TSTP Solution File: SWW613_2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW613_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 20:59:27 EDT 2022
% Result : Theorem 0.86s 0.84s
% Output : Proof 0.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW613_2 : TPTP v8.1.0. Released v6.1.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Sep 4 20:36:37 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.86/0.84 % SZS status Theorem
% 0.86/0.84 % SZS output start Proof
% 0.86/0.84 tff(tptp_fun_I_17_type, type, (
% 0.86/0.84 tptp_fun_I_17: $int)).
% 0.86/0.84 tff(tptp_fun_D1_13_type, type, (
% 0.86/0.84 tptp_fun_D1_13: $int)).
% 0.86/0.84 tff(divides_type, type, (
% 0.86/0.84 divides: ( $int * $int ) > $o)).
% 0.86/0.84 tff(tptp_fun_N_7_type, type, (
% 0.86/0.84 tptp_fun_N_7: $int)).
% 0.86/0.84 tff(prime_type, type, (
% 0.86/0.84 prime: $int > $o)).
% 0.86/0.84 tff(tptp_fun_Factor_11_type, type, (
% 0.86/0.84 tptp_fun_Factor_11: $int)).
% 0.86/0.84 tff(tptp_fun_Target_12_type, type, (
% 0.86/0.84 tptp_fun_Target_12: $int)).
% 0.86/0.84 tff(coprime_type, type, (
% 0.86/0.84 coprime: ( $int * $int ) > $o)).
% 0.86/0.84 tff(tptp_fun_Target1_16_type, type, (
% 0.86/0.84 tptp_fun_Target1_16: $int)).
% 0.86/0.84 tff(div_type, type, (
% 0.86/0.84 div: ( $int * $int ) > $int)).
% 0.86/0.84 tff(tb2t_type, type, (
% 0.86/0.84 tb2t: uni > list_int)).
% 0.86/0.84 tff(cons_type, type, (
% 0.86/0.84 cons: ( ty * uni * uni ) > uni)).
% 0.86/0.84 tff(t2tb_type, type, (
% 0.86/0.84 t2tb: list_int > uni)).
% 0.86/0.84 tff(tptp_fun_Factors1_10_type, type, (
% 0.86/0.84 tptp_fun_Factors1_10: list_int)).
% 0.86/0.84 tff(t2tb1_type, type, (
% 0.86/0.84 t2tb1: $int > uni)).
% 0.86/0.84 tff(int_type, type, (
% 0.86/0.84 int: ty)).
% 0.86/0.84 tff(tptp_fun_Factors2_15_type, type, (
% 0.86/0.84 tptp_fun_Factors2_15: list_int)).
% 0.86/0.84 tff(tptp_fun_Factor1_14_type, type, (
% 0.86/0.84 tptp_fun_Factor1_14: $int)).
% 0.86/0.84 tff(nil_type, type, (
% 0.86/0.84 nil: ty > uni)).
% 0.86/0.84 tff(tptp_fun_D_8_type, type, (
% 0.86/0.84 tptp_fun_D_8: $int)).
% 0.86/0.84 tff(tptp_fun_Factors_9_type, type, (
% 0.86/0.84 tptp_fun_Factors_9: list_int)).
% 0.86/0.84 tff(tptp_fun_N_6_type, type, (
% 0.86/0.84 tptp_fun_N_6: $int > $int)).
% 0.86/0.84 tff(1,plain,
% 0.86/0.84 (($greatereq(N!7, 2) & ($greatereq(D!8, 2) & $greatereq($sum(N!7, $product(-1, D!8)), 0) & divides(D!8, N!7) & ![I: $int] : ((~divides(I, N!7)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, D!8)), 0))))) & ![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$lesseq($sum(I, $product(-1, D!8)), 0)))) | (coprime(D!8, I) & divides(I, div(N!7, D!8)))) & ($sum(N!7, $product(-1, $product(D!8, div(N!7, D!8)))) = 0) & divides(div(N!7, D!8), N!7) & (Factors!9 = tb2t(cons(int, t2tb1(D!8), nil(int)))) & $greatereq(Target!12, 2) & $greatereq(Factor!11, 2) & $lesseq($sum(Factor!11, $product(-1, Target!12)), 0) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, Factor!11)), 0))))) & divides(Target!12, Target!12) & $greatereq(Target!12, 1) & $greatereq($sum(N!7, $product(-1, Target!12)), 0) & $greatereq($sum(N!7, $product(-1, Factor!11)), 0) & divides(Factor!11, N!7) & prime(Factor!11) & ![I: $int] : ((~(divides(I, Target!12) & $greatereq(I, 2))) | ($greatereq($sum(I, $product(-1, Factor!11)), 0) & divides(I, N!7))) & ![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$lesseq($sum(I, $product(-1, Factor!11)), 0)))) | divides(I, Target!12)) & prime(D1!13) & $lesseq($sum(Factor!11, $product(-1, D1!13)), 0) & $greatereq($sum(Target!12, $product(-1, D1!13)), 0) & divides(D1!13, Target!12) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, D1!13)), 0))))) & ($sum(D1!13, $product(-1, Factor1!14)) = 0) & (Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))) & (~(coprime(D1!13, I!17) | (~divides(I!17, Target!12)) | $greatereq($sum(Factor!11, $product(-1, I!17)), 0) | (~($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))) | (~(prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))))) & ($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12) & ($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0))) <=> ($greatereq(N!7, 2) & $greatereq(D!8, 2) & $greatereq($sum(N!7, $product(-1, D!8)), 0) & divides(D!8, N!7) & ![I: $int] : ((~divides(I, N!7)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, D!8)), 0))))) & ![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$lesseq($sum(I, $product(-1, D!8)), 0)))) | (coprime(D!8, I) & divides(I, div(N!7, D!8)))) & ($sum(N!7, $product(-1, $product(D!8, div(N!7, D!8)))) = 0) & divides(div(N!7, D!8), N!7) & (Factors!9 = tb2t(cons(int, t2tb1(D!8), nil(int)))) & $greatereq(Target!12, 2) & $greatereq(Factor!11, 2) & $lesseq($sum(Factor!11, $product(-1, Target!12)), 0) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, Factor!11)), 0))))) & divides(Target!12, Target!12) & $greatereq(Target!12, 1) & $greatereq($sum(N!7, $product(-1, Target!12)), 0) & $greatereq($sum(N!7, $product(-1, Factor!11)), 0) & divides(Factor!11, N!7) & prime(Factor!11) & ![I: $int] : ((~(divides(I, Target!12) & $greatereq(I, 2))) | ($greatereq($sum(I, $product(-1, Factor!11)), 0) & divides(I, N!7))) & ![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$lesseq($sum(I, $product(-1, Factor!11)), 0)))) | divides(I, Target!12)) & prime(D1!13) & $lesseq($sum(Factor!11, $product(-1, D1!13)), 0) & $greatereq($sum(Target!12, $product(-1, D1!13)), 0) & divides(D1!13, Target!12) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, D1!13)), 0))))) & ($sum(D1!13, $product(-1, Factor1!14)) = 0) & (Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))) & (~(coprime(D1!13, I!17) | (~divides(I!17, Target!12)) | $greatereq($sum(Factor!11, $product(-1, I!17)), 0) | (~($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))) | (~(prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))))) & ($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12) & ($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(2,plain,
% 0.86/0.84 ((($greatereq(D!8, 2) & $greatereq($sum(N!7, $product(-1, D!8)), 0) & divides(D!8, N!7) & ![I: $int] : ((~divides(I, N!7)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, D!8)), 0)))))) & (![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$lesseq($sum(I, $product(-1, D!8)), 0)))) | (coprime(D!8, I) & divides(I, div(N!7, D!8)))) & ($sum(N!7, $product(-1, $product(D!8, div(N!7, D!8)))) = 0) & divides(div(N!7, D!8), N!7) & (Factors!9 = tb2t(cons(int, t2tb1(D!8), nil(int)))) & $greatereq(Target!12, 2) & $greatereq(Factor!11, 2) & $lesseq($sum(Factor!11, $product(-1, Target!12)), 0) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, Factor!11)), 0))))) & divides(Target!12, Target!12) & $greatereq(Target!12, 1) & $greatereq($sum(N!7, $product(-1, Target!12)), 0) & $greatereq($sum(N!7, $product(-1, Factor!11)), 0) & divides(Factor!11, N!7) & prime(Factor!11) & ![I: $int] : ((~(divides(I, Target!12) & $greatereq(I, 2))) | ($greatereq($sum(I, $product(-1, Factor!11)), 0) & divides(I, N!7))) & ![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$lesseq($sum(I, $product(-1, Factor!11)), 0)))) | divides(I, Target!12)) & prime(D1!13) & $lesseq($sum(Factor!11, $product(-1, D1!13)), 0) & $greatereq($sum(Target!12, $product(-1, D1!13)), 0) & divides(D1!13, Target!12) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, D1!13)), 0))))) & ($sum(D1!13, $product(-1, Factor1!14)) = 0) & (Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))) & (~(coprime(D1!13, I!17) | (~divides(I!17, Target!12)) | $greatereq($sum(Factor!11, $product(-1, I!17)), 0) | (~($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))) | (~(prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))))) & ($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12) & ($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0))) <=> ($greatereq(D!8, 2) & $greatereq($sum(N!7, $product(-1, D!8)), 0) & divides(D!8, N!7) & ![I: $int] : ((~divides(I, N!7)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, D!8)), 0))))) & ![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$lesseq($sum(I, $product(-1, D!8)), 0)))) | (coprime(D!8, I) & divides(I, div(N!7, D!8)))) & ($sum(N!7, $product(-1, $product(D!8, div(N!7, D!8)))) = 0) & divides(div(N!7, D!8), N!7) & (Factors!9 = tb2t(cons(int, t2tb1(D!8), nil(int)))) & $greatereq(Target!12, 2) & $greatereq(Factor!11, 2) & $lesseq($sum(Factor!11, $product(-1, Target!12)), 0) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, Factor!11)), 0))))) & divides(Target!12, Target!12) & $greatereq(Target!12, 1) & $greatereq($sum(N!7, $product(-1, Target!12)), 0) & $greatereq($sum(N!7, $product(-1, Factor!11)), 0) & divides(Factor!11, N!7) & prime(Factor!11) & ![I: $int] : ((~(divides(I, Target!12) & $greatereq(I, 2))) | ($greatereq($sum(I, $product(-1, Factor!11)), 0) & divides(I, N!7))) & ![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$lesseq($sum(I, $product(-1, Factor!11)), 0)))) | divides(I, Target!12)) & prime(D1!13) & $lesseq($sum(Factor!11, $product(-1, D1!13)), 0) & $greatereq($sum(Target!12, $product(-1, D1!13)), 0) & divides(D1!13, Target!12) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, D1!13)), 0))))) & ($sum(D1!13, $product(-1, Factor1!14)) = 0) & (Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))) & (~(coprime(D1!13, I!17) | (~divides(I!17, Target!12)) | $greatereq($sum(Factor!11, $product(-1, I!17)), 0) | (~($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))) | (~(prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))))) & ($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12) & ($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(3,plain,
% 0.86/0.84 ((![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$lesseq($sum(I, $product(-1, D!8)), 0)))) | (coprime(D!8, I) & divides(I, div(N!7, D!8)))) & (($sum(N!7, $product(-1, $product(D!8, div(N!7, D!8)))) = 0) & divides(div(N!7, D!8), N!7)) & (Factors!9 = tb2t(cons(int, t2tb1(D!8), nil(int)))) & ($greatereq(Target!12, 2) & $greatereq(Factor!11, 2) & $lesseq($sum(Factor!11, $product(-1, Target!12)), 0) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, Factor!11)), 0))))) & divides(Target!12, Target!12) & $greatereq(Target!12, 1) & $greatereq($sum(N!7, $product(-1, Target!12)), 0) & $greatereq($sum(N!7, $product(-1, Factor!11)), 0) & divides(Factor!11, N!7) & prime(Factor!11) & ![I: $int] : ((~(divides(I, Target!12) & $greatereq(I, 2))) | ($greatereq($sum(I, $product(-1, Factor!11)), 0) & divides(I, N!7))) & ![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$lesseq($sum(I, $product(-1, Factor!11)), 0)))) | divides(I, Target!12)) & prime(D1!13) & $lesseq($sum(Factor!11, $product(-1, D1!13)), 0) & $greatereq($sum(Target!12, $product(-1, D1!13)), 0) & divides(D1!13, Target!12) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, D1!13)), 0))))) & ($sum(D1!13, $product(-1, Factor1!14)) = 0) & (Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))) & (~(coprime(D1!13, I!17) | (~divides(I!17, Target!12)) | $greatereq($sum(Factor!11, $product(-1, I!17)), 0) | (~($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))) | (~(prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))))) & ($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12) & ($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0))) <=> (![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$lesseq($sum(I, $product(-1, D!8)), 0)))) | (coprime(D!8, I) & divides(I, div(N!7, D!8)))) & ($sum(N!7, $product(-1, $product(D!8, div(N!7, D!8)))) = 0) & divides(div(N!7, D!8), N!7) & (Factors!9 = tb2t(cons(int, t2tb1(D!8), nil(int)))) & $greatereq(Target!12, 2) & $greatereq(Factor!11, 2) & $lesseq($sum(Factor!11, $product(-1, Target!12)), 0) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, Factor!11)), 0))))) & divides(Target!12, Target!12) & $greatereq(Target!12, 1) & $greatereq($sum(N!7, $product(-1, Target!12)), 0) & $greatereq($sum(N!7, $product(-1, Factor!11)), 0) & divides(Factor!11, N!7) & prime(Factor!11) & ![I: $int] : ((~(divides(I, Target!12) & $greatereq(I, 2))) | ($greatereq($sum(I, $product(-1, Factor!11)), 0) & divides(I, N!7))) & ![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$lesseq($sum(I, $product(-1, Factor!11)), 0)))) | divides(I, Target!12)) & prime(D1!13) & $lesseq($sum(Factor!11, $product(-1, D1!13)), 0) & $greatereq($sum(Target!12, $product(-1, D1!13)), 0) & divides(D1!13, Target!12) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, D1!13)), 0))))) & ($sum(D1!13, $product(-1, Factor1!14)) = 0) & (Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))) & (~(coprime(D1!13, I!17) | (~divides(I!17, Target!12)) | $greatereq($sum(Factor!11, $product(-1, I!17)), 0) | (~($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))) | (~(prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))))) & ($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12) & ($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(4,plain,
% 0.86/0.84 ((($greatereq(Target!12, 2) & $greatereq(Factor!11, 2) & $lesseq($sum(Factor!11, $product(-1, Target!12)), 0) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, Factor!11)), 0)))))) & (divides(Target!12, Target!12) & $greatereq(Target!12, 2) & $lesseq($sum(Factor!11, $product(-1, Target!12)), 0)) & $greatereq(Target!12, 2) & ($greatereq(Target!12, 1) & $greatereq($sum(N!7, $product(-1, Target!12)), 0) & $greatereq(Factor!11, 2) & $greatereq($sum(N!7, $product(-1, Factor!11)), 0) & divides(Factor!11, N!7) & prime(Factor!11) & ![I: $int] : ((~(divides(I, Target!12) & $greatereq(I, 2))) | ($greatereq($sum(I, $product(-1, Factor!11)), 0) & divides(I, N!7))) & ![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$lesseq($sum(I, $product(-1, Factor!11)), 0)))) | divides(I, Target!12))) & (prime(D1!13) & $lesseq($sum(Factor!11, $product(-1, D1!13)), 0) & $greatereq($sum(Target!12, $product(-1, D1!13)), 0) & divides(D1!13, Target!12) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, D1!13)), 0))))) & ($sum(D1!13, $product(-1, Factor1!14)) = 0) & (Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))) & (~(coprime(D1!13, I!17) | (~divides(I!17, Target!12)) | $greatereq($sum(Factor!11, $product(-1, I!17)), 0) | (~($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))) | (~(prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))))) & ($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12) & ($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0))) <=> ($greatereq(Target!12, 2) & $greatereq(Factor!11, 2) & $lesseq($sum(Factor!11, $product(-1, Target!12)), 0) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, Factor!11)), 0))))) & divides(Target!12, Target!12) & $greatereq(Target!12, 1) & $greatereq($sum(N!7, $product(-1, Target!12)), 0) & $greatereq($sum(N!7, $product(-1, Factor!11)), 0) & divides(Factor!11, N!7) & prime(Factor!11) & ![I: $int] : ((~(divides(I, Target!12) & $greatereq(I, 2))) | ($greatereq($sum(I, $product(-1, Factor!11)), 0) & divides(I, N!7))) & ![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$lesseq($sum(I, $product(-1, Factor!11)), 0)))) | divides(I, Target!12)) & prime(D1!13) & $lesseq($sum(Factor!11, $product(-1, D1!13)), 0) & $greatereq($sum(Target!12, $product(-1, D1!13)), 0) & divides(D1!13, Target!12) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, D1!13)), 0))))) & ($sum(D1!13, $product(-1, Factor1!14)) = 0) & (Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))) & (~(coprime(D1!13, I!17) | (~divides(I!17, Target!12)) | $greatereq($sum(Factor!11, $product(-1, I!17)), 0) | (~($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))) | (~(prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))))) & ($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12) & ($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(5,plain,
% 0.86/0.84 ((prime(D1!13) & ($lesseq($sum(Factor!11, $product(-1, D1!13)), 0) & $greatereq($sum(Target!12, $product(-1, D1!13)), 0) & divides(D1!13, Target!12) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, D1!13)), 0)))))) & (($sum(D1!13, $product(-1, Factor1!14)) = 0) & (Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))) & (~(coprime(D1!13, I!17) | (~divides(I!17, Target!12)) | $greatereq($sum(Factor!11, $product(-1, I!17)), 0) | (~($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))) | (~(prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))))) & ($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12) & ($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0))) <=> (prime(D1!13) & $lesseq($sum(Factor!11, $product(-1, D1!13)), 0) & $greatereq($sum(Target!12, $product(-1, D1!13)), 0) & divides(D1!13, Target!12) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, D1!13)), 0))))) & ($sum(D1!13, $product(-1, Factor1!14)) = 0) & (Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))) & (~(coprime(D1!13, I!17) | (~divides(I!17, Target!12)) | $greatereq($sum(Factor!11, $product(-1, I!17)), 0) | (~($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))) | (~(prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))))) & ($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12) & ($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(6,plain,
% 0.86/0.84 ((($sum(D1!13, $product(-1, Factor1!14)) = 0) & ((Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))) & (~(coprime(D1!13, I!17) | (~divides(I!17, Target!12)) | $greatereq($sum(Factor!11, $product(-1, I!17)), 0) | (~($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))) | (~(prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))))) & ($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12) & ($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0))) <=> (($sum(D1!13, $product(-1, Factor1!14)) = 0) & (Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))) & (~(coprime(D1!13, I!17) | (~divides(I!17, Target!12)) | $greatereq($sum(Factor!11, $product(-1, I!17)), 0) | (~($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))) | (~(prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))))) & ($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12) & ($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(7,plain,
% 0.86/0.84 (((Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))) & ((~(coprime(D1!13, I!17) | (~divides(I!17, Target!12)) | $greatereq($sum(Factor!11, $product(-1, I!17)), 0) | (~($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))) | (~(prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))))) & ($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12) & ($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0))) <=> ((Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))) & (~(coprime(D1!13, I!17) | (~divides(I!17, Target!12)) | $greatereq($sum(Factor!11, $product(-1, I!17)), 0) | (~($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))) | (~(prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))))) & ($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12) & ($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(8,plain,
% 0.86/0.84 (((~(coprime(D1!13, I!17) | (~divides(I!17, Target!12)) | $greatereq($sum(Factor!11, $product(-1, I!17)), 0) | (~($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))) | (~(prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))))) & (($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12)) & ($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0)) <=> ((~(coprime(D1!13, I!17) | (~divides(I!17, Target!12)) | $greatereq($sum(Factor!11, $product(-1, I!17)), 0) | (~($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))) | (~(prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))))) & ($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12) & ($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(9,plain,
% 0.86/0.84 ((~(~($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0))) <=> ($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0)),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(10,plain,
% 0.86/0.84 ((~($sum(Target1!16, $product(-1, div(Target!12, D1!13))) = 0)) <=> (~($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(11,plain,
% 0.86/0.84 ((~(~($sum(Target1!16, $product(-1, div(Target!12, D1!13))) = 0))) <=> (~(~($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0)))),
% 0.86/0.84 inference(monotonicity,[status(thm)],[10])).
% 0.86/0.84 tff(12,plain,
% 0.86/0.84 ((~(~($sum(Target1!16, $product(-1, div(Target!12, D1!13))) = 0))) <=> ($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0)),
% 0.86/0.84 inference(transitivity,[status(thm)],[11, 9])).
% 0.86/0.84 tff(13,plain,
% 0.86/0.84 ((~(~(($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12)))) <=> (($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(14,plain,
% 0.86/0.84 ((~(($sum(Target!12, $product(-1, $product(Target1!16, D1!13))) = 0) & divides(Target1!16, Target!12))) <=> (~(($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12)))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(15,plain,
% 0.86/0.84 ((~(~(($sum(Target!12, $product(-1, $product(Target1!16, D1!13))) = 0) & divides(Target1!16, Target!12)))) <=> (~(~(($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12))))),
% 0.86/0.84 inference(monotonicity,[status(thm)],[14])).
% 0.86/0.84 tff(16,plain,
% 0.86/0.84 ((~(~(($sum(Target!12, $product(-1, $product(Target1!16, D1!13))) = 0) & divides(Target1!16, Target!12)))) <=> (($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12))),
% 0.86/0.84 inference(transitivity,[status(thm)],[15, 13])).
% 0.86/0.84 tff(17,plain,
% 0.86/0.84 ((~(coprime(D1!13, I!17) | $lesseq($sum(I!17, $product(-1, Factor!11)), 0) | (~($greatereq(D1!13, 1) & (~$lesseq($sum(I!17, $product(-1, D1!13)), 0)))) | (~divides(I!17, Target!12)) | (~(prime(I!17) & divides(I!17, N!7) & (~$lesseq($sum(I!17, $product(-1, D1!13)), 0)))))) <=> (~(coprime(D1!13, I!17) | (~divides(I!17, Target!12)) | $greatereq($sum(Factor!11, $product(-1, I!17)), 0) | (~($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))) | (~(prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0))))))),
% 0.86/0.84 inference(rewrite,[status(thm)],[])).
% 0.86/0.84 tff(18,plain,
% 0.86/0.84 (((~(coprime(D1!13, I!17) | $lesseq($sum(I!17, $product(-1, Factor!11)), 0) | (~($greatereq(D1!13, 1) & (~$lesseq($sum(I!17, $product(-1, D1!13)), 0)))) | (~divides(I!17, Target!12)) | (~(prime(I!17) & divides(I!17, N!7) & (~$lesseq($sum(I!17, $product(-1, D1!13)), 0)))))) & (~(~(($sum(Target!12, $product(-1, $product(Target1!16, D1!13))) = 0) & divides(Target1!16, Target!12)))) & (~(~($sum(Target1!16, $product(-1, div(Target!12, D1!13))) = 0)))) <=> ((~(coprime(D1!13, I!17) | (~divides(I!17, Target!12)) | $greatereq($sum(Factor!11, $product(-1, I!17)), 0) | (~($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))) | (~(prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))))) & (($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12)) & ($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0))),
% 0.86/0.85 inference(monotonicity,[status(thm)],[17, 16, 12])).
% 0.86/0.85 tff(19,plain,
% 0.86/0.85 (((~(coprime(D1!13, I!17) | $lesseq($sum(I!17, $product(-1, Factor!11)), 0) | (~($greatereq(D1!13, 1) & (~$lesseq($sum(I!17, $product(-1, D1!13)), 0)))) | (~divides(I!17, Target!12)) | (~(prime(I!17) & divides(I!17, N!7) & (~$lesseq($sum(I!17, $product(-1, D1!13)), 0)))))) & (~(~(($sum(Target!12, $product(-1, $product(Target1!16, D1!13))) = 0) & divides(Target1!16, Target!12)))) & (~(~($sum(Target1!16, $product(-1, div(Target!12, D1!13))) = 0)))) <=> ((~(coprime(D1!13, I!17) | (~divides(I!17, Target!12)) | $greatereq($sum(Factor!11, $product(-1, I!17)), 0) | (~($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))) | (~(prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))))) & ($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12) & ($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0))),
% 0.86/0.85 inference(transitivity,[status(thm)],[18, 8])).
% 0.86/0.85 tff(20,plain,
% 0.86/0.85 ((~(~(Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))))) <=> (Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10))))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(21,plain,
% 0.86/0.85 (((~(~(Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))))) & ((~(coprime(D1!13, I!17) | $lesseq($sum(I!17, $product(-1, Factor!11)), 0) | (~($greatereq(D1!13, 1) & (~$lesseq($sum(I!17, $product(-1, D1!13)), 0)))) | (~divides(I!17, Target!12)) | (~(prime(I!17) & divides(I!17, N!7) & (~$lesseq($sum(I!17, $product(-1, D1!13)), 0)))))) & (~(~(($sum(Target!12, $product(-1, $product(Target1!16, D1!13))) = 0) & divides(Target1!16, Target!12)))) & (~(~($sum(Target1!16, $product(-1, div(Target!12, D1!13))) = 0))))) <=> ((Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))) & ((~(coprime(D1!13, I!17) | (~divides(I!17, Target!12)) | $greatereq($sum(Factor!11, $product(-1, I!17)), 0) | (~($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))) | (~(prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))))) & ($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12) & ($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0)))),
% 0.86/0.85 inference(monotonicity,[status(thm)],[20, 19])).
% 0.86/0.85 tff(22,plain,
% 0.86/0.85 (((~(~(Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))))) & ((~(coprime(D1!13, I!17) | $lesseq($sum(I!17, $product(-1, Factor!11)), 0) | (~($greatereq(D1!13, 1) & (~$lesseq($sum(I!17, $product(-1, D1!13)), 0)))) | (~divides(I!17, Target!12)) | (~(prime(I!17) & divides(I!17, N!7) & (~$lesseq($sum(I!17, $product(-1, D1!13)), 0)))))) & (~(~(($sum(Target!12, $product(-1, $product(Target1!16, D1!13))) = 0) & divides(Target1!16, Target!12)))) & (~(~($sum(Target1!16, $product(-1, div(Target!12, D1!13))) = 0))))) <=> ((Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))) & (~(coprime(D1!13, I!17) | (~divides(I!17, Target!12)) | $greatereq($sum(Factor!11, $product(-1, I!17)), 0) | (~($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))) | (~(prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))))) & ($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12) & ($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0))),
% 0.86/0.85 inference(transitivity,[status(thm)],[21, 7])).
% 0.86/0.85 tff(23,plain,
% 0.86/0.85 ((~(~($sum(D1!13, $product(-1, Factor1!14)) = 0))) <=> ($sum(D1!13, $product(-1, Factor1!14)) = 0)),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(24,plain,
% 0.86/0.85 (((~(~($sum(D1!13, $product(-1, Factor1!14)) = 0))) & ((~(~(Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))))) & ((~(coprime(D1!13, I!17) | $lesseq($sum(I!17, $product(-1, Factor!11)), 0) | (~($greatereq(D1!13, 1) & (~$lesseq($sum(I!17, $product(-1, D1!13)), 0)))) | (~divides(I!17, Target!12)) | (~(prime(I!17) & divides(I!17, N!7) & (~$lesseq($sum(I!17, $product(-1, D1!13)), 0)))))) & (~(~(($sum(Target!12, $product(-1, $product(Target1!16, D1!13))) = 0) & divides(Target1!16, Target!12)))) & (~(~($sum(Target1!16, $product(-1, div(Target!12, D1!13))) = 0)))))) <=> (($sum(D1!13, $product(-1, Factor1!14)) = 0) & ((Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))) & (~(coprime(D1!13, I!17) | (~divides(I!17, Target!12)) | $greatereq($sum(Factor!11, $product(-1, I!17)), 0) | (~($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))) | (~(prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))))) & ($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12) & ($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0)))),
% 0.86/0.85 inference(monotonicity,[status(thm)],[23, 22])).
% 0.86/0.85 tff(25,plain,
% 0.86/0.85 (((~(~($sum(D1!13, $product(-1, Factor1!14)) = 0))) & ((~(~(Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))))) & ((~(coprime(D1!13, I!17) | $lesseq($sum(I!17, $product(-1, Factor!11)), 0) | (~($greatereq(D1!13, 1) & (~$lesseq($sum(I!17, $product(-1, D1!13)), 0)))) | (~divides(I!17, Target!12)) | (~(prime(I!17) & divides(I!17, N!7) & (~$lesseq($sum(I!17, $product(-1, D1!13)), 0)))))) & (~(~(($sum(Target!12, $product(-1, $product(Target1!16, D1!13))) = 0) & divides(Target1!16, Target!12)))) & (~(~($sum(Target1!16, $product(-1, div(Target!12, D1!13))) = 0)))))) <=> (($sum(D1!13, $product(-1, Factor1!14)) = 0) & (Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))) & (~(coprime(D1!13, I!17) | (~divides(I!17, Target!12)) | $greatereq($sum(Factor!11, $product(-1, I!17)), 0) | (~($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))) | (~(prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))))) & ($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12) & ($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0))),
% 0.86/0.85 inference(transitivity,[status(thm)],[24, 6])).
% 0.86/0.85 tff(26,plain,
% 0.86/0.85 (($lesseq($sum(Factor!11, $product(-1, D1!13)), 0) & $lesseq($sum(D1!13, $product(-1, Target!12)), 0) & divides(D1!13, Target!12) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$lesseq($sum(D1!13, $product(-1, I)), 0)))))) <=> ($lesseq($sum(Factor!11, $product(-1, D1!13)), 0) & $greatereq($sum(Target!12, $product(-1, D1!13)), 0) & divides(D1!13, Target!12) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, D1!13)), 0))))))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(27,plain,
% 0.86/0.85 ((~(~prime(D1!13))) <=> prime(D1!13)),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(28,plain,
% 0.86/0.85 (((~(~prime(D1!13))) & ($lesseq($sum(Factor!11, $product(-1, D1!13)), 0) & $lesseq($sum(D1!13, $product(-1, Target!12)), 0) & divides(D1!13, Target!12) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$lesseq($sum(D1!13, $product(-1, I)), 0)))))) & ((~(~($sum(D1!13, $product(-1, Factor1!14)) = 0))) & ((~(~(Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))))) & ((~(coprime(D1!13, I!17) | $lesseq($sum(I!17, $product(-1, Factor!11)), 0) | (~($greatereq(D1!13, 1) & (~$lesseq($sum(I!17, $product(-1, D1!13)), 0)))) | (~divides(I!17, Target!12)) | (~(prime(I!17) & divides(I!17, N!7) & (~$lesseq($sum(I!17, $product(-1, D1!13)), 0)))))) & (~(~(($sum(Target!12, $product(-1, $product(Target1!16, D1!13))) = 0) & divides(Target1!16, Target!12)))) & (~(~($sum(Target1!16, $product(-1, div(Target!12, D1!13))) = 0))))))) <=> (prime(D1!13) & ($lesseq($sum(Factor!11, $product(-1, D1!13)), 0) & $greatereq($sum(Target!12, $product(-1, D1!13)), 0) & divides(D1!13, Target!12) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, D1!13)), 0)))))) & (($sum(D1!13, $product(-1, Factor1!14)) = 0) & (Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))) & (~(coprime(D1!13, I!17) | (~divides(I!17, Target!12)) | $greatereq($sum(Factor!11, $product(-1, I!17)), 0) | (~($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))) | (~(prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))))) & ($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12) & ($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0)))),
% 0.86/0.85 inference(monotonicity,[status(thm)],[27, 26, 25])).
% 0.86/0.85 tff(29,plain,
% 0.86/0.85 (((~(~prime(D1!13))) & ($lesseq($sum(Factor!11, $product(-1, D1!13)), 0) & $lesseq($sum(D1!13, $product(-1, Target!12)), 0) & divides(D1!13, Target!12) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$lesseq($sum(D1!13, $product(-1, I)), 0)))))) & ((~(~($sum(D1!13, $product(-1, Factor1!14)) = 0))) & ((~(~(Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))))) & ((~(coprime(D1!13, I!17) | $lesseq($sum(I!17, $product(-1, Factor!11)), 0) | (~($greatereq(D1!13, 1) & (~$lesseq($sum(I!17, $product(-1, D1!13)), 0)))) | (~divides(I!17, Target!12)) | (~(prime(I!17) & divides(I!17, N!7) & (~$lesseq($sum(I!17, $product(-1, D1!13)), 0)))))) & (~(~(($sum(Target!12, $product(-1, $product(Target1!16, D1!13))) = 0) & divides(Target1!16, Target!12)))) & (~(~($sum(Target1!16, $product(-1, div(Target!12, D1!13))) = 0))))))) <=> (prime(D1!13) & $lesseq($sum(Factor!11, $product(-1, D1!13)), 0) & $greatereq($sum(Target!12, $product(-1, D1!13)), 0) & divides(D1!13, Target!12) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, D1!13)), 0))))) & ($sum(D1!13, $product(-1, Factor1!14)) = 0) & (Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))) & (~(coprime(D1!13, I!17) | (~divides(I!17, Target!12)) | $greatereq($sum(Factor!11, $product(-1, I!17)), 0) | (~($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))) | (~(prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))))) & ($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12) & ($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0))),
% 0.86/0.85 inference(transitivity,[status(thm)],[28, 5])).
% 0.86/0.85 tff(30,plain,
% 0.86/0.85 (($greatereq(Target!12, 1) & $lesseq($sum(Target!12, $product(-1, N!7)), 0) & $greatereq(Factor!11, 2) & $lesseq($sum(Factor!11, $product(-1, N!7)), 0) & divides(Factor!11, N!7) & prime(Factor!11) & ![I: $int] : ((~(divides(I, Target!12) & $greatereq(I, 2))) | ($lesseq($sum(Factor!11, $product(-1, I)), 0) & divides(I, N!7))) & ![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$greatereq($sum(Factor!11, $product(-1, I)), 0)))) | divides(I, Target!12))) <=> ($greatereq(Target!12, 1) & $greatereq($sum(N!7, $product(-1, Target!12)), 0) & $greatereq(Factor!11, 2) & $greatereq($sum(N!7, $product(-1, Factor!11)), 0) & divides(Factor!11, N!7) & prime(Factor!11) & ![I: $int] : ((~(divides(I, Target!12) & $greatereq(I, 2))) | ($greatereq($sum(I, $product(-1, Factor!11)), 0) & divides(I, N!7))) & ![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$lesseq($sum(I, $product(-1, Factor!11)), 0)))) | divides(I, Target!12)))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(31,plain,
% 0.86/0.85 ((~(~$greatereq(Target!12, 2))) <=> $greatereq(Target!12, 2)),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(32,plain,
% 0.86/0.85 ((~(~(divides(Target!12, Target!12) & $greatereq(Target!12, 2) & $lesseq($sum(Factor!11, $product(-1, Target!12)), 0)))) <=> (divides(Target!12, Target!12) & $greatereq(Target!12, 2) & $lesseq($sum(Factor!11, $product(-1, Target!12)), 0))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(33,plain,
% 0.86/0.85 ((~(divides(Target!12, Target!12) & $greatereq(Target!12, 2) & $greatereq($sum(Target!12, $product(-1, Factor!11)), 0))) <=> (~(divides(Target!12, Target!12) & $greatereq(Target!12, 2) & $lesseq($sum(Factor!11, $product(-1, Target!12)), 0)))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(34,plain,
% 0.86/0.85 ((~(~(divides(Target!12, Target!12) & $greatereq(Target!12, 2) & $greatereq($sum(Target!12, $product(-1, Factor!11)), 0)))) <=> (~(~(divides(Target!12, Target!12) & $greatereq(Target!12, 2) & $lesseq($sum(Factor!11, $product(-1, Target!12)), 0))))),
% 0.86/0.85 inference(monotonicity,[status(thm)],[33])).
% 0.86/0.85 tff(35,plain,
% 0.86/0.85 ((~(~(divides(Target!12, Target!12) & $greatereq(Target!12, 2) & $greatereq($sum(Target!12, $product(-1, Factor!11)), 0)))) <=> (divides(Target!12, Target!12) & $greatereq(Target!12, 2) & $lesseq($sum(Factor!11, $product(-1, Target!12)), 0))),
% 0.86/0.85 inference(transitivity,[status(thm)],[34, 32])).
% 0.86/0.85 tff(36,plain,
% 0.86/0.85 (($greatereq(Target!12, 2) & $greatereq(Factor!11, 2) & $greatereq($sum(Target!12, $product(-1, Factor!11)), 0) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$lesseq($sum(Factor!11, $product(-1, I)), 0)))))) <=> ($greatereq(Target!12, 2) & $greatereq(Factor!11, 2) & $lesseq($sum(Factor!11, $product(-1, Target!12)), 0) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, Factor!11)), 0))))))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(37,plain,
% 0.86/0.85 ((($greatereq(Target!12, 2) & $greatereq(Factor!11, 2) & $greatereq($sum(Target!12, $product(-1, Factor!11)), 0) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$lesseq($sum(Factor!11, $product(-1, I)), 0)))))) & (~(~(divides(Target!12, Target!12) & $greatereq(Target!12, 2) & $greatereq($sum(Target!12, $product(-1, Factor!11)), 0)))) & (~(~$greatereq(Target!12, 2))) & ($greatereq(Target!12, 1) & $lesseq($sum(Target!12, $product(-1, N!7)), 0) & $greatereq(Factor!11, 2) & $lesseq($sum(Factor!11, $product(-1, N!7)), 0) & divides(Factor!11, N!7) & prime(Factor!11) & ![I: $int] : ((~(divides(I, Target!12) & $greatereq(I, 2))) | ($lesseq($sum(Factor!11, $product(-1, I)), 0) & divides(I, N!7))) & ![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$greatereq($sum(Factor!11, $product(-1, I)), 0)))) | divides(I, Target!12))) & ((~(~prime(D1!13))) & ($lesseq($sum(Factor!11, $product(-1, D1!13)), 0) & $lesseq($sum(D1!13, $product(-1, Target!12)), 0) & divides(D1!13, Target!12) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$lesseq($sum(D1!13, $product(-1, I)), 0)))))) & ((~(~($sum(D1!13, $product(-1, Factor1!14)) = 0))) & ((~(~(Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))))) & ((~(coprime(D1!13, I!17) | $lesseq($sum(I!17, $product(-1, Factor!11)), 0) | (~($greatereq(D1!13, 1) & (~$lesseq($sum(I!17, $product(-1, D1!13)), 0)))) | (~divides(I!17, Target!12)) | (~(prime(I!17) & divides(I!17, N!7) & (~$lesseq($sum(I!17, $product(-1, D1!13)), 0)))))) & (~(~(($sum(Target!12, $product(-1, $product(Target1!16, D1!13))) = 0) & divides(Target1!16, Target!12)))) & (~(~($sum(Target1!16, $product(-1, div(Target!12, D1!13))) = 0)))))))) <=> (($greatereq(Target!12, 2) & $greatereq(Factor!11, 2) & $lesseq($sum(Factor!11, $product(-1, Target!12)), 0) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, Factor!11)), 0)))))) & (divides(Target!12, Target!12) & $greatereq(Target!12, 2) & $lesseq($sum(Factor!11, $product(-1, Target!12)), 0)) & $greatereq(Target!12, 2) & ($greatereq(Target!12, 1) & $greatereq($sum(N!7, $product(-1, Target!12)), 0) & $greatereq(Factor!11, 2) & $greatereq($sum(N!7, $product(-1, Factor!11)), 0) & divides(Factor!11, N!7) & prime(Factor!11) & ![I: $int] : ((~(divides(I, Target!12) & $greatereq(I, 2))) | ($greatereq($sum(I, $product(-1, Factor!11)), 0) & divides(I, N!7))) & ![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$lesseq($sum(I, $product(-1, Factor!11)), 0)))) | divides(I, Target!12))) & (prime(D1!13) & $lesseq($sum(Factor!11, $product(-1, D1!13)), 0) & $greatereq($sum(Target!12, $product(-1, D1!13)), 0) & divides(D1!13, Target!12) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, D1!13)), 0))))) & ($sum(D1!13, $product(-1, Factor1!14)) = 0) & (Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))) & (~(coprime(D1!13, I!17) | (~divides(I!17, Target!12)) | $greatereq($sum(Factor!11, $product(-1, I!17)), 0) | (~($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))) | (~(prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))))) & ($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12) & ($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0)))),
% 0.86/0.85 inference(monotonicity,[status(thm)],[36, 35, 31, 30, 29])).
% 0.86/0.85 tff(38,plain,
% 0.86/0.85 ((($greatereq(Target!12, 2) & $greatereq(Factor!11, 2) & $greatereq($sum(Target!12, $product(-1, Factor!11)), 0) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$lesseq($sum(Factor!11, $product(-1, I)), 0)))))) & (~(~(divides(Target!12, Target!12) & $greatereq(Target!12, 2) & $greatereq($sum(Target!12, $product(-1, Factor!11)), 0)))) & (~(~$greatereq(Target!12, 2))) & ($greatereq(Target!12, 1) & $lesseq($sum(Target!12, $product(-1, N!7)), 0) & $greatereq(Factor!11, 2) & $lesseq($sum(Factor!11, $product(-1, N!7)), 0) & divides(Factor!11, N!7) & prime(Factor!11) & ![I: $int] : ((~(divides(I, Target!12) & $greatereq(I, 2))) | ($lesseq($sum(Factor!11, $product(-1, I)), 0) & divides(I, N!7))) & ![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$greatereq($sum(Factor!11, $product(-1, I)), 0)))) | divides(I, Target!12))) & ((~(~prime(D1!13))) & ($lesseq($sum(Factor!11, $product(-1, D1!13)), 0) & $lesseq($sum(D1!13, $product(-1, Target!12)), 0) & divides(D1!13, Target!12) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$lesseq($sum(D1!13, $product(-1, I)), 0)))))) & ((~(~($sum(D1!13, $product(-1, Factor1!14)) = 0))) & ((~(~(Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))))) & ((~(coprime(D1!13, I!17) | $lesseq($sum(I!17, $product(-1, Factor!11)), 0) | (~($greatereq(D1!13, 1) & (~$lesseq($sum(I!17, $product(-1, D1!13)), 0)))) | (~divides(I!17, Target!12)) | (~(prime(I!17) & divides(I!17, N!7) & (~$lesseq($sum(I!17, $product(-1, D1!13)), 0)))))) & (~(~(($sum(Target!12, $product(-1, $product(Target1!16, D1!13))) = 0) & divides(Target1!16, Target!12)))) & (~(~($sum(Target1!16, $product(-1, div(Target!12, D1!13))) = 0)))))))) <=> ($greatereq(Target!12, 2) & $greatereq(Factor!11, 2) & $lesseq($sum(Factor!11, $product(-1, Target!12)), 0) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, Factor!11)), 0))))) & divides(Target!12, Target!12) & $greatereq(Target!12, 1) & $greatereq($sum(N!7, $product(-1, Target!12)), 0) & $greatereq($sum(N!7, $product(-1, Factor!11)), 0) & divides(Factor!11, N!7) & prime(Factor!11) & ![I: $int] : ((~(divides(I, Target!12) & $greatereq(I, 2))) | ($greatereq($sum(I, $product(-1, Factor!11)), 0) & divides(I, N!7))) & ![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$lesseq($sum(I, $product(-1, Factor!11)), 0)))) | divides(I, Target!12)) & prime(D1!13) & $lesseq($sum(Factor!11, $product(-1, D1!13)), 0) & $greatereq($sum(Target!12, $product(-1, D1!13)), 0) & divides(D1!13, Target!12) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, D1!13)), 0))))) & ($sum(D1!13, $product(-1, Factor1!14)) = 0) & (Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))) & (~(coprime(D1!13, I!17) | (~divides(I!17, Target!12)) | $greatereq($sum(Factor!11, $product(-1, I!17)), 0) | (~($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))) | (~(prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))))) & ($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12) & ($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0))),
% 0.86/0.85 inference(transitivity,[status(thm)],[37, 4])).
% 0.86/0.85 tff(39,plain,
% 0.86/0.85 ((~(~(Factors!9 = tb2t(cons(int, t2tb1(D!8), nil(int)))))) <=> (Factors!9 = tb2t(cons(int, t2tb1(D!8), nil(int))))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(40,plain,
% 0.86/0.85 ((~(~(($sum(N!7, $product(-1, $product(D!8, div(N!7, D!8)))) = 0) & divides(div(N!7, D!8), N!7)))) <=> (($sum(N!7, $product(-1, $product(D!8, div(N!7, D!8)))) = 0) & divides(div(N!7, D!8), N!7))),
% 0.86/0.85 inference(rewrite,[status(thm)],[])).
% 0.86/0.85 tff(41,plain,
% 0.86/0.85 (^[I: $int] : rewrite(((~(prime(I) & divides(I, N!7) & (~$greatereq($sum(D!8, $product(-1, I)), 0)))) | (coprime(D!8, I) & divides(I, div(N!7, D!8)))) <=> ((~(prime(I) & divides(I, N!7) & (~$lesseq($sum(I, $product(-1, D!8)), 0)))) | (coprime(D!8, I) & divides(I, div(N!7, D!8)))))),
% 0.86/0.85 inference(bind,[status(th)],[])).
% 0.86/0.85 tff(42,plain,
% 0.86/0.85 (![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$greatereq($sum(D!8, $product(-1, I)), 0)))) | (coprime(D!8, I) & divides(I, div(N!7, D!8)))) <=> ![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$lesseq($sum(I, $product(-1, D!8)), 0)))) | (coprime(D!8, I) & divides(I, div(N!7, D!8))))),
% 0.86/0.85 inference(quant_intro,[status(thm)],[41])).
% 0.86/0.85 tff(43,plain,
% 0.86/0.85 ((![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$greatereq($sum(D!8, $product(-1, I)), 0)))) | (coprime(D!8, I) & divides(I, div(N!7, D!8)))) & (~(~(($sum(N!7, $product(-1, $product(D!8, div(N!7, D!8)))) = 0) & divides(div(N!7, D!8), N!7)))) & (~(~(Factors!9 = tb2t(cons(int, t2tb1(D!8), nil(int)))))) & (($greatereq(Target!12, 2) & $greatereq(Factor!11, 2) & $greatereq($sum(Target!12, $product(-1, Factor!11)), 0) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$lesseq($sum(Factor!11, $product(-1, I)), 0)))))) & (~(~(divides(Target!12, Target!12) & $greatereq(Target!12, 2) & $greatereq($sum(Target!12, $product(-1, Factor!11)), 0)))) & (~(~$greatereq(Target!12, 2))) & ($greatereq(Target!12, 1) & $lesseq($sum(Target!12, $product(-1, N!7)), 0) & $greatereq(Factor!11, 2) & $lesseq($sum(Factor!11, $product(-1, N!7)), 0) & divides(Factor!11, N!7) & prime(Factor!11) & ![I: $int] : ((~(divides(I, Target!12) & $greatereq(I, 2))) | ($lesseq($sum(Factor!11, $product(-1, I)), 0) & divides(I, N!7))) & ![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$greatereq($sum(Factor!11, $product(-1, I)), 0)))) | divides(I, Target!12))) & ((~(~prime(D1!13))) & ($lesseq($sum(Factor!11, $product(-1, D1!13)), 0) & $lesseq($sum(D1!13, $product(-1, Target!12)), 0) & divides(D1!13, Target!12) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$lesseq($sum(D1!13, $product(-1, I)), 0)))))) & ((~(~($sum(D1!13, $product(-1, Factor1!14)) = 0))) & ((~(~(Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))))) & ((~(coprime(D1!13, I!17) | $lesseq($sum(I!17, $product(-1, Factor!11)), 0) | (~($greatereq(D1!13, 1) & (~$lesseq($sum(I!17, $product(-1, D1!13)), 0)))) | (~divides(I!17, Target!12)) | (~(prime(I!17) & divides(I!17, N!7) & (~$lesseq($sum(I!17, $product(-1, D1!13)), 0)))))) & (~(~(($sum(Target!12, $product(-1, $product(Target1!16, D1!13))) = 0) & divides(Target1!16, Target!12)))) & (~(~($sum(Target1!16, $product(-1, div(Target!12, D1!13))) = 0))))))))) <=> (![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$lesseq($sum(I, $product(-1, D!8)), 0)))) | (coprime(D!8, I) & divides(I, div(N!7, D!8)))) & (($sum(N!7, $product(-1, $product(D!8, div(N!7, D!8)))) = 0) & divides(div(N!7, D!8), N!7)) & (Factors!9 = tb2t(cons(int, t2tb1(D!8), nil(int)))) & ($greatereq(Target!12, 2) & $greatereq(Factor!11, 2) & $lesseq($sum(Factor!11, $product(-1, Target!12)), 0) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, Factor!11)), 0))))) & divides(Target!12, Target!12) & $greatereq(Target!12, 1) & $greatereq($sum(N!7, $product(-1, Target!12)), 0) & $greatereq($sum(N!7, $product(-1, Factor!11)), 0) & divides(Factor!11, N!7) & prime(Factor!11) & ![I: $int] : ((~(divides(I, Target!12) & $greatereq(I, 2))) | ($greatereq($sum(I, $product(-1, Factor!11)), 0) & divides(I, N!7))) & ![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$lesseq($sum(I, $product(-1, Factor!11)), 0)))) | divides(I, Target!12)) & prime(D1!13) & $lesseq($sum(Factor!11, $product(-1, D1!13)), 0) & $greatereq($sum(Target!12, $product(-1, D1!13)), 0) & divides(D1!13, Target!12) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, D1!13)), 0))))) & ($sum(D1!13, $product(-1, Factor1!14)) = 0) & (Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))) & (~(coprime(D1!13, I!17) | (~divides(I!17, Target!12)) | $greatereq($sum(Factor!11, $product(-1, I!17)), 0) | (~($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))) | (~(prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))))) & ($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12) & ($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0)))),
% 0.86/0.86 inference(monotonicity,[status(thm)],[42, 40, 39, 38])).
% 0.86/0.86 tff(44,plain,
% 0.86/0.86 ((![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$greatereq($sum(D!8, $product(-1, I)), 0)))) | (coprime(D!8, I) & divides(I, div(N!7, D!8)))) & (~(~(($sum(N!7, $product(-1, $product(D!8, div(N!7, D!8)))) = 0) & divides(div(N!7, D!8), N!7)))) & (~(~(Factors!9 = tb2t(cons(int, t2tb1(D!8), nil(int)))))) & (($greatereq(Target!12, 2) & $greatereq(Factor!11, 2) & $greatereq($sum(Target!12, $product(-1, Factor!11)), 0) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$lesseq($sum(Factor!11, $product(-1, I)), 0)))))) & (~(~(divides(Target!12, Target!12) & $greatereq(Target!12, 2) & $greatereq($sum(Target!12, $product(-1, Factor!11)), 0)))) & (~(~$greatereq(Target!12, 2))) & ($greatereq(Target!12, 1) & $lesseq($sum(Target!12, $product(-1, N!7)), 0) & $greatereq(Factor!11, 2) & $lesseq($sum(Factor!11, $product(-1, N!7)), 0) & divides(Factor!11, N!7) & prime(Factor!11) & ![I: $int] : ((~(divides(I, Target!12) & $greatereq(I, 2))) | ($lesseq($sum(Factor!11, $product(-1, I)), 0) & divides(I, N!7))) & ![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$greatereq($sum(Factor!11, $product(-1, I)), 0)))) | divides(I, Target!12))) & ((~(~prime(D1!13))) & ($lesseq($sum(Factor!11, $product(-1, D1!13)), 0) & $lesseq($sum(D1!13, $product(-1, Target!12)), 0) & divides(D1!13, Target!12) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$lesseq($sum(D1!13, $product(-1, I)), 0)))))) & ((~(~($sum(D1!13, $product(-1, Factor1!14)) = 0))) & ((~(~(Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))))) & ((~(coprime(D1!13, I!17) | $lesseq($sum(I!17, $product(-1, Factor!11)), 0) | (~($greatereq(D1!13, 1) & (~$lesseq($sum(I!17, $product(-1, D1!13)), 0)))) | (~divides(I!17, Target!12)) | (~(prime(I!17) & divides(I!17, N!7) & (~$lesseq($sum(I!17, $product(-1, D1!13)), 0)))))) & (~(~(($sum(Target!12, $product(-1, $product(Target1!16, D1!13))) = 0) & divides(Target1!16, Target!12)))) & (~(~($sum(Target1!16, $product(-1, div(Target!12, D1!13))) = 0))))))))) <=> (![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$lesseq($sum(I, $product(-1, D!8)), 0)))) | (coprime(D!8, I) & divides(I, div(N!7, D!8)))) & ($sum(N!7, $product(-1, $product(D!8, div(N!7, D!8)))) = 0) & divides(div(N!7, D!8), N!7) & (Factors!9 = tb2t(cons(int, t2tb1(D!8), nil(int)))) & $greatereq(Target!12, 2) & $greatereq(Factor!11, 2) & $lesseq($sum(Factor!11, $product(-1, Target!12)), 0) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, Factor!11)), 0))))) & divides(Target!12, Target!12) & $greatereq(Target!12, 1) & $greatereq($sum(N!7, $product(-1, Target!12)), 0) & $greatereq($sum(N!7, $product(-1, Factor!11)), 0) & divides(Factor!11, N!7) & prime(Factor!11) & ![I: $int] : ((~(divides(I, Target!12) & $greatereq(I, 2))) | ($greatereq($sum(I, $product(-1, Factor!11)), 0) & divides(I, N!7))) & ![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$lesseq($sum(I, $product(-1, Factor!11)), 0)))) | divides(I, Target!12)) & prime(D1!13) & $lesseq($sum(Factor!11, $product(-1, D1!13)), 0) & $greatereq($sum(Target!12, $product(-1, D1!13)), 0) & divides(D1!13, Target!12) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, D1!13)), 0))))) & ($sum(D1!13, $product(-1, Factor1!14)) = 0) & (Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))) & (~(coprime(D1!13, I!17) | (~divides(I!17, Target!12)) | $greatereq($sum(Factor!11, $product(-1, I!17)), 0) | (~($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))) | (~(prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))))) & ($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12) & ($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0))),
% 0.86/0.86 inference(transitivity,[status(thm)],[43, 3])).
% 0.86/0.86 tff(45,plain,
% 0.86/0.86 (($greatereq(D!8, 2) & $greatereq($sum(N!7, $product(-1, D!8)), 0) & divides(D!8, N!7) & ![I: $int] : ((~divides(I, N!7)) | (~($greatereq(I, 2) & (~$lesseq($sum(D!8, $product(-1, I)), 0)))))) <=> ($greatereq(D!8, 2) & $greatereq($sum(N!7, $product(-1, D!8)), 0) & divides(D!8, N!7) & ![I: $int] : ((~divides(I, N!7)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, D!8)), 0))))))),
% 0.86/0.86 inference(rewrite,[status(thm)],[])).
% 0.86/0.86 tff(46,plain,
% 0.86/0.86 ((($greatereq(D!8, 2) & $greatereq($sum(N!7, $product(-1, D!8)), 0) & divides(D!8, N!7) & ![I: $int] : ((~divides(I, N!7)) | (~($greatereq(I, 2) & (~$lesseq($sum(D!8, $product(-1, I)), 0)))))) & (![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$greatereq($sum(D!8, $product(-1, I)), 0)))) | (coprime(D!8, I) & divides(I, div(N!7, D!8)))) & (~(~(($sum(N!7, $product(-1, $product(D!8, div(N!7, D!8)))) = 0) & divides(div(N!7, D!8), N!7)))) & (~(~(Factors!9 = tb2t(cons(int, t2tb1(D!8), nil(int)))))) & (($greatereq(Target!12, 2) & $greatereq(Factor!11, 2) & $greatereq($sum(Target!12, $product(-1, Factor!11)), 0) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$lesseq($sum(Factor!11, $product(-1, I)), 0)))))) & (~(~(divides(Target!12, Target!12) & $greatereq(Target!12, 2) & $greatereq($sum(Target!12, $product(-1, Factor!11)), 0)))) & (~(~$greatereq(Target!12, 2))) & ($greatereq(Target!12, 1) & $lesseq($sum(Target!12, $product(-1, N!7)), 0) & $greatereq(Factor!11, 2) & $lesseq($sum(Factor!11, $product(-1, N!7)), 0) & divides(Factor!11, N!7) & prime(Factor!11) & ![I: $int] : ((~(divides(I, Target!12) & $greatereq(I, 2))) | ($lesseq($sum(Factor!11, $product(-1, I)), 0) & divides(I, N!7))) & ![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$greatereq($sum(Factor!11, $product(-1, I)), 0)))) | divides(I, Target!12))) & ((~(~prime(D1!13))) & ($lesseq($sum(Factor!11, $product(-1, D1!13)), 0) & $lesseq($sum(D1!13, $product(-1, Target!12)), 0) & divides(D1!13, Target!12) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$lesseq($sum(D1!13, $product(-1, I)), 0)))))) & ((~(~($sum(D1!13, $product(-1, Factor1!14)) = 0))) & ((~(~(Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))))) & ((~(coprime(D1!13, I!17) | $lesseq($sum(I!17, $product(-1, Factor!11)), 0) | (~($greatereq(D1!13, 1) & (~$lesseq($sum(I!17, $product(-1, D1!13)), 0)))) | (~divides(I!17, Target!12)) | (~(prime(I!17) & divides(I!17, N!7) & (~$lesseq($sum(I!17, $product(-1, D1!13)), 0)))))) & (~(~(($sum(Target!12, $product(-1, $product(Target1!16, D1!13))) = 0) & divides(Target1!16, Target!12)))) & (~(~($sum(Target1!16, $product(-1, div(Target!12, D1!13))) = 0)))))))))) <=> (($greatereq(D!8, 2) & $greatereq($sum(N!7, $product(-1, D!8)), 0) & divides(D!8, N!7) & ![I: $int] : ((~divides(I, N!7)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, D!8)), 0)))))) & (![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$lesseq($sum(I, $product(-1, D!8)), 0)))) | (coprime(D!8, I) & divides(I, div(N!7, D!8)))) & ($sum(N!7, $product(-1, $product(D!8, div(N!7, D!8)))) = 0) & divides(div(N!7, D!8), N!7) & (Factors!9 = tb2t(cons(int, t2tb1(D!8), nil(int)))) & $greatereq(Target!12, 2) & $greatereq(Factor!11, 2) & $lesseq($sum(Factor!11, $product(-1, Target!12)), 0) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, Factor!11)), 0))))) & divides(Target!12, Target!12) & $greatereq(Target!12, 1) & $greatereq($sum(N!7, $product(-1, Target!12)), 0) & $greatereq($sum(N!7, $product(-1, Factor!11)), 0) & divides(Factor!11, N!7) & prime(Factor!11) & ![I: $int] : ((~(divides(I, Target!12) & $greatereq(I, 2))) | ($greatereq($sum(I, $product(-1, Factor!11)), 0) & divides(I, N!7))) & ![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$lesseq($sum(I, $product(-1, Factor!11)), 0)))) | divides(I, Target!12)) & prime(D1!13) & $lesseq($sum(Factor!11, $product(-1, D1!13)), 0) & $greatereq($sum(Target!12, $product(-1, D1!13)), 0) & divides(D1!13, Target!12) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, D1!13)), 0))))) & ($sum(D1!13, $product(-1, Factor1!14)) = 0) & (Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))) & (~(coprime(D1!13, I!17) | (~divides(I!17, Target!12)) | $greatereq($sum(Factor!11, $product(-1, I!17)), 0) | (~($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))) | (~(prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))))) & ($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12) & ($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0)))),
% 0.97/0.86 inference(monotonicity,[status(thm)],[45, 44])).
% 0.97/0.86 tff(47,plain,
% 0.97/0.86 ((($greatereq(D!8, 2) & $greatereq($sum(N!7, $product(-1, D!8)), 0) & divides(D!8, N!7) & ![I: $int] : ((~divides(I, N!7)) | (~($greatereq(I, 2) & (~$lesseq($sum(D!8, $product(-1, I)), 0)))))) & (![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$greatereq($sum(D!8, $product(-1, I)), 0)))) | (coprime(D!8, I) & divides(I, div(N!7, D!8)))) & (~(~(($sum(N!7, $product(-1, $product(D!8, div(N!7, D!8)))) = 0) & divides(div(N!7, D!8), N!7)))) & (~(~(Factors!9 = tb2t(cons(int, t2tb1(D!8), nil(int)))))) & (($greatereq(Target!12, 2) & $greatereq(Factor!11, 2) & $greatereq($sum(Target!12, $product(-1, Factor!11)), 0) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$lesseq($sum(Factor!11, $product(-1, I)), 0)))))) & (~(~(divides(Target!12, Target!12) & $greatereq(Target!12, 2) & $greatereq($sum(Target!12, $product(-1, Factor!11)), 0)))) & (~(~$greatereq(Target!12, 2))) & ($greatereq(Target!12, 1) & $lesseq($sum(Target!12, $product(-1, N!7)), 0) & $greatereq(Factor!11, 2) & $lesseq($sum(Factor!11, $product(-1, N!7)), 0) & divides(Factor!11, N!7) & prime(Factor!11) & ![I: $int] : ((~(divides(I, Target!12) & $greatereq(I, 2))) | ($lesseq($sum(Factor!11, $product(-1, I)), 0) & divides(I, N!7))) & ![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$greatereq($sum(Factor!11, $product(-1, I)), 0)))) | divides(I, Target!12))) & ((~(~prime(D1!13))) & ($lesseq($sum(Factor!11, $product(-1, D1!13)), 0) & $lesseq($sum(D1!13, $product(-1, Target!12)), 0) & divides(D1!13, Target!12) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$lesseq($sum(D1!13, $product(-1, I)), 0)))))) & ((~(~($sum(D1!13, $product(-1, Factor1!14)) = 0))) & ((~(~(Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))))) & ((~(coprime(D1!13, I!17) | $lesseq($sum(I!17, $product(-1, Factor!11)), 0) | (~($greatereq(D1!13, 1) & (~$lesseq($sum(I!17, $product(-1, D1!13)), 0)))) | (~divides(I!17, Target!12)) | (~(prime(I!17) & divides(I!17, N!7) & (~$lesseq($sum(I!17, $product(-1, D1!13)), 0)))))) & (~(~(($sum(Target!12, $product(-1, $product(Target1!16, D1!13))) = 0) & divides(Target1!16, Target!12)))) & (~(~($sum(Target1!16, $product(-1, div(Target!12, D1!13))) = 0)))))))))) <=> ($greatereq(D!8, 2) & $greatereq($sum(N!7, $product(-1, D!8)), 0) & divides(D!8, N!7) & ![I: $int] : ((~divides(I, N!7)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, D!8)), 0))))) & ![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$lesseq($sum(I, $product(-1, D!8)), 0)))) | (coprime(D!8, I) & divides(I, div(N!7, D!8)))) & ($sum(N!7, $product(-1, $product(D!8, div(N!7, D!8)))) = 0) & divides(div(N!7, D!8), N!7) & (Factors!9 = tb2t(cons(int, t2tb1(D!8), nil(int)))) & $greatereq(Target!12, 2) & $greatereq(Factor!11, 2) & $lesseq($sum(Factor!11, $product(-1, Target!12)), 0) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, Factor!11)), 0))))) & divides(Target!12, Target!12) & $greatereq(Target!12, 1) & $greatereq($sum(N!7, $product(-1, Target!12)), 0) & $greatereq($sum(N!7, $product(-1, Factor!11)), 0) & divides(Factor!11, N!7) & prime(Factor!11) & ![I: $int] : ((~(divides(I, Target!12) & $greatereq(I, 2))) | ($greatereq($sum(I, $product(-1, Factor!11)), 0) & divides(I, N!7))) & ![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$lesseq($sum(I, $product(-1, Factor!11)), 0)))) | divides(I, Target!12)) & prime(D1!13) & $lesseq($sum(Factor!11, $product(-1, D1!13)), 0) & $greatereq($sum(Target!12, $product(-1, D1!13)), 0) & divides(D1!13, Target!12) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, D1!13)), 0))))) & ($sum(D1!13, $product(-1, Factor1!14)) = 0) & (Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))) & (~(coprime(D1!13, I!17) | (~divides(I!17, Target!12)) | $greatereq($sum(Factor!11, $product(-1, I!17)), 0) | (~($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))) | (~(prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))))) & ($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12) & ($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0))),
% 0.97/0.86 inference(transitivity,[status(thm)],[46, 2])).
% 0.97/0.86 tff(48,plain,
% 0.97/0.86 ((~(~$greatereq(N!7, 2))) <=> $greatereq(N!7, 2)),
% 0.97/0.86 inference(rewrite,[status(thm)],[])).
% 0.97/0.86 tff(49,plain,
% 0.97/0.86 (((~(~$greatereq(N!7, 2))) & (($greatereq(D!8, 2) & $greatereq($sum(N!7, $product(-1, D!8)), 0) & divides(D!8, N!7) & ![I: $int] : ((~divides(I, N!7)) | (~($greatereq(I, 2) & (~$lesseq($sum(D!8, $product(-1, I)), 0)))))) & (![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$greatereq($sum(D!8, $product(-1, I)), 0)))) | (coprime(D!8, I) & divides(I, div(N!7, D!8)))) & (~(~(($sum(N!7, $product(-1, $product(D!8, div(N!7, D!8)))) = 0) & divides(div(N!7, D!8), N!7)))) & (~(~(Factors!9 = tb2t(cons(int, t2tb1(D!8), nil(int)))))) & (($greatereq(Target!12, 2) & $greatereq(Factor!11, 2) & $greatereq($sum(Target!12, $product(-1, Factor!11)), 0) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$lesseq($sum(Factor!11, $product(-1, I)), 0)))))) & (~(~(divides(Target!12, Target!12) & $greatereq(Target!12, 2) & $greatereq($sum(Target!12, $product(-1, Factor!11)), 0)))) & (~(~$greatereq(Target!12, 2))) & ($greatereq(Target!12, 1) & $lesseq($sum(Target!12, $product(-1, N!7)), 0) & $greatereq(Factor!11, 2) & $lesseq($sum(Factor!11, $product(-1, N!7)), 0) & divides(Factor!11, N!7) & prime(Factor!11) & ![I: $int] : ((~(divides(I, Target!12) & $greatereq(I, 2))) | ($lesseq($sum(Factor!11, $product(-1, I)), 0) & divides(I, N!7))) & ![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$greatereq($sum(Factor!11, $product(-1, I)), 0)))) | divides(I, Target!12))) & ((~(~prime(D1!13))) & ($lesseq($sum(Factor!11, $product(-1, D1!13)), 0) & $lesseq($sum(D1!13, $product(-1, Target!12)), 0) & divides(D1!13, Target!12) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$lesseq($sum(D1!13, $product(-1, I)), 0)))))) & ((~(~($sum(D1!13, $product(-1, Factor1!14)) = 0))) & ((~(~(Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))))) & ((~(coprime(D1!13, I!17) | $lesseq($sum(I!17, $product(-1, Factor!11)), 0) | (~($greatereq(D1!13, 1) & (~$lesseq($sum(I!17, $product(-1, D1!13)), 0)))) | (~divides(I!17, Target!12)) | (~(prime(I!17) & divides(I!17, N!7) & (~$lesseq($sum(I!17, $product(-1, D1!13)), 0)))))) & (~(~(($sum(Target!12, $product(-1, $product(Target1!16, D1!13))) = 0) & divides(Target1!16, Target!12)))) & (~(~($sum(Target1!16, $product(-1, div(Target!12, D1!13))) = 0))))))))))) <=> ($greatereq(N!7, 2) & ($greatereq(D!8, 2) & $greatereq($sum(N!7, $product(-1, D!8)), 0) & divides(D!8, N!7) & ![I: $int] : ((~divides(I, N!7)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, D!8)), 0))))) & ![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$lesseq($sum(I, $product(-1, D!8)), 0)))) | (coprime(D!8, I) & divides(I, div(N!7, D!8)))) & ($sum(N!7, $product(-1, $product(D!8, div(N!7, D!8)))) = 0) & divides(div(N!7, D!8), N!7) & (Factors!9 = tb2t(cons(int, t2tb1(D!8), nil(int)))) & $greatereq(Target!12, 2) & $greatereq(Factor!11, 2) & $lesseq($sum(Factor!11, $product(-1, Target!12)), 0) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, Factor!11)), 0))))) & divides(Target!12, Target!12) & $greatereq(Target!12, 1) & $greatereq($sum(N!7, $product(-1, Target!12)), 0) & $greatereq($sum(N!7, $product(-1, Factor!11)), 0) & divides(Factor!11, N!7) & prime(Factor!11) & ![I: $int] : ((~(divides(I, Target!12) & $greatereq(I, 2))) | ($greatereq($sum(I, $product(-1, Factor!11)), 0) & divides(I, N!7))) & ![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$lesseq($sum(I, $product(-1, Factor!11)), 0)))) | divides(I, Target!12)) & prime(D1!13) & $lesseq($sum(Factor!11, $product(-1, D1!13)), 0) & $greatereq($sum(Target!12, $product(-1, D1!13)), 0) & divides(D1!13, Target!12) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, D1!13)), 0))))) & ($sum(D1!13, $product(-1, Factor1!14)) = 0) & (Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))) & (~(coprime(D1!13, I!17) | (~divides(I!17, Target!12)) | $greatereq($sum(Factor!11, $product(-1, I!17)), 0) | (~($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))) | (~(prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))))) & ($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12) & ($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0)))),
% 0.97/0.86 inference(monotonicity,[status(thm)],[48, 47])).
% 0.97/0.86 tff(50,plain,
% 0.97/0.86 (((~(~$greatereq(N!7, 2))) & (($greatereq(D!8, 2) & $greatereq($sum(N!7, $product(-1, D!8)), 0) & divides(D!8, N!7) & ![I: $int] : ((~divides(I, N!7)) | (~($greatereq(I, 2) & (~$lesseq($sum(D!8, $product(-1, I)), 0)))))) & (![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$greatereq($sum(D!8, $product(-1, I)), 0)))) | (coprime(D!8, I) & divides(I, div(N!7, D!8)))) & (~(~(($sum(N!7, $product(-1, $product(D!8, div(N!7, D!8)))) = 0) & divides(div(N!7, D!8), N!7)))) & (~(~(Factors!9 = tb2t(cons(int, t2tb1(D!8), nil(int)))))) & (($greatereq(Target!12, 2) & $greatereq(Factor!11, 2) & $greatereq($sum(Target!12, $product(-1, Factor!11)), 0) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$lesseq($sum(Factor!11, $product(-1, I)), 0)))))) & (~(~(divides(Target!12, Target!12) & $greatereq(Target!12, 2) & $greatereq($sum(Target!12, $product(-1, Factor!11)), 0)))) & (~(~$greatereq(Target!12, 2))) & ($greatereq(Target!12, 1) & $lesseq($sum(Target!12, $product(-1, N!7)), 0) & $greatereq(Factor!11, 2) & $lesseq($sum(Factor!11, $product(-1, N!7)), 0) & divides(Factor!11, N!7) & prime(Factor!11) & ![I: $int] : ((~(divides(I, Target!12) & $greatereq(I, 2))) | ($lesseq($sum(Factor!11, $product(-1, I)), 0) & divides(I, N!7))) & ![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$greatereq($sum(Factor!11, $product(-1, I)), 0)))) | divides(I, Target!12))) & ((~(~prime(D1!13))) & ($lesseq($sum(Factor!11, $product(-1, D1!13)), 0) & $lesseq($sum(D1!13, $product(-1, Target!12)), 0) & divides(D1!13, Target!12) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$lesseq($sum(D1!13, $product(-1, I)), 0)))))) & ((~(~($sum(D1!13, $product(-1, Factor1!14)) = 0))) & ((~(~(Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))))) & ((~(coprime(D1!13, I!17) | $lesseq($sum(I!17, $product(-1, Factor!11)), 0) | (~($greatereq(D1!13, 1) & (~$lesseq($sum(I!17, $product(-1, D1!13)), 0)))) | (~divides(I!17, Target!12)) | (~(prime(I!17) & divides(I!17, N!7) & (~$lesseq($sum(I!17, $product(-1, D1!13)), 0)))))) & (~(~(($sum(Target!12, $product(-1, $product(Target1!16, D1!13))) = 0) & divides(Target1!16, Target!12)))) & (~(~($sum(Target1!16, $product(-1, div(Target!12, D1!13))) = 0))))))))))) <=> ($greatereq(N!7, 2) & $greatereq(D!8, 2) & $greatereq($sum(N!7, $product(-1, D!8)), 0) & divides(D!8, N!7) & ![I: $int] : ((~divides(I, N!7)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, D!8)), 0))))) & ![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$lesseq($sum(I, $product(-1, D!8)), 0)))) | (coprime(D!8, I) & divides(I, div(N!7, D!8)))) & ($sum(N!7, $product(-1, $product(D!8, div(N!7, D!8)))) = 0) & divides(div(N!7, D!8), N!7) & (Factors!9 = tb2t(cons(int, t2tb1(D!8), nil(int)))) & $greatereq(Target!12, 2) & $greatereq(Factor!11, 2) & $lesseq($sum(Factor!11, $product(-1, Target!12)), 0) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, Factor!11)), 0))))) & divides(Target!12, Target!12) & $greatereq(Target!12, 1) & $greatereq($sum(N!7, $product(-1, Target!12)), 0) & $greatereq($sum(N!7, $product(-1, Factor!11)), 0) & divides(Factor!11, N!7) & prime(Factor!11) & ![I: $int] : ((~(divides(I, Target!12) & $greatereq(I, 2))) | ($greatereq($sum(I, $product(-1, Factor!11)), 0) & divides(I, N!7))) & ![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$lesseq($sum(I, $product(-1, Factor!11)), 0)))) | divides(I, Target!12)) & prime(D1!13) & $lesseq($sum(Factor!11, $product(-1, D1!13)), 0) & $greatereq($sum(Target!12, $product(-1, D1!13)), 0) & divides(D1!13, Target!12) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, D1!13)), 0))))) & ($sum(D1!13, $product(-1, Factor1!14)) = 0) & (Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))) & (~(coprime(D1!13, I!17) | (~divides(I!17, Target!12)) | $greatereq($sum(Factor!11, $product(-1, I!17)), 0) | (~($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))) | (~(prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))))) & ($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12) & ($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0))),
% 0.97/0.86 inference(transitivity,[status(thm)],[49, 1])).
% 0.97/0.86 tff(51,plain,
% 0.97/0.86 ((~![N: $int] : ((~$greatereq(N, 2)) | ![D: $int] : ((~($greatereq(D, 2) & $greatereq($sum(N, $product(-1, D)), 0) & divides(D, N) & ![I: $int] : ((~divides(I, N)) | (~($greatereq(I, 2) & (~$lesseq($sum(D, $product(-1, I)), 0))))))) | ![Factors: list_int] : ((~![I: $int] : ((~(prime(I) & divides(I, N) & (~$greatereq($sum(D, $product(-1, I)), 0)))) | (coprime(D, I) & divides(I, div(N, D))))) | (~(($sum(N, $product(-1, $product(D, div(N, D)))) = 0) & divides(div(N, D), N))) | (~(Factors = tb2t(cons(int, t2tb1(D), nil(int))))) | ![Target: $int, Factor: $int, Factors1: list_int] : ((~($greatereq(Target, 2) & $greatereq(Factor, 2) & $greatereq($sum(Target, $product(-1, Factor)), 0) & ![I: $int] : ((~divides(I, Target)) | (~($greatereq(I, 2) & (~$lesseq($sum(Factor, $product(-1, I)), 0))))))) | (~(divides(Target, Target) & $greatereq(Target, 2) & $greatereq($sum(Target, $product(-1, Factor)), 0))) | (~$greatereq(Target, 2)) | (~($greatereq(Target, 1) & $lesseq($sum(Target, $product(-1, N)), 0) & $greatereq(Factor, 2) & $lesseq($sum(Factor, $product(-1, N)), 0) & divides(Factor, N) & prime(Factor) & ![I: $int] : ((~(divides(I, Target) & $greatereq(I, 2))) | ($lesseq($sum(Factor, $product(-1, I)), 0) & divides(I, N))) & ![I: $int] : ((~(prime(I) & divides(I, N) & (~$greatereq($sum(Factor, $product(-1, I)), 0)))) | divides(I, Target)))) | ![D1: $int] : ((~prime(D1)) | (~($lesseq($sum(Factor, $product(-1, D1)), 0) & $lesseq($sum(D1, $product(-1, Target)), 0) & divides(D1, Target) & ![I: $int] : ((~divides(I, Target)) | (~($greatereq(I, 2) & (~$lesseq($sum(D1, $product(-1, I)), 0))))))) | ![Factor1: $int] : ((~($sum(D1, $product(-1, Factor1)) = 0)) | ![Factors2: list_int] : ((~(Factors2 = tb2t(cons(int, t2tb1(D1), t2tb(Factors1))))) | ![Target1: $int] : (![I: $int] : (coprime(D1, I) | $lesseq($sum(I, $product(-1, Factor)), 0) | (~($greatereq(D1, 1) & (~$lesseq($sum(I, $product(-1, D1)), 0)))) | (~divides(I, Target)) | (~(prime(I) & divides(I, N) & (~$lesseq($sum(I, $product(-1, D1)), 0))))) | (~(($sum(Target, $product(-1, $product(Target1, D1))) = 0) & divides(Target1, Target))) | (~($sum(Target1, $product(-1, div(Target, D1))) = 0))))))))))) <=> (~![N: $int] : ((~$greatereq(N, 2)) | ![D: $int] : ((~($greatereq(D, 2) & $greatereq($sum(N, $product(-1, D)), 0) & divides(D, N) & ![I: $int] : ((~divides(I, N)) | (~($greatereq(I, 2) & (~$lesseq($sum(D, $product(-1, I)), 0))))))) | ![Factors: list_int] : ((~![I: $int] : ((~(prime(I) & divides(I, N) & (~$greatereq($sum(D, $product(-1, I)), 0)))) | (coprime(D, I) & divides(I, div(N, D))))) | (~(($sum(N, $product(-1, $product(D, div(N, D)))) = 0) & divides(div(N, D), N))) | (~(Factors = tb2t(cons(int, t2tb1(D), nil(int))))) | ![Target: $int, Factor: $int, Factors1: list_int] : ((~($greatereq(Target, 2) & $greatereq(Factor, 2) & $greatereq($sum(Target, $product(-1, Factor)), 0) & ![I: $int] : ((~divides(I, Target)) | (~($greatereq(I, 2) & (~$lesseq($sum(Factor, $product(-1, I)), 0))))))) | (~(divides(Target, Target) & $greatereq(Target, 2) & $greatereq($sum(Target, $product(-1, Factor)), 0))) | (~$greatereq(Target, 2)) | (~($greatereq(Target, 1) & $lesseq($sum(Target, $product(-1, N)), 0) & $greatereq(Factor, 2) & $lesseq($sum(Factor, $product(-1, N)), 0) & divides(Factor, N) & prime(Factor) & ![I: $int] : ((~(divides(I, Target) & $greatereq(I, 2))) | ($lesseq($sum(Factor, $product(-1, I)), 0) & divides(I, N))) & ![I: $int] : ((~(prime(I) & divides(I, N) & (~$greatereq($sum(Factor, $product(-1, I)), 0)))) | divides(I, Target)))) | ![D1: $int] : ((~prime(D1)) | (~($lesseq($sum(Factor, $product(-1, D1)), 0) & $lesseq($sum(D1, $product(-1, Target)), 0) & divides(D1, Target) & ![I: $int] : ((~divides(I, Target)) | (~($greatereq(I, 2) & (~$lesseq($sum(D1, $product(-1, I)), 0))))))) | ![Factor1: $int] : ((~($sum(D1, $product(-1, Factor1)) = 0)) | ![Factors2: list_int] : ((~(Factors2 = tb2t(cons(int, t2tb1(D1), t2tb(Factors1))))) | ![Target1: $int] : (![I: $int] : (coprime(D1, I) | $lesseq($sum(I, $product(-1, Factor)), 0) | (~($greatereq(D1, 1) & (~$lesseq($sum(I, $product(-1, D1)), 0)))) | (~divides(I, Target)) | (~(prime(I) & divides(I, N) & (~$lesseq($sum(I, $product(-1, D1)), 0))))) | (~(($sum(Target, $product(-1, $product(Target1, D1))) = 0) & divides(Target1, Target))) | (~($sum(Target1, $product(-1, div(Target, D1))) = 0)))))))))))),
% 0.97/0.86 inference(rewrite,[status(thm)],[])).
% 0.97/0.86 tff(52,plain,
% 0.97/0.86 ((~![N: $int] : ((~$greatereq(N, 2)) | ![D: $int] : ((~($greatereq(D, 2) & $lesseq($sum(D, $product(-1, N)), 0) & divides(D, N) & ![I: $int] : ((~divides(I, N)) | (~($greatereq(I, 2) & (~$lesseq($sum(D, $product(-1, I)), 0))))))) | ![Factors: list_int] : ((~(Factors = tb2t(cons(int, t2tb1(D), nil(int))))) | (~![I: $int] : ((~(prime(I) & divides(I, N) & (~$lesseq($sum(I, $product(-1, D)), 0)))) | (coprime(D, I) & divides(I, div(N, D))))) | (~(($sum($product(div(N, D), D), $product(-1, N)) = 0) & divides(div(N, D), N))) | ![Target: $int, Factor: $int, Factors1: list_int] : ((~$greatereq(Target, 2)) | ![D1: $int] : ((~prime(D1)) | (~($lesseq($sum(Factor, $product(-1, D1)), 0) & $lesseq($sum(D1, $product(-1, Target)), 0) & divides(D1, Target) & ![I: $int] : ((~divides(I, Target)) | (~($greatereq(I, 2) & (~$lesseq($sum(D1, $product(-1, I)), 0))))))) | ![Factor1: $int] : ((~($sum(Factor1, $product(-1, D1)) = 0)) | ![Factors2: list_int] : ((~(Factors2 = tb2t(cons(int, t2tb1(D1), t2tb(Factors1))))) | ![Target1: $int] : (![I: $int] : (coprime(D1, I) | $lesseq($sum(I, $product(-1, Factor)), 0) | (~($greatereq(D1, 1) & (~$lesseq($sum(I, $product(-1, D1)), 0)))) | (~divides(I, Target)) | (~(prime(I) & divides(I, N) & (~$lesseq($sum(I, $product(-1, D1)), 0))))) | (~($sum(Target1, $product(-1, div(Target, D1))) = 0)) | (~(($sum($product(Target1, D1), $product(-1, Target)) = 0) & divides(Target1, Target))))))) | (~(divides(Target, Target) & $greatereq(Target, 2) & $lesseq($sum(Factor, $product(-1, Target)), 0))) | (~($greatereq(Target, 2) & $greatereq(Factor, 2) & $lesseq($sum(Factor, $product(-1, Target)), 0) & ![I: $int] : ((~divides(I, Target)) | (~($greatereq(I, 2) & (~$lesseq($sum(Factor, $product(-1, I)), 0))))))) | (~($greatereq(Target, 1) & $lesseq($sum(Target, $product(-1, N)), 0) & $greatereq(Factor, 2) & $lesseq($sum(Factor, $product(-1, N)), 0) & divides(Factor, N) & prime(Factor) & ![I: $int] : ((~(divides(I, Target) & $greatereq(I, 2))) | ($lesseq($sum(Factor, $product(-1, I)), 0) & divides(I, N))) & ![I: $int] : ((~(prime(I) & divides(I, N) & (~$lesseq($sum(I, $product(-1, Factor)), 0)))) | divides(I, Target))))))))) <=> (~![N: $int] : ((~$greatereq(N, 2)) | ![D: $int] : ((~($greatereq(D, 2) & $greatereq($sum(N, $product(-1, D)), 0) & divides(D, N) & ![I: $int] : ((~divides(I, N)) | (~($greatereq(I, 2) & (~$lesseq($sum(D, $product(-1, I)), 0))))))) | ![Factors: list_int] : ((~![I: $int] : ((~(prime(I) & divides(I, N) & (~$greatereq($sum(D, $product(-1, I)), 0)))) | (coprime(D, I) & divides(I, div(N, D))))) | (~(($sum(N, $product(-1, $product(D, div(N, D)))) = 0) & divides(div(N, D), N))) | (~(Factors = tb2t(cons(int, t2tb1(D), nil(int))))) | ![Target: $int, Factor: $int, Factors1: list_int] : ((~($greatereq(Target, 2) & $greatereq(Factor, 2) & $greatereq($sum(Target, $product(-1, Factor)), 0) & ![I: $int] : ((~divides(I, Target)) | (~($greatereq(I, 2) & (~$lesseq($sum(Factor, $product(-1, I)), 0))))))) | (~(divides(Target, Target) & $greatereq(Target, 2) & $greatereq($sum(Target, $product(-1, Factor)), 0))) | (~$greatereq(Target, 2)) | (~($greatereq(Target, 1) & $lesseq($sum(Target, $product(-1, N)), 0) & $greatereq(Factor, 2) & $lesseq($sum(Factor, $product(-1, N)), 0) & divides(Factor, N) & prime(Factor) & ![I: $int] : ((~(divides(I, Target) & $greatereq(I, 2))) | ($lesseq($sum(Factor, $product(-1, I)), 0) & divides(I, N))) & ![I: $int] : ((~(prime(I) & divides(I, N) & (~$greatereq($sum(Factor, $product(-1, I)), 0)))) | divides(I, Target)))) | ![D1: $int] : ((~prime(D1)) | (~($lesseq($sum(Factor, $product(-1, D1)), 0) & $lesseq($sum(D1, $product(-1, Target)), 0) & divides(D1, Target) & ![I: $int] : ((~divides(I, Target)) | (~($greatereq(I, 2) & (~$lesseq($sum(D1, $product(-1, I)), 0))))))) | ![Factor1: $int] : ((~($sum(D1, $product(-1, Factor1)) = 0)) | ![Factors2: list_int] : ((~(Factors2 = tb2t(cons(int, t2tb1(D1), t2tb(Factors1))))) | ![Target1: $int] : (![I: $int] : (coprime(D1, I) | $lesseq($sum(I, $product(-1, Factor)), 0) | (~($greatereq(D1, 1) & (~$lesseq($sum(I, $product(-1, D1)), 0)))) | (~divides(I, Target)) | (~(prime(I) & divides(I, N) & (~$lesseq($sum(I, $product(-1, D1)), 0))))) | (~(($sum(Target, $product(-1, $product(Target1, D1))) = 0) & divides(Target1, Target))) | (~($sum(Target1, $product(-1, div(Target, D1))) = 0)))))))))))),
% 0.97/0.87 inference(rewrite,[status(thm)],[])).
% 0.97/0.87 tff(53,plain,
% 0.97/0.87 ((~![N: $int] : ((~$lesseq(2, N)) | ![D: $int] : ((~($lesseq(2, D) & $lesseq(D, N) & divides(D, N) & ![I: $int] : ((~divides(I, N)) | (~($lesseq(2, I) & (~$lesseq(D, I))))))) | ![Factors: list_int] : ((~(Factors = tb2t(cons(int, t2tb1(D), nil(int))))) | ![Target: $int, Factor: $int, Factors1: list_int] : (![D1: $int] : ((~prime(D1)) | ![Factor1: $int] : ((~(Factor1 = D1)) | ![Factors2: list_int] : ((~(Factors2 = tb2t(cons(int, t2tb1(D1), t2tb(Factors1))))) | ![Target1: $int] : ((~(Target1 = div(Target, D1))) | ![I: $int] : (coprime(D1, I) | (~divides(I, Target)) | $lesseq(I, Factor) | (~($lesseq(1, D1) & (~$lesseq(I, D1)))) | (~(prime(I) & divides(I, N) & (~$lesseq(I, D1))))) | (~(($product(Target1, D1) = Target) & divides(Target1, Target)))))) | (~($lesseq(Factor, D1) & $lesseq(D1, Target) & divides(D1, Target) & ![I: $int] : ((~divides(I, Target)) | (~($lesseq(2, I) & (~$lesseq(D1, I)))))))) | (~($lesseq(2, Target) & $lesseq(2, Factor) & $lesseq(Factor, Target) & ![I: $int] : ((~divides(I, Target)) | (~($lesseq(2, I) & (~$lesseq(Factor, I))))))) | (~(divides(Target, Target) & $lesseq(2, Target) & $lesseq(Factor, Target))) | (~$lesseq(2, Target)) | (~($lesseq(1, Target) & $lesseq(Target, N) & $lesseq(2, Factor) & $lesseq(Factor, N) & divides(Factor, N) & prime(Factor) & ![I: $int] : ((~(divides(I, Target) & $lesseq(2, I))) | ($lesseq(Factor, I) & divides(I, N))) & ![I: $int] : ((~(prime(I) & divides(I, N) & (~$lesseq(I, Factor)))) | divides(I, Target))))) | (~![I: $int] : ((~(prime(I) & divides(I, N) & (~$lesseq(I, D)))) | (coprime(D, I) & divides(I, div(N, D))))) | (~(($product(div(N, D), D) = N) & divides(div(N, D), N))))))) <=> (~![N: $int] : ((~$greatereq(N, 2)) | ![D: $int] : ((~($greatereq(D, 2) & $lesseq($sum(D, $product(-1, N)), 0) & divides(D, N) & ![I: $int] : ((~divides(I, N)) | (~($greatereq(I, 2) & (~$lesseq($sum(D, $product(-1, I)), 0))))))) | ![Factors: list_int] : ((~(Factors = tb2t(cons(int, t2tb1(D), nil(int))))) | (~![I: $int] : ((~(prime(I) & divides(I, N) & (~$lesseq($sum(I, $product(-1, D)), 0)))) | (coprime(D, I) & divides(I, div(N, D))))) | (~(($sum($product(div(N, D), D), $product(-1, N)) = 0) & divides(div(N, D), N))) | ![Target: $int, Factor: $int, Factors1: list_int] : ((~$greatereq(Target, 2)) | ![D1: $int] : ((~prime(D1)) | (~($lesseq($sum(Factor, $product(-1, D1)), 0) & $lesseq($sum(D1, $product(-1, Target)), 0) & divides(D1, Target) & ![I: $int] : ((~divides(I, Target)) | (~($greatereq(I, 2) & (~$lesseq($sum(D1, $product(-1, I)), 0))))))) | ![Factor1: $int] : ((~($sum(Factor1, $product(-1, D1)) = 0)) | ![Factors2: list_int] : ((~(Factors2 = tb2t(cons(int, t2tb1(D1), t2tb(Factors1))))) | ![Target1: $int] : (![I: $int] : (coprime(D1, I) | $lesseq($sum(I, $product(-1, Factor)), 0) | (~($greatereq(D1, 1) & (~$lesseq($sum(I, $product(-1, D1)), 0)))) | (~divides(I, Target)) | (~(prime(I) & divides(I, N) & (~$lesseq($sum(I, $product(-1, D1)), 0))))) | (~($sum(Target1, $product(-1, div(Target, D1))) = 0)) | (~(($sum($product(Target1, D1), $product(-1, Target)) = 0) & divides(Target1, Target))))))) | (~(divides(Target, Target) & $greatereq(Target, 2) & $lesseq($sum(Factor, $product(-1, Target)), 0))) | (~($greatereq(Target, 2) & $greatereq(Factor, 2) & $lesseq($sum(Factor, $product(-1, Target)), 0) & ![I: $int] : ((~divides(I, Target)) | (~($greatereq(I, 2) & (~$lesseq($sum(Factor, $product(-1, I)), 0))))))) | (~($greatereq(Target, 1) & $lesseq($sum(Target, $product(-1, N)), 0) & $greatereq(Factor, 2) & $lesseq($sum(Factor, $product(-1, N)), 0) & divides(Factor, N) & prime(Factor) & ![I: $int] : ((~(divides(I, Target) & $greatereq(I, 2))) | ($lesseq($sum(Factor, $product(-1, I)), 0) & divides(I, N))) & ![I: $int] : ((~(prime(I) & divides(I, N) & (~$lesseq($sum(I, $product(-1, Factor)), 0)))) | divides(I, Target)))))))))),
% 0.97/0.87 inference(rewrite,[status(thm)],[])).
% 0.97/0.87 tff(54,plain,
% 0.97/0.87 ((~![N: $int] : ((~$lesseq(2, N)) | ![D: $int] : ((~($lesseq(2, D) & $lesseq(D, N) & divides(D, N) & ![I: $int] : ((~divides(I, N)) | (~($lesseq(2, I) & (~$lesseq(D, I))))))) | ![Factors: list_int] : ((~(Factors = tb2t(cons(int, t2tb1(D), nil(int))))) | ![Target: $int, Factor: $int, Factors1: list_int] : (![D1: $int] : ((~prime(D1)) | ![Factor1: $int] : ((~(Factor1 = D1)) | ![Factors2: list_int] : ((~(Factors2 = tb2t(cons(int, t2tb1(D1), t2tb(Factors1))))) | ![Target1: $int] : ((~(Target1 = div(Target, D1))) | ![I: $int] : (coprime(D1, I) | (~divides(I, Target)) | $lesseq(I, Factor) | (~($lesseq(1, D1) & (~$lesseq(I, D1)))) | (~(prime(I) & divides(I, N) & (~$lesseq(I, D1))))) | (~(($product(Target1, D1) = Target) & divides(Target1, Target)))))) | (~($lesseq(Factor, D1) & $lesseq(D1, Target) & divides(D1, Target) & ![I: $int] : ((~divides(I, Target)) | (~($lesseq(2, I) & (~$lesseq(D1, I)))))))) | (~($lesseq(2, Target) & $lesseq(2, Factor) & $lesseq(Factor, Target) & ![I: $int] : ((~divides(I, Target)) | (~($lesseq(2, I) & (~$lesseq(Factor, I))))))) | (~(divides(Target, Target) & $lesseq(2, Target) & $lesseq(Factor, Target))) | (~$lesseq(2, Target)) | (~($lesseq(1, Target) & $lesseq(Target, N) & $lesseq(2, Factor) & $lesseq(Factor, N) & divides(Factor, N) & prime(Factor) & ![I: $int] : ((~(divides(I, Target) & $lesseq(2, I))) | ($lesseq(Factor, I) & divides(I, N))) & ![I: $int] : ((~(prime(I) & divides(I, N) & (~$lesseq(I, Factor)))) | divides(I, Target))))) | (~![I: $int] : ((~(prime(I) & divides(I, N) & (~$lesseq(I, D)))) | (coprime(D, I) & divides(I, div(N, D))))) | (~(($product(div(N, D), D) = N) & divides(div(N, D), N))))))) <=> (~![N: $int] : ((~$lesseq(2, N)) | ![D: $int] : ((~($lesseq(2, D) & $lesseq(D, N) & divides(D, N) & ![I: $int] : ((~divides(I, N)) | (~($lesseq(2, I) & (~$lesseq(D, I))))))) | ![Factors: list_int] : ((~(Factors = tb2t(cons(int, t2tb1(D), nil(int))))) | ![Target: $int, Factor: $int, Factors1: list_int] : (![D1: $int] : ((~prime(D1)) | ![Factor1: $int] : ((~(Factor1 = D1)) | ![Factors2: list_int] : ((~(Factors2 = tb2t(cons(int, t2tb1(D1), t2tb(Factors1))))) | ![Target1: $int] : ((~(Target1 = div(Target, D1))) | ![I: $int] : (coprime(D1, I) | (~divides(I, Target)) | $lesseq(I, Factor) | (~($lesseq(1, D1) & (~$lesseq(I, D1)))) | (~(prime(I) & divides(I, N) & (~$lesseq(I, D1))))) | (~(($product(Target1, D1) = Target) & divides(Target1, Target)))))) | (~($lesseq(Factor, D1) & $lesseq(D1, Target) & divides(D1, Target) & ![I: $int] : ((~divides(I, Target)) | (~($lesseq(2, I) & (~$lesseq(D1, I)))))))) | (~($lesseq(2, Target) & $lesseq(2, Factor) & $lesseq(Factor, Target) & ![I: $int] : ((~divides(I, Target)) | (~($lesseq(2, I) & (~$lesseq(Factor, I))))))) | (~(divides(Target, Target) & $lesseq(2, Target) & $lesseq(Factor, Target))) | (~$lesseq(2, Target)) | (~($lesseq(1, Target) & $lesseq(Target, N) & $lesseq(2, Factor) & $lesseq(Factor, N) & divides(Factor, N) & prime(Factor) & ![I: $int] : ((~(divides(I, Target) & $lesseq(2, I))) | ($lesseq(Factor, I) & divides(I, N))) & ![I: $int] : ((~(prime(I) & divides(I, N) & (~$lesseq(I, Factor)))) | divides(I, Target))))) | (~![I: $int] : ((~(prime(I) & divides(I, N) & (~$lesseq(I, D)))) | (coprime(D, I) & divides(I, div(N, D))))) | (~(($product(div(N, D), D) = N) & divides(div(N, D), N)))))))),
% 0.97/0.87 inference(rewrite,[status(thm)],[])).
% 0.97/0.87 tff(55,plain,
% 0.97/0.87 ((~![N: $int] : ($lesseq(2, N) => (((($lesseq(2, N) & $lesseq(2, 2)) & $lesseq(2, N)) & ![I: $int] : (($lesseq(2, I) & $less(I, 2)) => (~divides(I, N)))) => ![D: $int] : (((($lesseq(2, D) & $lesseq(D, N)) & divides(D, N)) & ![I: $int] : (($lesseq(2, I) & $less(I, D)) => (~divides(I, N)))) => ![Factors: list_int] : ((Factors = tb2t(cons(int, t2tb1(D), nil(int)))) => ((($product(div(N, D), D) = N) & divides(div(N, D), N)) => (![I: $int] : (((prime(I) & divides(I, N)) & $less(D, I)) => (coprime(D, I) & divides(I, div(N, D)))) => ![Target: $int, Factor: $int, Factors1: list_int] : (((((((($lesseq(1, Target) & $lesseq(Target, N)) & $lesseq(2, Factor)) & $lesseq(Factor, N)) & divides(Factor, N)) & prime(Factor)) & ![I: $int] : ((divides(I, Target) & $lesseq(2, I)) => ($lesseq(Factor, I) & divides(I, N)))) & ![I: $int] : (((prime(I) & divides(I, N)) & $less(Factor, I)) => divides(I, Target))) => ($lesseq(2, Target) => (((divides(Target, Target) & $lesseq(2, Target)) & $lesseq(Factor, Target)) => (((($lesseq(2, Target) & $lesseq(2, Factor)) & $lesseq(Factor, Target)) & ![I: $int] : (($lesseq(2, I) & $less(I, Factor)) => (~divides(I, Target)))) => ![D1: $int] : (((($lesseq(Factor, D1) & $lesseq(D1, Target)) & divides(D1, Target)) & ![I: $int] : (($lesseq(2, I) & $less(I, D1)) => (~divides(I, Target)))) => (prime(D1) => ![Factor1: $int] : ((Factor1 = D1) => ![Factors2: list_int] : ((Factors2 = tb2t(cons(int, t2tb1(D1), t2tb(Factors1)))) => ![Target1: $int] : ((Target1 = div(Target, D1)) => ((($product(Target1, D1) = Target) & divides(Target1, Target)) => ![I: $int] : (((prime(I) & divides(I, N)) & $less(D1, I)) => ($less(Factor, I) => (divides(I, Target) => (($lesseq(1, D1) & $less(D1, I)) => coprime(D1, I)))))))))))))))))))))) <=> (~![N: $int] : ((~$lesseq(2, N)) | ![D: $int] : ((~($lesseq(2, D) & $lesseq(D, N) & divides(D, N) & ![I: $int] : ((~divides(I, N)) | (~($lesseq(2, I) & (~$lesseq(D, I))))))) | ![Factors: list_int] : ((~(Factors = tb2t(cons(int, t2tb1(D), nil(int))))) | ![Target: $int, Factor: $int, Factors1: list_int] : (![D1: $int] : ((~prime(D1)) | ![Factor1: $int] : ((~(Factor1 = D1)) | ![Factors2: list_int] : ((~(Factors2 = tb2t(cons(int, t2tb1(D1), t2tb(Factors1))))) | ![Target1: $int] : ((~(Target1 = div(Target, D1))) | ![I: $int] : (coprime(D1, I) | (~divides(I, Target)) | $lesseq(I, Factor) | (~($lesseq(1, D1) & (~$lesseq(I, D1)))) | (~(prime(I) & divides(I, N) & (~$lesseq(I, D1))))) | (~(($product(Target1, D1) = Target) & divides(Target1, Target)))))) | (~($lesseq(Factor, D1) & $lesseq(D1, Target) & divides(D1, Target) & ![I: $int] : ((~divides(I, Target)) | (~($lesseq(2, I) & (~$lesseq(D1, I)))))))) | (~($lesseq(2, Target) & $lesseq(2, Factor) & $lesseq(Factor, Target) & ![I: $int] : ((~divides(I, Target)) | (~($lesseq(2, I) & (~$lesseq(Factor, I))))))) | (~(divides(Target, Target) & $lesseq(2, Target) & $lesseq(Factor, Target))) | (~$lesseq(2, Target)) | (~($lesseq(1, Target) & $lesseq(Target, N) & $lesseq(2, Factor) & $lesseq(Factor, N) & divides(Factor, N) & prime(Factor) & ![I: $int] : ((~(divides(I, Target) & $lesseq(2, I))) | ($lesseq(Factor, I) & divides(I, N))) & ![I: $int] : ((~(prime(I) & divides(I, N) & (~$lesseq(I, Factor)))) | divides(I, Target))))) | (~![I: $int] : ((~(prime(I) & divides(I, N) & (~$lesseq(I, D)))) | (coprime(D, I) & divides(I, div(N, D))))) | (~(($product(div(N, D), D) = N) & divides(div(N, D), N)))))))),
% 0.97/0.87 inference(rewrite,[status(thm)],[])).
% 0.97/0.87 tff(56,axiom,(~![N: $int] : ($lesseq(2, N) => (((($lesseq(2, N) & $lesseq(2, 2)) & $lesseq(2, N)) & ![I: $int] : (($lesseq(2, I) & $less(I, 2)) => (~divides(I, N)))) => ![D: $int] : (((($lesseq(2, D) & $lesseq(D, N)) & divides(D, N)) & ![I: $int] : (($lesseq(2, I) & $less(I, D)) => (~divides(I, N)))) => ![Factors: list_int] : ((Factors = tb2t(cons(int, t2tb1(D), nil(int)))) => ((($product(div(N, D), D) = N) & divides(div(N, D), N)) => (![I: $int] : (((prime(I) & divides(I, N)) & $less(D, I)) => (coprime(D, I) & divides(I, div(N, D)))) => ![Target: $int, Factor: $int, Factors1: list_int] : (((((((($lesseq(1, Target) & $lesseq(Target, N)) & $lesseq(2, Factor)) & $lesseq(Factor, N)) & divides(Factor, N)) & prime(Factor)) & ![I: $int] : ((divides(I, Target) & $lesseq(2, I)) => ($lesseq(Factor, I) & divides(I, N)))) & ![I: $int] : (((prime(I) & divides(I, N)) & $less(Factor, I)) => divides(I, Target))) => ($lesseq(2, Target) => (((divides(Target, Target) & $lesseq(2, Target)) & $lesseq(Factor, Target)) => (((($lesseq(2, Target) & $lesseq(2, Factor)) & $lesseq(Factor, Target)) & ![I: $int] : (($lesseq(2, I) & $less(I, Factor)) => (~divides(I, Target)))) => ![D1: $int] : (((($lesseq(Factor, D1) & $lesseq(D1, Target)) & divides(D1, Target)) & ![I: $int] : (($lesseq(2, I) & $less(I, D1)) => (~divides(I, Target)))) => (prime(D1) => ![Factor1: $int] : ((Factor1 = D1) => ![Factors2: list_int] : ((Factors2 = tb2t(cons(int, t2tb1(D1), t2tb(Factors1)))) => ![Target1: $int] : ((Target1 = div(Target, D1)) => ((($product(Target1, D1) = Target) & divides(Target1, Target)) => ![I: $int] : (((prime(I) & divides(I, N)) & $less(D1, I)) => ($less(Factor, I) => (divides(I, Target) => (($lesseq(1, D1) & $less(D1, I)) => coprime(D1, I)))))))))))))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','wP_parameter_largest_prime_factor')).
% 0.97/0.87 tff(57,plain,
% 0.97/0.87 (~![N: $int] : ((~$lesseq(2, N)) | ![D: $int] : ((~($lesseq(2, D) & $lesseq(D, N) & divides(D, N) & ![I: $int] : ((~divides(I, N)) | (~($lesseq(2, I) & (~$lesseq(D, I))))))) | ![Factors: list_int] : ((~(Factors = tb2t(cons(int, t2tb1(D), nil(int))))) | ![Target: $int, Factor: $int, Factors1: list_int] : (![D1: $int] : ((~prime(D1)) | ![Factor1: $int] : ((~(Factor1 = D1)) | ![Factors2: list_int] : ((~(Factors2 = tb2t(cons(int, t2tb1(D1), t2tb(Factors1))))) | ![Target1: $int] : ((~(Target1 = div(Target, D1))) | ![I: $int] : (coprime(D1, I) | (~divides(I, Target)) | $lesseq(I, Factor) | (~($lesseq(1, D1) & (~$lesseq(I, D1)))) | (~(prime(I) & divides(I, N) & (~$lesseq(I, D1))))) | (~(($product(Target1, D1) = Target) & divides(Target1, Target)))))) | (~($lesseq(Factor, D1) & $lesseq(D1, Target) & divides(D1, Target) & ![I: $int] : ((~divides(I, Target)) | (~($lesseq(2, I) & (~$lesseq(D1, I)))))))) | (~($lesseq(2, Target) & $lesseq(2, Factor) & $lesseq(Factor, Target) & ![I: $int] : ((~divides(I, Target)) | (~($lesseq(2, I) & (~$lesseq(Factor, I))))))) | (~(divides(Target, Target) & $lesseq(2, Target) & $lesseq(Factor, Target))) | (~$lesseq(2, Target)) | (~($lesseq(1, Target) & $lesseq(Target, N) & $lesseq(2, Factor) & $lesseq(Factor, N) & divides(Factor, N) & prime(Factor) & ![I: $int] : ((~(divides(I, Target) & $lesseq(2, I))) | ($lesseq(Factor, I) & divides(I, N))) & ![I: $int] : ((~(prime(I) & divides(I, N) & (~$lesseq(I, Factor)))) | divides(I, Target))))) | (~![I: $int] : ((~(prime(I) & divides(I, N) & (~$lesseq(I, D)))) | (coprime(D, I) & divides(I, div(N, D))))) | (~(($product(div(N, D), D) = N) & divides(div(N, D), N))))))),
% 0.97/0.87 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.97/0.87 tff(58,plain,
% 0.97/0.87 (~![N: $int] : ((~$lesseq(2, N)) | ![D: $int] : ((~($lesseq(2, D) & $lesseq(D, N) & divides(D, N) & ![I: $int] : ((~divides(I, N)) | (~($lesseq(2, I) & (~$lesseq(D, I))))))) | ![Factors: list_int] : ((~(Factors = tb2t(cons(int, t2tb1(D), nil(int))))) | ![Target: $int, Factor: $int, Factors1: list_int] : (![D1: $int] : ((~prime(D1)) | ![Factor1: $int] : ((~(Factor1 = D1)) | ![Factors2: list_int] : ((~(Factors2 = tb2t(cons(int, t2tb1(D1), t2tb(Factors1))))) | ![Target1: $int] : ((~(Target1 = div(Target, D1))) | ![I: $int] : (coprime(D1, I) | (~divides(I, Target)) | $lesseq(I, Factor) | (~($lesseq(1, D1) & (~$lesseq(I, D1)))) | (~(prime(I) & divides(I, N) & (~$lesseq(I, D1))))) | (~(($product(Target1, D1) = Target) & divides(Target1, Target)))))) | (~($lesseq(Factor, D1) & $lesseq(D1, Target) & divides(D1, Target) & ![I: $int] : ((~divides(I, Target)) | (~($lesseq(2, I) & (~$lesseq(D1, I)))))))) | (~($lesseq(2, Target) & $lesseq(2, Factor) & $lesseq(Factor, Target) & ![I: $int] : ((~divides(I, Target)) | (~($lesseq(2, I) & (~$lesseq(Factor, I))))))) | (~(divides(Target, Target) & $lesseq(2, Target) & $lesseq(Factor, Target))) | (~$lesseq(2, Target)) | (~($lesseq(1, Target) & $lesseq(Target, N) & $lesseq(2, Factor) & $lesseq(Factor, N) & divides(Factor, N) & prime(Factor) & ![I: $int] : ((~(divides(I, Target) & $lesseq(2, I))) | ($lesseq(Factor, I) & divides(I, N))) & ![I: $int] : ((~(prime(I) & divides(I, N) & (~$lesseq(I, Factor)))) | divides(I, Target))))) | (~![I: $int] : ((~(prime(I) & divides(I, N) & (~$lesseq(I, D)))) | (coprime(D, I) & divides(I, div(N, D))))) | (~(($product(div(N, D), D) = N) & divides(div(N, D), N))))))),
% 0.97/0.87 inference(modus_ponens,[status(thm)],[57, 54])).
% 0.97/0.87 tff(59,plain,
% 0.97/0.87 (~![N: $int] : ((~$lesseq(2, N)) | ![D: $int] : ((~($lesseq(2, D) & $lesseq(D, N) & divides(D, N) & ![I: $int] : ((~divides(I, N)) | (~($lesseq(2, I) & (~$lesseq(D, I))))))) | ![Factors: list_int] : ((~(Factors = tb2t(cons(int, t2tb1(D), nil(int))))) | ![Target: $int, Factor: $int, Factors1: list_int] : (![D1: $int] : ((~prime(D1)) | ![Factor1: $int] : ((~(Factor1 = D1)) | ![Factors2: list_int] : ((~(Factors2 = tb2t(cons(int, t2tb1(D1), t2tb(Factors1))))) | ![Target1: $int] : ((~(Target1 = div(Target, D1))) | ![I: $int] : (coprime(D1, I) | (~divides(I, Target)) | $lesseq(I, Factor) | (~($lesseq(1, D1) & (~$lesseq(I, D1)))) | (~(prime(I) & divides(I, N) & (~$lesseq(I, D1))))) | (~(($product(Target1, D1) = Target) & divides(Target1, Target)))))) | (~($lesseq(Factor, D1) & $lesseq(D1, Target) & divides(D1, Target) & ![I: $int] : ((~divides(I, Target)) | (~($lesseq(2, I) & (~$lesseq(D1, I)))))))) | (~($lesseq(2, Target) & $lesseq(2, Factor) & $lesseq(Factor, Target) & ![I: $int] : ((~divides(I, Target)) | (~($lesseq(2, I) & (~$lesseq(Factor, I))))))) | (~(divides(Target, Target) & $lesseq(2, Target) & $lesseq(Factor, Target))) | (~$lesseq(2, Target)) | (~($lesseq(1, Target) & $lesseq(Target, N) & $lesseq(2, Factor) & $lesseq(Factor, N) & divides(Factor, N) & prime(Factor) & ![I: $int] : ((~(divides(I, Target) & $lesseq(2, I))) | ($lesseq(Factor, I) & divides(I, N))) & ![I: $int] : ((~(prime(I) & divides(I, N) & (~$lesseq(I, Factor)))) | divides(I, Target))))) | (~![I: $int] : ((~(prime(I) & divides(I, N) & (~$lesseq(I, D)))) | (coprime(D, I) & divides(I, div(N, D))))) | (~(($product(div(N, D), D) = N) & divides(div(N, D), N))))))),
% 0.97/0.87 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.97/0.87 tff(60,plain,
% 0.97/0.87 (~![N: $int] : ((~$lesseq(2, N)) | ![D: $int] : ((~($lesseq(2, D) & $lesseq(D, N) & divides(D, N) & ![I: $int] : ((~divides(I, N)) | (~($lesseq(2, I) & (~$lesseq(D, I))))))) | ![Factors: list_int] : ((~(Factors = tb2t(cons(int, t2tb1(D), nil(int))))) | ![Target: $int, Factor: $int, Factors1: list_int] : (![D1: $int] : ((~prime(D1)) | ![Factor1: $int] : ((~(Factor1 = D1)) | ![Factors2: list_int] : ((~(Factors2 = tb2t(cons(int, t2tb1(D1), t2tb(Factors1))))) | ![Target1: $int] : ((~(Target1 = div(Target, D1))) | ![I: $int] : (coprime(D1, I) | (~divides(I, Target)) | $lesseq(I, Factor) | (~($lesseq(1, D1) & (~$lesseq(I, D1)))) | (~(prime(I) & divides(I, N) & (~$lesseq(I, D1))))) | (~(($product(Target1, D1) = Target) & divides(Target1, Target)))))) | (~($lesseq(Factor, D1) & $lesseq(D1, Target) & divides(D1, Target) & ![I: $int] : ((~divides(I, Target)) | (~($lesseq(2, I) & (~$lesseq(D1, I)))))))) | (~($lesseq(2, Target) & $lesseq(2, Factor) & $lesseq(Factor, Target) & ![I: $int] : ((~divides(I, Target)) | (~($lesseq(2, I) & (~$lesseq(Factor, I))))))) | (~(divides(Target, Target) & $lesseq(2, Target) & $lesseq(Factor, Target))) | (~$lesseq(2, Target)) | (~($lesseq(1, Target) & $lesseq(Target, N) & $lesseq(2, Factor) & $lesseq(Factor, N) & divides(Factor, N) & prime(Factor) & ![I: $int] : ((~(divides(I, Target) & $lesseq(2, I))) | ($lesseq(Factor, I) & divides(I, N))) & ![I: $int] : ((~(prime(I) & divides(I, N) & (~$lesseq(I, Factor)))) | divides(I, Target))))) | (~![I: $int] : ((~(prime(I) & divides(I, N) & (~$lesseq(I, D)))) | (coprime(D, I) & divides(I, div(N, D))))) | (~(($product(div(N, D), D) = N) & divides(div(N, D), N))))))),
% 0.97/0.87 inference(modus_ponens,[status(thm)],[59, 54])).
% 0.97/0.87 tff(61,plain,
% 0.97/0.87 (~![N: $int] : ((~$greatereq(N, 2)) | ![D: $int] : ((~($greatereq(D, 2) & $lesseq($sum(D, $product(-1, N)), 0) & divides(D, N) & ![I: $int] : ((~divides(I, N)) | (~($greatereq(I, 2) & (~$lesseq($sum(D, $product(-1, I)), 0))))))) | ![Factors: list_int] : ((~(Factors = tb2t(cons(int, t2tb1(D), nil(int))))) | (~![I: $int] : ((~(prime(I) & divides(I, N) & (~$lesseq($sum(I, $product(-1, D)), 0)))) | (coprime(D, I) & divides(I, div(N, D))))) | (~(($sum($product(div(N, D), D), $product(-1, N)) = 0) & divides(div(N, D), N))) | ![Target: $int, Factor: $int, Factors1: list_int] : ((~$greatereq(Target, 2)) | ![D1: $int] : ((~prime(D1)) | (~($lesseq($sum(Factor, $product(-1, D1)), 0) & $lesseq($sum(D1, $product(-1, Target)), 0) & divides(D1, Target) & ![I: $int] : ((~divides(I, Target)) | (~($greatereq(I, 2) & (~$lesseq($sum(D1, $product(-1, I)), 0))))))) | ![Factor1: $int] : ((~($sum(Factor1, $product(-1, D1)) = 0)) | ![Factors2: list_int] : ((~(Factors2 = tb2t(cons(int, t2tb1(D1), t2tb(Factors1))))) | ![Target1: $int] : (![I: $int] : (coprime(D1, I) | $lesseq($sum(I, $product(-1, Factor)), 0) | (~($greatereq(D1, 1) & (~$lesseq($sum(I, $product(-1, D1)), 0)))) | (~divides(I, Target)) | (~(prime(I) & divides(I, N) & (~$lesseq($sum(I, $product(-1, D1)), 0))))) | (~($sum(Target1, $product(-1, div(Target, D1))) = 0)) | (~(($sum($product(Target1, D1), $product(-1, Target)) = 0) & divides(Target1, Target))))))) | (~(divides(Target, Target) & $greatereq(Target, 2) & $lesseq($sum(Factor, $product(-1, Target)), 0))) | (~($greatereq(Target, 2) & $greatereq(Factor, 2) & $lesseq($sum(Factor, $product(-1, Target)), 0) & ![I: $int] : ((~divides(I, Target)) | (~($greatereq(I, 2) & (~$lesseq($sum(Factor, $product(-1, I)), 0))))))) | (~($greatereq(Target, 1) & $lesseq($sum(Target, $product(-1, N)), 0) & $greatereq(Factor, 2) & $lesseq($sum(Factor, $product(-1, N)), 0) & divides(Factor, N) & prime(Factor) & ![I: $int] : ((~(divides(I, Target) & $greatereq(I, 2))) | ($lesseq($sum(Factor, $product(-1, I)), 0) & divides(I, N))) & ![I: $int] : ((~(prime(I) & divides(I, N) & (~$lesseq($sum(I, $product(-1, Factor)), 0)))) | divides(I, Target))))))))),
% 0.97/0.87 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.97/0.87 tff(62,plain,
% 0.97/0.87 (~![N: $int] : ((~$greatereq(N, 2)) | ![D: $int] : ((~($greatereq(D, 2) & $greatereq($sum(N, $product(-1, D)), 0) & divides(D, N) & ![I: $int] : ((~divides(I, N)) | (~($greatereq(I, 2) & (~$lesseq($sum(D, $product(-1, I)), 0))))))) | ![Factors: list_int] : ((~![I: $int] : ((~(prime(I) & divides(I, N) & (~$greatereq($sum(D, $product(-1, I)), 0)))) | (coprime(D, I) & divides(I, div(N, D))))) | (~(($sum(N, $product(-1, $product(D, div(N, D)))) = 0) & divides(div(N, D), N))) | (~(Factors = tb2t(cons(int, t2tb1(D), nil(int))))) | ![Target: $int, Factor: $int, Factors1: list_int] : ((~($greatereq(Target, 2) & $greatereq(Factor, 2) & $greatereq($sum(Target, $product(-1, Factor)), 0) & ![I: $int] : ((~divides(I, Target)) | (~($greatereq(I, 2) & (~$lesseq($sum(Factor, $product(-1, I)), 0))))))) | (~(divides(Target, Target) & $greatereq(Target, 2) & $greatereq($sum(Target, $product(-1, Factor)), 0))) | (~$greatereq(Target, 2)) | (~($greatereq(Target, 1) & $lesseq($sum(Target, $product(-1, N)), 0) & $greatereq(Factor, 2) & $lesseq($sum(Factor, $product(-1, N)), 0) & divides(Factor, N) & prime(Factor) & ![I: $int] : ((~(divides(I, Target) & $greatereq(I, 2))) | ($lesseq($sum(Factor, $product(-1, I)), 0) & divides(I, N))) & ![I: $int] : ((~(prime(I) & divides(I, N) & (~$greatereq($sum(Factor, $product(-1, I)), 0)))) | divides(I, Target)))) | ![D1: $int] : ((~prime(D1)) | (~($lesseq($sum(Factor, $product(-1, D1)), 0) & $lesseq($sum(D1, $product(-1, Target)), 0) & divides(D1, Target) & ![I: $int] : ((~divides(I, Target)) | (~($greatereq(I, 2) & (~$lesseq($sum(D1, $product(-1, I)), 0))))))) | ![Factor1: $int] : ((~($sum(D1, $product(-1, Factor1)) = 0)) | ![Factors2: list_int] : ((~(Factors2 = tb2t(cons(int, t2tb1(D1), t2tb(Factors1))))) | ![Target1: $int] : (![I: $int] : (coprime(D1, I) | $lesseq($sum(I, $product(-1, Factor)), 0) | (~($greatereq(D1, 1) & (~$lesseq($sum(I, $product(-1, D1)), 0)))) | (~divides(I, Target)) | (~(prime(I) & divides(I, N) & (~$lesseq($sum(I, $product(-1, D1)), 0))))) | (~(($sum(Target, $product(-1, $product(Target1, D1))) = 0) & divides(Target1, Target))) | (~($sum(Target1, $product(-1, div(Target, D1))) = 0))))))))))),
% 0.97/0.87 inference(modus_ponens,[status(thm)],[61, 52])).
% 0.97/0.87 tff(63,plain,
% 0.97/0.87 (~![N: $int] : ((~$greatereq(N, 2)) | ![D: $int] : ((~($greatereq(D, 2) & $greatereq($sum(N, $product(-1, D)), 0) & divides(D, N) & ![I: $int] : ((~divides(I, N)) | (~($greatereq(I, 2) & (~$lesseq($sum(D, $product(-1, I)), 0))))))) | ![Factors: list_int] : ((~![I: $int] : ((~(prime(I) & divides(I, N) & (~$greatereq($sum(D, $product(-1, I)), 0)))) | (coprime(D, I) & divides(I, div(N, D))))) | (~(($sum(N, $product(-1, $product(D, div(N, D)))) = 0) & divides(div(N, D), N))) | (~(Factors = tb2t(cons(int, t2tb1(D), nil(int))))) | ![Target: $int, Factor: $int, Factors1: list_int] : ((~($greatereq(Target, 2) & $greatereq(Factor, 2) & $greatereq($sum(Target, $product(-1, Factor)), 0) & ![I: $int] : ((~divides(I, Target)) | (~($greatereq(I, 2) & (~$lesseq($sum(Factor, $product(-1, I)), 0))))))) | (~(divides(Target, Target) & $greatereq(Target, 2) & $greatereq($sum(Target, $product(-1, Factor)), 0))) | (~$greatereq(Target, 2)) | (~($greatereq(Target, 1) & $lesseq($sum(Target, $product(-1, N)), 0) & $greatereq(Factor, 2) & $lesseq($sum(Factor, $product(-1, N)), 0) & divides(Factor, N) & prime(Factor) & ![I: $int] : ((~(divides(I, Target) & $greatereq(I, 2))) | ($lesseq($sum(Factor, $product(-1, I)), 0) & divides(I, N))) & ![I: $int] : ((~(prime(I) & divides(I, N) & (~$greatereq($sum(Factor, $product(-1, I)), 0)))) | divides(I, Target)))) | ![D1: $int] : ((~prime(D1)) | (~($lesseq($sum(Factor, $product(-1, D1)), 0) & $lesseq($sum(D1, $product(-1, Target)), 0) & divides(D1, Target) & ![I: $int] : ((~divides(I, Target)) | (~($greatereq(I, 2) & (~$lesseq($sum(D1, $product(-1, I)), 0))))))) | ![Factor1: $int] : ((~($sum(D1, $product(-1, Factor1)) = 0)) | ![Factors2: list_int] : ((~(Factors2 = tb2t(cons(int, t2tb1(D1), t2tb(Factors1))))) | ![Target1: $int] : (![I: $int] : (coprime(D1, I) | $lesseq($sum(I, $product(-1, Factor)), 0) | (~($greatereq(D1, 1) & (~$lesseq($sum(I, $product(-1, D1)), 0)))) | (~divides(I, Target)) | (~(prime(I) & divides(I, N) & (~$lesseq($sum(I, $product(-1, D1)), 0))))) | (~(($sum(Target, $product(-1, $product(Target1, D1))) = 0) & divides(Target1, Target))) | (~($sum(Target1, $product(-1, div(Target, D1))) = 0))))))))))),
% 0.97/0.87 inference(modus_ponens,[status(thm)],[62, 51])).
% 0.97/0.87 tff(64,plain,
% 0.97/0.87 (~![N: $int] : ((~$greatereq(N, 2)) | ![D: $int] : ((~($greatereq(D, 2) & $greatereq($sum(N, $product(-1, D)), 0) & divides(D, N) & ![I: $int] : ((~divides(I, N)) | (~($greatereq(I, 2) & (~$lesseq($sum(D, $product(-1, I)), 0))))))) | ![Factors: list_int] : ((~![I: $int] : ((~(prime(I) & divides(I, N) & (~$greatereq($sum(D, $product(-1, I)), 0)))) | (coprime(D, I) & divides(I, div(N, D))))) | (~(($sum(N, $product(-1, $product(D, div(N, D)))) = 0) & divides(div(N, D), N))) | (~(Factors = tb2t(cons(int, t2tb1(D), nil(int))))) | ![Target: $int, Factor: $int, Factors1: list_int] : ((~($greatereq(Target, 2) & $greatereq(Factor, 2) & $greatereq($sum(Target, $product(-1, Factor)), 0) & ![I: $int] : ((~divides(I, Target)) | (~($greatereq(I, 2) & (~$lesseq($sum(Factor, $product(-1, I)), 0))))))) | (~(divides(Target, Target) & $greatereq(Target, 2) & $greatereq($sum(Target, $product(-1, Factor)), 0))) | (~$greatereq(Target, 2)) | (~($greatereq(Target, 1) & $lesseq($sum(Target, $product(-1, N)), 0) & $greatereq(Factor, 2) & $lesseq($sum(Factor, $product(-1, N)), 0) & divides(Factor, N) & prime(Factor) & ![I: $int] : ((~(divides(I, Target) & $greatereq(I, 2))) | ($lesseq($sum(Factor, $product(-1, I)), 0) & divides(I, N))) & ![I: $int] : ((~(prime(I) & divides(I, N) & (~$greatereq($sum(Factor, $product(-1, I)), 0)))) | divides(I, Target)))) | ![D1: $int] : ((~prime(D1)) | (~($lesseq($sum(Factor, $product(-1, D1)), 0) & $lesseq($sum(D1, $product(-1, Target)), 0) & divides(D1, Target) & ![I: $int] : ((~divides(I, Target)) | (~($greatereq(I, 2) & (~$lesseq($sum(D1, $product(-1, I)), 0))))))) | ![Factor1: $int] : ((~($sum(D1, $product(-1, Factor1)) = 0)) | ![Factors2: list_int] : ((~(Factors2 = tb2t(cons(int, t2tb1(D1), t2tb(Factors1))))) | ![Target1: $int] : (![I: $int] : (coprime(D1, I) | $lesseq($sum(I, $product(-1, Factor)), 0) | (~($greatereq(D1, 1) & (~$lesseq($sum(I, $product(-1, D1)), 0)))) | (~divides(I, Target)) | (~(prime(I) & divides(I, N) & (~$lesseq($sum(I, $product(-1, D1)), 0))))) | (~(($sum(Target, $product(-1, $product(Target1, D1))) = 0) & divides(Target1, Target))) | (~($sum(Target1, $product(-1, div(Target, D1))) = 0))))))))))),
% 0.97/0.87 inference(modus_ponens,[status(thm)],[63, 51])).
% 0.97/0.87 tff(65,plain,
% 0.97/0.87 ($greatereq(N!7, 2) & $greatereq(D!8, 2) & $greatereq($sum(N!7, $product(-1, D!8)), 0) & divides(D!8, N!7) & ![I: $int] : ((~divides(I, N!7)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, D!8)), 0))))) & ![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$lesseq($sum(I, $product(-1, D!8)), 0)))) | (coprime(D!8, I) & divides(I, div(N!7, D!8)))) & ($sum(N!7, $product(-1, $product(D!8, div(N!7, D!8)))) = 0) & divides(div(N!7, D!8), N!7) & (Factors!9 = tb2t(cons(int, t2tb1(D!8), nil(int)))) & $greatereq(Target!12, 2) & $greatereq(Factor!11, 2) & $lesseq($sum(Factor!11, $product(-1, Target!12)), 0) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, Factor!11)), 0))))) & divides(Target!12, Target!12) & $greatereq(Target!12, 1) & $greatereq($sum(N!7, $product(-1, Target!12)), 0) & $greatereq($sum(N!7, $product(-1, Factor!11)), 0) & divides(Factor!11, N!7) & prime(Factor!11) & ![I: $int] : ((~(divides(I, Target!12) & $greatereq(I, 2))) | ($greatereq($sum(I, $product(-1, Factor!11)), 0) & divides(I, N!7))) & ![I: $int] : ((~(prime(I) & divides(I, N!7) & (~$lesseq($sum(I, $product(-1, Factor!11)), 0)))) | divides(I, Target!12)) & prime(D1!13) & $lesseq($sum(Factor!11, $product(-1, D1!13)), 0) & $greatereq($sum(Target!12, $product(-1, D1!13)), 0) & divides(D1!13, Target!12) & ![I: $int] : ((~divides(I, Target!12)) | (~($greatereq(I, 2) & (~$greatereq($sum(I, $product(-1, D1!13)), 0))))) & ($sum(D1!13, $product(-1, Factor1!14)) = 0) & (Factors2!15 = tb2t(cons(int, t2tb1(D1!13), t2tb(Factors1!10)))) & (~(coprime(D1!13, I!17) | (~divides(I!17, Target!12)) | $greatereq($sum(Factor!11, $product(-1, I!17)), 0) | (~($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))) | (~(prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))))) & ($sum(Target!12, $product(-1, $product(D1!13, Target1!16))) = 0) & divides(Target1!16, Target!12) & ($sum(div(Target!12, D1!13), $product(-1, Target1!16)) = 0)),
% 0.97/0.87 inference(modus_ponens,[status(thm)],[64, 50])).
% 0.97/0.87 tff(66,plain,
% 0.97/0.87 (~(coprime(D1!13, I!17) | (~divides(I!17, Target!12)) | $greatereq($sum(Factor!11, $product(-1, I!17)), 0) | (~($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))) | (~(prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)))))),
% 0.97/0.87 inference(and_elim,[status(thm)],[65])).
% 0.97/0.87 tff(67,plain,
% 0.97/0.87 ($greatereq(D1!13, 1) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0))),
% 0.97/0.87 inference(or_elim,[status(thm)],[66])).
% 0.97/0.87 tff(68,plain,
% 0.97/0.87 (~$greatereq($sum(D1!13, $product(-1, I!17)), 0)),
% 0.97/0.87 inference(and_elim,[status(thm)],[67])).
% 0.97/0.87 tff(69,plain,
% 0.97/0.87 ($greatereq(D1!13, 1)),
% 0.97/0.87 inference(and_elim,[status(thm)],[67])).
% 0.97/0.87 tff(70,plain,
% 0.97/0.87 ($greatereq(D1!13, 0) | (~$greatereq(D1!13, 1))),
% 0.97/0.87 inference(theory_lemma,[status(thm)],[])).
% 0.97/0.87 tff(71,plain,
% 0.97/0.87 ($greatereq(D1!13, 0)),
% 0.97/0.87 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.97/0.87 tff(72,plain,
% 0.97/0.87 ((~$greatereq(D1!13, 0)) | (D1!13 = ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)))),
% 0.97/0.87 inference(tautology,[status(thm)],[])).
% 0.97/0.87 tff(73,plain,
% 0.97/0.87 (D1!13 = ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13))),
% 0.97/0.87 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.97/0.87 tff(74,plain,
% 0.97/0.87 ((~(D1!13 = ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)))) | $greatereq($sum(D1!13, $product(-1, ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)))), 0)),
% 0.97/0.87 inference(theory_lemma,[status(thm)],[])).
% 0.97/0.87 tff(75,plain,
% 0.97/0.87 ($greatereq($sum(D1!13, $product(-1, ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)))), 0)),
% 0.97/0.87 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.97/0.87 tff(76,plain,
% 0.97/0.87 (ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)) = D1!13),
% 0.97/0.87 inference(symmetry,[status(thm)],[73])).
% 0.97/0.87 tff(77,plain,
% 0.97/0.87 (coprime(ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)), I!17) <=> coprime(D1!13, I!17)),
% 0.97/0.87 inference(monotonicity,[status(thm)],[76])).
% 0.97/0.87 tff(78,plain,
% 0.97/0.87 (coprime(D1!13, I!17) <=> coprime(ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)), I!17)),
% 0.97/0.87 inference(symmetry,[status(thm)],[77])).
% 0.97/0.87 tff(79,plain,
% 0.97/0.87 ((~coprime(D1!13, I!17)) <=> (~coprime(ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)), I!17))),
% 0.97/0.87 inference(monotonicity,[status(thm)],[78])).
% 0.97/0.87 tff(80,plain,
% 0.97/0.87 (~coprime(D1!13, I!17)),
% 0.97/0.87 inference(or_elim,[status(thm)],[66])).
% 0.97/0.87 tff(81,plain,
% 0.97/0.87 (~coprime(ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)), I!17)),
% 0.97/0.87 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.97/0.87 tff(82,plain,
% 0.97/0.87 ($greatereq(Factor!11, 2)),
% 0.97/0.87 inference(and_elim,[status(thm)],[65])).
% 0.97/0.87 tff(83,plain,
% 0.97/0.87 ((~(D1!13 = ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)))) | $lesseq($sum(D1!13, $product(-1, ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)))), 0)),
% 0.97/0.87 inference(theory_lemma,[status(thm)],[])).
% 0.97/0.87 tff(84,plain,
% 0.97/0.87 ($lesseq($sum(D1!13, $product(-1, ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)))), 0)),
% 0.97/0.87 inference(unit_resolution,[status(thm)],[83, 73])).
% 0.97/0.87 tff(85,plain,
% 0.97/0.87 ($lesseq($sum(Factor!11, $product(-1, D1!13)), 0)),
% 0.97/0.87 inference(and_elim,[status(thm)],[65])).
% 0.97/0.87 tff(86,plain,
% 0.97/0.87 ($greatereq(ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)), 1) | (~$lesseq($sum(D1!13, $product(-1, ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)))), 0)) | (~$greatereq(Factor!11, 2)) | (~$lesseq($sum(Factor!11, $product(-1, D1!13)), 0))),
% 0.97/0.87 inference(theory_lemma,[status(thm)],[])).
% 0.97/0.87 tff(87,plain,
% 0.97/0.87 ($greatereq(ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)), 1)),
% 0.97/0.87 inference(unit_resolution,[status(thm)],[86, 85, 84, 82])).
% 0.97/0.87 tff(88,plain,
% 0.97/0.87 (^[P: $int] : rewrite((~((~((~prime(P)) | (~((~$greatereq(P, 2)) | (~![N: $int] : (coprime(N, P) | $lesseq($sum(P, $product(-1, N)), 0) | (~$greatereq(N, 1)))))))) | (~(prime(P) | (~$greatereq(P, 2)) | (~($lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0) | coprime(tptp_fun_N_6(P), P) | (~$greatereq(tptp_fun_N_6(P), 1)))))))) <=> (~((~(prime(P) | (~$greatereq(P, 2)) | (~($lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0) | coprime(tptp_fun_N_6(P), P) | (~$greatereq(tptp_fun_N_6(P), 1)))))) | (~((~prime(P)) | (~((~$greatereq(P, 2)) | (~![N: $int] : (coprime(N, P) | $lesseq($sum(P, $product(-1, N)), 0) | (~$greatereq(N, 1)))))))))))),
% 0.97/0.87 inference(bind,[status(th)],[])).
% 0.97/0.87 tff(89,plain,
% 0.97/0.87 (![P: $int] : (~((~((~prime(P)) | (~((~$greatereq(P, 2)) | (~![N: $int] : (coprime(N, P) | $lesseq($sum(P, $product(-1, N)), 0) | (~$greatereq(N, 1)))))))) | (~(prime(P) | (~$greatereq(P, 2)) | (~($lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0) | coprime(tptp_fun_N_6(P), P) | (~$greatereq(tptp_fun_N_6(P), 1)))))))) <=> ![P: $int] : (~((~(prime(P) | (~$greatereq(P, 2)) | (~($lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0) | coprime(tptp_fun_N_6(P), P) | (~$greatereq(tptp_fun_N_6(P), 1)))))) | (~((~prime(P)) | (~((~$greatereq(P, 2)) | (~![N: $int] : (coprime(N, P) | $lesseq($sum(P, $product(-1, N)), 0) | (~$greatereq(N, 1))))))))))),
% 0.97/0.87 inference(quant_intro,[status(thm)],[88])).
% 0.97/0.87 tff(90,plain,
% 0.97/0.87 (^[P: $int] : refl((~((~((~prime(P)) | (~((~$greatereq(P, 2)) | (~![N: $int] : (coprime(N, P) | $lesseq($sum(P, $product(-1, N)), 0) | (~$greatereq(N, 1)))))))) | (~(prime(P) | (~$greatereq(P, 2)) | (~($lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0) | coprime(tptp_fun_N_6(P), P) | (~$greatereq(tptp_fun_N_6(P), 1)))))))) <=> (~((~((~prime(P)) | (~((~$greatereq(P, 2)) | (~![N: $int] : (coprime(N, P) | $lesseq($sum(P, $product(-1, N)), 0) | (~$greatereq(N, 1)))))))) | (~(prime(P) | (~$greatereq(P, 2)) | (~($lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0) | coprime(tptp_fun_N_6(P), P) | (~$greatereq(tptp_fun_N_6(P), 1)))))))))),
% 0.97/0.87 inference(bind,[status(th)],[])).
% 0.97/0.87 tff(91,plain,
% 0.97/0.87 (![P: $int] : (~((~((~prime(P)) | (~((~$greatereq(P, 2)) | (~![N: $int] : (coprime(N, P) | $lesseq($sum(P, $product(-1, N)), 0) | (~$greatereq(N, 1)))))))) | (~(prime(P) | (~$greatereq(P, 2)) | (~($lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0) | coprime(tptp_fun_N_6(P), P) | (~$greatereq(tptp_fun_N_6(P), 1)))))))) <=> ![P: $int] : (~((~((~prime(P)) | (~((~$greatereq(P, 2)) | (~![N: $int] : (coprime(N, P) | $lesseq($sum(P, $product(-1, N)), 0) | (~$greatereq(N, 1)))))))) | (~(prime(P) | (~$greatereq(P, 2)) | (~($lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0) | coprime(tptp_fun_N_6(P), P) | (~$greatereq(tptp_fun_N_6(P), 1))))))))),
% 0.97/0.87 inference(quant_intro,[status(thm)],[90])).
% 0.97/0.87 tff(92,plain,
% 0.97/0.87 (^[P: $int] : rewrite((~((~((~prime(P)) | (~((~$greatereq(P, 2)) | (~![N: $int] : (coprime(N, P) | $lesseq($sum(P, $product(-1, N)), 0) | (~$greatereq(N, 1)))))))) | (~(prime(P) | (~$greatereq(P, 2)) | (~($lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0) | coprime(tptp_fun_N_6(P), P) | (~$greatereq(tptp_fun_N_6(P), 1)))))))) <=> (~((~((~prime(P)) | (~((~$greatereq(P, 2)) | (~![N: $int] : (coprime(N, P) | $lesseq($sum(P, $product(-1, N)), 0) | (~$greatereq(N, 1)))))))) | (~(prime(P) | (~$greatereq(P, 2)) | (~($lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0) | coprime(tptp_fun_N_6(P), P) | (~$greatereq(tptp_fun_N_6(P), 1)))))))))),
% 0.97/0.87 inference(bind,[status(th)],[])).
% 0.97/0.87 tff(93,plain,
% 0.97/0.87 (![P: $int] : (~((~((~prime(P)) | (~((~$greatereq(P, 2)) | (~![N: $int] : (coprime(N, P) | $lesseq($sum(P, $product(-1, N)), 0) | (~$greatereq(N, 1)))))))) | (~(prime(P) | (~$greatereq(P, 2)) | (~($lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0) | coprime(tptp_fun_N_6(P), P) | (~$greatereq(tptp_fun_N_6(P), 1)))))))) <=> ![P: $int] : (~((~((~prime(P)) | (~((~$greatereq(P, 2)) | (~![N: $int] : (coprime(N, P) | $lesseq($sum(P, $product(-1, N)), 0) | (~$greatereq(N, 1)))))))) | (~(prime(P) | (~$greatereq(P, 2)) | (~($lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0) | coprime(tptp_fun_N_6(P), P) | (~$greatereq(tptp_fun_N_6(P), 1))))))))),
% 0.97/0.87 inference(quant_intro,[status(thm)],[92])).
% 0.97/0.87 tff(94,plain,
% 0.97/0.87 (![P: $int] : (~((~((~prime(P)) | (~((~$greatereq(P, 2)) | (~![N: $int] : (coprime(N, P) | $lesseq($sum(P, $product(-1, N)), 0) | (~$greatereq(N, 1)))))))) | (~(prime(P) | (~$greatereq(P, 2)) | (~($lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0) | coprime(tptp_fun_N_6(P), P) | (~$greatereq(tptp_fun_N_6(P), 1)))))))) <=> ![P: $int] : (~((~((~prime(P)) | (~((~$greatereq(P, 2)) | (~![N: $int] : (coprime(N, P) | $lesseq($sum(P, $product(-1, N)), 0) | (~$greatereq(N, 1)))))))) | (~(prime(P) | (~$greatereq(P, 2)) | (~($lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0) | coprime(tptp_fun_N_6(P), P) | (~$greatereq(tptp_fun_N_6(P), 1))))))))),
% 0.97/0.87 inference(transitivity,[status(thm)],[93, 91])).
% 0.97/0.87 tff(95,plain,
% 0.97/0.87 (^[P: $int] : trans(monotonicity(rewrite(((~prime(P)) | ($greatereq(P, 2) & ![N: $int] : ((~($greatereq(N, 1) & (~$lesseq($sum(P, $product(-1, N)), 0)))) | coprime(N, P)))) <=> ((~prime(P)) | (~((~$greatereq(P, 2)) | (~![N: $int] : (coprime(N, P) | $lesseq($sum(P, $product(-1, N)), 0) | (~$greatereq(N, 1)))))))), rewrite((prime(P) | (~$greatereq(P, 2)) | (~((~($greatereq(tptp_fun_N_6(P), 1) & (~$lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0)))) | coprime(tptp_fun_N_6(P), P)))) <=> (prime(P) | (~$greatereq(P, 2)) | (~($lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0) | coprime(tptp_fun_N_6(P), P) | (~$greatereq(tptp_fun_N_6(P), 1)))))), ((((~prime(P)) | ($greatereq(P, 2) & ![N: $int] : ((~($greatereq(N, 1) & (~$lesseq($sum(P, $product(-1, N)), 0)))) | coprime(N, P)))) & (prime(P) | (~$greatereq(P, 2)) | (~((~($greatereq(tptp_fun_N_6(P), 1) & (~$lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0)))) | coprime(tptp_fun_N_6(P), P))))) <=> (((~prime(P)) | (~((~$greatereq(P, 2)) | (~![N: $int] : (coprime(N, P) | $lesseq($sum(P, $product(-1, N)), 0) | (~$greatereq(N, 1))))))) & (prime(P) | (~$greatereq(P, 2)) | (~($lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0) | coprime(tptp_fun_N_6(P), P) | (~$greatereq(tptp_fun_N_6(P), 1)))))))), rewrite((((~prime(P)) | (~((~$greatereq(P, 2)) | (~![N: $int] : (coprime(N, P) | $lesseq($sum(P, $product(-1, N)), 0) | (~$greatereq(N, 1))))))) & (prime(P) | (~$greatereq(P, 2)) | (~($lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0) | coprime(tptp_fun_N_6(P), P) | (~$greatereq(tptp_fun_N_6(P), 1)))))) <=> (~((~((~prime(P)) | (~((~$greatereq(P, 2)) | (~![N: $int] : (coprime(N, P) | $lesseq($sum(P, $product(-1, N)), 0) | (~$greatereq(N, 1)))))))) | (~(prime(P) | (~$greatereq(P, 2)) | (~($lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0) | coprime(tptp_fun_N_6(P), P) | (~$greatereq(tptp_fun_N_6(P), 1))))))))), ((((~prime(P)) | ($greatereq(P, 2) & ![N: $int] : ((~($greatereq(N, 1) & (~$lesseq($sum(P, $product(-1, N)), 0)))) | coprime(N, P)))) & (prime(P) | (~$greatereq(P, 2)) | (~((~($greatereq(tptp_fun_N_6(P), 1) & (~$lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0)))) | coprime(tptp_fun_N_6(P), P))))) <=> (~((~((~prime(P)) | (~((~$greatereq(P, 2)) | (~![N: $int] : (coprime(N, P) | $lesseq($sum(P, $product(-1, N)), 0) | (~$greatereq(N, 1)))))))) | (~(prime(P) | (~$greatereq(P, 2)) | (~($lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0) | coprime(tptp_fun_N_6(P), P) | (~$greatereq(tptp_fun_N_6(P), 1))))))))))),
% 0.97/0.87 inference(bind,[status(th)],[])).
% 0.97/0.87 tff(96,plain,
% 0.97/0.87 (![P: $int] : (((~prime(P)) | ($greatereq(P, 2) & ![N: $int] : ((~($greatereq(N, 1) & (~$lesseq($sum(P, $product(-1, N)), 0)))) | coprime(N, P)))) & (prime(P) | (~$greatereq(P, 2)) | (~((~($greatereq(tptp_fun_N_6(P), 1) & (~$lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0)))) | coprime(tptp_fun_N_6(P), P))))) <=> ![P: $int] : (~((~((~prime(P)) | (~((~$greatereq(P, 2)) | (~![N: $int] : (coprime(N, P) | $lesseq($sum(P, $product(-1, N)), 0) | (~$greatereq(N, 1)))))))) | (~(prime(P) | (~$greatereq(P, 2)) | (~($lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0) | coprime(tptp_fun_N_6(P), P) | (~$greatereq(tptp_fun_N_6(P), 1))))))))),
% 0.97/0.87 inference(quant_intro,[status(thm)],[95])).
% 0.97/0.87 tff(97,plain,
% 0.97/0.87 (^[P: $int] : rewrite((((~prime(P)) | ($greatereq(P, 2) & ![N: $int] : ((~($greatereq(N, 1) & (~$lesseq($sum(P, $product(-1, N)), 0)))) | coprime(N, P)))) & (prime(P) | ((~$greatereq(P, 2)) | (~((~($greatereq(tptp_fun_N_6(P), 1) & (~$lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0)))) | coprime(tptp_fun_N_6(P), P)))))) <=> (((~prime(P)) | ($greatereq(P, 2) & ![N: $int] : ((~($greatereq(N, 1) & (~$lesseq($sum(P, $product(-1, N)), 0)))) | coprime(N, P)))) & (prime(P) | (~$greatereq(P, 2)) | (~((~($greatereq(tptp_fun_N_6(P), 1) & (~$lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0)))) | coprime(tptp_fun_N_6(P), P))))))),
% 0.97/0.87 inference(bind,[status(th)],[])).
% 0.97/0.87 tff(98,plain,
% 0.97/0.87 (![P: $int] : (((~prime(P)) | ($greatereq(P, 2) & ![N: $int] : ((~($greatereq(N, 1) & (~$lesseq($sum(P, $product(-1, N)), 0)))) | coprime(N, P)))) & (prime(P) | ((~$greatereq(P, 2)) | (~((~($greatereq(tptp_fun_N_6(P), 1) & (~$lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0)))) | coprime(tptp_fun_N_6(P), P)))))) <=> ![P: $int] : (((~prime(P)) | ($greatereq(P, 2) & ![N: $int] : ((~($greatereq(N, 1) & (~$lesseq($sum(P, $product(-1, N)), 0)))) | coprime(N, P)))) & (prime(P) | (~$greatereq(P, 2)) | (~((~($greatereq(tptp_fun_N_6(P), 1) & (~$lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0)))) | coprime(tptp_fun_N_6(P), P)))))),
% 0.97/0.87 inference(quant_intro,[status(thm)],[97])).
% 0.97/0.87 tff(99,plain,
% 0.97/0.87 (^[P: $int] : rewrite((prime(P) <=> ($lesseq(2, P) & ![N: $int] : ((~($lesseq(1, N) & (~$lesseq(P, N)))) | coprime(N, P)))) <=> (prime(P) <=> ($greatereq(P, 2) & ![N: $int] : ((~($greatereq(N, 1) & (~$lesseq($sum(P, $product(-1, N)), 0)))) | coprime(N, P)))))),
% 0.97/0.87 inference(bind,[status(th)],[])).
% 0.97/0.87 tff(100,plain,
% 0.97/0.87 (![P: $int] : (prime(P) <=> ($lesseq(2, P) & ![N: $int] : ((~($lesseq(1, N) & (~$lesseq(P, N)))) | coprime(N, P)))) <=> ![P: $int] : (prime(P) <=> ($greatereq(P, 2) & ![N: $int] : ((~($greatereq(N, 1) & (~$lesseq($sum(P, $product(-1, N)), 0)))) | coprime(N, P))))),
% 0.97/0.87 inference(quant_intro,[status(thm)],[99])).
% 0.97/0.87 tff(101,plain,
% 0.97/0.87 (![P: $int] : (prime(P) <=> ($lesseq(2, P) & ![N: $int] : ((~($lesseq(1, N) & (~$lesseq(P, N)))) | coprime(N, P)))) <=> ![P: $int] : (prime(P) <=> ($lesseq(2, P) & ![N: $int] : ((~($lesseq(1, N) & (~$lesseq(P, N)))) | coprime(N, P))))),
% 0.97/0.87 inference(rewrite,[status(thm)],[])).
% 0.97/0.87 tff(102,plain,
% 0.97/0.87 (^[P: $int] : rewrite((prime(P) <=> ($lesseq(2, P) & ![N: $int] : (($lesseq(1, N) & $less(N, P)) => coprime(N, P)))) <=> (prime(P) <=> ($lesseq(2, P) & ![N: $int] : ((~($lesseq(1, N) & (~$lesseq(P, N)))) | coprime(N, P)))))),
% 0.97/0.87 inference(bind,[status(th)],[])).
% 0.97/0.87 tff(103,plain,
% 0.97/0.87 (![P: $int] : (prime(P) <=> ($lesseq(2, P) & ![N: $int] : (($lesseq(1, N) & $less(N, P)) => coprime(N, P)))) <=> ![P: $int] : (prime(P) <=> ($lesseq(2, P) & ![N: $int] : ((~($lesseq(1, N) & (~$lesseq(P, N)))) | coprime(N, P))))),
% 0.97/0.87 inference(quant_intro,[status(thm)],[102])).
% 0.97/0.87 tff(104,axiom,(![P: $int] : (prime(P) <=> ($lesseq(2, P) & ![N: $int] : (($lesseq(1, N) & $less(N, P)) => coprime(N, P))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prime_coprime')).
% 0.97/0.87 tff(105,plain,
% 0.97/0.87 (![P: $int] : (prime(P) <=> ($lesseq(2, P) & ![N: $int] : ((~($lesseq(1, N) & (~$lesseq(P, N)))) | coprime(N, P))))),
% 0.97/0.87 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.97/0.87 tff(106,plain,
% 0.97/0.87 (![P: $int] : (prime(P) <=> ($lesseq(2, P) & ![N: $int] : ((~($lesseq(1, N) & (~$lesseq(P, N)))) | coprime(N, P))))),
% 0.97/0.87 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.97/0.87 tff(107,plain,
% 0.97/0.87 (![P: $int] : (prime(P) <=> ($greatereq(P, 2) & ![N: $int] : ((~($greatereq(N, 1) & (~$lesseq($sum(P, $product(-1, N)), 0)))) | coprime(N, P))))),
% 0.97/0.87 inference(modus_ponens,[status(thm)],[106, 100])).
% 0.97/0.87 tff(108,plain,(
% 0.97/0.87 ![P: $int] : (((~prime(P)) | ($greatereq(P, 2) & ![N: $int] : ((~($greatereq(N, 1) & (~$lesseq($sum(P, $product(-1, N)), 0)))) | coprime(N, P)))) & (prime(P) | ((~$greatereq(P, 2)) | (~((~($greatereq(tptp_fun_N_6(P), 1) & (~$lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0)))) | coprime(tptp_fun_N_6(P), P))))))),
% 0.97/0.87 inference(skolemize,[status(sab)],[107])).
% 0.97/0.87 tff(109,plain,
% 0.97/0.87 (![P: $int] : (((~prime(P)) | ($greatereq(P, 2) & ![N: $int] : ((~($greatereq(N, 1) & (~$lesseq($sum(P, $product(-1, N)), 0)))) | coprime(N, P)))) & (prime(P) | (~$greatereq(P, 2)) | (~((~($greatereq(tptp_fun_N_6(P), 1) & (~$lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0)))) | coprime(tptp_fun_N_6(P), P)))))),
% 0.97/0.87 inference(modus_ponens,[status(thm)],[108, 98])).
% 0.97/0.87 tff(110,plain,
% 0.97/0.87 (![P: $int] : (~((~((~prime(P)) | (~((~$greatereq(P, 2)) | (~![N: $int] : (coprime(N, P) | $lesseq($sum(P, $product(-1, N)), 0) | (~$greatereq(N, 1)))))))) | (~(prime(P) | (~$greatereq(P, 2)) | (~($lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0) | coprime(tptp_fun_N_6(P), P) | (~$greatereq(tptp_fun_N_6(P), 1))))))))),
% 0.97/0.87 inference(modus_ponens,[status(thm)],[109, 96])).
% 0.97/0.87 tff(111,plain,
% 0.97/0.87 (![P: $int] : (~((~((~prime(P)) | (~((~$greatereq(P, 2)) | (~![N: $int] : (coprime(N, P) | $lesseq($sum(P, $product(-1, N)), 0) | (~$greatereq(N, 1)))))))) | (~(prime(P) | (~$greatereq(P, 2)) | (~($lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0) | coprime(tptp_fun_N_6(P), P) | (~$greatereq(tptp_fun_N_6(P), 1))))))))),
% 0.97/0.87 inference(modus_ponens,[status(thm)],[110, 94])).
% 0.97/0.87 tff(112,plain,
% 0.97/0.87 (![P: $int] : (~((~(prime(P) | (~$greatereq(P, 2)) | (~($lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0) | coprime(tptp_fun_N_6(P), P) | (~$greatereq(tptp_fun_N_6(P), 1)))))) | (~((~prime(P)) | (~((~$greatereq(P, 2)) | (~![N: $int] : (coprime(N, P) | $lesseq($sum(P, $product(-1, N)), 0) | (~$greatereq(N, 1))))))))))),
% 0.97/0.87 inference(modus_ponens,[status(thm)],[111, 89])).
% 0.97/0.87 tff(113,plain,
% 0.97/0.87 (((~![P: $int] : (~((~(prime(P) | (~$greatereq(P, 2)) | (~($lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0) | coprime(tptp_fun_N_6(P), P) | (~$greatereq(tptp_fun_N_6(P), 1)))))) | (~((~prime(P)) | (~((~$greatereq(P, 2)) | (~![N: $int] : (coprime(N, P) | $lesseq($sum(P, $product(-1, N)), 0) | (~$greatereq(N, 1))))))))))) | (~((~(prime(I!17) | (~$greatereq(I!17, 2)) | (~($lesseq($sum(I!17, $product(-1, tptp_fun_N_6(I!17))), 0) | coprime(tptp_fun_N_6(I!17), I!17) | (~$greatereq(tptp_fun_N_6(I!17), 1)))))) | (~((~prime(I!17)) | (~((~$greatereq(I!17, 2)) | (~![N: $int] : ((~$greatereq(N, 1)) | coprime(N, I!17) | $greatereq($sum(N, $product(-1, I!17)), 0)))))))))) <=> ((~![P: $int] : (~((~(prime(P) | (~$greatereq(P, 2)) | (~($lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0) | coprime(tptp_fun_N_6(P), P) | (~$greatereq(tptp_fun_N_6(P), 1)))))) | (~((~prime(P)) | (~((~$greatereq(P, 2)) | (~![N: $int] : (coprime(N, P) | $lesseq($sum(P, $product(-1, N)), 0) | (~$greatereq(N, 1))))))))))) | (~((~(prime(I!17) | (~$greatereq(I!17, 2)) | (~($lesseq($sum(I!17, $product(-1, tptp_fun_N_6(I!17))), 0) | coprime(tptp_fun_N_6(I!17), I!17) | (~$greatereq(tptp_fun_N_6(I!17), 1)))))) | (~((~prime(I!17)) | (~((~$greatereq(I!17, 2)) | (~![N: $int] : ((~$greatereq(N, 1)) | coprime(N, I!17) | $greatereq($sum(N, $product(-1, I!17)), 0))))))))))),
% 0.97/0.87 inference(rewrite,[status(thm)],[])).
% 0.97/0.87 tff(114,plain,
% 0.97/0.87 ((~((~(prime(I!17) | (~$greatereq(I!17, 2)) | (~($lesseq($sum(I!17, $product(-1, tptp_fun_N_6(I!17))), 0) | coprime(tptp_fun_N_6(I!17), I!17) | (~$greatereq(tptp_fun_N_6(I!17), 1)))))) | (~((~prime(I!17)) | (~((~$greatereq(I!17, 2)) | (~![N: $int] : (coprime(N, I!17) | $lesseq($sum(I!17, $product(-1, N)), 0) | (~$greatereq(N, 1)))))))))) <=> (~((~(prime(I!17) | (~$greatereq(I!17, 2)) | (~($lesseq($sum(I!17, $product(-1, tptp_fun_N_6(I!17))), 0) | coprime(tptp_fun_N_6(I!17), I!17) | (~$greatereq(tptp_fun_N_6(I!17), 1)))))) | (~((~prime(I!17)) | (~((~$greatereq(I!17, 2)) | (~![N: $int] : ((~$greatereq(N, 1)) | coprime(N, I!17) | $greatereq($sum(N, $product(-1, I!17)), 0)))))))))),
% 0.97/0.87 inference(rewrite,[status(thm)],[])).
% 0.97/0.87 tff(115,plain,
% 0.97/0.87 (((~![P: $int] : (~((~(prime(P) | (~$greatereq(P, 2)) | (~($lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0) | coprime(tptp_fun_N_6(P), P) | (~$greatereq(tptp_fun_N_6(P), 1)))))) | (~((~prime(P)) | (~((~$greatereq(P, 2)) | (~![N: $int] : (coprime(N, P) | $lesseq($sum(P, $product(-1, N)), 0) | (~$greatereq(N, 1))))))))))) | (~((~(prime(I!17) | (~$greatereq(I!17, 2)) | (~($lesseq($sum(I!17, $product(-1, tptp_fun_N_6(I!17))), 0) | coprime(tptp_fun_N_6(I!17), I!17) | (~$greatereq(tptp_fun_N_6(I!17), 1)))))) | (~((~prime(I!17)) | (~((~$greatereq(I!17, 2)) | (~![N: $int] : (coprime(N, I!17) | $lesseq($sum(I!17, $product(-1, N)), 0) | (~$greatereq(N, 1))))))))))) <=> ((~![P: $int] : (~((~(prime(P) | (~$greatereq(P, 2)) | (~($lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0) | coprime(tptp_fun_N_6(P), P) | (~$greatereq(tptp_fun_N_6(P), 1)))))) | (~((~prime(P)) | (~((~$greatereq(P, 2)) | (~![N: $int] : (coprime(N, P) | $lesseq($sum(P, $product(-1, N)), 0) | (~$greatereq(N, 1))))))))))) | (~((~(prime(I!17) | (~$greatereq(I!17, 2)) | (~($lesseq($sum(I!17, $product(-1, tptp_fun_N_6(I!17))), 0) | coprime(tptp_fun_N_6(I!17), I!17) | (~$greatereq(tptp_fun_N_6(I!17), 1)))))) | (~((~prime(I!17)) | (~((~$greatereq(I!17, 2)) | (~![N: $int] : ((~$greatereq(N, 1)) | coprime(N, I!17) | $greatereq($sum(N, $product(-1, I!17)), 0))))))))))),
% 0.97/0.88 inference(monotonicity,[status(thm)],[114])).
% 0.97/0.88 tff(116,plain,
% 0.97/0.88 (((~![P: $int] : (~((~(prime(P) | (~$greatereq(P, 2)) | (~($lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0) | coprime(tptp_fun_N_6(P), P) | (~$greatereq(tptp_fun_N_6(P), 1)))))) | (~((~prime(P)) | (~((~$greatereq(P, 2)) | (~![N: $int] : (coprime(N, P) | $lesseq($sum(P, $product(-1, N)), 0) | (~$greatereq(N, 1))))))))))) | (~((~(prime(I!17) | (~$greatereq(I!17, 2)) | (~($lesseq($sum(I!17, $product(-1, tptp_fun_N_6(I!17))), 0) | coprime(tptp_fun_N_6(I!17), I!17) | (~$greatereq(tptp_fun_N_6(I!17), 1)))))) | (~((~prime(I!17)) | (~((~$greatereq(I!17, 2)) | (~![N: $int] : (coprime(N, I!17) | $lesseq($sum(I!17, $product(-1, N)), 0) | (~$greatereq(N, 1))))))))))) <=> ((~![P: $int] : (~((~(prime(P) | (~$greatereq(P, 2)) | (~($lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0) | coprime(tptp_fun_N_6(P), P) | (~$greatereq(tptp_fun_N_6(P), 1)))))) | (~((~prime(P)) | (~((~$greatereq(P, 2)) | (~![N: $int] : (coprime(N, P) | $lesseq($sum(P, $product(-1, N)), 0) | (~$greatereq(N, 1))))))))))) | (~((~(prime(I!17) | (~$greatereq(I!17, 2)) | (~($lesseq($sum(I!17, $product(-1, tptp_fun_N_6(I!17))), 0) | coprime(tptp_fun_N_6(I!17), I!17) | (~$greatereq(tptp_fun_N_6(I!17), 1)))))) | (~((~prime(I!17)) | (~((~$greatereq(I!17, 2)) | (~![N: $int] : ((~$greatereq(N, 1)) | coprime(N, I!17) | $greatereq($sum(N, $product(-1, I!17)), 0))))))))))),
% 0.97/0.88 inference(transitivity,[status(thm)],[115, 113])).
% 0.97/0.88 tff(117,plain,
% 0.97/0.88 ((~![P: $int] : (~((~(prime(P) | (~$greatereq(P, 2)) | (~($lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0) | coprime(tptp_fun_N_6(P), P) | (~$greatereq(tptp_fun_N_6(P), 1)))))) | (~((~prime(P)) | (~((~$greatereq(P, 2)) | (~![N: $int] : (coprime(N, P) | $lesseq($sum(P, $product(-1, N)), 0) | (~$greatereq(N, 1))))))))))) | (~((~(prime(I!17) | (~$greatereq(I!17, 2)) | (~($lesseq($sum(I!17, $product(-1, tptp_fun_N_6(I!17))), 0) | coprime(tptp_fun_N_6(I!17), I!17) | (~$greatereq(tptp_fun_N_6(I!17), 1)))))) | (~((~prime(I!17)) | (~((~$greatereq(I!17, 2)) | (~![N: $int] : (coprime(N, I!17) | $lesseq($sum(I!17, $product(-1, N)), 0) | (~$greatereq(N, 1))))))))))),
% 0.97/0.88 inference(quant_inst,[status(thm)],[])).
% 0.97/0.88 tff(118,plain,
% 0.97/0.88 ((~![P: $int] : (~((~(prime(P) | (~$greatereq(P, 2)) | (~($lesseq($sum(P, $product(-1, tptp_fun_N_6(P))), 0) | coprime(tptp_fun_N_6(P), P) | (~$greatereq(tptp_fun_N_6(P), 1)))))) | (~((~prime(P)) | (~((~$greatereq(P, 2)) | (~![N: $int] : (coprime(N, P) | $lesseq($sum(P, $product(-1, N)), 0) | (~$greatereq(N, 1))))))))))) | (~((~(prime(I!17) | (~$greatereq(I!17, 2)) | (~($lesseq($sum(I!17, $product(-1, tptp_fun_N_6(I!17))), 0) | coprime(tptp_fun_N_6(I!17), I!17) | (~$greatereq(tptp_fun_N_6(I!17), 1)))))) | (~((~prime(I!17)) | (~((~$greatereq(I!17, 2)) | (~![N: $int] : ((~$greatereq(N, 1)) | coprime(N, I!17) | $greatereq($sum(N, $product(-1, I!17)), 0)))))))))),
% 0.97/0.88 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.97/0.88 tff(119,plain,
% 0.97/0.88 (~((~(prime(I!17) | (~$greatereq(I!17, 2)) | (~($lesseq($sum(I!17, $product(-1, tptp_fun_N_6(I!17))), 0) | coprime(tptp_fun_N_6(I!17), I!17) | (~$greatereq(tptp_fun_N_6(I!17), 1)))))) | (~((~prime(I!17)) | (~((~$greatereq(I!17, 2)) | (~![N: $int] : ((~$greatereq(N, 1)) | coprime(N, I!17) | $greatereq($sum(N, $product(-1, I!17)), 0))))))))),
% 0.97/0.88 inference(unit_resolution,[status(thm)],[118, 112])).
% 0.97/0.88 tff(120,plain,
% 0.97/0.88 (((~(prime(I!17) | (~$greatereq(I!17, 2)) | (~($lesseq($sum(I!17, $product(-1, tptp_fun_N_6(I!17))), 0) | coprime(tptp_fun_N_6(I!17), I!17) | (~$greatereq(tptp_fun_N_6(I!17), 1)))))) | (~((~prime(I!17)) | (~((~$greatereq(I!17, 2)) | (~![N: $int] : ((~$greatereq(N, 1)) | coprime(N, I!17) | $greatereq($sum(N, $product(-1, I!17)), 0)))))))) | ((~prime(I!17)) | (~((~$greatereq(I!17, 2)) | (~![N: $int] : ((~$greatereq(N, 1)) | coprime(N, I!17) | $greatereq($sum(N, $product(-1, I!17)), 0))))))),
% 0.97/0.88 inference(tautology,[status(thm)],[])).
% 0.97/0.88 tff(121,plain,
% 0.97/0.88 ((~prime(I!17)) | (~((~$greatereq(I!17, 2)) | (~![N: $int] : ((~$greatereq(N, 1)) | coprime(N, I!17) | $greatereq($sum(N, $product(-1, I!17)), 0)))))),
% 0.97/0.88 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.97/0.88 tff(122,plain,
% 0.97/0.88 (prime(I!17) & divides(I!17, N!7) & (~$greatereq($sum(D1!13, $product(-1, I!17)), 0))),
% 0.97/0.88 inference(or_elim,[status(thm)],[66])).
% 0.97/0.88 tff(123,plain,
% 0.97/0.88 (prime(I!17)),
% 0.97/0.88 inference(and_elim,[status(thm)],[122])).
% 0.97/0.88 tff(124,plain,
% 0.97/0.88 ((~((~prime(I!17)) | (~((~$greatereq(I!17, 2)) | (~![N: $int] : ((~$greatereq(N, 1)) | coprime(N, I!17) | $greatereq($sum(N, $product(-1, I!17)), 0))))))) | (~prime(I!17)) | (~((~$greatereq(I!17, 2)) | (~![N: $int] : ((~$greatereq(N, 1)) | coprime(N, I!17) | $greatereq($sum(N, $product(-1, I!17)), 0)))))),
% 0.97/0.88 inference(tautology,[status(thm)],[])).
% 0.97/0.88 tff(125,plain,
% 0.97/0.88 ((~((~prime(I!17)) | (~((~$greatereq(I!17, 2)) | (~![N: $int] : ((~$greatereq(N, 1)) | coprime(N, I!17) | $greatereq($sum(N, $product(-1, I!17)), 0))))))) | (~((~$greatereq(I!17, 2)) | (~![N: $int] : ((~$greatereq(N, 1)) | coprime(N, I!17) | $greatereq($sum(N, $product(-1, I!17)), 0)))))),
% 0.97/0.88 inference(unit_resolution,[status(thm)],[124, 123])).
% 0.97/0.88 tff(126,plain,
% 0.97/0.88 (~((~$greatereq(I!17, 2)) | (~![N: $int] : ((~$greatereq(N, 1)) | coprime(N, I!17) | $greatereq($sum(N, $product(-1, I!17)), 0))))),
% 0.97/0.88 inference(unit_resolution,[status(thm)],[125, 121])).
% 0.97/0.88 tff(127,plain,
% 0.97/0.88 (((~$greatereq(I!17, 2)) | (~![N: $int] : ((~$greatereq(N, 1)) | coprime(N, I!17) | $greatereq($sum(N, $product(-1, I!17)), 0)))) | ![N: $int] : ((~$greatereq(N, 1)) | coprime(N, I!17) | $greatereq($sum(N, $product(-1, I!17)), 0))),
% 0.97/0.88 inference(tautology,[status(thm)],[])).
% 0.97/0.88 tff(128,plain,
% 0.97/0.88 (![N: $int] : ((~$greatereq(N, 1)) | coprime(N, I!17) | $greatereq($sum(N, $product(-1, I!17)), 0))),
% 0.97/0.88 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.97/0.88 tff(129,plain,
% 0.97/0.88 (((~![N: $int] : ((~$greatereq(N, 1)) | coprime(N, I!17) | $greatereq($sum(N, $product(-1, I!17)), 0))) | ((~$greatereq(ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)), 1)) | coprime(ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)), I!17) | $lesseq($sum(I!17, $product(-1, ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)))), 0))) <=> ((~![N: $int] : ((~$greatereq(N, 1)) | coprime(N, I!17) | $greatereq($sum(N, $product(-1, I!17)), 0))) | (~$greatereq(ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)), 1)) | coprime(ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)), I!17) | $lesseq($sum(I!17, $product(-1, ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)))), 0))),
% 0.97/0.88 inference(rewrite,[status(thm)],[])).
% 0.97/0.88 tff(130,plain,
% 0.97/0.88 (((~$greatereq(ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)), 1)) | coprime(ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)), I!17) | $greatereq($sum(ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)), $product(-1, I!17)), 0)) <=> ((~$greatereq(ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)), 1)) | coprime(ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)), I!17) | $lesseq($sum(I!17, $product(-1, ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)))), 0))),
% 0.97/0.88 inference(rewrite,[status(thm)],[])).
% 0.97/0.88 tff(131,plain,
% 0.97/0.88 (((~![N: $int] : ((~$greatereq(N, 1)) | coprime(N, I!17) | $greatereq($sum(N, $product(-1, I!17)), 0))) | ((~$greatereq(ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)), 1)) | coprime(ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)), I!17) | $greatereq($sum(ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)), $product(-1, I!17)), 0))) <=> ((~![N: $int] : ((~$greatereq(N, 1)) | coprime(N, I!17) | $greatereq($sum(N, $product(-1, I!17)), 0))) | ((~$greatereq(ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)), 1)) | coprime(ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)), I!17) | $lesseq($sum(I!17, $product(-1, ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)))), 0)))),
% 0.97/0.88 inference(monotonicity,[status(thm)],[130])).
% 0.97/0.88 tff(132,plain,
% 0.97/0.88 (((~![N: $int] : ((~$greatereq(N, 1)) | coprime(N, I!17) | $greatereq($sum(N, $product(-1, I!17)), 0))) | ((~$greatereq(ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)), 1)) | coprime(ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)), I!17) | $greatereq($sum(ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)), $product(-1, I!17)), 0))) <=> ((~![N: $int] : ((~$greatereq(N, 1)) | coprime(N, I!17) | $greatereq($sum(N, $product(-1, I!17)), 0))) | (~$greatereq(ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)), 1)) | coprime(ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)), I!17) | $lesseq($sum(I!17, $product(-1, ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)))), 0))),
% 0.97/0.88 inference(transitivity,[status(thm)],[131, 129])).
% 0.97/0.88 tff(133,plain,
% 0.97/0.88 ((~![N: $int] : ((~$greatereq(N, 1)) | coprime(N, I!17) | $greatereq($sum(N, $product(-1, I!17)), 0))) | ((~$greatereq(ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)), 1)) | coprime(ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)), I!17) | $greatereq($sum(ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)), $product(-1, I!17)), 0))),
% 0.97/0.88 inference(quant_inst,[status(thm)],[])).
% 0.97/0.88 tff(134,plain,
% 0.97/0.88 ((~![N: $int] : ((~$greatereq(N, 1)) | coprime(N, I!17) | $greatereq($sum(N, $product(-1, I!17)), 0))) | (~$greatereq(ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)), 1)) | coprime(ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)), I!17) | $lesseq($sum(I!17, $product(-1, ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)))), 0)),
% 0.97/0.88 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.97/0.88 tff(135,plain,
% 0.97/0.88 ((~$greatereq(ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)), 1)) | coprime(ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)), I!17) | $lesseq($sum(I!17, $product(-1, ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)))), 0)),
% 0.97/0.88 inference(unit_resolution,[status(thm)],[134, 128])).
% 0.97/0.88 tff(136,plain,
% 0.97/0.88 ($lesseq($sum(I!17, $product(-1, ite_t($greatereq(D1!13, 0), D1!13, $product(-1, D1!13)))), 0)),
% 0.97/0.88 inference(unit_resolution,[status(thm)],[135, 87, 81])).
% 0.97/0.88 tff(137,plain,
% 0.97/0.88 ($false),
% 0.97/0.88 inference(theory_lemma,[status(thm)],[136, 75, 68])).
% 0.97/0.88 % SZS output end Proof
%------------------------------------------------------------------------------