TSTP Solution File: PLA050_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : PLA050_1 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 : Sun Sep 18 13:40:05 EDT 2022
% Result : Theorem 25.93s 17.00s
% Output : Proof 26.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PLA050_1 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n018.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 : Fri Sep 2 17:50:29 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.
% 25.93/17.00 % SZS status Theorem
% 25.93/17.00 % SZS output start Proof
% 25.93/17.00 tff(imp_type, type, (
% 25.93/17.00 imp: ( $real * $int * $int ) > $real)).
% 25.93/17.00 tff(ns_type, type, (
% 25.93/17.00 ns: $int > $int)).
% 25.93/17.00 tff(problen_type, type, (
% 25.93/17.00 problen: $int)).
% 25.93/17.00 tff(mysump_type, type, (
% 25.93/17.00 mysump: ( $real * $int * $int * $int ) > $real)).
% 25.93/17.00 tff(lk_type, type, (
% 25.93/17.00 lk: $int > $int)).
% 25.93/17.00 tff(tptp_fun_Problen_1_type, type, (
% 25.93/17.00 tptp_fun_Problen_1: $int)).
% 25.93/17.00 tff(tptp_fun_S_3_type, type, (
% 25.93/17.00 tptp_fun_S_3: $real)).
% 25.93/17.00 tff(recexp_type, type, (
% 25.93/17.00 recexp: ( $real * $int * $int ) > $real)).
% 25.93/17.00 tff(tptp_fun_C_2_type, type, (
% 25.93/17.00 tptp_fun_C_2: $int)).
% 25.93/17.00 tff(probsize_type, type, (
% 25.93/17.00 probsize: $int)).
% 25.93/17.00 tff(tptp_fun_Probsize_0_type, type, (
% 25.93/17.00 tptp_fun_Probsize_0: $int)).
% 25.93/17.00 tff(dc_type, type, (
% 25.93/17.00 dc: ( $real * $int * $int ) > $real)).
% 25.93/17.00 tff(1,plain,
% 25.93/17.00 ((0 = $sum($product(17/2, $to_real(lk(1))), $sum(mysump(17/2, ns($sum(-1, problen)), 2, 0), $product(-1, $product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2)))))) <=> ($sum($product(17/2, $to_real(lk(1))), $sum(mysump(17/2, ns($sum(-1, problen)), 2, 0), $product(-1, $product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2))))) = 0)),
% 25.93/17.00 inference(commutativity,[status(thm)],[])).
% 25.93/17.00 tff(2,plain,
% 25.93/17.00 (($sum($product(17/2, $to_real(lk(1))), $sum(mysump(17/2, ns($sum(-1, problen)), 2, 0), $product(-1, $product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2))))) = 0) <=> (0 = $sum($product(17/2, $to_real(lk(1))), $sum(mysump(17/2, ns($sum(-1, problen)), 2, 0), $product(-1, $product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2))))))),
% 25.93/17.00 inference(symmetry,[status(thm)],[1])).
% 25.93/17.00 tff(3,plain,
% 25.93/17.00 (^[D: $real, T: $int, C: $int] : refl(((~$greatereq(C, 1)) | ($sum($product($to_real(T), imp(D, T, C)), $sum($product(-1, $product(D, $to_real(lk($sum(-1, C))))), $product(-1, mysump(D, T, C, $sum(-2, C))))) = 0)) <=> ((~$greatereq(C, 1)) | ($sum($product($to_real(T), imp(D, T, C)), $sum($product(-1, $product(D, $to_real(lk($sum(-1, C))))), $product(-1, mysump(D, T, C, $sum(-2, C))))) = 0)))),
% 25.93/17.00 inference(bind,[status(th)],[])).
% 25.93/17.00 tff(4,plain,
% 25.93/17.00 (![D: $real, T: $int, C: $int] : ((~$greatereq(C, 1)) | ($sum($product($to_real(T), imp(D, T, C)), $sum($product(-1, $product(D, $to_real(lk($sum(-1, C))))), $product(-1, mysump(D, T, C, $sum(-2, C))))) = 0)) <=> ![D: $real, T: $int, C: $int] : ((~$greatereq(C, 1)) | ($sum($product($to_real(T), imp(D, T, C)), $sum($product(-1, $product(D, $to_real(lk($sum(-1, C))))), $product(-1, mysump(D, T, C, $sum(-2, C))))) = 0))),
% 25.93/17.00 inference(quant_intro,[status(thm)],[3])).
% 25.93/17.00 tff(5,plain,
% 25.93/17.00 (^[D: $real, T: $int, C: $int] : rewrite(((~$greatereq(C, 1)) | ($sum($product($to_real(T), imp(D, T, C)), $sum($product(-1, $product($to_real(lk($sum(-1, C))), D)), $product(-1, mysump(D, T, C, $sum(-2, C))))) = 0)) <=> ((~$greatereq(C, 1)) | ($sum($product($to_real(T), imp(D, T, C)), $sum($product(-1, $product(D, $to_real(lk($sum(-1, C))))), $product(-1, mysump(D, T, C, $sum(-2, C))))) = 0)))),
% 25.93/17.00 inference(bind,[status(th)],[])).
% 25.93/17.00 tff(6,plain,
% 25.93/17.00 (![D: $real, T: $int, C: $int] : ((~$greatereq(C, 1)) | ($sum($product($to_real(T), imp(D, T, C)), $sum($product(-1, $product($to_real(lk($sum(-1, C))), D)), $product(-1, mysump(D, T, C, $sum(-2, C))))) = 0)) <=> ![D: $real, T: $int, C: $int] : ((~$greatereq(C, 1)) | ($sum($product($to_real(T), imp(D, T, C)), $sum($product(-1, $product(D, $to_real(lk($sum(-1, C))))), $product(-1, mysump(D, T, C, $sum(-2, C))))) = 0))),
% 25.93/17.00 inference(quant_intro,[status(thm)],[5])).
% 25.93/17.00 tff(7,plain,
% 25.93/17.00 (^[D: $real, T: $int, C: $int] : rewrite(((~$lesseq(1, C)) | ($product($to_real(T), imp(D, T, C)) = $sum($product($to_real(lk($sum(-1, C))), D), mysump(D, T, C, $sum(-2, C))))) <=> ((~$greatereq(C, 1)) | ($sum($product($to_real(T), imp(D, T, C)), $sum($product(-1, $product($to_real(lk($sum(-1, C))), D)), $product(-1, mysump(D, T, C, $sum(-2, C))))) = 0)))),
% 25.93/17.00 inference(bind,[status(th)],[])).
% 25.93/17.00 tff(8,plain,
% 25.93/17.00 (![D: $real, T: $int, C: $int] : ((~$lesseq(1, C)) | ($product($to_real(T), imp(D, T, C)) = $sum($product($to_real(lk($sum(-1, C))), D), mysump(D, T, C, $sum(-2, C))))) <=> ![D: $real, T: $int, C: $int] : ((~$greatereq(C, 1)) | ($sum($product($to_real(T), imp(D, T, C)), $sum($product(-1, $product($to_real(lk($sum(-1, C))), D)), $product(-1, mysump(D, T, C, $sum(-2, C))))) = 0))),
% 25.93/17.00 inference(quant_intro,[status(thm)],[7])).
% 25.93/17.00 tff(9,plain,
% 25.93/17.00 (![D: $real, T: $int, C: $int] : ((~$lesseq(1, C)) | ($product($to_real(T), imp(D, T, C)) = $sum($product($to_real(lk($sum(-1, C))), D), mysump(D, T, C, $sum(-2, C))))) <=> ![D: $real, T: $int, C: $int] : ((~$lesseq(1, C)) | ($product($to_real(T), imp(D, T, C)) = $sum($product($to_real(lk($sum(-1, C))), D), mysump(D, T, C, $sum(-2, C)))))),
% 25.93/17.00 inference(rewrite,[status(thm)],[])).
% 25.93/17.00 tff(10,plain,
% 25.93/17.00 (^[D: $real, T: $int, C: $int] : trans(monotonicity(rewrite(($product($to_real(T), imp(D, T, C)) = $sum($product(D, $to_real(lk($difference(C, 1)))), mysump(D, T, C, $difference(C, 2)))) <=> ($product($to_real(T), imp(D, T, C)) = $sum($product($to_real(lk($sum(-1, C))), D), mysump(D, T, C, $sum(-2, C))))), (($lesseq(1, C) => ($product($to_real(T), imp(D, T, C)) = $sum($product(D, $to_real(lk($difference(C, 1)))), mysump(D, T, C, $difference(C, 2))))) <=> ($lesseq(1, C) => ($product($to_real(T), imp(D, T, C)) = $sum($product($to_real(lk($sum(-1, C))), D), mysump(D, T, C, $sum(-2, C))))))), rewrite(($lesseq(1, C) => ($product($to_real(T), imp(D, T, C)) = $sum($product($to_real(lk($sum(-1, C))), D), mysump(D, T, C, $sum(-2, C))))) <=> ((~$lesseq(1, C)) | ($product($to_real(T), imp(D, T, C)) = $sum($product($to_real(lk($sum(-1, C))), D), mysump(D, T, C, $sum(-2, C)))))), (($lesseq(1, C) => ($product($to_real(T), imp(D, T, C)) = $sum($product(D, $to_real(lk($difference(C, 1)))), mysump(D, T, C, $difference(C, 2))))) <=> ((~$lesseq(1, C)) | ($product($to_real(T), imp(D, T, C)) = $sum($product($to_real(lk($sum(-1, C))), D), mysump(D, T, C, $sum(-2, C)))))))),
% 25.93/17.00 inference(bind,[status(th)],[])).
% 25.93/17.00 tff(11,plain,
% 25.93/17.00 (![D: $real, T: $int, C: $int] : ($lesseq(1, C) => ($product($to_real(T), imp(D, T, C)) = $sum($product(D, $to_real(lk($difference(C, 1)))), mysump(D, T, C, $difference(C, 2))))) <=> ![D: $real, T: $int, C: $int] : ((~$lesseq(1, C)) | ($product($to_real(T), imp(D, T, C)) = $sum($product($to_real(lk($sum(-1, C))), D), mysump(D, T, C, $sum(-2, C)))))),
% 25.93/17.00 inference(quant_intro,[status(thm)],[10])).
% 25.93/17.00 tff(12,axiom,(![D: $real, T: $int, C: $int] : ($lesseq(1, C) => ($product($to_real(T), imp(D, T, C)) = $sum($product(D, $to_real(lk($difference(C, 1)))), mysump(D, T, C, $difference(C, 2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','imp_n')).
% 25.93/17.00 tff(13,plain,
% 25.93/17.00 (![D: $real, T: $int, C: $int] : ((~$lesseq(1, C)) | ($product($to_real(T), imp(D, T, C)) = $sum($product($to_real(lk($sum(-1, C))), D), mysump(D, T, C, $sum(-2, C)))))),
% 25.93/17.00 inference(modus_ponens,[status(thm)],[12, 11])).
% 25.93/17.00 tff(14,plain,
% 25.93/17.00 (![D: $real, T: $int, C: $int] : ((~$lesseq(1, C)) | ($product($to_real(T), imp(D, T, C)) = $sum($product($to_real(lk($sum(-1, C))), D), mysump(D, T, C, $sum(-2, C)))))),
% 25.93/17.00 inference(modus_ponens,[status(thm)],[13, 9])).
% 25.93/17.00 tff(15,plain,
% 25.93/17.00 (![D: $real, T: $int, C: $int] : ((~$greatereq(C, 1)) | ($sum($product($to_real(T), imp(D, T, C)), $sum($product(-1, $product($to_real(lk($sum(-1, C))), D)), $product(-1, mysump(D, T, C, $sum(-2, C))))) = 0))),
% 25.93/17.00 inference(modus_ponens,[status(thm)],[14, 8])).
% 25.93/17.00 tff(16,plain,
% 25.93/17.00 (![D: $real, T: $int, C: $int] : ((~$greatereq(C, 1)) | ($sum($product($to_real(T), imp(D, T, C)), $sum($product(-1, $product(D, $to_real(lk($sum(-1, C))))), $product(-1, mysump(D, T, C, $sum(-2, C))))) = 0))),
% 25.93/17.00 inference(modus_ponens,[status(thm)],[15, 6])).
% 25.93/17.00 tff(17,plain,(
% 25.93/17.00 ![D: $real, T: $int, C: $int] : ((~$greatereq(C, 1)) | ($sum($product($to_real(T), imp(D, T, C)), $sum($product(-1, $product(D, $to_real(lk($sum(-1, C))))), $product(-1, mysump(D, T, C, $sum(-2, C))))) = 0))),
% 25.93/17.00 inference(skolemize,[status(sab)],[16])).
% 25.93/17.00 tff(18,plain,
% 25.93/17.00 (![D: $real, T: $int, C: $int] : ((~$greatereq(C, 1)) | ($sum($product($to_real(T), imp(D, T, C)), $sum($product(-1, $product(D, $to_real(lk($sum(-1, C))))), $product(-1, mysump(D, T, C, $sum(-2, C))))) = 0))),
% 25.93/17.00 inference(modus_ponens,[status(thm)],[17, 4])).
% 25.93/17.00 tff(19,plain,
% 25.93/17.00 (((~![D: $real, T: $int, C: $int] : ((~$greatereq(C, 1)) | ($sum($product($to_real(T), imp(D, T, C)), $sum($product(-1, $product(D, $to_real(lk($sum(-1, C))))), $product(-1, mysump(D, T, C, $sum(-2, C))))) = 0))) | ($sum($product(17/2, $to_real(lk(1))), $sum(mysump(17/2, ns($sum(-1, problen)), 2, 0), $product(-1, $product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2))))) = 0)) <=> ((~![D: $real, T: $int, C: $int] : ((~$greatereq(C, 1)) | ($sum($product($to_real(T), imp(D, T, C)), $sum($product(-1, $product(D, $to_real(lk($sum(-1, C))))), $product(-1, mysump(D, T, C, $sum(-2, C))))) = 0))) | ($sum($product(17/2, $to_real(lk(1))), $sum(mysump(17/2, ns($sum(-1, problen)), 2, 0), $product(-1, $product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2))))) = 0))),
% 25.93/17.00 inference(rewrite,[status(thm)],[])).
% 25.93/17.00 tff(20,plain,
% 25.93/17.00 (($false | ($sum($product(17/2, $to_real(lk(1))), $sum(mysump(17/2, ns($sum(-1, problen)), 2, 0), $product(-1, $product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2))))) = 0)) <=> ($sum($product(17/2, $to_real(lk(1))), $sum(mysump(17/2, ns($sum(-1, problen)), 2, 0), $product(-1, $product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2))))) = 0)),
% 25.93/17.00 inference(rewrite,[status(thm)],[])).
% 25.93/17.00 tff(21,plain,
% 25.93/17.00 (($sum($product(-17/2, $to_real(lk(1))), $sum($product(-1, mysump(17/2, ns($sum(-1, problen)), 2, 0)), $product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2)))) = 0) <=> ($sum($product(17/2, $to_real(lk(1))), $sum(mysump(17/2, ns($sum(-1, problen)), 2, 0), $product(-1, $product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2))))) = 0)),
% 25.93/17.00 inference(rewrite,[status(thm)],[])).
% 25.93/17.00 tff(22,plain,
% 25.93/17.00 ($sum($product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2)), $sum($product(-17/2, $to_real(lk(1))), $product(-1, mysump(17/2, ns($sum(-1, problen)), 2, 0)))) = $sum($product(-17/2, $to_real(lk(1))), $sum($product(-1, mysump(17/2, ns($sum(-1, problen)), 2, 0)), $product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2))))),
% 25.93/17.00 inference(rewrite,[status(thm)],[])).
% 25.93/17.00 tff(23,plain,
% 25.93/17.00 ($product(-1, mysump(17/2, ns($sum(-1, problen)), 2, $sum(-2, 2))) = $product(-1, mysump(17/2, ns($sum(-1, problen)), 2, 0))),
% 25.93/17.00 inference(rewrite,[status(thm)],[])).
% 25.93/17.00 tff(24,plain,
% 25.93/17.00 ($product(-1, $product(17/2, $to_real(lk(1)))) = $product(-17/2, $to_real(lk(1)))),
% 25.93/17.00 inference(rewrite,[status(thm)],[])).
% 25.93/17.00 tff(25,plain,
% 25.93/17.00 ($product(17/2, $to_real(lk($sum(-1, 2)))) = $product(17/2, $to_real(lk(1)))),
% 25.93/17.00 inference(rewrite,[status(thm)],[])).
% 25.93/17.00 tff(26,plain,
% 25.93/17.00 ($product(-1, $product(17/2, $to_real(lk($sum(-1, 2))))) = $product(-1, $product(17/2, $to_real(lk(1))))),
% 25.93/17.00 inference(monotonicity,[status(thm)],[25])).
% 25.93/17.00 tff(27,plain,
% 25.93/17.00 ($product(-1, $product(17/2, $to_real(lk($sum(-1, 2))))) = $product(-17/2, $to_real(lk(1)))),
% 25.93/17.00 inference(transitivity,[status(thm)],[26, 24])).
% 25.93/17.00 tff(28,plain,
% 25.93/17.00 ($sum($product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2)), $sum($product(-1, $product(17/2, $to_real(lk($sum(-1, 2))))), $product(-1, mysump(17/2, ns($sum(-1, problen)), 2, $sum(-2, 2))))) = $sum($product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2)), $sum($product(-17/2, $to_real(lk(1))), $product(-1, mysump(17/2, ns($sum(-1, problen)), 2, 0))))),
% 25.93/17.00 inference(monotonicity,[status(thm)],[27, 23])).
% 25.93/17.00 tff(29,plain,
% 25.93/17.00 ($sum($product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2)), $sum($product(-1, $product(17/2, $to_real(lk($sum(-1, 2))))), $product(-1, mysump(17/2, ns($sum(-1, problen)), 2, $sum(-2, 2))))) = $sum($product(-17/2, $to_real(lk(1))), $sum($product(-1, mysump(17/2, ns($sum(-1, problen)), 2, 0)), $product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2))))),
% 25.93/17.00 inference(transitivity,[status(thm)],[28, 22])).
% 25.93/17.00 tff(30,plain,
% 25.93/17.00 (($sum($product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2)), $sum($product(-1, $product(17/2, $to_real(lk($sum(-1, 2))))), $product(-1, mysump(17/2, ns($sum(-1, problen)), 2, $sum(-2, 2))))) = 0) <=> ($sum($product(-17/2, $to_real(lk(1))), $sum($product(-1, mysump(17/2, ns($sum(-1, problen)), 2, 0)), $product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2)))) = 0)),
% 25.93/17.00 inference(monotonicity,[status(thm)],[29])).
% 25.93/17.00 tff(31,plain,
% 25.93/17.00 (($sum($product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2)), $sum($product(-1, $product(17/2, $to_real(lk($sum(-1, 2))))), $product(-1, mysump(17/2, ns($sum(-1, problen)), 2, $sum(-2, 2))))) = 0) <=> ($sum($product(17/2, $to_real(lk(1))), $sum(mysump(17/2, ns($sum(-1, problen)), 2, 0), $product(-1, $product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2))))) = 0)),
% 25.93/17.00 inference(transitivity,[status(thm)],[30, 21])).
% 25.93/17.00 tff(32,plain,
% 25.93/17.00 ((~$true) <=> $false),
% 25.93/17.00 inference(rewrite,[status(thm)],[])).
% 25.93/17.00 tff(33,plain,
% 25.93/17.00 ($greatereq(2, 1) <=> $true),
% 25.93/17.00 inference(rewrite,[status(thm)],[])).
% 25.93/17.00 tff(34,plain,
% 25.93/17.00 ((~$greatereq(2, 1)) <=> (~$true)),
% 25.93/17.00 inference(monotonicity,[status(thm)],[33])).
% 25.93/17.00 tff(35,plain,
% 25.93/17.00 ((~$greatereq(2, 1)) <=> $false),
% 25.93/17.00 inference(transitivity,[status(thm)],[34, 32])).
% 25.93/17.00 tff(36,plain,
% 25.93/17.00 (((~$greatereq(2, 1)) | ($sum($product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2)), $sum($product(-1, $product(17/2, $to_real(lk($sum(-1, 2))))), $product(-1, mysump(17/2, ns($sum(-1, problen)), 2, $sum(-2, 2))))) = 0)) <=> ($false | ($sum($product(17/2, $to_real(lk(1))), $sum(mysump(17/2, ns($sum(-1, problen)), 2, 0), $product(-1, $product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2))))) = 0))),
% 25.93/17.00 inference(monotonicity,[status(thm)],[35, 31])).
% 25.93/17.00 tff(37,plain,
% 25.93/17.00 (((~$greatereq(2, 1)) | ($sum($product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2)), $sum($product(-1, $product(17/2, $to_real(lk($sum(-1, 2))))), $product(-1, mysump(17/2, ns($sum(-1, problen)), 2, $sum(-2, 2))))) = 0)) <=> ($sum($product(17/2, $to_real(lk(1))), $sum(mysump(17/2, ns($sum(-1, problen)), 2, 0), $product(-1, $product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2))))) = 0)),
% 25.93/17.00 inference(transitivity,[status(thm)],[36, 20])).
% 25.93/17.00 tff(38,plain,
% 25.93/17.00 (((~![D: $real, T: $int, C: $int] : ((~$greatereq(C, 1)) | ($sum($product($to_real(T), imp(D, T, C)), $sum($product(-1, $product(D, $to_real(lk($sum(-1, C))))), $product(-1, mysump(D, T, C, $sum(-2, C))))) = 0))) | ((~$greatereq(2, 1)) | ($sum($product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2)), $sum($product(-1, $product(17/2, $to_real(lk($sum(-1, 2))))), $product(-1, mysump(17/2, ns($sum(-1, problen)), 2, $sum(-2, 2))))) = 0))) <=> ((~![D: $real, T: $int, C: $int] : ((~$greatereq(C, 1)) | ($sum($product($to_real(T), imp(D, T, C)), $sum($product(-1, $product(D, $to_real(lk($sum(-1, C))))), $product(-1, mysump(D, T, C, $sum(-2, C))))) = 0))) | ($sum($product(17/2, $to_real(lk(1))), $sum(mysump(17/2, ns($sum(-1, problen)), 2, 0), $product(-1, $product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2))))) = 0))),
% 25.93/17.00 inference(monotonicity,[status(thm)],[37])).
% 25.93/17.00 tff(39,plain,
% 25.93/17.00 (((~![D: $real, T: $int, C: $int] : ((~$greatereq(C, 1)) | ($sum($product($to_real(T), imp(D, T, C)), $sum($product(-1, $product(D, $to_real(lk($sum(-1, C))))), $product(-1, mysump(D, T, C, $sum(-2, C))))) = 0))) | ((~$greatereq(2, 1)) | ($sum($product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2)), $sum($product(-1, $product(17/2, $to_real(lk($sum(-1, 2))))), $product(-1, mysump(17/2, ns($sum(-1, problen)), 2, $sum(-2, 2))))) = 0))) <=> ((~![D: $real, T: $int, C: $int] : ((~$greatereq(C, 1)) | ($sum($product($to_real(T), imp(D, T, C)), $sum($product(-1, $product(D, $to_real(lk($sum(-1, C))))), $product(-1, mysump(D, T, C, $sum(-2, C))))) = 0))) | ($sum($product(17/2, $to_real(lk(1))), $sum(mysump(17/2, ns($sum(-1, problen)), 2, 0), $product(-1, $product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2))))) = 0))),
% 25.93/17.01 inference(transitivity,[status(thm)],[38, 19])).
% 25.93/17.01 tff(40,plain,
% 25.93/17.01 ((~![D: $real, T: $int, C: $int] : ((~$greatereq(C, 1)) | ($sum($product($to_real(T), imp(D, T, C)), $sum($product(-1, $product(D, $to_real(lk($sum(-1, C))))), $product(-1, mysump(D, T, C, $sum(-2, C))))) = 0))) | ((~$greatereq(2, 1)) | ($sum($product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2)), $sum($product(-1, $product(17/2, $to_real(lk($sum(-1, 2))))), $product(-1, mysump(17/2, ns($sum(-1, problen)), 2, $sum(-2, 2))))) = 0))),
% 25.93/17.01 inference(quant_inst,[status(thm)],[])).
% 25.93/17.01 tff(41,plain,
% 25.93/17.01 ((~![D: $real, T: $int, C: $int] : ((~$greatereq(C, 1)) | ($sum($product($to_real(T), imp(D, T, C)), $sum($product(-1, $product(D, $to_real(lk($sum(-1, C))))), $product(-1, mysump(D, T, C, $sum(-2, C))))) = 0))) | ($sum($product(17/2, $to_real(lk(1))), $sum(mysump(17/2, ns($sum(-1, problen)), 2, 0), $product(-1, $product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2))))) = 0)),
% 25.93/17.01 inference(modus_ponens,[status(thm)],[40, 39])).
% 25.93/17.01 tff(42,plain,
% 25.93/17.01 ($sum($product(17/2, $to_real(lk(1))), $sum(mysump(17/2, ns($sum(-1, problen)), 2, 0), $product(-1, $product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2))))) = 0),
% 25.93/17.01 inference(unit_resolution,[status(thm)],[41, 18])).
% 25.93/17.01 tff(43,plain,
% 25.93/17.01 (0 = $sum($product(17/2, $to_real(lk(1))), $sum(mysump(17/2, ns($sum(-1, problen)), 2, 0), $product(-1, $product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2)))))),
% 25.93/17.01 inference(modus_ponens,[status(thm)],[42, 2])).
% 25.93/17.01 tff(44,plain,
% 25.93/17.01 ((~(0 = $sum($product(17/2, $to_real(lk(1))), $sum(mysump(17/2, ns($sum(-1, problen)), 2, 0), $product(-1, $product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2))))))) | $lesseq($sum($product(17/2, $to_real(lk(1))), $sum(mysump(17/2, ns($sum(-1, problen)), 2, 0), $product(-1, $product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2))))), 0)),
% 25.93/17.01 inference(theory_lemma,[status(thm)],[])).
% 25.93/17.01 tff(45,plain,
% 25.93/17.01 ($lesseq($sum($product(17/2, $to_real(lk(1))), $sum(mysump(17/2, ns($sum(-1, problen)), 2, 0), $product(-1, $product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2))))), 0)),
% 25.93/17.01 inference(unit_resolution,[status(thm)],[44, 43])).
% 25.93/17.01 tff(46,plain,
% 25.93/17.01 ((0 = mysump(17/2, ns($sum(-1, problen)), 2, 0)) <=> (mysump(17/2, ns($sum(-1, problen)), 2, 0) = 0)),
% 25.93/17.01 inference(commutativity,[status(thm)],[])).
% 25.93/17.01 tff(47,plain,
% 25.93/17.01 ((mysump(17/2, ns($sum(-1, problen)), 2, 0) = 0) <=> (0 = mysump(17/2, ns($sum(-1, problen)), 2, 0))),
% 25.93/17.01 inference(symmetry,[status(thm)],[46])).
% 25.93/17.01 tff(48,plain,
% 25.93/17.01 (^[D: $real, T: $int, C: $int] : refl((mysump(D, T, C, 0) = 0) <=> (mysump(D, T, C, 0) = 0))),
% 25.93/17.01 inference(bind,[status(th)],[])).
% 25.93/17.01 tff(49,plain,
% 25.93/17.01 (![D: $real, T: $int, C: $int] : (mysump(D, T, C, 0) = 0) <=> ![D: $real, T: $int, C: $int] : (mysump(D, T, C, 0) = 0)),
% 25.93/17.01 inference(quant_intro,[status(thm)],[48])).
% 25.93/17.01 tff(50,plain,
% 25.93/17.01 (![D: $real, T: $int, C: $int] : (mysump(D, T, C, 0) = 0) <=> ![D: $real, T: $int, C: $int] : (mysump(D, T, C, 0) = 0)),
% 25.93/17.01 inference(rewrite,[status(thm)],[])).
% 25.93/17.01 tff(51,axiom,(![D: $real, T: $int, C: $int] : (mysump(D, T, C, 0) = 0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mysump_0')).
% 25.93/17.01 tff(52,plain,
% 25.93/17.01 (![D: $real, T: $int, C: $int] : (mysump(D, T, C, 0) = 0)),
% 25.93/17.01 inference(modus_ponens,[status(thm)],[51, 50])).
% 25.93/17.01 tff(53,plain,(
% 25.93/17.01 ![D: $real, T: $int, C: $int] : (mysump(D, T, C, 0) = 0)),
% 25.93/17.01 inference(skolemize,[status(sab)],[52])).
% 25.93/17.01 tff(54,plain,
% 25.93/17.01 (![D: $real, T: $int, C: $int] : (mysump(D, T, C, 0) = 0)),
% 25.93/17.01 inference(modus_ponens,[status(thm)],[53, 49])).
% 25.93/17.01 tff(55,plain,
% 25.93/17.01 ((~![D: $real, T: $int, C: $int] : (mysump(D, T, C, 0) = 0)) | (mysump(17/2, ns($sum(-1, problen)), 2, 0) = 0)),
% 25.93/17.01 inference(quant_inst,[status(thm)],[])).
% 25.93/17.01 tff(56,plain,
% 25.93/17.01 (mysump(17/2, ns($sum(-1, problen)), 2, 0) = 0),
% 25.93/17.01 inference(unit_resolution,[status(thm)],[55, 54])).
% 25.93/17.01 tff(57,plain,
% 25.93/17.01 (0 = mysump(17/2, ns($sum(-1, problen)), 2, 0)),
% 25.93/17.01 inference(modus_ponens,[status(thm)],[56, 47])).
% 25.93/17.01 tff(58,plain,
% 25.93/17.01 ((~(0 = mysump(17/2, ns($sum(-1, problen)), 2, 0))) | $greatereq(mysump(17/2, ns($sum(-1, problen)), 2, 0), 0)),
% 25.93/17.01 inference(theory_lemma,[status(thm)],[])).
% 25.93/17.01 tff(59,plain,
% 25.93/17.01 ($greatereq(mysump(17/2, ns($sum(-1, problen)), 2, 0), 0)),
% 25.93/17.01 inference(unit_resolution,[status(thm)],[58, 57])).
% 25.93/17.01 tff(60,assumption,($lesseq(lk(1), 0)), introduced(assumption)).
% 25.93/17.01 tff(61,plain,
% 25.93/17.01 ((~![S: $real, C: $int, Problen: $int, Probsize: $int] : ((~($greatereq(Problen, 2) & ($sum(problen, $product(-1, Problen)) = 0) & $greatereq($sum(Probsize, $product(-1, $product(Problen, Problen))), 0) & ($sum(probsize, $product(-1, Probsize)) = 0) & $greatereq($sum(problen, $product(-2, C)), 0) & $lesseq($sum($to_real(probsize), $product(-1, recexp(S, probsize, C))), 0) & $greatereq(S, 9/10) & $lesseq(S, 10))) | $lesseq(S, 1))) <=> (~![S: $real, C: $int, Problen: $int, Probsize: $int] : ((~($greatereq(Problen, 2) & ($sum(problen, $product(-1, Problen)) = 0) & $greatereq($sum(Probsize, $product(-1, $product(Problen, Problen))), 0) & ($sum(probsize, $product(-1, Probsize)) = 0) & $greatereq($sum(problen, $product(-2, C)), 0) & $lesseq($sum($to_real(probsize), $product(-1, recexp(S, probsize, C))), 0) & $greatereq(S, 9/10) & $lesseq(S, 10))) | $lesseq(S, 1)))),
% 25.93/17.01 inference(rewrite,[status(thm)],[])).
% 25.93/17.01 tff(62,plain,
% 25.93/17.01 ((~![S: $real, C: $int, Problen: $int, Probsize: $int] : ((~($greatereq(Problen, 2) & ($sum(problen, $product(-1, Problen)) = 0) & $lesseq($sum($product(Problen, Problen), $product(-1, Probsize)), 0) & ($sum(probsize, $product(-1, Probsize)) = 0) & $lesseq($sum($product(2, C), $product(-1, problen)), 0) & $lesseq($sum($to_real(probsize), $product(-1, recexp(S, probsize, C))), 0) & $greatereq(S, 9/10) & $lesseq(S, 10))) | $lesseq(S, 1))) <=> (~![S: $real, C: $int, Problen: $int, Probsize: $int] : ((~($greatereq(Problen, 2) & ($sum(problen, $product(-1, Problen)) = 0) & $greatereq($sum(Probsize, $product(-1, $product(Problen, Problen))), 0) & ($sum(probsize, $product(-1, Probsize)) = 0) & $greatereq($sum(problen, $product(-2, C)), 0) & $lesseq($sum($to_real(probsize), $product(-1, recexp(S, probsize, C))), 0) & $greatereq(S, 9/10) & $lesseq(S, 10))) | $lesseq(S, 1)))),
% 25.93/17.01 inference(rewrite,[status(thm)],[])).
% 25.93/17.01 tff(63,plain,
% 25.93/17.01 ((~![S: $real, C: $int, Problen: $int, Probsize: $int] : ((~($lesseq(2, Problen) & (problen = Problen) & $lesseq($product(Problen, Problen), Probsize) & (probsize = Probsize) & $lesseq($product(2, C), problen) & $lesseq($to_real(probsize), recexp(S, probsize, C)) & $lesseq(9/10, S) & $lesseq(S, 10))) | $lesseq(S, 1))) <=> (~![S: $real, C: $int, Problen: $int, Probsize: $int] : ((~($greatereq(Problen, 2) & ($sum(problen, $product(-1, Problen)) = 0) & $lesseq($sum($product(Problen, Problen), $product(-1, Probsize)), 0) & ($sum(probsize, $product(-1, Probsize)) = 0) & $lesseq($sum($product(2, C), $product(-1, problen)), 0) & $lesseq($sum($to_real(probsize), $product(-1, recexp(S, probsize, C))), 0) & $greatereq(S, 9/10) & $lesseq(S, 10))) | $lesseq(S, 1)))),
% 25.93/17.01 inference(rewrite,[status(thm)],[])).
% 25.93/17.01 tff(64,plain,
% 25.93/17.01 ((~![S: $real, C: $int, Problen: $int, Probsize: $int] : ((~($lesseq(2, Problen) & (problen = Problen) & $lesseq($product(Problen, Problen), Probsize) & (probsize = Probsize) & $lesseq($product(2, C), problen) & $lesseq($to_real(probsize), recexp(S, probsize, C)) & $lesseq(9/10, S) & $lesseq(S, 10))) | $lesseq(S, 1))) <=> (~![S: $real, C: $int, Problen: $int, Probsize: $int] : ((~($lesseq(2, Problen) & (problen = Problen) & $lesseq($product(Problen, Problen), Probsize) & (probsize = Probsize) & $lesseq($product(2, C), problen) & $lesseq($to_real(probsize), recexp(S, probsize, C)) & $lesseq(9/10, S) & $lesseq(S, 10))) | $lesseq(S, 1)))),
% 25.93/17.01 inference(rewrite,[status(thm)],[])).
% 25.93/17.01 tff(65,plain,
% 25.93/17.01 ((~![S: $real, C: $int, Problen: $int, Probsize: $int] : (((((((($lesseq(2, Problen) & (problen = Problen)) & $lesseq($product(Problen, Problen), Probsize)) & (probsize = Probsize)) & $lesseq($product(C, 2), problen)) & $lesseq($to_real(probsize), recexp(S, probsize, C))) & $lesseq(9/10, S)) & $lesseq(S, 10)) => $lesseq(S, 1))) <=> (~![S: $real, C: $int, Problen: $int, Probsize: $int] : ((~($lesseq(2, Problen) & (problen = Problen) & $lesseq($product(Problen, Problen), Probsize) & (probsize = Probsize) & $lesseq($product(2, C), problen) & $lesseq($to_real(probsize), recexp(S, probsize, C)) & $lesseq(9/10, S) & $lesseq(S, 10))) | $lesseq(S, 1)))),
% 25.93/17.01 inference(rewrite,[status(thm)],[])).
% 25.93/17.01 tff(66,axiom,(~![S: $real, C: $int, Problen: $int, Probsize: $int] : (((((((($lesseq(2, Problen) & (problen = Problen)) & $lesseq($product(Problen, Problen), Probsize)) & (probsize = Probsize)) & $lesseq($product(C, 2), problen)) & $lesseq($to_real(probsize), recexp(S, probsize, C))) & $lesseq(9/10, S)) & $lesseq(S, 10)) => $lesseq(S, 1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','tougher_local_search')).
% 25.93/17.01 tff(67,plain,
% 25.93/17.01 (~![S: $real, C: $int, Problen: $int, Probsize: $int] : ((~($lesseq(2, Problen) & (problen = Problen) & $lesseq($product(Problen, Problen), Probsize) & (probsize = Probsize) & $lesseq($product(2, C), problen) & $lesseq($to_real(probsize), recexp(S, probsize, C)) & $lesseq(9/10, S) & $lesseq(S, 10))) | $lesseq(S, 1))),
% 25.93/17.01 inference(modus_ponens,[status(thm)],[66, 65])).
% 25.93/17.01 tff(68,plain,
% 25.93/17.01 (~![S: $real, C: $int, Problen: $int, Probsize: $int] : ((~($lesseq(2, Problen) & (problen = Problen) & $lesseq($product(Problen, Problen), Probsize) & (probsize = Probsize) & $lesseq($product(2, C), problen) & $lesseq($to_real(probsize), recexp(S, probsize, C)) & $lesseq(9/10, S) & $lesseq(S, 10))) | $lesseq(S, 1))),
% 25.93/17.01 inference(modus_ponens,[status(thm)],[67, 64])).
% 25.93/17.01 tff(69,plain,
% 25.93/17.01 (~![S: $real, C: $int, Problen: $int, Probsize: $int] : ((~($lesseq(2, Problen) & (problen = Problen) & $lesseq($product(Problen, Problen), Probsize) & (probsize = Probsize) & $lesseq($product(2, C), problen) & $lesseq($to_real(probsize), recexp(S, probsize, C)) & $lesseq(9/10, S) & $lesseq(S, 10))) | $lesseq(S, 1))),
% 25.93/17.01 inference(modus_ponens,[status(thm)],[68, 64])).
% 25.93/17.01 tff(70,plain,
% 25.93/17.01 (~![S: $real, C: $int, Problen: $int, Probsize: $int] : ((~($lesseq(2, Problen) & (problen = Problen) & $lesseq($product(Problen, Problen), Probsize) & (probsize = Probsize) & $lesseq($product(2, C), problen) & $lesseq($to_real(probsize), recexp(S, probsize, C)) & $lesseq(9/10, S) & $lesseq(S, 10))) | $lesseq(S, 1))),
% 25.93/17.01 inference(modus_ponens,[status(thm)],[69, 64])).
% 25.93/17.01 tff(71,plain,
% 25.93/17.01 (~![S: $real, C: $int, Problen: $int, Probsize: $int] : ((~($greatereq(Problen, 2) & ($sum(problen, $product(-1, Problen)) = 0) & $lesseq($sum($product(Problen, Problen), $product(-1, Probsize)), 0) & ($sum(probsize, $product(-1, Probsize)) = 0) & $lesseq($sum($product(2, C), $product(-1, problen)), 0) & $lesseq($sum($to_real(probsize), $product(-1, recexp(S, probsize, C))), 0) & $greatereq(S, 9/10) & $lesseq(S, 10))) | $lesseq(S, 1))),
% 25.93/17.01 inference(modus_ponens,[status(thm)],[70, 63])).
% 25.93/17.01 tff(72,plain,
% 25.93/17.01 (~![S: $real, C: $int, Problen: $int, Probsize: $int] : ((~($greatereq(Problen, 2) & ($sum(problen, $product(-1, Problen)) = 0) & $greatereq($sum(Probsize, $product(-1, $product(Problen, Problen))), 0) & ($sum(probsize, $product(-1, Probsize)) = 0) & $greatereq($sum(problen, $product(-2, C)), 0) & $lesseq($sum($to_real(probsize), $product(-1, recexp(S, probsize, C))), 0) & $greatereq(S, 9/10) & $lesseq(S, 10))) | $lesseq(S, 1))),
% 25.93/17.01 inference(modus_ponens,[status(thm)],[71, 62])).
% 25.93/17.01 tff(73,plain,
% 25.93/17.01 (~![S: $real, C: $int, Problen: $int, Probsize: $int] : ((~($greatereq(Problen, 2) & ($sum(problen, $product(-1, Problen)) = 0) & $greatereq($sum(Probsize, $product(-1, $product(Problen, Problen))), 0) & ($sum(probsize, $product(-1, Probsize)) = 0) & $greatereq($sum(problen, $product(-2, C)), 0) & $lesseq($sum($to_real(probsize), $product(-1, recexp(S, probsize, C))), 0) & $greatereq(S, 9/10) & $lesseq(S, 10))) | $lesseq(S, 1))),
% 25.93/17.01 inference(modus_ponens,[status(thm)],[72, 61])).
% 25.93/17.01 tff(74,plain,
% 25.93/17.01 (~![S: $real, C: $int, Problen: $int, Probsize: $int] : ((~($greatereq(Problen, 2) & ($sum(problen, $product(-1, Problen)) = 0) & $greatereq($sum(Probsize, $product(-1, $product(Problen, Problen))), 0) & ($sum(probsize, $product(-1, Probsize)) = 0) & $greatereq($sum(problen, $product(-2, C)), 0) & $lesseq($sum($to_real(probsize), $product(-1, recexp(S, probsize, C))), 0) & $greatereq(S, 9/10) & $lesseq(S, 10))) | $lesseq(S, 1))),
% 25.93/17.01 inference(modus_ponens,[status(thm)],[73, 61])).
% 25.93/17.01 tff(75,plain,(
% 25.93/17.01 ~((~($greatereq(Problen!1, 2) & ($sum(problen, $product(-1, Problen!1)) = 0) & $greatereq($sum(Probsize!0, $product(-1, $product(Problen!1, Problen!1))), 0) & ($sum(probsize, $product(-1, Probsize!0)) = 0) & $greatereq($sum(problen, $product(-2, C!2)), 0) & $lesseq($sum($to_real(probsize), $product(-1, recexp(S!3, probsize, C!2))), 0) & $greatereq(S!3, 9/10) & $lesseq(S!3, 10))) | $lesseq(S!3, 1))),
% 25.93/17.01 inference(skolemize,[status(sab)],[74])).
% 25.93/17.01 tff(76,plain,
% 25.93/17.01 ($greatereq(Problen!1, 2) & ($sum(problen, $product(-1, Problen!1)) = 0) & $greatereq($sum(Probsize!0, $product(-1, $product(Problen!1, Problen!1))), 0) & ($sum(probsize, $product(-1, Probsize!0)) = 0) & $greatereq($sum(problen, $product(-2, C!2)), 0) & $lesseq($sum($to_real(probsize), $product(-1, recexp(S!3, probsize, C!2))), 0) & $greatereq(S!3, 9/10) & $lesseq(S!3, 10)),
% 25.93/17.01 inference(or_elim,[status(thm)],[75])).
% 25.93/17.01 tff(77,plain,
% 25.93/17.01 ($greatereq(Problen!1, 2)),
% 25.93/17.01 inference(and_elim,[status(thm)],[76])).
% 25.93/17.01 tff(78,plain,
% 25.93/17.01 ((0 = $sum(problen, $product(-1, Problen!1))) <=> ($sum(problen, $product(-1, Problen!1)) = 0)),
% 25.93/17.01 inference(commutativity,[status(thm)],[])).
% 25.93/17.01 tff(79,plain,
% 25.93/17.01 (($sum(problen, $product(-1, Problen!1)) = 0) <=> (0 = $sum(problen, $product(-1, Problen!1)))),
% 25.93/17.01 inference(symmetry,[status(thm)],[78])).
% 25.93/17.01 tff(80,plain,
% 25.93/17.01 ($sum(problen, $product(-1, Problen!1)) = 0),
% 25.93/17.01 inference(and_elim,[status(thm)],[76])).
% 25.93/17.01 tff(81,plain,
% 25.93/17.01 (0 = $sum(problen, $product(-1, Problen!1))),
% 25.93/17.01 inference(modus_ponens,[status(thm)],[80, 79])).
% 25.93/17.01 tff(82,plain,
% 25.93/17.01 ((~(0 = $sum(problen, $product(-1, Problen!1)))) | $greatereq($sum(problen, $product(-1, Problen!1)), 0)),
% 25.93/17.01 inference(theory_lemma,[status(thm)],[])).
% 25.93/17.01 tff(83,plain,
% 25.93/17.01 ($greatereq($sum(problen, $product(-1, Problen!1)), 0)),
% 25.93/17.01 inference(unit_resolution,[status(thm)],[82, 81])).
% 25.93/17.01 tff(84,plain,
% 25.93/17.01 ((~$greatereq(Problen!1, 2)) | (~$greatereq($sum(problen, $product(-1, Problen!1)), 0)) | $greatereq(problen, 1)),
% 25.93/17.01 inference(theory_lemma,[status(thm)],[])).
% 25.93/17.01 tff(85,plain,
% 25.93/17.01 ($greatereq(problen, 1)),
% 25.93/17.01 inference(unit_resolution,[status(thm)],[84, 83, 77])).
% 25.93/17.01 tff(86,plain,
% 25.93/17.01 (^[K: $int] : refl(($greatereq($sum(lk(K), $product(-1, lk($sum(-1, K)))), 0) | (~$greatereq(K, 1)) | (~$greatereq($sum(problen, $product(-1, K)), 0))) <=> ($greatereq($sum(lk(K), $product(-1, lk($sum(-1, K)))), 0) | (~$greatereq(K, 1)) | (~$greatereq($sum(problen, $product(-1, K)), 0))))),
% 25.93/17.01 inference(bind,[status(th)],[])).
% 25.93/17.01 tff(87,plain,
% 25.93/17.01 (![K: $int] : ($greatereq($sum(lk(K), $product(-1, lk($sum(-1, K)))), 0) | (~$greatereq(K, 1)) | (~$greatereq($sum(problen, $product(-1, K)), 0))) <=> ![K: $int] : ($greatereq($sum(lk(K), $product(-1, lk($sum(-1, K)))), 0) | (~$greatereq(K, 1)) | (~$greatereq($sum(problen, $product(-1, K)), 0)))),
% 25.93/17.01 inference(quant_intro,[status(thm)],[86])).
% 25.93/17.01 tff(88,plain,
% 25.93/17.01 (^[K: $int] : trans(monotonicity(trans(monotonicity(rewrite(($greatereq(K, 1) & $greatereq($sum(problen, $product(-1, K)), 0)) <=> (~((~$greatereq(K, 1)) | (~$greatereq($sum(problen, $product(-1, K)), 0))))), ((~($greatereq(K, 1) & $greatereq($sum(problen, $product(-1, K)), 0))) <=> (~(~((~$greatereq(K, 1)) | (~$greatereq($sum(problen, $product(-1, K)), 0))))))), rewrite((~(~((~$greatereq(K, 1)) | (~$greatereq($sum(problen, $product(-1, K)), 0))))) <=> ((~$greatereq(K, 1)) | (~$greatereq($sum(problen, $product(-1, K)), 0)))), ((~($greatereq(K, 1) & $greatereq($sum(problen, $product(-1, K)), 0))) <=> ((~$greatereq(K, 1)) | (~$greatereq($sum(problen, $product(-1, K)), 0))))), (((~($greatereq(K, 1) & $greatereq($sum(problen, $product(-1, K)), 0))) | $greatereq($sum(lk(K), $product(-1, lk($sum(-1, K)))), 0)) <=> (((~$greatereq(K, 1)) | (~$greatereq($sum(problen, $product(-1, K)), 0))) | $greatereq($sum(lk(K), $product(-1, lk($sum(-1, K)))), 0)))), rewrite((((~$greatereq(K, 1)) | (~$greatereq($sum(problen, $product(-1, K)), 0))) | $greatereq($sum(lk(K), $product(-1, lk($sum(-1, K)))), 0)) <=> ($greatereq($sum(lk(K), $product(-1, lk($sum(-1, K)))), 0) | (~$greatereq(K, 1)) | (~$greatereq($sum(problen, $product(-1, K)), 0)))), (((~($greatereq(K, 1) & $greatereq($sum(problen, $product(-1, K)), 0))) | $greatereq($sum(lk(K), $product(-1, lk($sum(-1, K)))), 0)) <=> ($greatereq($sum(lk(K), $product(-1, lk($sum(-1, K)))), 0) | (~$greatereq(K, 1)) | (~$greatereq($sum(problen, $product(-1, K)), 0)))))),
% 25.93/17.01 inference(bind,[status(th)],[])).
% 25.93/17.01 tff(89,plain,
% 25.93/17.01 (![K: $int] : ((~($greatereq(K, 1) & $greatereq($sum(problen, $product(-1, K)), 0))) | $greatereq($sum(lk(K), $product(-1, lk($sum(-1, K)))), 0)) <=> ![K: $int] : ($greatereq($sum(lk(K), $product(-1, lk($sum(-1, K)))), 0) | (~$greatereq(K, 1)) | (~$greatereq($sum(problen, $product(-1, K)), 0)))),
% 25.93/17.01 inference(quant_intro,[status(thm)],[88])).
% 25.93/17.01 tff(90,plain,
% 25.93/17.01 (^[K: $int] : rewrite(((~($greatereq(K, 1) & $lesseq($sum(K, $product(-1, problen)), 0))) | $lesseq($sum(lk($sum(-1, K)), $product(-1, lk(K))), 0)) <=> ((~($greatereq(K, 1) & $greatereq($sum(problen, $product(-1, K)), 0))) | $greatereq($sum(lk(K), $product(-1, lk($sum(-1, K)))), 0)))),
% 25.93/17.01 inference(bind,[status(th)],[])).
% 25.93/17.01 tff(91,plain,
% 25.93/17.01 (![K: $int] : ((~($greatereq(K, 1) & $lesseq($sum(K, $product(-1, problen)), 0))) | $lesseq($sum(lk($sum(-1, K)), $product(-1, lk(K))), 0)) <=> ![K: $int] : ((~($greatereq(K, 1) & $greatereq($sum(problen, $product(-1, K)), 0))) | $greatereq($sum(lk(K), $product(-1, lk($sum(-1, K)))), 0))),
% 25.93/17.01 inference(quant_intro,[status(thm)],[90])).
% 25.93/17.01 tff(92,plain,
% 25.93/17.01 (^[K: $int] : rewrite(((~($lesseq(1, K) & $lesseq(K, problen))) | $lesseq(lk($sum(-1, K)), lk(K))) <=> ((~($greatereq(K, 1) & $lesseq($sum(K, $product(-1, problen)), 0))) | $lesseq($sum(lk($sum(-1, K)), $product(-1, lk(K))), 0)))),
% 25.93/17.01 inference(bind,[status(th)],[])).
% 25.93/17.01 tff(93,plain,
% 25.93/17.01 (![K: $int] : ((~($lesseq(1, K) & $lesseq(K, problen))) | $lesseq(lk($sum(-1, K)), lk(K))) <=> ![K: $int] : ((~($greatereq(K, 1) & $lesseq($sum(K, $product(-1, problen)), 0))) | $lesseq($sum(lk($sum(-1, K)), $product(-1, lk(K))), 0))),
% 25.93/17.01 inference(quant_intro,[status(thm)],[92])).
% 25.93/17.01 tff(94,plain,
% 25.93/17.01 (![K: $int] : ((~($lesseq(1, K) & $lesseq(K, problen))) | $lesseq(lk($sum(-1, K)), lk(K))) <=> ![K: $int] : ((~($lesseq(1, K) & $lesseq(K, problen))) | $lesseq(lk($sum(-1, K)), lk(K)))),
% 25.93/17.01 inference(rewrite,[status(thm)],[])).
% 25.93/17.01 tff(95,plain,
% 25.93/17.01 (^[K: $int] : trans(monotonicity(rewrite($lesseq(lk($difference(K, 1)), lk(K)) <=> $lesseq(lk($sum(-1, K)), lk(K))), ((($lesseq(1, K) & $lesseq(K, problen)) => $lesseq(lk($difference(K, 1)), lk(K))) <=> (($lesseq(1, K) & $lesseq(K, problen)) => $lesseq(lk($sum(-1, K)), lk(K))))), rewrite((($lesseq(1, K) & $lesseq(K, problen)) => $lesseq(lk($sum(-1, K)), lk(K))) <=> ((~($lesseq(1, K) & $lesseq(K, problen))) | $lesseq(lk($sum(-1, K)), lk(K)))), ((($lesseq(1, K) & $lesseq(K, problen)) => $lesseq(lk($difference(K, 1)), lk(K))) <=> ((~($lesseq(1, K) & $lesseq(K, problen))) | $lesseq(lk($sum(-1, K)), lk(K)))))),
% 25.93/17.01 inference(bind,[status(th)],[])).
% 25.93/17.01 tff(96,plain,
% 25.93/17.01 (![K: $int] : (($lesseq(1, K) & $lesseq(K, problen)) => $lesseq(lk($difference(K, 1)), lk(K))) <=> ![K: $int] : ((~($lesseq(1, K) & $lesseq(K, problen))) | $lesseq(lk($sum(-1, K)), lk(K)))),
% 25.93/17.01 inference(quant_intro,[status(thm)],[95])).
% 25.93/17.01 tff(97,axiom,(![K: $int] : (($lesseq(1, K) & $lesseq(K, problen)) => $lesseq(lk($difference(K, 1)), lk(K)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lk_n')).
% 25.93/17.01 tff(98,plain,
% 25.93/17.01 (![K: $int] : ((~($lesseq(1, K) & $lesseq(K, problen))) | $lesseq(lk($sum(-1, K)), lk(K)))),
% 25.93/17.01 inference(modus_ponens,[status(thm)],[97, 96])).
% 25.93/17.01 tff(99,plain,
% 25.93/17.01 (![K: $int] : ((~($lesseq(1, K) & $lesseq(K, problen))) | $lesseq(lk($sum(-1, K)), lk(K)))),
% 25.93/17.01 inference(modus_ponens,[status(thm)],[98, 94])).
% 25.93/17.01 tff(100,plain,
% 25.93/17.01 (![K: $int] : ((~($greatereq(K, 1) & $lesseq($sum(K, $product(-1, problen)), 0))) | $lesseq($sum(lk($sum(-1, K)), $product(-1, lk(K))), 0))),
% 25.93/17.01 inference(modus_ponens,[status(thm)],[99, 93])).
% 25.93/17.01 tff(101,plain,
% 25.93/17.01 (![K: $int] : ((~($greatereq(K, 1) & $greatereq($sum(problen, $product(-1, K)), 0))) | $greatereq($sum(lk(K), $product(-1, lk($sum(-1, K)))), 0))),
% 25.93/17.01 inference(modus_ponens,[status(thm)],[100, 91])).
% 25.93/17.01 tff(102,plain,(
% 25.93/17.01 ![K: $int] : ((~($greatereq(K, 1) & $greatereq($sum(problen, $product(-1, K)), 0))) | $greatereq($sum(lk(K), $product(-1, lk($sum(-1, K)))), 0))),
% 25.93/17.01 inference(skolemize,[status(sab)],[101])).
% 25.93/17.01 tff(103,plain,
% 25.93/17.01 (![K: $int] : ($greatereq($sum(lk(K), $product(-1, lk($sum(-1, K)))), 0) | (~$greatereq(K, 1)) | (~$greatereq($sum(problen, $product(-1, K)), 0)))),
% 25.93/17.01 inference(modus_ponens,[status(thm)],[102, 89])).
% 25.93/17.01 tff(104,plain,
% 25.93/17.01 (![K: $int] : ($greatereq($sum(lk(K), $product(-1, lk($sum(-1, K)))), 0) | (~$greatereq(K, 1)) | (~$greatereq($sum(problen, $product(-1, K)), 0)))),
% 25.93/17.01 inference(modus_ponens,[status(thm)],[103, 87])).
% 25.93/17.01 tff(105,plain,
% 25.93/17.01 (((~![K: $int] : ($greatereq($sum(lk(K), $product(-1, lk($sum(-1, K)))), 0) | (~$greatereq(K, 1)) | (~$greatereq($sum(problen, $product(-1, K)), 0)))) | ((~$greatereq(problen, 1)) | $lesseq($sum(lk(0), $product(-1, lk(1))), 0))) <=> ((~![K: $int] : ($greatereq($sum(lk(K), $product(-1, lk($sum(-1, K)))), 0) | (~$greatereq(K, 1)) | (~$greatereq($sum(problen, $product(-1, K)), 0)))) | (~$greatereq(problen, 1)) | $lesseq($sum(lk(0), $product(-1, lk(1))), 0))),
% 25.93/17.01 inference(rewrite,[status(thm)],[])).
% 25.93/17.01 tff(106,plain,
% 25.93/17.01 (($lesseq($sum(lk(0), $product(-1, lk(1))), 0) | $false | (~$greatereq(problen, 1))) <=> ((~$greatereq(problen, 1)) | $lesseq($sum(lk(0), $product(-1, lk(1))), 0))),
% 25.93/17.01 inference(rewrite,[status(thm)],[])).
% 25.93/17.01 tff(107,plain,
% 25.93/17.01 ((~$greatereq($sum(problen, $product(-1, 1)), 0)) <=> (~$greatereq(problen, 1))),
% 25.93/17.01 inference(rewrite,[status(thm)],[])).
% 25.93/17.01 tff(108,plain,
% 25.93/17.01 ($greatereq(1, 1) <=> $true),
% 25.93/17.01 inference(rewrite,[status(thm)],[])).
% 25.93/17.01 tff(109,plain,
% 25.93/17.01 ((~$greatereq(1, 1)) <=> (~$true)),
% 25.93/17.01 inference(monotonicity,[status(thm)],[108])).
% 25.93/17.01 tff(110,plain,
% 25.93/17.01 ((~$greatereq(1, 1)) <=> $false),
% 25.93/17.01 inference(transitivity,[status(thm)],[109, 32])).
% 25.93/17.01 tff(111,plain,
% 25.93/17.01 ($greatereq($sum($product(-1, lk(0)), lk(1)), 0) <=> $lesseq($sum(lk(0), $product(-1, lk(1))), 0)),
% 25.93/17.01 inference(rewrite,[status(thm)],[])).
% 25.93/17.01 tff(112,plain,
% 25.93/17.01 ($sum(lk(1), $product(-1, lk(0))) = $sum($product(-1, lk(0)), lk(1))),
% 25.93/17.01 inference(rewrite,[status(thm)],[])).
% 25.93/17.01 tff(113,plain,
% 25.93/17.01 ($product(-1, lk($sum(-1, 1))) = $product(-1, lk(0))),
% 25.93/17.01 inference(rewrite,[status(thm)],[])).
% 25.93/17.01 tff(114,plain,
% 25.93/17.01 ($sum(lk(1), $product(-1, lk($sum(-1, 1)))) = $sum(lk(1), $product(-1, lk(0)))),
% 25.93/17.01 inference(monotonicity,[status(thm)],[113])).
% 25.93/17.01 tff(115,plain,
% 25.93/17.01 ($sum(lk(1), $product(-1, lk($sum(-1, 1)))) = $sum($product(-1, lk(0)), lk(1))),
% 25.93/17.01 inference(transitivity,[status(thm)],[114, 112])).
% 25.93/17.01 tff(116,plain,
% 25.93/17.01 ($greatereq($sum(lk(1), $product(-1, lk($sum(-1, 1)))), 0) <=> $greatereq($sum($product(-1, lk(0)), lk(1)), 0)),
% 25.93/17.01 inference(monotonicity,[status(thm)],[115])).
% 25.93/17.01 tff(117,plain,
% 25.93/17.01 ($greatereq($sum(lk(1), $product(-1, lk($sum(-1, 1)))), 0) <=> $lesseq($sum(lk(0), $product(-1, lk(1))), 0)),
% 25.93/17.01 inference(transitivity,[status(thm)],[116, 111])).
% 25.93/17.01 tff(118,plain,
% 25.93/17.01 (($greatereq($sum(lk(1), $product(-1, lk($sum(-1, 1)))), 0) | (~$greatereq(1, 1)) | (~$greatereq($sum(problen, $product(-1, 1)), 0))) <=> ($lesseq($sum(lk(0), $product(-1, lk(1))), 0) | $false | (~$greatereq(problen, 1)))),
% 25.93/17.01 inference(monotonicity,[status(thm)],[117, 110, 107])).
% 25.93/17.01 tff(119,plain,
% 25.93/17.01 (($greatereq($sum(lk(1), $product(-1, lk($sum(-1, 1)))), 0) | (~$greatereq(1, 1)) | (~$greatereq($sum(problen, $product(-1, 1)), 0))) <=> ((~$greatereq(problen, 1)) | $lesseq($sum(lk(0), $product(-1, lk(1))), 0))),
% 25.93/17.01 inference(transitivity,[status(thm)],[118, 106])).
% 25.93/17.01 tff(120,plain,
% 25.93/17.01 (((~![K: $int] : ($greatereq($sum(lk(K), $product(-1, lk($sum(-1, K)))), 0) | (~$greatereq(K, 1)) | (~$greatereq($sum(problen, $product(-1, K)), 0)))) | ($greatereq($sum(lk(1), $product(-1, lk($sum(-1, 1)))), 0) | (~$greatereq(1, 1)) | (~$greatereq($sum(problen, $product(-1, 1)), 0)))) <=> ((~![K: $int] : ($greatereq($sum(lk(K), $product(-1, lk($sum(-1, K)))), 0) | (~$greatereq(K, 1)) | (~$greatereq($sum(problen, $product(-1, K)), 0)))) | ((~$greatereq(problen, 1)) | $lesseq($sum(lk(0), $product(-1, lk(1))), 0)))),
% 25.93/17.01 inference(monotonicity,[status(thm)],[119])).
% 25.93/17.01 tff(121,plain,
% 25.93/17.01 (((~![K: $int] : ($greatereq($sum(lk(K), $product(-1, lk($sum(-1, K)))), 0) | (~$greatereq(K, 1)) | (~$greatereq($sum(problen, $product(-1, K)), 0)))) | ($greatereq($sum(lk(1), $product(-1, lk($sum(-1, 1)))), 0) | (~$greatereq(1, 1)) | (~$greatereq($sum(problen, $product(-1, 1)), 0)))) <=> ((~![K: $int] : ($greatereq($sum(lk(K), $product(-1, lk($sum(-1, K)))), 0) | (~$greatereq(K, 1)) | (~$greatereq($sum(problen, $product(-1, K)), 0)))) | (~$greatereq(problen, 1)) | $lesseq($sum(lk(0), $product(-1, lk(1))), 0))),
% 25.93/17.01 inference(transitivity,[status(thm)],[120, 105])).
% 25.93/17.01 tff(122,plain,
% 25.93/17.01 ((~![K: $int] : ($greatereq($sum(lk(K), $product(-1, lk($sum(-1, K)))), 0) | (~$greatereq(K, 1)) | (~$greatereq($sum(problen, $product(-1, K)), 0)))) | ($greatereq($sum(lk(1), $product(-1, lk($sum(-1, 1)))), 0) | (~$greatereq(1, 1)) | (~$greatereq($sum(problen, $product(-1, 1)), 0)))),
% 25.93/17.01 inference(quant_inst,[status(thm)],[])).
% 25.93/17.01 tff(123,plain,
% 25.93/17.01 ((~![K: $int] : ($greatereq($sum(lk(K), $product(-1, lk($sum(-1, K)))), 0) | (~$greatereq(K, 1)) | (~$greatereq($sum(problen, $product(-1, K)), 0)))) | (~$greatereq(problen, 1)) | $lesseq($sum(lk(0), $product(-1, lk(1))), 0)),
% 25.93/17.01 inference(modus_ponens,[status(thm)],[122, 121])).
% 25.93/17.01 tff(124,plain,
% 25.93/17.01 ((~$greatereq(problen, 1)) | $lesseq($sum(lk(0), $product(-1, lk(1))), 0)),
% 25.93/17.01 inference(unit_resolution,[status(thm)],[123, 104])).
% 25.93/17.01 tff(125,plain,
% 25.93/17.01 ($lesseq($sum(lk(0), $product(-1, lk(1))), 0)),
% 25.93/17.01 inference(unit_resolution,[status(thm)],[124, 85])).
% 25.93/17.01 tff(126,plain,
% 25.93/17.01 ((lk(0) = 1) <=> (lk(0) = 1)),
% 25.93/17.01 inference(rewrite,[status(thm)],[])).
% 25.93/17.01 tff(127,axiom,(lk(0) = 1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lk_0')).
% 25.93/17.01 tff(128,plain,
% 25.93/17.01 (lk(0) = 1),
% 25.93/17.01 inference(modus_ponens,[status(thm)],[127, 126])).
% 25.93/17.01 tff(129,plain,
% 25.93/17.01 (1 = lk(0)),
% 25.93/17.01 inference(symmetry,[status(thm)],[128])).
% 25.93/17.01 tff(130,plain,
% 25.93/17.01 ((~(1 = lk(0))) | $greatereq(lk(0), 1)),
% 25.93/17.01 inference(theory_lemma,[status(thm)],[])).
% 25.93/17.01 tff(131,plain,
% 25.93/17.01 ($greatereq(lk(0), 1)),
% 25.93/17.01 inference(unit_resolution,[status(thm)],[130, 129])).
% 25.93/17.01 tff(132,plain,
% 25.93/17.01 ($false),
% 25.93/17.01 inference(theory_lemma,[status(thm)],[131, 125, 60])).
% 25.93/17.01 tff(133,plain,(~$lesseq(lk(1), 0)), inference(lemma,lemma(discharge,[]))).
% 25.93/17.01 tff(134,assumption,($lesseq($product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2)), 0)), introduced(assumption)).
% 25.93/17.01 tff(135,plain,
% 25.93/17.01 ($false),
% 25.93/17.01 inference(theory_lemma,[status(thm)],[134, 133, 59, 45])).
% 25.93/17.01 tff(136,plain,(~$lesseq($product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2)), 0)), inference(lemma,lemma(discharge,[]))).
% 25.93/17.01 tff(137,plain,
% 25.93/17.01 ((0 = $to_real(ns($sum(-1, problen)))) <=> ($to_real(ns($sum(-1, problen))) = 0)),
% 25.93/17.01 inference(commutativity,[status(thm)],[])).
% 25.93/17.01 tff(138,plain,
% 25.93/17.01 (($to_real(ns($sum(-1, problen))) = 0) <=> (0 = $to_real(ns($sum(-1, problen))))),
% 25.93/17.01 inference(symmetry,[status(thm)],[137])).
% 25.93/17.01 tff(139,plain,
% 25.93/17.01 (^[D: $real, T: $int, C: $int] : refl(($sum($product(D, $to_real(ns(C))), $sum($product(-1, $to_real(T)), $sum($product(-1, $product($to_real(ns(C)), dc(D, T, C))), $product($to_real(T), dc(D, T, C))))) = 0) <=> ($sum($product(D, $to_real(ns(C))), $sum($product(-1, $to_real(T)), $sum($product(-1, $product($to_real(ns(C)), dc(D, T, C))), $product($to_real(T), dc(D, T, C))))) = 0))),
% 25.93/17.01 inference(bind,[status(th)],[])).
% 25.93/17.01 tff(140,plain,
% 25.93/17.01 (![D: $real, T: $int, C: $int] : ($sum($product(D, $to_real(ns(C))), $sum($product(-1, $to_real(T)), $sum($product(-1, $product($to_real(ns(C)), dc(D, T, C))), $product($to_real(T), dc(D, T, C))))) = 0) <=> ![D: $real, T: $int, C: $int] : ($sum($product(D, $to_real(ns(C))), $sum($product(-1, $to_real(T)), $sum($product(-1, $product($to_real(ns(C)), dc(D, T, C))), $product($to_real(T), dc(D, T, C))))) = 0)),
% 26.03/17.01 inference(quant_intro,[status(thm)],[139])).
% 26.03/17.01 tff(141,plain,
% 26.03/17.01 (^[D: $real, T: $int, C: $int] : rewrite(($sum($product($sum($to_real(T), $product(-1, $to_real(ns(C)))), dc(D, T, C)), $sum($product(-1, $to_real(T)), $product($to_real(ns(C)), D))) = 0) <=> ($sum($product(D, $to_real(ns(C))), $sum($product(-1, $to_real(T)), $sum($product(-1, $product($to_real(ns(C)), dc(D, T, C))), $product($to_real(T), dc(D, T, C))))) = 0))),
% 26.03/17.01 inference(bind,[status(th)],[])).
% 26.03/17.01 tff(142,plain,
% 26.03/17.01 (![D: $real, T: $int, C: $int] : ($sum($product($sum($to_real(T), $product(-1, $to_real(ns(C)))), dc(D, T, C)), $sum($product(-1, $to_real(T)), $product($to_real(ns(C)), D))) = 0) <=> ![D: $real, T: $int, C: $int] : ($sum($product(D, $to_real(ns(C))), $sum($product(-1, $to_real(T)), $sum($product(-1, $product($to_real(ns(C)), dc(D, T, C))), $product($to_real(T), dc(D, T, C))))) = 0)),
% 26.03/17.01 inference(quant_intro,[status(thm)],[141])).
% 26.03/17.01 tff(143,plain,
% 26.03/17.01 (^[D: $real, T: $int, C: $int] : rewrite(($product($sum($to_real(T), $product(-1, $to_real(ns(C)))), dc(D, T, C)) = $sum($to_real(T), $product(-1, $product($to_real(ns(C)), D)))) <=> ($sum($product($sum($to_real(T), $product(-1, $to_real(ns(C)))), dc(D, T, C)), $sum($product(-1, $to_real(T)), $product($to_real(ns(C)), D))) = 0))),
% 26.03/17.01 inference(bind,[status(th)],[])).
% 26.03/17.01 tff(144,plain,
% 26.03/17.01 (![D: $real, T: $int, C: $int] : ($product($sum($to_real(T), $product(-1, $to_real(ns(C)))), dc(D, T, C)) = $sum($to_real(T), $product(-1, $product($to_real(ns(C)), D)))) <=> ![D: $real, T: $int, C: $int] : ($sum($product($sum($to_real(T), $product(-1, $to_real(ns(C)))), dc(D, T, C)), $sum($product(-1, $to_real(T)), $product($to_real(ns(C)), D))) = 0)),
% 26.03/17.01 inference(quant_intro,[status(thm)],[143])).
% 26.03/17.01 tff(145,plain,
% 26.03/17.01 (![D: $real, T: $int, C: $int] : ($product($sum($to_real(T), $product(-1, $to_real(ns(C)))), dc(D, T, C)) = $sum($to_real(T), $product(-1, $product($to_real(ns(C)), D)))) <=> ![D: $real, T: $int, C: $int] : ($product($sum($to_real(T), $product(-1, $to_real(ns(C)))), dc(D, T, C)) = $sum($to_real(T), $product(-1, $product($to_real(ns(C)), D))))),
% 26.03/17.01 inference(rewrite,[status(thm)],[])).
% 26.03/17.01 tff(146,plain,
% 26.03/17.01 (^[D: $real, T: $int, C: $int] : rewrite(($product(dc(D, T, C), $to_real($difference(T, ns(C)))) = $difference($to_real(T), $product(D, $to_real(ns(C))))) <=> ($product($sum($to_real(T), $product(-1, $to_real(ns(C)))), dc(D, T, C)) = $sum($to_real(T), $product(-1, $product($to_real(ns(C)), D)))))),
% 26.03/17.01 inference(bind,[status(th)],[])).
% 26.03/17.01 tff(147,plain,
% 26.03/17.01 (![D: $real, T: $int, C: $int] : ($product(dc(D, T, C), $to_real($difference(T, ns(C)))) = $difference($to_real(T), $product(D, $to_real(ns(C))))) <=> ![D: $real, T: $int, C: $int] : ($product($sum($to_real(T), $product(-1, $to_real(ns(C)))), dc(D, T, C)) = $sum($to_real(T), $product(-1, $product($to_real(ns(C)), D))))),
% 26.03/17.01 inference(quant_intro,[status(thm)],[146])).
% 26.03/17.01 tff(148,axiom,(![D: $real, T: $int, C: $int] : ($product(dc(D, T, C), $to_real($difference(T, ns(C)))) = $difference($to_real(T), $product(D, $to_real(ns(C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dc')).
% 26.03/17.01 tff(149,plain,
% 26.03/17.01 (![D: $real, T: $int, C: $int] : ($product($sum($to_real(T), $product(-1, $to_real(ns(C)))), dc(D, T, C)) = $sum($to_real(T), $product(-1, $product($to_real(ns(C)), D))))),
% 26.03/17.01 inference(modus_ponens,[status(thm)],[148, 147])).
% 26.03/17.01 tff(150,plain,
% 26.03/17.01 (![D: $real, T: $int, C: $int] : ($product($sum($to_real(T), $product(-1, $to_real(ns(C)))), dc(D, T, C)) = $sum($to_real(T), $product(-1, $product($to_real(ns(C)), D))))),
% 26.03/17.01 inference(modus_ponens,[status(thm)],[149, 145])).
% 26.03/17.01 tff(151,plain,
% 26.03/17.01 (![D: $real, T: $int, C: $int] : ($sum($product($sum($to_real(T), $product(-1, $to_real(ns(C)))), dc(D, T, C)), $sum($product(-1, $to_real(T)), $product($to_real(ns(C)), D))) = 0)),
% 26.03/17.01 inference(modus_ponens,[status(thm)],[150, 144])).
% 26.03/17.01 tff(152,plain,
% 26.03/17.01 (![D: $real, T: $int, C: $int] : ($sum($product(D, $to_real(ns(C))), $sum($product(-1, $to_real(T)), $sum($product(-1, $product($to_real(ns(C)), dc(D, T, C))), $product($to_real(T), dc(D, T, C))))) = 0)),
% 26.03/17.01 inference(modus_ponens,[status(thm)],[151, 142])).
% 26.03/17.01 tff(153,plain,(
% 26.03/17.01 ![D: $real, T: $int, C: $int] : ($sum($product(D, $to_real(ns(C))), $sum($product(-1, $to_real(T)), $sum($product(-1, $product($to_real(ns(C)), dc(D, T, C))), $product($to_real(T), dc(D, T, C))))) = 0)),
% 26.03/17.01 inference(skolemize,[status(sab)],[152])).
% 26.03/17.01 tff(154,plain,
% 26.03/17.01 (![D: $real, T: $int, C: $int] : ($sum($product(D, $to_real(ns(C))), $sum($product(-1, $to_real(T)), $sum($product(-1, $product($to_real(ns(C)), dc(D, T, C))), $product($to_real(T), dc(D, T, C))))) = 0)),
% 26.03/17.01 inference(modus_ponens,[status(thm)],[153, 140])).
% 26.03/17.01 tff(155,plain,
% 26.03/17.01 (((~![D: $real, T: $int, C: $int] : ($sum($product(D, $to_real(ns(C))), $sum($product(-1, $to_real(T)), $sum($product(-1, $product($to_real(ns(C)), dc(D, T, C))), $product($to_real(T), dc(D, T, C))))) = 0)) | ($to_real(ns($sum(-1, problen))) = 0)) <=> ((~![D: $real, T: $int, C: $int] : ($sum($product(D, $to_real(ns(C))), $sum($product(-1, $to_real(T)), $sum($product(-1, $product($to_real(ns(C)), dc(D, T, C))), $product($to_real(T), dc(D, T, C))))) = 0)) | ($to_real(ns($sum(-1, problen))) = 0))),
% 26.03/17.01 inference(rewrite,[status(thm)],[])).
% 26.03/17.01 tff(156,plain,
% 26.03/17.01 (($product(15/2, $to_real(ns($sum(-1, problen)))) = 0) <=> ($to_real(ns($sum(-1, problen))) = 0)),
% 26.03/17.01 inference(rewrite,[status(thm)],[])).
% 26.03/17.01 tff(157,plain,
% 26.03/17.01 ($sum($product(17/2, $to_real(ns($sum(-1, problen)))), $sum($product(-1, $to_real(ns($sum(-1, problen)))), $sum($product(-1, $product($to_real(ns($sum(-1, problen))), dc(17/2, ns($sum(-1, problen)), $sum(-1, problen)))), $product($to_real(ns($sum(-1, problen))), dc(17/2, ns($sum(-1, problen)), $sum(-1, problen)))))) = $product(15/2, $to_real(ns($sum(-1, problen))))),
% 26.03/17.01 inference(rewrite,[status(thm)],[])).
% 26.03/17.01 tff(158,plain,
% 26.03/17.01 (($sum($product(17/2, $to_real(ns($sum(-1, problen)))), $sum($product(-1, $to_real(ns($sum(-1, problen)))), $sum($product(-1, $product($to_real(ns($sum(-1, problen))), dc(17/2, ns($sum(-1, problen)), $sum(-1, problen)))), $product($to_real(ns($sum(-1, problen))), dc(17/2, ns($sum(-1, problen)), $sum(-1, problen)))))) = 0) <=> ($product(15/2, $to_real(ns($sum(-1, problen)))) = 0)),
% 26.03/17.01 inference(monotonicity,[status(thm)],[157])).
% 26.03/17.01 tff(159,plain,
% 26.03/17.01 (($sum($product(17/2, $to_real(ns($sum(-1, problen)))), $sum($product(-1, $to_real(ns($sum(-1, problen)))), $sum($product(-1, $product($to_real(ns($sum(-1, problen))), dc(17/2, ns($sum(-1, problen)), $sum(-1, problen)))), $product($to_real(ns($sum(-1, problen))), dc(17/2, ns($sum(-1, problen)), $sum(-1, problen)))))) = 0) <=> ($to_real(ns($sum(-1, problen))) = 0)),
% 26.03/17.01 inference(transitivity,[status(thm)],[158, 156])).
% 26.03/17.01 tff(160,plain,
% 26.03/17.01 (((~![D: $real, T: $int, C: $int] : ($sum($product(D, $to_real(ns(C))), $sum($product(-1, $to_real(T)), $sum($product(-1, $product($to_real(ns(C)), dc(D, T, C))), $product($to_real(T), dc(D, T, C))))) = 0)) | ($sum($product(17/2, $to_real(ns($sum(-1, problen)))), $sum($product(-1, $to_real(ns($sum(-1, problen)))), $sum($product(-1, $product($to_real(ns($sum(-1, problen))), dc(17/2, ns($sum(-1, problen)), $sum(-1, problen)))), $product($to_real(ns($sum(-1, problen))), dc(17/2, ns($sum(-1, problen)), $sum(-1, problen)))))) = 0)) <=> ((~![D: $real, T: $int, C: $int] : ($sum($product(D, $to_real(ns(C))), $sum($product(-1, $to_real(T)), $sum($product(-1, $product($to_real(ns(C)), dc(D, T, C))), $product($to_real(T), dc(D, T, C))))) = 0)) | ($to_real(ns($sum(-1, problen))) = 0))),
% 26.03/17.01 inference(monotonicity,[status(thm)],[159])).
% 26.03/17.01 tff(161,plain,
% 26.03/17.01 (((~![D: $real, T: $int, C: $int] : ($sum($product(D, $to_real(ns(C))), $sum($product(-1, $to_real(T)), $sum($product(-1, $product($to_real(ns(C)), dc(D, T, C))), $product($to_real(T), dc(D, T, C))))) = 0)) | ($sum($product(17/2, $to_real(ns($sum(-1, problen)))), $sum($product(-1, $to_real(ns($sum(-1, problen)))), $sum($product(-1, $product($to_real(ns($sum(-1, problen))), dc(17/2, ns($sum(-1, problen)), $sum(-1, problen)))), $product($to_real(ns($sum(-1, problen))), dc(17/2, ns($sum(-1, problen)), $sum(-1, problen)))))) = 0)) <=> ((~![D: $real, T: $int, C: $int] : ($sum($product(D, $to_real(ns(C))), $sum($product(-1, $to_real(T)), $sum($product(-1, $product($to_real(ns(C)), dc(D, T, C))), $product($to_real(T), dc(D, T, C))))) = 0)) | ($to_real(ns($sum(-1, problen))) = 0))),
% 26.03/17.02 inference(transitivity,[status(thm)],[160, 155])).
% 26.03/17.02 tff(162,plain,
% 26.03/17.02 ((~![D: $real, T: $int, C: $int] : ($sum($product(D, $to_real(ns(C))), $sum($product(-1, $to_real(T)), $sum($product(-1, $product($to_real(ns(C)), dc(D, T, C))), $product($to_real(T), dc(D, T, C))))) = 0)) | ($sum($product(17/2, $to_real(ns($sum(-1, problen)))), $sum($product(-1, $to_real(ns($sum(-1, problen)))), $sum($product(-1, $product($to_real(ns($sum(-1, problen))), dc(17/2, ns($sum(-1, problen)), $sum(-1, problen)))), $product($to_real(ns($sum(-1, problen))), dc(17/2, ns($sum(-1, problen)), $sum(-1, problen)))))) = 0)),
% 26.03/17.02 inference(quant_inst,[status(thm)],[])).
% 26.03/17.02 tff(163,plain,
% 26.03/17.02 ((~![D: $real, T: $int, C: $int] : ($sum($product(D, $to_real(ns(C))), $sum($product(-1, $to_real(T)), $sum($product(-1, $product($to_real(ns(C)), dc(D, T, C))), $product($to_real(T), dc(D, T, C))))) = 0)) | ($to_real(ns($sum(-1, problen))) = 0)),
% 26.03/17.02 inference(modus_ponens,[status(thm)],[162, 161])).
% 26.03/17.02 tff(164,plain,
% 26.03/17.02 ($to_real(ns($sum(-1, problen))) = 0),
% 26.03/17.02 inference(unit_resolution,[status(thm)],[163, 154])).
% 26.03/17.02 tff(165,plain,
% 26.03/17.02 (0 = $to_real(ns($sum(-1, problen)))),
% 26.03/17.02 inference(modus_ponens,[status(thm)],[164, 138])).
% 26.03/17.02 tff(166,assumption,(~(0 = $to_real(ns($sum(-1, problen))))), introduced(assumption)).
% 26.03/17.02 tff(167,plain,
% 26.03/17.02 ($false),
% 26.03/17.02 inference(unit_resolution,[status(thm)],[166, 165])).
% 26.03/17.02 tff(168,plain,(0 = $to_real(ns($sum(-1, problen)))), inference(lemma,lemma(discharge,[]))).
% 26.03/17.02 tff(169,plain,
% 26.03/17.02 ((~(0 = $to_real(ns($sum(-1, problen))))) | $greatereq($to_real(ns($sum(-1, problen))), 0)),
% 26.03/17.02 inference(theory_lemma,[status(thm)],[])).
% 26.03/17.02 tff(170,plain,
% 26.03/17.02 ($greatereq($to_real(ns($sum(-1, problen))), 0)),
% 26.03/17.02 inference(unit_resolution,[status(thm)],[169, 168])).
% 26.03/17.02 tff(171,plain,
% 26.03/17.02 ((~(0 = $to_real(ns($sum(-1, problen))))) | $lesseq($to_real(ns($sum(-1, problen))), 0)),
% 26.03/17.02 inference(theory_lemma,[status(thm)],[])).
% 26.03/17.02 tff(172,plain,
% 26.03/17.02 ($lesseq($to_real(ns($sum(-1, problen))), 0)),
% 26.03/17.02 inference(unit_resolution,[status(thm)],[171, 168])).
% 26.03/17.02 tff(173,plain,
% 26.03/17.02 ($lesseq($product($to_real(ns($sum(-1, problen))), imp(17/2, ns($sum(-1, problen)), 2)), 0) | (~$lesseq($to_real(ns($sum(-1, problen))), 0)) | (~$greatereq($to_real(ns($sum(-1, problen))), 0))),
% 26.03/17.02 inference(theory_lemma,[status(thm)],[])).
% 26.03/17.02 tff(174,plain,
% 26.03/17.02 ($false),
% 26.03/17.02 inference(unit_resolution,[status(thm)],[173, 172, 170, 136])).
% 26.03/17.02 % SZS output end Proof
%------------------------------------------------------------------------------