-1, $product(B!0, Q!2)))) = 0),
% 70.08/45.37 inference(unit_resolution,[status(thm)],[48, 47])).
% 70.08/45.37 tff(50,plain,
% 70.08/45.37 ((~($sum(A!1, $sum($product(-1, R!3), $product(-1, $product(B!0, Q!2)))) = 0)) | $lesseq($sum(A!1, $sum($product(-1, R!3), $product(-1, $product(B!0, Q!2)))), 0)),
% 70.08/45.37 inference(theory_lemma,[status(thm)],[])).
% 70.08/45.37 tff(51,plain,
% 70.08/45.37 ($lesseq($sum(A!1, $sum($product(-1, R!3), $product(-1, $product(B!0, Q!2)))), 0)),
% 70.08/45.37 inference(unit_resolution,[status(thm)],[50, 49])).
% 70.08/45.37 tff(52,plain,
% 70.08/45.37 ((~($sum(A!1, $sum($product(-1, R!3), $product(-1, $product(B!0, Q!2)))) = 0)) | $greatereq($sum(A!1, $sum($product(-1, R!3), $product(-1, $product(B!0, Q!2)))), 0)),
% 70.08/45.37 inference(theory_lemma,[status(thm)],[])).
% 70.08/45.37 tff(53,plain,
% 70.08/45.37 ($greatereq($sum(A!1, $sum($product(-1, R!3), $product(-1, $product(B!0, Q!2)))), 0)),
% 70.08/45.37 inference(unit_resolution,[status(thm)],[52, 49])).
% 70.08/45.37 tff(54,assumption,($lesseq($sum(Q!2, $product(-1, Q1!4)), -1)), introduced(assumption)).
% 70.08/45.37 tff(55,assumption,($greatereq($sum(Q!2, $product(-1, Q1!4)), -1)), introduced(assumption)).
% 70.08/45.37 tff(56,assumption,(~$greatereq($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))), 0)), introduced(assumption)).
% 70.08/45.37 tff(57,plain,
% 70.08/45.37 ($false),
% 70.08/45.37 inference(theory_lemma,[status(thm)],[56, 55, 54, 53, 51, 42, 41])).
% 70.08/45.37 tff(58,plain,($greatereq($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))), 0) | (~$greatereq($sum(Q!2, $product(-1, Q1!4)), -1)) | (~$lesseq($sum(Q!2, $product(-1, Q1!4)), -1)) | (~$greatereq($sum(B!0, $sum($product(-1, R!3), R1!5)), 0)) | (~$lesseq($sum(B!0, $sum($product(-1, R!3), R1!5)), 0))), inference(lemma,lemma(discharge,[]))).
% 70.08/45.37 tff(59,plain,
% 70.08/45.37 ($greatereq($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))), 0)),
% 70.08/45.37 inference(unit_resolution,[status(thm)],[58, 40, 38, 30, 26])).
% 70.08/45.37 tff(60,assumption,(~$lesseq($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))), 0)), introduced(assumption)).
% 70.08/45.37 tff(61,plain,
% 70.08/45.37 ($false),
% 70.08/45.37 inference(theory_lemma,[status(thm)],[60, 42, 41, 42, 41, 53, 51, 55, 54])).
% 70.08/45.37 tff(62,plain,($lesseq($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))), 0) | (~$greatereq($sum(B!0, $sum($product(-1, R!3), R1!5)), 0)) | (~$lesseq($sum(B!0, $sum($product(-1, R!3), R1!5)), 0)) | (~$greatereq($sum(Q!2, $product(-1, Q1!4)), -1)) | (~$lesseq($sum(Q!2, $product(-1, Q1!4)), -1))), inference(lemma,lemma(discharge,[]))).
% 70.08/45.37 tff(63,plain,
% 70.08/45.37 ($lesseq($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))), 0)),
% 70.08/45.37 inference(unit_resolution,[status(thm)],[62, 30, 26, 40, 38])).
% 70.08/45.37 tff(64,plain,
% 70.08/45.37 (($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))) = 0) | (~$lesseq($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))), 0)) | (~$greatereq($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))), 0))),
% 70.08/45.37 inference(theory_lemma,[status(thm)],[])).
% 70.08/45.37 tff(65,plain,
% 70.08/45.37 ($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))) = 0),
% 70.08/45.37 inference(unit_resolution,[status(thm)],[64, 63, 59])).
% 70.08/45.37 tff(66,plain,
% 70.08/45.37 (((~$greatereq(R!3, 0)) | (~($sum(A!1, $sum($product(-1, R!3), $product(-1, $product(B!0, Q!2)))) = 0)) | (~((~($lesseq($sum(B!0, $product(-1, R!3)), 0) | (~![R1: $int] : ((~$greatereq(R1, 0)) | $greatereq($sum(R1, $product(-1, B!0)), 0) | (~($sum(R1, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0)))))) | (~((~$lesseq($sum(B!0, $product(-1, R!3)), 0)) | (~($sum(Q!2, $product(-1, Q1!4)) = -1)) | (~($sum(B!0, $sum($product(-1, R!3), R1!5)) = 0)) | (~((~$greatereq(R!3, 0)) | (~$greatereq(R1!5, 0)) | (~($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))) = 0)) | $lesseq($sum(R!3, $product(-1, R1!5)), 0)))))))) | $greatereq(R!3, 0)),
% 70.08/45.37 inference(tautology,[status(thm)],[])).
% 70.08/45.37 tff(67,plain,
% 70.08/45.37 ($greatereq(R!3, 0)),
% 70.08/45.37 inference(unit_resolution,[status(thm)],[66, 47])).
% 70.08/45.37 tff(68,plain,
% 70.08/45.37 ((~((~$greatereq(R!3, 0)) | (~$greatereq(R1!5, 0)) | (~($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))) = 0)) | $lesseq($sum(R!3, $product(-1, R1!5)), 0))) | (~$greatereq(R!3, 0)) | (~$greatereq(R1!5, 0)) | (~($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))) = 0)) | $lesseq($sum(R!3, $product(-1, R1!5)), 0)),
% 70.08/45.37 inference(tautology,[status(thm)],[])).
% 70.08/45.37 tff(69,plain,
% 70.08/45.37 ((~((~$greatereq(R!3, 0)) | (~$greatereq(R1!5, 0)) | (~($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))) = 0)) | $lesseq($sum(R!3, $product(-1, R1!5)), 0))) | (~$greatereq(R1!5, 0)) | (~($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))) = 0)) | $lesseq($sum(R!3, $product(-1, R1!5)), 0)),
% 70.08/45.37 inference(unit_resolution,[status(thm)],[68, 67])).
% 70.08/45.37 tff(70,plain,
% 70.08/45.37 ($lesseq($sum(R!3, $product(-1, R1!5)), 0)),
% 70.08/45.37 inference(unit_resolution,[status(thm)],[69, 65, 34, 32])).
% 70.08/45.37 tff(71,plain,
% 70.08/45.37 ($false),
% 70.08/45.37 inference(theory_lemma,[status(thm)],[70, 26, 21])).
% 70.08/45.37 tff(72,plain,((~$lesseq($sum(B!0, $product(-1, R!3)), 0)) | (~($sum(Q!2, $product(-1, Q1!4)) = -1)) | (~($sum(B!0, $sum($product(-1, R!3), R1!5)) = 0)) | (~((~$greatereq(R!3, 0)) | (~$greatereq(R1!5, 0)) | (~($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))) = 0)) | $lesseq($sum(R!3, $product(-1, R1!5)), 0)))), inference(lemma,lemma(discharge,[]))).
% 70.08/45.37 tff(73,plain,
% 70.08/45.37 (((~$greatereq(R!3, 0)) | (~($sum(A!1, $sum($product(-1, R!3), $product(-1, $product(B!0, Q!2)))) = 0)) | (~((~($lesseq($sum(B!0, $product(-1, R!3)), 0) | (~![R1: $int] : ((~$greatereq(R1, 0)) | $greatereq($sum(R1, $product(-1, B!0)), 0) | (~($sum(R1, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0)))))) | (~((~$lesseq($sum(B!0, $product(-1, R!3)), 0)) | (~($sum(Q!2, $product(-1, Q1!4)) = -1)) | (~($sum(B!0, $sum($product(-1, R!3), R1!5)) = 0)) | (~((~$greatereq(R!3, 0)) | (~$greatereq(R1!5, 0)) | (~($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))) = 0)) | $lesseq($sum(R!3, $product(-1, R1!5)), 0)))))))) | ((~($lesseq($sum(B!0, $product(-1, R!3)), 0) | (~![R1: $int] : ((~$greatereq(R1, 0)) | $greatereq($sum(R1, $product(-1, B!0)), 0) | (~($sum(R1, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0)))))) | (~((~$lesseq($sum(B!0, $product(-1, R!3)), 0)) | (~($sum(Q!2, $product(-1, Q1!4)) = -1)) | (~($sum(B!0, $sum($product(-1, R!3), R1!5)) = 0)) | (~((~$greatereq(R!3, 0)) | (~$greatereq(R1!5, 0)) | (~($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))) = 0)) | $lesseq($sum(R!3, $product(-1, R1!5)), 0))))))),
% 70.08/45.37 inference(tautology,[status(thm)],[])).
% 70.08/45.37 tff(74,plain,
% 70.08/45.37 ((~($lesseq($sum(B!0, $product(-1, R!3)), 0) | (~![R1: $int] : ((~$greatereq(R1, 0)) | $greatereq($sum(R1, $product(-1, B!0)), 0) | (~($sum(R1, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0)))))) | (~((~$lesseq($sum(B!0, $product(-1, R!3)), 0)) | (~($sum(Q!2, $product(-1, Q1!4)) = -1)) | (~($sum(B!0, $sum($product(-1, R!3), R1!5)) = 0)) | (~((~$greatereq(R!3, 0)) | (~$greatereq(R1!5, 0)) | (~($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))) = 0)) | $lesseq($sum(R!3, $product(-1, R1!5)), 0)))))),
% 70.08/45.37 inference(unit_resolution,[status(thm)],[73, 47])).
% 70.08/45.37 tff(75,plain,
% 70.08/45.37 ((~((~($lesseq($sum(B!0, $product(-1, R!3)), 0) | (~![R1: $int] : ((~$greatereq(R1, 0)) | $greatereq($sum(R1, $product(-1, B!0)), 0) | (~($sum(R1, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0)))))) | (~((~$lesseq($sum(B!0, $product(-1, R!3)), 0)) | (~($sum(Q!2, $product(-1, Q1!4)) = -1)) | (~($sum(B!0, $sum($product(-1, R!3), R1!5)) = 0)) | (~((~$greatereq(R!3, 0)) | (~$greatereq(R1!5, 0)) | (~($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))) = 0)) | $lesseq($sum(R!3, $product(-1, R1!5)), 0))))))) | (~($lesseq($sum(B!0, $product(-1, R!3)), 0) | (~![R1: $int] : ((~$greatereq(R1, 0)) | $greatereq($sum(R1, $product(-1, B!0)), 0) | (~($sum(R1, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0)))))) | (~((~$lesseq($sum(B!0, $product(-1, R!3)), 0)) | (~($sum(Q!2, $product(-1, Q1!4)) = -1)) | (~($sum(B!0, $sum($product(-1, R!3), R1!5)) = 0)) | (~((~$greatereq(R!3, 0)) | (~$greatereq(R1!5, 0)) | (~($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))) = 0)) | $lesseq($sum(R!3, $product(-1, R1!5)), 0)))))),
% 70.08/45.37 inference(tautology,[status(thm)],[])).
% 70.08/45.37 tff(76,plain,
% 70.08/45.37 ((~($lesseq($sum(B!0, $product(-1, R!3)), 0) | (~![R1: $int] : ((~$greatereq(R1, 0)) | $greatereq($sum(R1, $product(-1, B!0)), 0) | (~($sum(R1, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0)))))) | (~((~$lesseq($sum(B!0, $product(-1, R!3)), 0)) | (~($sum(Q!2, $product(-1, Q1!4)) = -1)) | (~($sum(B!0, $sum($product(-1, R!3), R1!5)) = 0)) | (~((~$greatereq(R!3, 0)) | (~$greatereq(R1!5, 0)) | (~($sum(A!1, $sum($product(-1, R1!5), $product(-1, $product(B!0, Q1!4)))) = 0)) | $lesseq($sum(R!3, $product(-1, R1!5)), 0)))))),
% 70.08/45.37 inference(unit_resolution,[status(thm)],[75, 74])).
% 70.08/45.37 tff(77,plain,
% 70.08/45.37 (~($lesseq($sum(B!0, $product(-1, R!3)), 0) | (~![R1: $int] : ((~$greatereq(R1, 0)) | $greatereq($sum(R1, $product(-1, B!0)), 0) | (~($sum(R1, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0)))))),
% 70.08/45.37 inference(unit_resolution,[status(thm)],[76, 72])).
% 70.08/45.37 tff(78,plain,
% 70.08/45.37 (($lesseq($sum(B!0, $product(-1, R!3)), 0) | (~![R1: $int] : ((~$greatereq(R1, 0)) | $greatereq($sum(R1, $product(-1, B!0)), 0) | (~($sum(R1, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0))))) | ![R1: $int] : ((~$greatereq(R1, 0)) | $greatereq($sum(R1, $product(-1, B!0)), 0) | (~($sum(R1, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0)))),
% 70.08/45.37 inference(tautology,[status(thm)],[])).
% 70.08/45.37 tff(79,plain,
% 70.08/45.37 (![R1: $int] : ((~$greatereq(R1, 0)) | $greatereq($sum(R1, $product(-1, B!0)), 0) | (~($sum(R1, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0)))),
% 70.08/45.37 inference(unit_resolution,[status(thm)],[78, 77])).
% 70.08/45.37 tff(80,plain,
% 70.08/45.37 (($lesseq($sum(B!0, $product(-1, R!3)), 0) | (~![R1: $int] : ((~$greatereq(R1, 0)) | $greatereq($sum(R1, $product(-1, B!0)), 0) | (~($sum(R1, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0))))) | (~$lesseq($sum(B!0, $product(-1, R!3)), 0))),
% 70.08/45.37 inference(tautology,[status(thm)],[])).
% 70.08/45.37 tff(81,plain,
% 70.08/45.37 (~$lesseq($sum(B!0, $product(-1, R!3)), 0)),
% 70.08/45.37 inference(unit_resolution,[status(thm)],[80, 77])).
% 70.08/45.37 tff(82,plain,
% 70.08/45.37 (((~![R1: $int] : ((~$greatereq(R1, 0)) | $greatereq($sum(R1, $product(-1, B!0)), 0) | (~($sum(R1, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0)))) | ($lesseq($sum(B!0, $product(-1, R!3)), 0) | (~$greatereq(R!3, 0)) | (~($sum(A!1, $sum($product(-1, R!3), $product(-1, $product(B!0, Q!2)))) = 0)))) <=> ((~![R1: $int] : ((~$greatereq(R1, 0)) | $greatereq($sum(R1, $product(-1, B!0)), 0) | (~($sum(R1, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0)))) | $lesseq($sum(B!0, $product(-1, R!3)), 0) | (~$greatereq(R!3, 0)) | (~($sum(A!1, $sum($product(-1, R!3), $product(-1, $product(B!0, Q!2)))) = 0)))),
% 70.08/45.37 inference(rewrite,[status(thm)],[])).
% 70.08/45.37 tff(83,plain,
% 70.08/45.37 (((~$greatereq(R!3, 0)) | $lesseq($sum(B!0, $product(-1, R!3)), 0) | (~($sum(A!1, $sum($product(-1, R!3), $product(-1, $product(B!0, Q!2)))) = 0))) <=> ($lesseq($sum(B!0, $product(-1, R!3)), 0) | (~$greatereq(R!3, 0)) | (~($sum(A!1, $sum($product(-1, R!3), $product(-1, $product(B!0, Q!2)))) = 0)))),
% 70.08/45.37 inference(rewrite,[status(thm)],[])).
% 70.08/45.37 tff(84,plain,
% 70.08/45.37 ((~($sum(R!3, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0)) <=> (~($sum(A!1, $sum($product(-1, R!3), $product(-1, $product(B!0, Q!2)))) = 0))),
% 70.08/45.37 inference(rewrite,[status(thm)],[])).
% 70.08/45.37 tff(85,plain,
% 70.08/45.37 ($greatereq($sum($product(-1, B!0), R!3), 0) <=> $lesseq($sum(B!0, $product(-1, R!3)), 0)),
% 70.08/45.37 inference(rewrite,[status(thm)],[])).
% 70.08/45.37 tff(86,plain,
% 70.08/45.37 ($sum(R!3, $product(-1, B!0)) = $sum($product(-1, B!0), R!3)),
% 70.08/45.37 inference(rewrite,[status(thm)],[])).
% 70.08/45.37 tff(87,plain,
% 70.08/45.37 ($greatereq($sum(R!3, $product(-1, B!0)), 0) <=> $greatereq($sum($product(-1, B!0), R!3), 0)),
% 70.08/45.37 inference(monotonicity,[status(thm)],[86])).
% 70.08/45.37 tff(88,plain,
% 70.08/45.37 ($greatereq($sum(R!3, $product(-1, B!0)), 0) <=> $lesseq($sum(B!0, $product(-1, R!3)), 0)),
% 70.08/45.37 inference(transitivity,[status(thm)],[87, 85])).
% 70.08/45.37 tff(89,plain,
% 70.08/45.37 (((~$greatereq(R!3, 0)) | $greatereq($sum(R!3, $product(-1, B!0)), 0) | (~($sum(R!3, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0))) <=> ((~$greatereq(R!3, 0)) | $lesseq($sum(B!0, $product(-1, R!3)), 0) | (~($sum(A!1, $sum($product(-1, R!3), $product(-1, $product(B!0, Q!2)))) = 0)))),
% 70.08/45.37 inference(monotonicity,[status(thm)],[88, 84])).
% 70.08/45.37 tff(90,plain,
% 70.08/45.37 (((~$greatereq(R!3, 0)) | $greatereq($sum(R!3, $product(-1, B!0)), 0) | (~($sum(R!3, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0))) <=> ($lesseq($sum(B!0, $product(-1, R!3)), 0) | (~$greatereq(R!3, 0)) | (~($sum(A!1, $sum($product(-1, R!3), $product(-1, $product(B!0, Q!2)))) = 0)))),
% 70.08/45.37 inference(transitivity,[status(thm)],[89, 83])).
% 70.08/45.37 tff(91,plain,
% 70.08/45.37 (((~![R1: $int] : ((~$greatereq(R1, 0)) | $greatereq($sum(R1, $product(-1, B!0)), 0) | (~($sum(R1, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0)))) | ((~$greatereq(R!3, 0)) | $greatereq($sum(R!3, $product(-1, B!0)), 0) | (~($sum(R!3, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0)))) <=> ((~![R1: $int] : ((~$greatereq(R1, 0)) | $greatereq($sum(R1, $product(-1, B!0)), 0) | (~($sum(R1, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0)))) | ($lesseq($sum(B!0, $product(-1, R!3)), 0) | (~$greatereq(R!3, 0)) | (~($sum(A!1, $sum($product(-1, R!3), $product(-1, $product(B!0, Q!2)))) = 0))))),
% 70.08/45.38 inference(monotonicity,[status(thm)],[90])).
% 70.08/45.38 tff(92,plain,
% 70.08/45.38 (((~![R1: $int] : ((~$greatereq(R1, 0)) | $greatereq($sum(R1, $product(-1, B!0)), 0) | (~($sum(R1, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0)))) | ((~$greatereq(R!3, 0)) | $greatereq($sum(R!3, $product(-1, B!0)), 0) | (~($sum(R!3, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0)))) <=> ((~![R1: $int] : ((~$greatereq(R1, 0)) | $greatereq($sum(R1, $product(-1, B!0)), 0) | (~($sum(R1, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0)))) | $lesseq($sum(B!0, $product(-1, R!3)), 0) | (~$greatereq(R!3, 0)) | (~($sum(A!1, $sum($product(-1, R!3), $product(-1, $product(B!0, Q!2)))) = 0)))),
% 70.08/45.38 inference(transitivity,[status(thm)],[91, 82])).
% 70.08/45.38 tff(93,plain,
% 70.08/45.38 ((~![R1: $int] : ((~$greatereq(R1, 0)) | $greatereq($sum(R1, $product(-1, B!0)), 0) | (~($sum(R1, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0)))) | ((~$greatereq(R!3, 0)) | $greatereq($sum(R!3, $product(-1, B!0)), 0) | (~($sum(R!3, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0)))),
% 70.08/45.38 inference(quant_inst,[status(thm)],[])).
% 70.08/45.38 tff(94,plain,
% 70.08/45.38 ((~![R1: $int] : ((~$greatereq(R1, 0)) | $greatereq($sum(R1, $product(-1, B!0)), 0) | (~($sum(R1, $sum($product(-1, A!1), $product(B!0, Q!2))) = 0)))) | $lesseq($sum(B!0, $product(-1, R!3)), 0) | (~$greatereq(R!3, 0)) | (~($sum(A!1, $sum($product(-1, R!3), $product(-1, $product(B!0, Q!2)))) = 0))),
% 70.08/45.38 inference(modus_ponens,[status(thm)],[93, 92])).
% 70.08/45.38 tff(95,plain,
% 70.08/45.38 ($false),
% 70.08/45.38 inference(unit_resolution,[status(thm)],[94, 67, 49, 81, 79])).
% 70.08/45.38 % SZS output end Proof
%------------------------------------------------------------------------------