TSTP Solution File: SWW581_2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW581_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 20:59:20 EDT 2022
% Result : Theorem 0.19s 0.53s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW581_2 : TPTP v8.1.0. Released v6.1.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n004.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 20:06:04 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.19/0.53 % SZS status Theorem
% 0.19/0.53 % SZS output start Proof
% 0.19/0.53 tff(tptp_fun_S_4_type, type, (
% 0.19/0.53 tptp_fun_S_4: $int)).
% 0.19/0.53 tff(fact_type, type, (
% 0.19/0.53 fact: $int > $int)).
% 0.19/0.53 tff(tptp_fun_R_1_type, type, (
% 0.19/0.53 tptp_fun_R_1: $int)).
% 0.19/0.53 tff(tptp_fun_U1_3_type, type, (
% 0.19/0.53 tptp_fun_U1_3: $int)).
% 0.19/0.53 tff(tptp_fun_U_2_type, type, (
% 0.19/0.53 tptp_fun_U_2: $int)).
% 0.19/0.53 tff(tptp_fun_N_0_type, type, (
% 0.19/0.53 tptp_fun_N_0: $int)).
% 0.19/0.53 tff(tptp_fun_R1_5_type, type, (
% 0.19/0.53 tptp_fun_R1_5: $int)).
% 0.19/0.53 tff(1,plain,
% 0.19/0.53 (($greatereq(N!0, 0) & ((~$lesseq($sum(N!0, $product(-1, R!1)), 0)) & (~$greatereq($sum(R!1, $product(-1, S!4)), 0)) & $greatereq(S!4, 1) & $greatereq($sum(R!1, $product(-1, S!4)), -1) & ($sum(U1!3, $product(-1, $product(fact(R!1), S!4))) = 0) & (~((~($sum(R!1, $product(-1, R1!5)) = -1)) | ($greatereq(R1!5, 0) & $greatereq($sum(N!0, $product(-1, R1!5)), 0) & ($sum(U1!3, $product(-1, fact(R1!5))) = 0)))) & $greatereq(R!1, 0) & $greatereq($sum(N!0, $product(-1, R!1)), 0) & ($sum(U!2, $product(-1, fact(R!1))) = 0))) <=> ($greatereq(N!0, 0) & (~$lesseq($sum(N!0, $product(-1, R!1)), 0)) & (~$greatereq($sum(R!1, $product(-1, S!4)), 0)) & $greatereq(S!4, 1) & $greatereq($sum(R!1, $product(-1, S!4)), -1) & ($sum(U1!3, $product(-1, $product(fact(R!1), S!4))) = 0) & (~((~($sum(R!1, $product(-1, R1!5)) = -1)) | ($greatereq(R1!5, 0) & $greatereq($sum(N!0, $product(-1, R1!5)), 0) & ($sum(U1!3, $product(-1, fact(R1!5))) = 0)))) & $greatereq(R!1, 0) & $greatereq($sum(N!0, $product(-1, R!1)), 0) & ($sum(U!2, $product(-1, fact(R!1))) = 0))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(2,plain,
% 0.19/0.53 (((~$lesseq($sum(N!0, $product(-1, R!1)), 0)) & ((~$greatereq($sum(R!1, $product(-1, S!4)), 0)) & $greatereq(S!4, 1) & $greatereq($sum(R!1, $product(-1, S!4)), -1) & ($sum(U1!3, $product(-1, $product(fact(R!1), S!4))) = 0) & (~((~($sum(R!1, $product(-1, R1!5)) = -1)) | ($greatereq(R1!5, 0) & $greatereq($sum(N!0, $product(-1, R1!5)), 0) & ($sum(U1!3, $product(-1, fact(R1!5))) = 0))))) & ($greatereq(R!1, 0) & $greatereq($sum(N!0, $product(-1, R!1)), 0) & ($sum(U!2, $product(-1, fact(R!1))) = 0))) <=> ((~$lesseq($sum(N!0, $product(-1, R!1)), 0)) & (~$greatereq($sum(R!1, $product(-1, S!4)), 0)) & $greatereq(S!4, 1) & $greatereq($sum(R!1, $product(-1, S!4)), -1) & ($sum(U1!3, $product(-1, $product(fact(R!1), S!4))) = 0) & (~((~($sum(R!1, $product(-1, R1!5)) = -1)) | ($greatereq(R1!5, 0) & $greatereq($sum(N!0, $product(-1, R1!5)), 0) & ($sum(U1!3, $product(-1, fact(R1!5))) = 0)))) & $greatereq(R!1, 0) & $greatereq($sum(N!0, $product(-1, R!1)), 0) & ($sum(U!2, $product(-1, fact(R!1))) = 0))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(3,plain,
% 0.19/0.53 ((~(~($greatereq(R!1, 0) & $greatereq($sum(N!0, $product(-1, R!1)), 0) & ($sum(U!2, $product(-1, fact(R!1))) = 0)))) <=> ($greatereq(R!1, 0) & $greatereq($sum(N!0, $product(-1, R!1)), 0) & ($sum(U!2, $product(-1, fact(R!1))) = 0))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(4,plain,
% 0.19/0.53 (((~$greatereq($sum(R!1, $product(-1, S!4)), 0)) & ($greatereq(S!4, 1) & $greatereq($sum(R!1, $product(-1, S!4)), -1) & ($sum(U1!3, $product(-1, $product(fact(R!1), S!4))) = 0)) & (~((~($sum(R!1, $product(-1, R1!5)) = -1)) | ($greatereq(R1!5, 0) & $greatereq($sum(N!0, $product(-1, R1!5)), 0) & ($sum(U1!3, $product(-1, fact(R1!5))) = 0))))) <=> ((~$greatereq($sum(R!1, $product(-1, S!4)), 0)) & $greatereq(S!4, 1) & $greatereq($sum(R!1, $product(-1, S!4)), -1) & ($sum(U1!3, $product(-1, $product(fact(R!1), S!4))) = 0) & (~((~($sum(R!1, $product(-1, R1!5)) = -1)) | ($greatereq(R1!5, 0) & $greatereq($sum(N!0, $product(-1, R1!5)), 0) & ($sum(U1!3, $product(-1, fact(R1!5))) = 0)))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(5,plain,
% 0.19/0.53 ((~((~($sum(R1!5, $product(-1, R!1)) = 1)) | ($greatereq(R1!5, 0) & $greatereq($sum(N!0, $product(-1, R1!5)), 0) & ($sum(U1!3, $product(-1, fact(R1!5))) = 0)))) <=> (~((~($sum(R!1, $product(-1, R1!5)) = -1)) | ($greatereq(R1!5, 0) & $greatereq($sum(N!0, $product(-1, R1!5)), 0) & ($sum(U1!3, $product(-1, fact(R1!5))) = 0))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(6,plain,
% 0.19/0.53 ((~(~($greatereq(S!4, 1) & $greatereq($sum(R!1, $product(-1, S!4)), -1) & ($sum(U1!3, $product(-1, $product(fact(R!1), S!4))) = 0)))) <=> ($greatereq(S!4, 1) & $greatereq($sum(R!1, $product(-1, S!4)), -1) & ($sum(U1!3, $product(-1, $product(fact(R!1), S!4))) = 0))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(7,plain,
% 0.19/0.53 ((~($greatereq(S!4, 1) & $greatereq($sum(R!1, $product(-1, S!4)), -1) & ($sum(U1!3, $product(-1, $product(S!4, fact(R!1)))) = 0))) <=> (~($greatereq(S!4, 1) & $greatereq($sum(R!1, $product(-1, S!4)), -1) & ($sum(U1!3, $product(-1, $product(fact(R!1), S!4))) = 0)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(8,plain,
% 0.19/0.53 ((~(~($greatereq(S!4, 1) & $greatereq($sum(R!1, $product(-1, S!4)), -1) & ($sum(U1!3, $product(-1, $product(S!4, fact(R!1)))) = 0)))) <=> (~(~($greatereq(S!4, 1) & $greatereq($sum(R!1, $product(-1, S!4)), -1) & ($sum(U1!3, $product(-1, $product(fact(R!1), S!4))) = 0))))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[7])).
% 0.19/0.53 tff(9,plain,
% 0.19/0.53 ((~(~($greatereq(S!4, 1) & $greatereq($sum(R!1, $product(-1, S!4)), -1) & ($sum(U1!3, $product(-1, $product(S!4, fact(R!1)))) = 0)))) <=> ($greatereq(S!4, 1) & $greatereq($sum(R!1, $product(-1, S!4)), -1) & ($sum(U1!3, $product(-1, $product(fact(R!1), S!4))) = 0))),
% 0.19/0.53 inference(transitivity,[status(thm)],[8, 6])).
% 0.19/0.53 tff(10,plain,
% 0.19/0.53 (((~$greatereq($sum(R!1, $product(-1, S!4)), 0)) & (~(~($greatereq(S!4, 1) & $greatereq($sum(R!1, $product(-1, S!4)), -1) & ($sum(U1!3, $product(-1, $product(S!4, fact(R!1)))) = 0)))) & (~((~($sum(R1!5, $product(-1, R!1)) = 1)) | ($greatereq(R1!5, 0) & $greatereq($sum(N!0, $product(-1, R1!5)), 0) & ($sum(U1!3, $product(-1, fact(R1!5))) = 0))))) <=> ((~$greatereq($sum(R!1, $product(-1, S!4)), 0)) & ($greatereq(S!4, 1) & $greatereq($sum(R!1, $product(-1, S!4)), -1) & ($sum(U1!3, $product(-1, $product(fact(R!1), S!4))) = 0)) & (~((~($sum(R!1, $product(-1, R1!5)) = -1)) | ($greatereq(R1!5, 0) & $greatereq($sum(N!0, $product(-1, R1!5)), 0) & ($sum(U1!3, $product(-1, fact(R1!5))) = 0)))))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[9, 5])).
% 0.19/0.53 tff(11,plain,
% 0.19/0.53 (((~$greatereq($sum(R!1, $product(-1, S!4)), 0)) & (~(~($greatereq(S!4, 1) & $greatereq($sum(R!1, $product(-1, S!4)), -1) & ($sum(U1!3, $product(-1, $product(S!4, fact(R!1)))) = 0)))) & (~((~($sum(R1!5, $product(-1, R!1)) = 1)) | ($greatereq(R1!5, 0) & $greatereq($sum(N!0, $product(-1, R1!5)), 0) & ($sum(U1!3, $product(-1, fact(R1!5))) = 0))))) <=> ((~$greatereq($sum(R!1, $product(-1, S!4)), 0)) & $greatereq(S!4, 1) & $greatereq($sum(R!1, $product(-1, S!4)), -1) & ($sum(U1!3, $product(-1, $product(fact(R!1), S!4))) = 0) & (~((~($sum(R!1, $product(-1, R1!5)) = -1)) | ($greatereq(R1!5, 0) & $greatereq($sum(N!0, $product(-1, R1!5)), 0) & ($sum(U1!3, $product(-1, fact(R1!5))) = 0)))))),
% 0.19/0.53 inference(transitivity,[status(thm)],[10, 4])).
% 0.19/0.53 tff(12,plain,
% 0.19/0.53 (((~$lesseq($sum(N!0, $product(-1, R!1)), 0)) & ((~$greatereq($sum(R!1, $product(-1, S!4)), 0)) & (~(~($greatereq(S!4, 1) & $greatereq($sum(R!1, $product(-1, S!4)), -1) & ($sum(U1!3, $product(-1, $product(S!4, fact(R!1)))) = 0)))) & (~((~($sum(R1!5, $product(-1, R!1)) = 1)) | ($greatereq(R1!5, 0) & $greatereq($sum(N!0, $product(-1, R1!5)), 0) & ($sum(U1!3, $product(-1, fact(R1!5))) = 0))))) & (~(~($greatereq(R!1, 0) & $greatereq($sum(N!0, $product(-1, R!1)), 0) & ($sum(U!2, $product(-1, fact(R!1))) = 0))))) <=> ((~$lesseq($sum(N!0, $product(-1, R!1)), 0)) & ((~$greatereq($sum(R!1, $product(-1, S!4)), 0)) & $greatereq(S!4, 1) & $greatereq($sum(R!1, $product(-1, S!4)), -1) & ($sum(U1!3, $product(-1, $product(fact(R!1), S!4))) = 0) & (~((~($sum(R!1, $product(-1, R1!5)) = -1)) | ($greatereq(R1!5, 0) & $greatereq($sum(N!0, $product(-1, R1!5)), 0) & ($sum(U1!3, $product(-1, fact(R1!5))) = 0))))) & ($greatereq(R!1, 0) & $greatereq($sum(N!0, $product(-1, R!1)), 0) & ($sum(U!2, $product(-1, fact(R!1))) = 0)))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[11, 3])).
% 0.19/0.53 tff(13,plain,
% 0.19/0.53 (((~$lesseq($sum(N!0, $product(-1, R!1)), 0)) & ((~$greatereq($sum(R!1, $product(-1, S!4)), 0)) & (~(~($greatereq(S!4, 1) & $greatereq($sum(R!1, $product(-1, S!4)), -1) & ($sum(U1!3, $product(-1, $product(S!4, fact(R!1)))) = 0)))) & (~((~($sum(R1!5, $product(-1, R!1)) = 1)) | ($greatereq(R1!5, 0) & $greatereq($sum(N!0, $product(-1, R1!5)), 0) & ($sum(U1!3, $product(-1, fact(R1!5))) = 0))))) & (~(~($greatereq(R!1, 0) & $greatereq($sum(N!0, $product(-1, R!1)), 0) & ($sum(U!2, $product(-1, fact(R!1))) = 0))))) <=> ((~$lesseq($sum(N!0, $product(-1, R!1)), 0)) & (~$greatereq($sum(R!1, $product(-1, S!4)), 0)) & $greatereq(S!4, 1) & $greatereq($sum(R!1, $product(-1, S!4)), -1) & ($sum(U1!3, $product(-1, $product(fact(R!1), S!4))) = 0) & (~((~($sum(R!1, $product(-1, R1!5)) = -1)) | ($greatereq(R1!5, 0) & $greatereq($sum(N!0, $product(-1, R1!5)), 0) & ($sum(U1!3, $product(-1, fact(R1!5))) = 0)))) & $greatereq(R!1, 0) & $greatereq($sum(N!0, $product(-1, R!1)), 0) & ($sum(U!2, $product(-1, fact(R!1))) = 0))),
% 0.19/0.53 inference(transitivity,[status(thm)],[12, 2])).
% 0.19/0.53 tff(14,plain,
% 0.19/0.53 ((~(~$greatereq(N!0, 0))) <=> $greatereq(N!0, 0)),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(15,plain,
% 0.19/0.53 (((~(~$greatereq(N!0, 0))) & ((~$lesseq($sum(N!0, $product(-1, R!1)), 0)) & ((~$greatereq($sum(R!1, $product(-1, S!4)), 0)) & (~(~($greatereq(S!4, 1) & $greatereq($sum(R!1, $product(-1, S!4)), -1) & ($sum(U1!3, $product(-1, $product(S!4, fact(R!1)))) = 0)))) & (~((~($sum(R1!5, $product(-1, R!1)) = 1)) | ($greatereq(R1!5, 0) & $greatereq($sum(N!0, $product(-1, R1!5)), 0) & ($sum(U1!3, $product(-1, fact(R1!5))) = 0))))) & (~(~($greatereq(R!1, 0) & $greatereq($sum(N!0, $product(-1, R!1)), 0) & ($sum(U!2, $product(-1, fact(R!1))) = 0)))))) <=> ($greatereq(N!0, 0) & ((~$lesseq($sum(N!0, $product(-1, R!1)), 0)) & (~$greatereq($sum(R!1, $product(-1, S!4)), 0)) & $greatereq(S!4, 1) & $greatereq($sum(R!1, $product(-1, S!4)), -1) & ($sum(U1!3, $product(-1, $product(fact(R!1), S!4))) = 0) & (~((~($sum(R!1, $product(-1, R1!5)) = -1)) | ($greatereq(R1!5, 0) & $greatereq($sum(N!0, $product(-1, R1!5)), 0) & ($sum(U1!3, $product(-1, fact(R1!5))) = 0)))) & $greatereq(R!1, 0) & $greatereq($sum(N!0, $product(-1, R!1)), 0) & ($sum(U!2, $product(-1, fact(R!1))) = 0)))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[14, 13])).
% 0.19/0.53 tff(16,plain,
% 0.19/0.53 (((~(~$greatereq(N!0, 0))) & ((~$lesseq($sum(N!0, $product(-1, R!1)), 0)) & ((~$greatereq($sum(R!1, $product(-1, S!4)), 0)) & (~(~($greatereq(S!4, 1) & $greatereq($sum(R!1, $product(-1, S!4)), -1) & ($sum(U1!3, $product(-1, $product(S!4, fact(R!1)))) = 0)))) & (~((~($sum(R1!5, $product(-1, R!1)) = 1)) | ($greatereq(R1!5, 0) & $greatereq($sum(N!0, $product(-1, R1!5)), 0) & ($sum(U1!3, $product(-1, fact(R1!5))) = 0))))) & (~(~($greatereq(R!1, 0) & $greatereq($sum(N!0, $product(-1, R!1)), 0) & ($sum(U!2, $product(-1, fact(R!1))) = 0)))))) <=> ($greatereq(N!0, 0) & (~$lesseq($sum(N!0, $product(-1, R!1)), 0)) & (~$greatereq($sum(R!1, $product(-1, S!4)), 0)) & $greatereq(S!4, 1) & $greatereq($sum(R!1, $product(-1, S!4)), -1) & ($sum(U1!3, $product(-1, $product(fact(R!1), S!4))) = 0) & (~((~($sum(R!1, $product(-1, R1!5)) = -1)) | ($greatereq(R1!5, 0) & $greatereq($sum(N!0, $product(-1, R1!5)), 0) & ($sum(U1!3, $product(-1, fact(R1!5))) = 0)))) & $greatereq(R!1, 0) & $greatereq($sum(N!0, $product(-1, R!1)), 0) & ($sum(U!2, $product(-1, fact(R!1))) = 0))),
% 0.19/0.53 inference(transitivity,[status(thm)],[15, 1])).
% 0.19/0.53 tff(17,plain,
% 0.19/0.53 ((~![N: $int] : ((~$greatereq(N, 0)) | ![U: $int, R: $int] : ($lesseq($sum(N, $product(-1, R)), 0) | ![S: $int, U1: $int] : ($greatereq($sum(R, $product(-1, S)), 0) | (~($greatereq(S, 1) & $greatereq($sum(R, $product(-1, S)), -1) & ($sum(U1, $product(-1, $product(S, fact(R)))) = 0))) | ![R1: $int] : ((~($sum(R1, $product(-1, R)) = 1)) | ($greatereq(R1, 0) & $greatereq($sum(N, $product(-1, R1)), 0) & ($sum(U1, $product(-1, fact(R1))) = 0)))) | (~($greatereq(R, 0) & $greatereq($sum(N, $product(-1, R)), 0) & ($sum(U, $product(-1, fact(R))) = 0)))))) <=> (~![N: $int] : ((~$greatereq(N, 0)) | ![U: $int, R: $int] : ($lesseq($sum(N, $product(-1, R)), 0) | ![S: $int, U1: $int] : ($greatereq($sum(R, $product(-1, S)), 0) | (~($greatereq(S, 1) & $greatereq($sum(R, $product(-1, S)), -1) & ($sum(U1, $product(-1, $product(S, fact(R)))) = 0))) | ![R1: $int] : ((~($sum(R1, $product(-1, R)) = 1)) | ($greatereq(R1, 0) & $greatereq($sum(N, $product(-1, R1)), 0) & ($sum(U1, $product(-1, fact(R1))) = 0)))) | (~($greatereq(R, 0) & $greatereq($sum(N, $product(-1, R)), 0) & ($sum(U, $product(-1, fact(R))) = 0))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(18,plain,
% 0.19/0.53 ((~![N: $int] : ((~$greatereq(N, 0)) | ![U: $int, R: $int] : ($lesseq($sum(N, $product(-1, R)), 0) | ![S: $int, U1: $int] : ($lesseq($sum(S, $product(-1, R)), 0) | ![R1: $int] : ((~($sum(R1, $product(-1, R)) = 1)) | ($greatereq(R1, 0) & $lesseq($sum(R1, $product(-1, N)), 0) & ($sum(U1, $product(-1, fact(R1))) = 0))) | (~($greatereq(S, 1) & $lesseq($sum(S, $product(-1, R)), 1) & ($sum(U1, $product(-1, $product(fact(R), S))) = 0)))) | (~($greatereq(R, 0) & $lesseq($sum(R, $product(-1, N)), 0) & ($sum(U, $product(-1, fact(R))) = 0)))))) <=> (~![N: $int] : ((~$greatereq(N, 0)) | ![U: $int, R: $int] : ($lesseq($sum(N, $product(-1, R)), 0) | ![S: $int, U1: $int] : ($greatereq($sum(R, $product(-1, S)), 0) | (~($greatereq(S, 1) & $greatereq($sum(R, $product(-1, S)), -1) & ($sum(U1, $product(-1, $product(S, fact(R)))) = 0))) | ![R1: $int] : ((~($sum(R1, $product(-1, R)) = 1)) | ($greatereq(R1, 0) & $greatereq($sum(N, $product(-1, R1)), 0) & ($sum(U1, $product(-1, fact(R1))) = 0)))) | (~($greatereq(R, 0) & $greatereq($sum(N, $product(-1, R)), 0) & ($sum(U, $product(-1, fact(R))) = 0))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(19,plain,
% 0.19/0.53 ((~![N: $int] : ((~$lesseq(0, N)) | ![U: $int, R: $int] : ($lesseq(N, R) | ![S: $int, U1: $int] : ($lesseq(S, R) | ![R1: $int] : ((~(R1 = $sum(1, R))) | ($lesseq(0, R1) & $lesseq(R1, N) & (U1 = fact(R1)))) | (~($lesseq(1, S) & $lesseq(S, $sum(1, R)) & (U1 = $product(fact(R), S))))) | (~($lesseq(0, R) & $lesseq(R, N) & (U = fact(R))))))) <=> (~![N: $int] : ((~$greatereq(N, 0)) | ![U: $int, R: $int] : ($lesseq($sum(N, $product(-1, R)), 0) | ![S: $int, U1: $int] : ($lesseq($sum(S, $product(-1, R)), 0) | ![R1: $int] : ((~($sum(R1, $product(-1, R)) = 1)) | ($greatereq(R1, 0) & $lesseq($sum(R1, $product(-1, N)), 0) & ($sum(U1, $product(-1, fact(R1))) = 0))) | (~($greatereq(S, 1) & $lesseq($sum(S, $product(-1, R)), 1) & ($sum(U1, $product(-1, $product(fact(R), S))) = 0)))) | (~($greatereq(R, 0) & $lesseq($sum(R, $product(-1, N)), 0) & ($sum(U, $product(-1, fact(R))) = 0))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(20,plain,
% 0.19/0.53 ((~![N: $int] : ((~$lesseq(0, N)) | ![U: $int, R: $int] : ($lesseq(N, R) | ![S: $int, U1: $int] : ($lesseq(S, R) | ![R1: $int] : ((~(R1 = $sum(1, R))) | ($lesseq(0, R1) & $lesseq(R1, N) & (U1 = fact(R1)))) | (~($lesseq(1, S) & $lesseq(S, $sum(1, R)) & (U1 = $product(fact(R), S))))) | (~($lesseq(0, R) & $lesseq(R, N) & (U = fact(R))))))) <=> (~![N: $int] : ((~$lesseq(0, N)) | ![U: $int, R: $int] : ($lesseq(N, R) | ![S: $int, U1: $int] : ($lesseq(S, R) | ![R1: $int] : ((~(R1 = $sum(1, R))) | ($lesseq(0, R1) & $lesseq(R1, N) & (U1 = fact(R1)))) | (~($lesseq(1, S) & $lesseq(S, $sum(1, R)) & (U1 = $product(fact(R), S))))) | (~($lesseq(0, R) & $lesseq(R, N) & (U = fact(R)))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(21,plain,
% 0.19/0.53 ((~![N: $int] : ($lesseq(0, N) => ![U: $int, R: $int] : ((($lesseq(0, R) & $lesseq(R, N)) & (U = fact(R))) => ($less(R, N) => ![S: $int, U1: $int] : ((($lesseq(1, S) & $lesseq(S, $sum(R, 1))) & (U1 = $product(S, fact(R)))) => ((~$lesseq(S, R)) => ![R1: $int] : ((R1 = $sum(R, 1)) => (($lesseq(0, R1) & $lesseq(R1, N)) & (U1 = fact(R1)))))))))) <=> (~![N: $int] : ((~$lesseq(0, N)) | ![U: $int, R: $int] : ($lesseq(N, R) | ![S: $int, U1: $int] : ($lesseq(S, R) | ![R1: $int] : ((~(R1 = $sum(1, R))) | ($lesseq(0, R1) & $lesseq(R1, N) & (U1 = fact(R1)))) | (~($lesseq(1, S) & $lesseq(S, $sum(1, R)) & (U1 = $product(fact(R), S))))) | (~($lesseq(0, R) & $lesseq(R, N) & (U = fact(R)))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(22,axiom,(~![N: $int] : ($lesseq(0, N) => ![U: $int, R: $int] : ((($lesseq(0, R) & $lesseq(R, N)) & (U = fact(R))) => ($less(R, N) => ![S: $int, U1: $int] : ((($lesseq(1, S) & $lesseq(S, $sum(R, 1))) & (U1 = $product(S, fact(R)))) => ((~$lesseq(S, R)) => ![R1: $int] : ((R1 = $sum(R, 1)) => (($lesseq(0, R1) & $lesseq(R1, N)) & (U1 = fact(R1)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','wP_parameter_routine')).
% 0.19/0.53 tff(23,plain,
% 0.19/0.53 (~![N: $int] : ((~$lesseq(0, N)) | ![U: $int, R: $int] : ($lesseq(N, R) | ![S: $int, U1: $int] : ($lesseq(S, R) | ![R1: $int] : ((~(R1 = $sum(1, R))) | ($lesseq(0, R1) & $lesseq(R1, N) & (U1 = fact(R1)))) | (~($lesseq(1, S) & $lesseq(S, $sum(1, R)) & (U1 = $product(fact(R), S))))) | (~($lesseq(0, R) & $lesseq(R, N) & (U = fact(R))))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.19/0.53 tff(24,plain,
% 0.19/0.53 (~![N: $int] : ((~$lesseq(0, N)) | ![U: $int, R: $int] : ($lesseq(N, R) | ![S: $int, U1: $int] : ($lesseq(S, R) | ![R1: $int] : ((~(R1 = $sum(1, R))) | ($lesseq(0, R1) & $lesseq(R1, N) & (U1 = fact(R1)))) | (~($lesseq(1, S) & $lesseq(S, $sum(1, R)) & (U1 = $product(fact(R), S))))) | (~($lesseq(0, R) & $lesseq(R, N) & (U = fact(R))))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[23, 20])).
% 0.19/0.53 tff(25,plain,
% 0.19/0.53 (~![N: $int] : ((~$lesseq(0, N)) | ![U: $int, R: $int] : ($lesseq(N, R) | ![S: $int, U1: $int] : ($lesseq(S, R) | ![R1: $int] : ((~(R1 = $sum(1, R))) | ($lesseq(0, R1) & $lesseq(R1, N) & (U1 = fact(R1)))) | (~($lesseq(1, S) & $lesseq(S, $sum(1, R)) & (U1 = $product(fact(R), S))))) | (~($lesseq(0, R) & $lesseq(R, N) & (U = fact(R))))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.19/0.53 tff(26,plain,
% 0.19/0.53 (~![N: $int] : ((~$lesseq(0, N)) | ![U: $int, R: $int] : ($lesseq(N, R) | ![S: $int, U1: $int] : ($lesseq(S, R) | ![R1: $int] : ((~(R1 = $sum(1, R))) | ($lesseq(0, R1) & $lesseq(R1, N) & (U1 = fact(R1)))) | (~($lesseq(1, S) & $lesseq(S, $sum(1, R)) & (U1 = $product(fact(R), S))))) | (~($lesseq(0, R) & $lesseq(R, N) & (U = fact(R))))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[25, 20])).
% 0.19/0.53 tff(27,plain,
% 0.19/0.53 (~![N: $int] : ((~$greatereq(N, 0)) | ![U: $int, R: $int] : ($lesseq($sum(N, $product(-1, R)), 0) | ![S: $int, U1: $int] : ($lesseq($sum(S, $product(-1, R)), 0) | ![R1: $int] : ((~($sum(R1, $product(-1, R)) = 1)) | ($greatereq(R1, 0) & $lesseq($sum(R1, $product(-1, N)), 0) & ($sum(U1, $product(-1, fact(R1))) = 0))) | (~($greatereq(S, 1) & $lesseq($sum(S, $product(-1, R)), 1) & ($sum(U1, $product(-1, $product(fact(R), S))) = 0)))) | (~($greatereq(R, 0) & $lesseq($sum(R, $product(-1, N)), 0) & ($sum(U, $product(-1, fact(R))) = 0)))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.19/0.53 tff(28,plain,
% 0.19/0.53 (~![N: $int] : ((~$greatereq(N, 0)) | ![U: $int, R: $int] : ($lesseq($sum(N, $product(-1, R)), 0) | ![S: $int, U1: $int] : ($greatereq($sum(R, $product(-1, S)), 0) | (~($greatereq(S, 1) & $greatereq($sum(R, $product(-1, S)), -1) & ($sum(U1, $product(-1, $product(S, fact(R)))) = 0))) | ![R1: $int] : ((~($sum(R1, $product(-1, R)) = 1)) | ($greatereq(R1, 0) & $greatereq($sum(N, $product(-1, R1)), 0) & ($sum(U1, $product(-1, fact(R1))) = 0)))) | (~($greatereq(R, 0) & $greatereq($sum(N, $product(-1, R)), 0) & ($sum(U, $product(-1, fact(R))) = 0)))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[27, 18])).
% 0.19/0.53 tff(29,plain,
% 0.19/0.53 (~![N: $int] : ((~$greatereq(N, 0)) | ![U: $int, R: $int] : ($lesseq($sum(N, $product(-1, R)), 0) | ![S: $int, U1: $int] : ($greatereq($sum(R, $product(-1, S)), 0) | (~($greatereq(S, 1) & $greatereq($sum(R, $product(-1, S)), -1) & ($sum(U1, $product(-1, $product(S, fact(R)))) = 0))) | ![R1: $int] : ((~($sum(R1, $product(-1, R)) = 1)) | ($greatereq(R1, 0) & $greatereq($sum(N, $product(-1, R1)), 0) & ($sum(U1, $product(-1, fact(R1))) = 0)))) | (~($greatereq(R, 0) & $greatereq($sum(N, $product(-1, R)), 0) & ($sum(U, $product(-1, fact(R))) = 0)))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[28, 17])).
% 0.19/0.53 tff(30,plain,
% 0.19/0.53 (~![N: $int] : ((~$greatereq(N, 0)) | ![U: $int, R: $int] : ($lesseq($sum(N, $product(-1, R)), 0) | ![S: $int, U1: $int] : ($greatereq($sum(R, $product(-1, S)), 0) | (~($greatereq(S, 1) & $greatereq($sum(R, $product(-1, S)), -1) & ($sum(U1, $product(-1, $product(S, fact(R)))) = 0))) | ![R1: $int] : ((~($sum(R1, $product(-1, R)) = 1)) | ($greatereq(R1, 0) & $greatereq($sum(N, $product(-1, R1)), 0) & ($sum(U1, $product(-1, fact(R1))) = 0)))) | (~($greatereq(R, 0) & $greatereq($sum(N, $product(-1, R)), 0) & ($sum(U, $product(-1, fact(R))) = 0)))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[29, 17])).
% 0.19/0.53 tff(31,plain,
% 0.19/0.53 ($greatereq(N!0, 0) & (~$lesseq($sum(N!0, $product(-1, R!1)), 0)) & (~$greatereq($sum(R!1, $product(-1, S!4)), 0)) & $greatereq(S!4, 1) & $greatereq($sum(R!1, $product(-1, S!4)), -1) & ($sum(U1!3, $product(-1, $product(fact(R!1), S!4))) = 0) & (~((~($sum(R!1, $product(-1, R1!5)) = -1)) | ($greatereq(R1!5, 0) & $greatereq($sum(N!0, $product(-1, R1!5)), 0) & ($sum(U1!3, $product(-1, fact(R1!5))) = 0)))) & $greatereq(R!1, 0) & $greatereq($sum(N!0, $product(-1, R!1)), 0) & ($sum(U!2, $product(-1, fact(R!1))) = 0)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[30, 16])).
% 0.19/0.53 tff(32,plain,
% 0.19/0.53 ($sum(U1!3, $product(-1, $product(fact(R!1), S!4))) = 0),
% 0.19/0.53 inference(and_elim,[status(thm)],[31])).
% 0.19/0.53 tff(33,plain,
% 0.19/0.53 ((~($sum(U1!3, $product(-1, $product(fact(R!1), S!4))) = 0)) | $lesseq($sum(U1!3, $product(-1, $product(fact(R!1), S!4))), 0)),
% 0.19/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.53 tff(34,plain,
% 0.19/0.53 ($lesseq($sum(U1!3, $product(-1, $product(fact(R!1), S!4))), 0)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.19/0.53 tff(35,plain,
% 0.19/0.53 ((~($sum(U1!3, $product(-1, $product(fact(R!1), S!4))) = 0)) | $greatereq($sum(U1!3, $product(-1, $product(fact(R!1), S!4))), 0)),
% 0.19/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.53 tff(36,plain,
% 0.19/0.53 ($greatereq($sum(U1!3, $product(-1, $product(fact(R!1), S!4))), 0)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[35, 32])).
% 0.19/0.53 tff(37,assumption,(~$greatereq(R1!5, 1)), introduced(assumption)).
% 0.19/0.53 tff(38,plain,
% 0.19/0.53 (~((~($sum(R!1, $product(-1, R1!5)) = -1)) | ($greatereq(R1!5, 0) & $greatereq($sum(N!0, $product(-1, R1!5)), 0) & ($sum(U1!3, $product(-1, fact(R1!5))) = 0)))),
% 0.19/0.53 inference(and_elim,[status(thm)],[31])).
% 0.19/0.53 tff(39,plain,
% 0.19/0.53 ($sum(R!1, $product(-1, R1!5)) = -1),
% 0.19/0.53 inference(or_elim,[status(thm)],[38])).
% 0.19/0.53 tff(40,plain,
% 0.19/0.53 ((~($sum(R!1, $product(-1, R1!5)) = -1)) | $lesseq($sum(R!1, $product(-1, R1!5)), -1)),
% 0.19/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.53 tff(41,plain,
% 0.19/0.53 ($lesseq($sum(R!1, $product(-1, R1!5)), -1)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.19/0.53 tff(42,plain,
% 0.19/0.53 ($greatereq(R!1, 0)),
% 0.19/0.53 inference(and_elim,[status(thm)],[31])).
% 0.19/0.53 tff(43,plain,
% 0.19/0.53 ($false),
% 0.19/0.53 inference(theory_lemma,[status(thm)],[42, 41, 37])).
% 0.19/0.53 tff(44,plain,($greatereq(R1!5, 1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.53 tff(45,plain,
% 0.19/0.53 (^[N: $int] : refl(((~$greatereq(N, 1)) | ($sum(fact(N), $product(-1, $product(N, fact($sum(-1, N))))) = 0)) <=> ((~$greatereq(N, 1)) | ($sum(fact(N), $product(-1, $product(N, fact($sum(-1, N))))) = 0)))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(46,plain,
% 0.19/0.53 (![N: $int] : ((~$greatereq(N, 1)) | ($sum(fact(N), $product(-1, $product(N, fact($sum(-1, N))))) = 0)) <=> ![N: $int] : ((~$greatereq(N, 1)) | ($sum(fact(N), $product(-1, $product(N, fact($sum(-1, N))))) = 0))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[45])).
% 0.19/0.53 tff(47,plain,
% 0.19/0.53 (^[N: $int] : rewrite(((~$greatereq(N, 1)) | ($sum(fact(N), $product(-1, $product(fact($sum(-1, N)), N))) = 0)) <=> ((~$greatereq(N, 1)) | ($sum(fact(N), $product(-1, $product(N, fact($sum(-1, N))))) = 0)))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(48,plain,
% 0.19/0.53 (![N: $int] : ((~$greatereq(N, 1)) | ($sum(fact(N), $product(-1, $product(fact($sum(-1, N)), N))) = 0)) <=> ![N: $int] : ((~$greatereq(N, 1)) | ($sum(fact(N), $product(-1, $product(N, fact($sum(-1, N))))) = 0))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[47])).
% 0.19/0.53 tff(49,plain,
% 0.19/0.53 (^[N: $int] : rewrite(((~$lesseq(1, N)) | (fact(N) = $product(fact($sum(-1, N)), N))) <=> ((~$greatereq(N, 1)) | ($sum(fact(N), $product(-1, $product(fact($sum(-1, N)), N))) = 0)))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(50,plain,
% 0.19/0.53 (![N: $int] : ((~$lesseq(1, N)) | (fact(N) = $product(fact($sum(-1, N)), N))) <=> ![N: $int] : ((~$greatereq(N, 1)) | ($sum(fact(N), $product(-1, $product(fact($sum(-1, N)), N))) = 0))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[49])).
% 0.19/0.53 tff(51,plain,
% 0.19/0.53 (![N: $int] : ((~$lesseq(1, N)) | (fact(N) = $product(fact($sum(-1, N)), N))) <=> ![N: $int] : ((~$lesseq(1, N)) | (fact(N) = $product(fact($sum(-1, N)), N)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(52,plain,
% 0.19/0.53 (^[N: $int] : trans(monotonicity(rewrite((fact(N) = $product(N, fact($difference(N, 1)))) <=> (fact(N) = $product(fact($sum(-1, N)), N))), (($lesseq(1, N) => (fact(N) = $product(N, fact($difference(N, 1))))) <=> ($lesseq(1, N) => (fact(N) = $product(fact($sum(-1, N)), N))))), rewrite(($lesseq(1, N) => (fact(N) = $product(fact($sum(-1, N)), N))) <=> ((~$lesseq(1, N)) | (fact(N) = $product(fact($sum(-1, N)), N)))), (($lesseq(1, N) => (fact(N) = $product(N, fact($difference(N, 1))))) <=> ((~$lesseq(1, N)) | (fact(N) = $product(fact($sum(-1, N)), N)))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(53,plain,
% 0.19/0.53 (![N: $int] : ($lesseq(1, N) => (fact(N) = $product(N, fact($difference(N, 1))))) <=> ![N: $int] : ((~$lesseq(1, N)) | (fact(N) = $product(fact($sum(-1, N)), N)))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[52])).
% 0.19/0.53 tff(54,axiom,(![N: $int] : ($lesseq(1, N) => (fact(N) = $product(N, fact($difference(N, 1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','factn')).
% 0.19/0.53 tff(55,plain,
% 0.19/0.53 (![N: $int] : ((~$lesseq(1, N)) | (fact(N) = $product(fact($sum(-1, N)), N)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.53 tff(56,plain,
% 0.19/0.53 (![N: $int] : ((~$lesseq(1, N)) | (fact(N) = $product(fact($sum(-1, N)), N)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.19/0.53 tff(57,plain,
% 0.19/0.53 (![N: $int] : ((~$greatereq(N, 1)) | ($sum(fact(N), $product(-1, $product(fact($sum(-1, N)), N))) = 0))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[56, 50])).
% 0.19/0.53 tff(58,plain,
% 0.19/0.53 (![N: $int] : ((~$greatereq(N, 1)) | ($sum(fact(N), $product(-1, $product(N, fact($sum(-1, N))))) = 0))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[57, 48])).
% 0.19/0.53 tff(59,plain,(
% 0.19/0.53 ![N: $int] : ((~$greatereq(N, 1)) | ($sum(fact(N), $product(-1, $product(N, fact($sum(-1, N))))) = 0))),
% 0.19/0.53 inference(skolemize,[status(sab)],[58])).
% 0.19/0.53 tff(60,plain,
% 0.19/0.53 (![N: $int] : ((~$greatereq(N, 1)) | ($sum(fact(N), $product(-1, $product(N, fact($sum(-1, N))))) = 0))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[59, 46])).
% 0.19/0.53 tff(61,plain,
% 0.19/0.53 (((~![N: $int] : ((~$greatereq(N, 1)) | ($sum(fact(N), $product(-1, $product(N, fact($sum(-1, N))))) = 0))) | ((~$greatereq(R1!5, 1)) | ($sum(fact(R1!5), $product(-1, $product(R1!5, fact($sum(-1, R1!5))))) = 0))) <=> ((~![N: $int] : ((~$greatereq(N, 1)) | ($sum(fact(N), $product(-1, $product(N, fact($sum(-1, N))))) = 0))) | (~$greatereq(R1!5, 1)) | ($sum(fact(R1!5), $product(-1, $product(R1!5, fact($sum(-1, R1!5))))) = 0))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(62,plain,
% 0.19/0.53 ((~![N: $int] : ((~$greatereq(N, 1)) | ($sum(fact(N), $product(-1, $product(N, fact($sum(-1, N))))) = 0))) | ((~$greatereq(R1!5, 1)) | ($sum(fact(R1!5), $product(-1, $product(R1!5, fact($sum(-1, R1!5))))) = 0))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(63,plain,
% 0.19/0.53 ((~![N: $int] : ((~$greatereq(N, 1)) | ($sum(fact(N), $product(-1, $product(N, fact($sum(-1, N))))) = 0))) | (~$greatereq(R1!5, 1)) | ($sum(fact(R1!5), $product(-1, $product(R1!5, fact($sum(-1, R1!5))))) = 0)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.53 tff(64,plain,
% 0.19/0.53 ((~$greatereq(R1!5, 1)) | ($sum(fact(R1!5), $product(-1, $product(R1!5, fact($sum(-1, R1!5))))) = 0)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[63, 60])).
% 0.19/0.53 tff(65,plain,
% 0.19/0.53 ($sum(fact(R1!5), $product(-1, $product(R1!5, fact($sum(-1, R1!5))))) = 0),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[64, 44])).
% 0.19/0.53 tff(66,plain,
% 0.19/0.53 ((~($sum(fact(R1!5), $product(-1, $product(R1!5, fact($sum(-1, R1!5))))) = 0)) | $lesseq($sum(fact(R1!5), $product(-1, $product(R1!5, fact($sum(-1, R1!5))))), 0)),
% 0.19/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.53 tff(67,plain,
% 0.19/0.53 ($lesseq($sum(fact(R1!5), $product(-1, $product(R1!5, fact($sum(-1, R1!5))))), 0)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.19/0.53 tff(68,plain,
% 0.19/0.53 ((~($sum(fact(R1!5), $product(-1, $product(R1!5, fact($sum(-1, R1!5))))) = 0)) | $greatereq($sum(fact(R1!5), $product(-1, $product(R1!5, fact($sum(-1, R1!5))))), 0)),
% 0.19/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.53 tff(69,plain,
% 0.19/0.53 ($greatereq($sum(fact(R1!5), $product(-1, $product(R1!5, fact($sum(-1, R1!5))))), 0)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[68, 65])).
% 0.19/0.53 tff(70,plain,
% 0.19/0.53 (~$greatereq($sum(R!1, $product(-1, S!4)), 0)),
% 0.19/0.53 inference(and_elim,[status(thm)],[31])).
% 0.19/0.53 tff(71,plain,
% 0.19/0.53 ($greatereq($sum(R!1, $product(-1, S!4)), -1)),
% 0.19/0.53 inference(and_elim,[status(thm)],[31])).
% 0.19/0.53 tff(72,plain,
% 0.19/0.53 ((~($sum(R!1, $product(-1, R1!5)) = -1)) | $greatereq($sum(R!1, $product(-1, R1!5)), -1)),
% 0.19/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.53 tff(73,plain,
% 0.19/0.53 ($greatereq($sum(R!1, $product(-1, R1!5)), -1)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[72, 39])).
% 0.19/0.53 tff(74,plain,
% 0.19/0.53 (R!1 = $sum(-1, R1!5)),
% 0.19/0.53 inference(theory_lemma,[status(thm)],[73, 41])).
% 0.19/0.53 tff(75,plain,
% 0.19/0.53 ($sum(-1, R1!5) = R!1),
% 0.19/0.53 inference(symmetry,[status(thm)],[74])).
% 0.19/0.53 tff(76,plain,
% 0.19/0.53 (fact($sum(-1, R1!5)) = fact(R!1)),
% 0.19/0.53 inference(monotonicity,[status(thm)],[75])).
% 0.19/0.53 tff(77,plain,
% 0.19/0.53 (fact(R!1) = fact($sum(-1, R1!5))),
% 0.19/0.53 inference(symmetry,[status(thm)],[76])).
% 0.19/0.53 tff(78,plain,
% 0.19/0.53 ((~(fact(R!1) = fact($sum(-1, R1!5)))) | $lesseq($sum(fact(R!1), $product(-1, fact($sum(-1, R1!5)))), 0)),
% 0.19/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.53 tff(79,plain,
% 0.19/0.53 ($lesseq($sum(fact(R!1), $product(-1, fact($sum(-1, R1!5)))), 0)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.19/0.53 tff(80,plain,
% 0.19/0.53 ((~(fact(R!1) = fact($sum(-1, R1!5)))) | $greatereq($sum(fact(R!1), $product(-1, fact($sum(-1, R1!5)))), 0)),
% 0.19/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.53 tff(81,plain,
% 0.19/0.53 ($greatereq($sum(fact(R!1), $product(-1, fact($sum(-1, R1!5)))), 0)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[80, 77])).
% 0.19/0.53 tff(82,assumption,(~$lesseq($sum(U1!3, $product(-1, fact(R1!5))), 0)), introduced(assumption)).
% 0.19/0.53 tff(83,assumption,(~$greatereq(R!1, 1)), introduced(assumption)).
% 0.19/0.53 tff(84,plain,
% 0.19/0.53 ((~$greatereq(R1!5, 2)) | $greatereq(R!1, 1) | (~$greatereq($sum(R!1, $product(-1, R1!5)), -1))),
% 0.19/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.53 tff(85,plain,
% 0.19/0.53 (~$greatereq(R1!5, 2)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[84, 83, 73])).
% 0.19/0.53 tff(86,plain,
% 0.19/0.53 ((fact(0) = 1) <=> (fact(0) = 1)),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(87,axiom,(fact(0) = 1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fact0')).
% 0.19/0.53 tff(88,plain,
% 0.19/0.53 (fact(0) = 1),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.19/0.53 tff(89,plain,
% 0.19/0.53 ($sum(-1, R1!5) = 0),
% 0.19/0.53 inference(theory_lemma,[status(thm)],[42, 83, 73, 41])).
% 0.19/0.53 tff(90,plain,
% 0.19/0.53 (fact($sum(-1, R1!5)) = fact(0)),
% 0.19/0.53 inference(monotonicity,[status(thm)],[89])).
% 0.19/0.53 tff(91,plain,
% 0.19/0.53 (fact($sum(-1, R1!5)) = 1),
% 0.19/0.53 inference(transitivity,[status(thm)],[90, 88])).
% 0.19/0.53 tff(92,plain,
% 0.19/0.53 ((~(fact($sum(-1, R1!5)) = 1)) | $greatereq(fact($sum(-1, R1!5)), 1)),
% 0.19/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.53 tff(93,plain,
% 0.19/0.53 ($greatereq(fact($sum(-1, R1!5)), 1)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.19/0.53 tff(94,plain,
% 0.19/0.53 (R!1 = 0),
% 0.19/0.53 inference(theory_lemma,[status(thm)],[42, 83])).
% 0.19/0.53 tff(95,plain,
% 0.19/0.53 (fact(R!1) = fact(0)),
% 0.19/0.53 inference(monotonicity,[status(thm)],[94])).
% 0.19/0.53 tff(96,plain,
% 0.19/0.53 (fact(R!1) = 1),
% 0.19/0.53 inference(transitivity,[status(thm)],[95, 88])).
% 0.19/0.53 tff(97,plain,
% 0.19/0.53 ((~(fact(R!1) = 1)) | $lesseq(fact(R!1), 1)),
% 0.19/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.53 tff(98,plain,
% 0.19/0.53 ($lesseq(fact(R!1), 1)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.19/0.53 tff(99,plain,
% 0.19/0.53 ((~(fact(R!1) = 1)) | $greatereq(fact(R!1), 1)),
% 0.19/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.53 tff(100,plain,
% 0.19/0.53 ($greatereq(fact(R!1), 1)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[99, 96])).
% 0.19/0.53 tff(101,plain,
% 0.19/0.53 ($false),
% 0.19/0.53 inference(theory_lemma,[status(thm)],[83, 100, 98, 34, 93, 44, 85, 69, 82, 71])).
% 0.19/0.53 tff(102,plain,($greatereq(R!1, 1) | $lesseq($sum(U1!3, $product(-1, fact(R1!5))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.53 tff(103,plain,
% 0.19/0.53 ($greatereq(R!1, 1)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[102, 82])).
% 0.19/0.53 tff(104,plain,
% 0.19/0.53 (((~![N: $int] : ((~$greatereq(N, 1)) | ($sum(fact(N), $product(-1, $product(N, fact($sum(-1, N))))) = 0))) | ((~$greatereq(R!1, 1)) | ($sum(fact(R!1), $product(-1, $product(R!1, fact($sum(-1, R!1))))) = 0))) <=> ((~![N: $int] : ((~$greatereq(N, 1)) | ($sum(fact(N), $product(-1, $product(N, fact($sum(-1, N))))) = 0))) | (~$greatereq(R!1, 1)) | ($sum(fact(R!1), $product(-1, $product(R!1, fact($sum(-1, R!1))))) = 0))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(105,plain,
% 0.19/0.53 ((~![N: $int] : ((~$greatereq(N, 1)) | ($sum(fact(N), $product(-1, $product(N, fact($sum(-1, N))))) = 0))) | ((~$greatereq(R!1, 1)) | ($sum(fact(R!1), $product(-1, $product(R!1, fact($sum(-1, R!1))))) = 0))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(106,plain,
% 0.19/0.53 ((~![N: $int] : ((~$greatereq(N, 1)) | ($sum(fact(N), $product(-1, $product(N, fact($sum(-1, N))))) = 0))) | (~$greatereq(R!1, 1)) | ($sum(fact(R!1), $product(-1, $product(R!1, fact($sum(-1, R!1))))) = 0)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.19/0.53 tff(107,plain,
% 0.19/0.53 ((~$greatereq(R!1, 1)) | ($sum(fact(R!1), $product(-1, $product(R!1, fact($sum(-1, R!1))))) = 0)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[106, 60])).
% 0.19/0.53 tff(108,plain,
% 0.19/0.53 ($sum(fact(R!1), $product(-1, $product(R!1, fact($sum(-1, R!1))))) = 0),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[107, 103])).
% 0.19/0.53 tff(109,plain,
% 0.19/0.53 ((~($sum(fact(R!1), $product(-1, $product(R!1, fact($sum(-1, R!1))))) = 0)) | $lesseq($sum(fact(R!1), $product(-1, $product(R!1, fact($sum(-1, R!1))))), 0)),
% 0.19/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.53 tff(110,plain,
% 0.19/0.53 ($lesseq($sum(fact(R!1), $product(-1, $product(R!1, fact($sum(-1, R!1))))), 0)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.19/0.53 tff(111,plain,
% 0.19/0.53 ((~($sum(fact(R!1), $product(-1, $product(R!1, fact($sum(-1, R!1))))) = 0)) | $greatereq($sum(fact(R!1), $product(-1, $product(R!1, fact($sum(-1, R!1))))), 0)),
% 0.19/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.53 tff(112,plain,
% 0.19/0.53 ($greatereq($sum(fact(R!1), $product(-1, $product(R!1, fact($sum(-1, R!1))))), 0)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[111, 108])).
% 0.19/0.53 tff(113,plain,
% 0.19/0.53 ($sum(-1, R!1) = $sum(-2, R1!5)),
% 0.19/0.53 inference(theory_lemma,[status(thm)],[73, 41])).
% 0.19/0.53 tff(114,plain,
% 0.19/0.53 ($sum(-2, R1!5) = $sum(-1, R!1)),
% 0.19/0.53 inference(symmetry,[status(thm)],[113])).
% 0.19/0.53 tff(115,plain,
% 0.19/0.53 (fact($sum(-2, R1!5)) = fact($sum(-1, R!1))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[114])).
% 0.19/0.53 tff(116,plain,
% 0.19/0.53 (fact($sum(-1, R!1)) = fact($sum(-2, R1!5))),
% 0.19/0.53 inference(symmetry,[status(thm)],[115])).
% 0.19/0.53 tff(117,plain,
% 0.19/0.53 ((~(fact($sum(-1, R!1)) = fact($sum(-2, R1!5)))) | $lesseq($sum(fact($sum(-1, R!1)), $product(-1, fact($sum(-2, R1!5)))), 0)),
% 0.19/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.53 tff(118,plain,
% 0.19/0.53 ($lesseq($sum(fact($sum(-1, R!1)), $product(-1, fact($sum(-2, R1!5)))), 0)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.19/0.53 tff(119,plain,
% 0.19/0.53 ((~(fact($sum(-1, R!1)) = fact($sum(-2, R1!5)))) | $greatereq($sum(fact($sum(-1, R!1)), $product(-1, fact($sum(-2, R1!5)))), 0)),
% 0.19/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.53 tff(120,plain,
% 0.19/0.53 ($greatereq($sum(fact($sum(-1, R!1)), $product(-1, fact($sum(-2, R1!5)))), 0)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[119, 116])).
% 0.19/0.53 tff(121,plain,
% 0.19/0.53 ($false),
% 0.19/0.53 inference(theory_lemma,[status(thm)],[82, 69, 67, 36, 34, 73, 41, 71, 70, 120, 118, 112, 110, 81, 79, 112, 110])).
% 0.19/0.53 tff(122,plain,($lesseq($sum(U1!3, $product(-1, fact(R1!5))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.53 tff(123,plain,
% 0.19/0.53 ($greatereq(R1!5, 0) | (~$greatereq(R!1, 0)) | (~$lesseq($sum(R!1, $product(-1, R1!5)), -1))),
% 0.19/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.53 tff(124,plain,
% 0.19/0.53 ($greatereq(R1!5, 0)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[123, 41, 42])).
% 0.19/0.53 tff(125,plain,
% 0.19/0.53 (~$lesseq($sum(N!0, $product(-1, R!1)), 0)),
% 0.19/0.53 inference(and_elim,[status(thm)],[31])).
% 0.19/0.53 tff(126,plain,
% 0.19/0.53 ($greatereq($sum(N!0, $product(-1, R1!5)), 0) | $lesseq($sum(N!0, $product(-1, R!1)), 0) | (~$greatereq($sum(R!1, $product(-1, R1!5)), -1))),
% 0.19/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.54 tff(127,plain,
% 0.19/0.54 ($greatereq($sum(N!0, $product(-1, R1!5)), 0)),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[126, 73, 125])).
% 0.19/0.54 tff(128,plain,
% 0.19/0.54 ((~(~((~$greatereq(R1!5, 0)) | (~$greatereq($sum(N!0, $product(-1, R1!5)), 0)) | (~($sum(U1!3, $product(-1, fact(R1!5))) = 0))))) <=> ((~$greatereq(R1!5, 0)) | (~$greatereq($sum(N!0, $product(-1, R1!5)), 0)) | (~($sum(U1!3, $product(-1, fact(R1!5))) = 0)))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(129,plain,
% 0.19/0.54 (($greatereq(R1!5, 0) & $greatereq($sum(N!0, $product(-1, R1!5)), 0) & ($sum(U1!3, $product(-1, fact(R1!5))) = 0)) <=> (~((~$greatereq(R1!5, 0)) | (~$greatereq($sum(N!0, $product(-1, R1!5)), 0)) | (~($sum(U1!3, $product(-1, fact(R1!5))) = 0))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(130,plain,
% 0.19/0.54 ((~($greatereq(R1!5, 0) & $greatereq($sum(N!0, $product(-1, R1!5)), 0) & ($sum(U1!3, $product(-1, fact(R1!5))) = 0))) <=> (~(~((~$greatereq(R1!5, 0)) | (~$greatereq($sum(N!0, $product(-1, R1!5)), 0)) | (~($sum(U1!3, $product(-1, fact(R1!5))) = 0)))))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[129])).
% 0.19/0.54 tff(131,plain,
% 0.19/0.54 ((~($greatereq(R1!5, 0) & $greatereq($sum(N!0, $product(-1, R1!5)), 0) & ($sum(U1!3, $product(-1, fact(R1!5))) = 0))) <=> ((~$greatereq(R1!5, 0)) | (~$greatereq($sum(N!0, $product(-1, R1!5)), 0)) | (~($sum(U1!3, $product(-1, fact(R1!5))) = 0)))),
% 0.19/0.54 inference(transitivity,[status(thm)],[130, 128])).
% 0.19/0.54 tff(132,plain,
% 0.19/0.54 (~($greatereq(R1!5, 0) & $greatereq($sum(N!0, $product(-1, R1!5)), 0) & ($sum(U1!3, $product(-1, fact(R1!5))) = 0))),
% 0.19/0.54 inference(or_elim,[status(thm)],[38])).
% 0.19/0.54 tff(133,plain,
% 0.19/0.54 ((~$greatereq(R1!5, 0)) | (~$greatereq($sum(N!0, $product(-1, R1!5)), 0)) | (~($sum(U1!3, $product(-1, fact(R1!5))) = 0))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.19/0.54 tff(134,plain,
% 0.19/0.54 (~($sum(U1!3, $product(-1, fact(R1!5))) = 0)),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[133, 127, 124])).
% 0.19/0.54 tff(135,plain,
% 0.19/0.54 (($sum(U1!3, $product(-1, fact(R1!5))) = 0) | (~$lesseq($sum(U1!3, $product(-1, fact(R1!5))), 0)) | (~$greatereq($sum(U1!3, $product(-1, fact(R1!5))), 0))),
% 0.19/0.54 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.54 tff(136,plain,
% 0.19/0.54 ((~$lesseq($sum(U1!3, $product(-1, fact(R1!5))), 0)) | (~$greatereq($sum(U1!3, $product(-1, fact(R1!5))), 0))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.19/0.54 tff(137,plain,
% 0.19/0.54 (~$greatereq($sum(U1!3, $product(-1, fact(R1!5))), 0)),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[136, 122])).
% 0.19/0.54 tff(138,plain,
% 0.19/0.54 ($false),
% 0.19/0.54 inference(theory_lemma,[status(thm)],[137, 81, 79, 73, 41, 71, 70, 69, 67, 36, 34])).
% 0.19/0.54 % SZS output end Proof
%------------------------------------------------------------------------------