%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : TOP052-1 : TPTP v9.0.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n002.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 : Tue Jul 15 08:44:18 AM UTC 2025
% Result : Unsatisfiable 74.16s 74.33s
% Output : CNFRefutation 74.16s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
tuple(a1,a2,a41,a42,a3,a40,a4,a13,a14,a5,a38,a39,a6,a135,a136,a7,a52,a51,a8,a16,a17,a9,a55,a56,a10,a133,a134,a11,a36,a37,a12,a21,a20,a23,a31,a32,a15,a53,a28,a29,a18,a132,a19,a58,a57,a20,a25,a26,a34,a35,a140,a44,a45,a24,a48,a49,a138,a137,a27,a30,a33,a130,a131,a59,a60,a139,a46,a47,a43,a61,a62,a127,a128,a50,a54,a63,a95,a96,a64,a126,a65,a66,a67,a91,a92,a68,a97,a98,a69,a70,a71,a118,a117,a72,a108,a109,a73,a81,a82,a74,a75,a76,a77,a113,a114,a78,a79,a80,a119,a83,a84,a85,a86,a87,a103,a104,a88,a89,a90,a99,a100,a123,a124,a93,a94,a101,a102,a105,a106,a107,a110,a111,a112,a115,a116,a120,a121,a122,a125,a129) != tuple(a2,a3,a42,a43,a4,a41,a5,a14,a15,a6,a39,a40,a7,a136,a137,a8,a53,a52,a9,a17,a18,a10,a56,a57,a11,a134,a135,a12,a37,a38,a13,a23,a21,a24,a32,a33,a16,a54,a29,a30,a19,a133,a20,a59,a58,a22,a26,a27,a35,a36,a141,a45,a46,a25,a49,a50,a139,a138,a28,a31,a34,a131,a132,a60,a61,a140,a47,a48,a44,a62,a63,a128,a129,a51,a55,a64,a96,a97,a65,a127,a66,a67,a68,a92,a93,a69,a98,a99,a70,a71,a72,a119,a118,a73,a109,a110,a74,a82,a83,a75,a76,a77,a78,a114,a115,a79,a80,a81,a120,a84,a85,a86,a87,a88,a104,a105,a89,a90,a91,a100,a101,a124,a125,a94,a95,a102,a103,a106,a107,a108,a111,a112,a113,a116,a117,a121,a122,a123,a126,a130),
file('theBenchmark.p',goal) ).
cnf(c1,axiom,
product(X,X) = X,
file('theBenchmark.p',involutory_quandle) ).
cnf(c2,axiom,
a2 = product(a1,a42),
file('theBenchmark.p',knot) ).
cnf(c3,plain,
product(a1,a42) = a2,
inference(equational,[status(thm)],[c2]) ).
cnf(c4,axiom,
a3 = product(a2,a41),
file('theBenchmark.p',knot_03) ).
cnf(c5,plain,
product(a2,a41) = a3,
inference(equational,[status(thm)],[c4]) ).
cnf(c6,axiom,
a4 = product(a3,a14),
file('theBenchmark.p',knot_04) ).
cnf(c7,plain,
product(a3,a14) = a4,
inference(equational,[status(thm)],[c6]) ).
cnf(c8,axiom,
a5 = product(a4,a39),
file('theBenchmark.p',knot_05) ).
cnf(c9,plain,
product(a4,a39) = a5,
inference(equational,[status(thm)],[c8]) ).
cnf(c10,axiom,
a6 = product(a5,a136),
file('theBenchmark.p',knot_06) ).
cnf(c11,plain,
product(a5,a136) = a6,
inference(equational,[status(thm)],[c10]) ).
cnf(c12,axiom,
a7 = product(a6,a52),
file('theBenchmark.p',knot_07) ).
cnf(c13,plain,
product(a6,a52) = a7,
inference(equational,[status(thm)],[c12]) ).
cnf(c14,axiom,
a8 = product(a7,a17),
file('theBenchmark.p',knot_08) ).
cnf(c15,plain,
product(a7,a17) = a8,
inference(equational,[status(thm)],[c14]) ).
cnf(c16,axiom,
a9 = product(a8,a56),
file('theBenchmark.p',knot_09) ).
cnf(c17,plain,
product(a8,a56) = a9,
inference(equational,[status(thm)],[c16]) ).
cnf(c18,axiom,
a10 = product(a9,a134),
file('theBenchmark.p',knot_10) ).
cnf(c19,plain,
product(a9,a134) = a10,
inference(equational,[status(thm)],[c18]) ).
cnf(c20,axiom,
a11 = product(a10,a37),
file('theBenchmark.p',knot_11) ).
cnf(c21,plain,
product(a10,a37) = a11,
inference(equational,[status(thm)],[c20]) ).
cnf(c22,axiom,
a12 = product(a11,a21),
file('theBenchmark.p',knot_12) ).
cnf(c23,plain,
product(a11,a21) = a12,
inference(equational,[status(thm)],[c22]) ).
cnf(c24,axiom,
a13 = product(a12,a23),
file('theBenchmark.p',knot_13) ).
cnf(c25,plain,
product(a12,a23) = a13,
inference(equational,[status(thm)],[c24]) ).
cnf(c26,axiom,
a14 = product(a13,a32),
file('theBenchmark.p',knot_14) ).
cnf(c27,plain,
product(a13,a32) = a14,
inference(equational,[status(thm)],[c26]) ).
cnf(c28,axiom,
a15 = product(a14,a53),
file('theBenchmark.p',knot_15) ).
cnf(c29,plain,
product(a14,a53) = a15,
inference(equational,[status(thm)],[c28]) ).
cnf(c30,axiom,
a16 = product(a15,a136),
file('theBenchmark.p',knot_16) ).
cnf(c31,plain,
product(a15,a136) = a16,
inference(equational,[status(thm)],[c30]) ).
cnf(c32,axiom,
a17 = product(a16,a29),
file('theBenchmark.p',knot_17) ).
cnf(c33,plain,
product(a16,a29) = a17,
inference(equational,[status(thm)],[c32]) ).
cnf(c34,axiom,
a18 = product(a17,a133),
file('theBenchmark.p',knot_18) ).
cnf(c35,plain,
product(a17,a133) = a18,
inference(equational,[status(thm)],[c34]) ).
cnf(c36,axiom,
a19 = product(a18,a58),
file('theBenchmark.p',knot_19) ).
cnf(c37,plain,
product(a18,a58) = a19,
inference(equational,[status(thm)],[c36]) ).
cnf(c38,axiom,
a20 = product(a19,a26),
file('theBenchmark.p',knot_20) ).
cnf(c39,plain,
product(a19,a26) = a20,
inference(equational,[status(thm)],[c38]) ).
cnf(c40,axiom,
a21 = product(a20,a35),
file('theBenchmark.p',knot_21) ).
cnf(c41,plain,
product(a20,a35) = a21,
inference(equational,[status(thm)],[c40]) ).
cnf(c42,axiom,
a22 = product(a21,a141),
file('theBenchmark.p',knot_22) ).
cnf(c43,plain,
product(a21,a141) = a22,
inference(equational,[status(thm)],[c42]) ).
cnf(c44,axiom,
a23 = product(a22,a45),
file('theBenchmark.p',knot_23) ).
cnf(c45,plain,
product(a22,a45) = a23,
inference(equational,[status(thm)],[c44]) ).
cnf(c46,axiom,
a24 = product(a23,a35),
file('theBenchmark.p',knot_24) ).
cnf(c47,plain,
product(a23,a35) = a24,
inference(equational,[status(thm)],[c46]) ).
cnf(c48,axiom,
a25 = product(a24,a49),
file('theBenchmark.p',knot_25) ).
cnf(c49,plain,
product(a24,a49) = a25,
inference(equational,[status(thm)],[c48]) ).
cnf(c50,axiom,
a26 = product(a25,a138),
file('theBenchmark.p',knot_26) ).
cnf(c51,plain,
product(a25,a138) = a26,
inference(equational,[status(thm)],[c50]) ).
cnf(c52,axiom,
a27 = product(a26,a8),
file('theBenchmark.p',knot_27) ).
cnf(c53,plain,
product(a26,a8) = a27,
inference(equational,[status(thm)],[c52]) ).
cnf(c54,axiom,
a28 = product(a27,a37),
file('theBenchmark.p',knot_28) ).
cnf(c55,plain,
product(a27,a37) = a28,
inference(equational,[status(thm)],[c54]) ).
cnf(c56,axiom,
a29 = product(a28,a17),
file('theBenchmark.p',knot_29) ).
cnf(c57,plain,
product(a28,a17) = a29,
inference(equational,[status(thm)],[c56]) ).
cnf(c58,axiom,
a30 = product(a29,a14),
file('theBenchmark.p',knot_30) ).
cnf(c59,plain,
product(a29,a14) = a30,
inference(equational,[status(thm)],[c58]) ).
cnf(c60,axiom,
a31 = product(a30,a5),
file('theBenchmark.p',knot_31) ).
cnf(c61,plain,
product(a30,a5) = a31,
inference(equational,[status(thm)],[c60]) ).
cnf(c62,axiom,
a32 = product(a31,a39),
file('theBenchmark.p',knot_32) ).
cnf(c63,plain,
product(a31,a39) = a32,
inference(equational,[status(thm)],[c62]) ).
cnf(c64,axiom,
a33 = product(a32,a13),
file('theBenchmark.p',knot_33) ).
cnf(c65,plain,
product(a32,a13) = a33,
inference(equational,[status(thm)],[c64]) ).
cnf(c66,axiom,
a34 = product(a33,a131),
file('theBenchmark.p',knot_34) ).
cnf(c67,plain,
product(a33,a131) = a34,
inference(equational,[status(thm)],[c66]) ).
cnf(c68,axiom,
a35 = product(a34,a60),
file('theBenchmark.p',knot_35) ).
cnf(c69,plain,
product(a34,a60) = a35,
inference(equational,[status(thm)],[c68]) ).
cnf(c70,axiom,
a36 = product(a35,a139),
file('theBenchmark.p',knot_36) ).
cnf(c71,plain,
product(a35,a139) = a36,
inference(equational,[status(thm)],[c70]) ).
cnf(c72,axiom,
a37 = product(a36,a47),
file('theBenchmark.p',knot_37) ).
cnf(c73,plain,
product(a36,a47) = a37,
inference(equational,[status(thm)],[c72]) ).
cnf(c74,axiom,
a38 = product(a37,a17),
file('theBenchmark.p',knot_38) ).
cnf(c75,plain,
product(a37,a17) = a38,
inference(equational,[status(thm)],[c74]) ).
cnf(c76,axiom,
a39 = product(a38,a7),
file('theBenchmark.p',knot_39) ).
cnf(c77,plain,
product(a38,a7) = a39,
inference(equational,[status(thm)],[c76]) ).
cnf(c78,axiom,
a40 = product(a39,a4),
file('theBenchmark.p',knot_40) ).
cnf(c79,plain,
product(a39,a4) = a40,
inference(equational,[status(thm)],[c78]) ).
cnf(c80,axiom,
a41 = product(a40,a14),
file('theBenchmark.p',knot_41) ).
cnf(c81,plain,
product(a40,a14) = a41,
inference(equational,[status(thm)],[c80]) ).
cnf(c82,axiom,
a42 = product(a41,a2),
file('theBenchmark.p',knot_42) ).
cnf(c83,plain,
product(a41,a2) = a42,
inference(equational,[status(thm)],[c82]) ).
cnf(c84,axiom,
a43 = product(a42,a62),
file('theBenchmark.p',knot_43) ).
cnf(c85,plain,
product(a42,a62) = a43,
inference(equational,[status(thm)],[c84]) ).
cnf(c86,axiom,
a44 = product(a43,a128),
file('theBenchmark.p',knot_44) ).
cnf(c87,plain,
product(a43,a128) = a44,
inference(equational,[status(thm)],[c86]) ).
cnf(c88,axiom,
a45 = product(a44,a23),
file('theBenchmark.p',knot_45) ).
cnf(c89,plain,
product(a44,a23) = a45,
inference(equational,[status(thm)],[c88]) ).
cnf(c90,axiom,
a46 = product(a45,a141),
file('theBenchmark.p',knot_46) ).
cnf(c91,plain,
product(a45,a141) = a46,
inference(equational,[status(thm)],[c90]) ).
cnf(c92,axiom,
a47 = product(a46,a11),
file('theBenchmark.p',knot_47) ).
cnf(c93,plain,
product(a46,a11) = a47,
inference(equational,[status(thm)],[c92]) ).
cnf(c94,axiom,
a48 = product(a47,a20),
file('theBenchmark.p',knot_48) ).
cnf(c95,plain,
product(a47,a20) = a48,
inference(equational,[status(thm)],[c94]) ).
cnf(c96,axiom,
a49 = product(a48,a138),
file('theBenchmark.p',knot_49) ).
cnf(c97,plain,
product(a48,a138) = a49,
inference(equational,[status(thm)],[c96]) ).
cnf(c98,axiom,
a50 = product(a49,a131),
file('theBenchmark.p',knot_50) ).
cnf(c99,plain,
product(a49,a131) = a50,
inference(equational,[status(thm)],[c98]) ).
cnf(c100,axiom,
a51 = product(a50,a59),
file('theBenchmark.p',knot_51) ).
cnf(c101,plain,
product(a50,a59) = a51,
inference(equational,[status(thm)],[c100]) ).
cnf(c102,axiom,
a52 = product(a51,a39),
file('theBenchmark.p',knot_52) ).
cnf(c103,plain,
product(a51,a39) = a52,
inference(equational,[status(thm)],[c102]) ).
cnf(c104,axiom,
a53 = product(a52,a136),
file('theBenchmark.p',knot_53) ).
cnf(c105,plain,
product(a52,a136) = a53,
inference(equational,[status(thm)],[c104]) ).
cnf(c106,axiom,
a54 = product(a53,a29),
file('theBenchmark.p',knot_54) ).
cnf(c107,plain,
product(a53,a29) = a54,
inference(equational,[status(thm)],[c106]) ).
cnf(c108,axiom,
a55 = product(a54,a135),
file('theBenchmark.p',knot_55) ).
cnf(c109,plain,
product(a54,a135) = a55,
inference(equational,[status(thm)],[c108]) ).
cnf(c110,axiom,
a56 = product(a55,a37),
file('theBenchmark.p',knot_56) ).
cnf(c111,plain,
product(a55,a37) = a56,
inference(equational,[status(thm)],[c110]) ).
cnf(c112,axiom,
a57 = product(a56,a134),
file('theBenchmark.p',knot_57) ).
cnf(c113,plain,
product(a56,a134) = a57,
inference(equational,[status(thm)],[c112]) ).
cnf(c114,axiom,
a58 = product(a57,a26),
file('theBenchmark.p',knot_58) ).
cnf(c115,plain,
product(a57,a26) = a58,
inference(equational,[status(thm)],[c114]) ).
cnf(c116,axiom,
a59 = product(a58,a138),
file('theBenchmark.p',knot_59) ).
cnf(c117,plain,
product(a58,a138) = a59,
inference(equational,[status(thm)],[c116]) ).
cnf(c118,axiom,
a60 = product(a59,a131),
file('theBenchmark.p',knot_60) ).
cnf(c119,plain,
product(a59,a131) = a60,
inference(equational,[status(thm)],[c118]) ).
cnf(c120,axiom,
a61 = product(a60,a13),
file('theBenchmark.p',knot_61) ).
cnf(c121,plain,
product(a60,a13) = a61,
inference(equational,[status(thm)],[c120]) ).
cnf(c122,axiom,
a62 = product(a61,a1),
file('theBenchmark.p',knot_62) ).
cnf(c123,plain,
product(a61,a1) = a62,
inference(equational,[status(thm)],[c122]) ).
cnf(c124,axiom,
a63 = product(a62,a96),
file('theBenchmark.p',knot_63) ).
cnf(c125,plain,
product(a62,a96) = a63,
inference(equational,[status(thm)],[c124]) ).
cnf(c126,axiom,
a64 = product(a63,a127),
file('theBenchmark.p',knot_64) ).
cnf(c127,plain,
product(a63,a127) = a64,
inference(equational,[status(thm)],[c126]) ).
cnf(c128,axiom,
a65 = product(a64,a41),
file('theBenchmark.p',knot_65) ).
cnf(c129,plain,
product(a64,a41) = a65,
inference(equational,[status(thm)],[c128]) ).
cnf(c130,axiom,
a66 = product(a65,a2),
file('theBenchmark.p',knot_66) ).
cnf(c131,plain,
product(a65,a2) = a66,
inference(equational,[status(thm)],[c130]) ).
cnf(c132,axiom,
a67 = product(a66,a92),
file('theBenchmark.p',knot_67) ).
cnf(c133,plain,
product(a66,a92) = a67,
inference(equational,[status(thm)],[c132]) ).
cnf(c134,axiom,
a68 = product(a67,a98),
file('theBenchmark.p',knot_68) ).
cnf(c135,plain,
product(a67,a98) = a68,
inference(equational,[status(thm)],[c134]) ).
cnf(c136,axiom,
a69 = product(a68,a32),
file('theBenchmark.p',knot_69) ).
cnf(c137,plain,
product(a68,a32) = a69,
inference(equational,[status(thm)],[c136]) ).
cnf(c138,axiom,
a70 = product(a69,a13),
file('theBenchmark.p',knot_70) ).
cnf(c139,plain,
product(a69,a13) = a70,
inference(equational,[status(thm)],[c138]) ).
cnf(c140,axiom,
a71 = product(a70,a118),
file('theBenchmark.p',knot_71) ).
cnf(c141,plain,
product(a70,a118) = a71,
inference(equational,[status(thm)],[c140]) ).
cnf(c142,axiom,
a72 = product(a71,a109),
file('theBenchmark.p',knot_72) ).
cnf(c143,plain,
product(a71,a109) = a72,
inference(equational,[status(thm)],[c142]) ).
cnf(c144,axiom,
a73 = product(a72,a82),
file('theBenchmark.p',knot_73) ).
cnf(c145,plain,
product(a72,a82) = a73,
inference(equational,[status(thm)],[c144]) ).
cnf(c146,axiom,
a74 = product(a73,a32),
file('theBenchmark.p',knot_74) ).
cnf(c147,plain,
product(a73,a32) = a74,
inference(equational,[status(thm)],[c146]) ).
cnf(c148,axiom,
a75 = product(a74,a14),
file('theBenchmark.p',knot_75) ).
cnf(c149,plain,
product(a74,a14) = a75,
inference(equational,[status(thm)],[c148]) ).
cnf(c150,axiom,
a76 = product(a75,a68),
file('theBenchmark.p',knot_76) ).
cnf(c151,plain,
product(a75,a68) = a76,
inference(equational,[status(thm)],[c150]) ).
cnf(c152,axiom,
a77 = product(a76,a114),
file('theBenchmark.p',knot_77) ).
cnf(c153,plain,
product(a76,a114) = a77,
inference(equational,[status(thm)],[c152]) ).
cnf(c154,axiom,
a78 = product(a77,a13),
file('theBenchmark.p',knot_78) ).
cnf(c155,plain,
product(a77,a13) = a78,
inference(equational,[status(thm)],[c154]) ).
cnf(c156,axiom,
a79 = product(a78,a33),
file('theBenchmark.p',knot_79) ).
cnf(c157,plain,
product(a78,a33) = a79,
inference(equational,[status(thm)],[c156]) ).
cnf(c158,axiom,
a80 = product(a79,a119),
file('theBenchmark.p',knot_80) ).
cnf(c159,plain,
product(a79,a119) = a80,
inference(equational,[status(thm)],[c158]) ).
cnf(c160,axiom,
a81 = product(a80,a70),
file('theBenchmark.p',knot_81) ).
cnf(c161,plain,
product(a80,a70) = a81,
inference(equational,[status(thm)],[c160]) ).
cnf(c162,axiom,
a82 = product(a81,a109),
file('theBenchmark.p',knot_82) ).
cnf(c163,plain,
product(a81,a109) = a82,
inference(equational,[status(thm)],[c162]) ).
cnf(c164,axiom,
a83 = product(a82,a118),
file('theBenchmark.p',knot_83) ).
cnf(c165,plain,
product(a82,a118) = a83,
inference(equational,[status(thm)],[c164]) ).
cnf(c166,axiom,
a84 = product(a83,a39),
file('theBenchmark.p',knot_84) ).
cnf(c167,plain,
product(a83,a39) = a84,
inference(equational,[status(thm)],[c166]) ).
cnf(c168,axiom,
a85 = product(a84,a5),
file('theBenchmark.p',knot_85) ).
cnf(c169,plain,
product(a84,a5) = a85,
inference(equational,[status(thm)],[c168]) ).
cnf(c170,axiom,
a86 = product(a85,a30),
file('theBenchmark.p',knot_86) ).
cnf(c171,plain,
product(a85,a30) = a86,
inference(equational,[status(thm)],[c170]) ).
cnf(c172,axiom,
a87 = product(a86,a104),
file('theBenchmark.p',knot_87) ).
cnf(c173,plain,
product(a86,a104) = a87,
inference(equational,[status(thm)],[c172]) ).
cnf(c174,axiom,
a88 = product(a87,a4),
file('theBenchmark.p',knot_88) ).
cnf(c175,plain,
product(a87,a4) = a88,
inference(equational,[status(thm)],[c174]) ).
cnf(c176,axiom,
a89 = product(a88,a14),
file('theBenchmark.p',knot_89) ).
cnf(c177,plain,
product(a88,a14) = a89,
inference(equational,[status(thm)],[c176]) ).
cnf(c178,axiom,
a90 = product(a89,a41),
file('theBenchmark.p',knot_90) ).
cnf(c179,plain,
product(a89,a41) = a90,
inference(equational,[status(thm)],[c178]) ).
cnf(c180,axiom,
a91 = product(a90,a100),
file('theBenchmark.p',knot_91) ).
cnf(c181,plain,
product(a90,a100) = a91,
inference(equational,[status(thm)],[c180]) ).
cnf(c182,axiom,
a92 = product(a91,a124),
file('theBenchmark.p',knot_92) ).
cnf(c183,plain,
product(a91,a124) = a92,
inference(equational,[status(thm)],[c182]) ).
cnf(c184,axiom,
a93 = product(a92,a2),
file('theBenchmark.p',knot_93) ).
cnf(c185,plain,
product(a92,a2) = a93,
inference(equational,[status(thm)],[c184]) ).
cnf(c186,axiom,
a94 = product(a93,a41),
file('theBenchmark.p',knot_94) ).
cnf(c187,plain,
product(a93,a41) = a94,
inference(equational,[status(thm)],[c186]) ).
cnf(c188,axiom,
a95 = product(a94,a127),
file('theBenchmark.p',knot_95) ).
cnf(c189,plain,
product(a94,a127) = a95,
inference(equational,[status(thm)],[c188]) ).
cnf(c190,axiom,
a96 = product(a95,a64),
file('theBenchmark.p',knot_96) ).
cnf(c191,plain,
product(a95,a64) = a96,
inference(equational,[status(thm)],[c190]) ).
cnf(c192,axiom,
a97 = product(a96,a42),
file('theBenchmark.p',knot_97) ).
cnf(c193,plain,
product(a96,a42) = a97,
inference(equational,[status(thm)],[c192]) ).
cnf(c194,axiom,
a98 = product(a97,a1),
file('theBenchmark.p',knot_98) ).
cnf(c195,plain,
product(a97,a1) = a98,
inference(equational,[status(thm)],[c194]) ).
cnf(c196,axiom,
a99 = product(a98,a92),
file('theBenchmark.p',knot_99) ).
cnf(c197,plain,
product(a98,a92) = a99,
inference(equational,[status(thm)],[c196]) ).
cnf(c198,axiom,
a100 = product(a99,a124),
file('theBenchmark.p',knot_100) ).
cnf(c199,plain,
product(a99,a124) = a100,
inference(equational,[status(thm)],[c198]) ).
cnf(c200,axiom,
a101 = product(a100,a14),
file('theBenchmark.p',knot_101) ).
cnf(c201,plain,
product(a100,a14) = a101,
inference(equational,[status(thm)],[c200]) ).
cnf(c202,axiom,
a102 = product(a101,a40),
file('theBenchmark.p',knot_102) ).
cnf(c203,plain,
product(a101,a40) = a102,
inference(equational,[status(thm)],[c202]) ).
cnf(c204,axiom,
a103 = product(a102,a4),
file('theBenchmark.p',knot_103) ).
cnf(c205,plain,
product(a102,a4) = a103,
inference(equational,[status(thm)],[c204]) ).
cnf(c206,axiom,
a104 = product(a103,a87),
file('theBenchmark.p',knot_104) ).
cnf(c207,plain,
product(a103,a87) = a104,
inference(equational,[status(thm)],[c206]) ).
cnf(c208,axiom,
a105 = product(a104,a30),
file('theBenchmark.p',knot_105) ).
cnf(c209,plain,
product(a104,a30) = a105,
inference(equational,[status(thm)],[c208]) ).
cnf(c210,axiom,
a106 = product(a105,a5),
file('theBenchmark.p',knot_106) ).
cnf(c211,plain,
product(a105,a5) = a106,
inference(equational,[status(thm)],[c210]) ).
cnf(c212,axiom,
a107 = product(a106,a84),
file('theBenchmark.p',knot_107) ).
cnf(c213,plain,
product(a106,a84) = a107,
inference(equational,[status(thm)],[c212]) ).
cnf(c214,axiom,
a108 = product(a107,a39),
file('theBenchmark.p',knot_108) ).
cnf(c215,plain,
product(a107,a39) = a108,
inference(equational,[status(thm)],[c214]) ).
cnf(c216,axiom,
a109 = product(a108,a118),
file('theBenchmark.p',knot_109) ).
cnf(c217,plain,
product(a108,a118) = a109,
inference(equational,[status(thm)],[c216]) ).
cnf(c218,axiom,
a110 = product(a109,a70),
file('theBenchmark.p',knot_110) ).
cnf(c219,plain,
product(a109,a70) = a110,
inference(equational,[status(thm)],[c218]) ).
cnf(c220,axiom,
a111 = product(a110,a119),
file('theBenchmark.p',knot_111) ).
cnf(c221,plain,
product(a110,a119) = a111,
inference(equational,[status(thm)],[c220]) ).
cnf(c222,axiom,
a112 = product(a111,a79),
file('theBenchmark.p',knot_112) ).
cnf(c223,plain,
product(a111,a79) = a112,
inference(equational,[status(thm)],[c222]) ).
cnf(c224,axiom,
a113 = product(a112,a33),
file('theBenchmark.p',knot_113) ).
cnf(c225,plain,
product(a112,a33) = a113,
inference(equational,[status(thm)],[c224]) ).
cnf(c226,axiom,
a114 = product(a113,a13),
file('theBenchmark.p',knot_114) ).
cnf(c227,plain,
product(a113,a13) = a114,
inference(equational,[status(thm)],[c226]) ).
cnf(c228,axiom,
a115 = product(a114,a68),
file('theBenchmark.p',knot_115) ).
cnf(c229,plain,
product(a114,a68) = a115,
inference(equational,[status(thm)],[c228]) ).
cnf(c230,axiom,
a116 = product(a115,a14),
file('theBenchmark.p',knot_116) ).
cnf(c231,plain,
product(a115,a14) = a116,
inference(equational,[status(thm)],[c230]) ).
cnf(c232,axiom,
a117 = product(a116,a74),
file('theBenchmark.p',knot_117) ).
cnf(c233,plain,
product(a116,a74) = a117,
inference(equational,[status(thm)],[c232]) ).
cnf(c234,axiom,
a118 = product(a117,a32),
file('theBenchmark.p',knot_118) ).
cnf(c235,plain,
product(a117,a32) = a118,
inference(equational,[status(thm)],[c234]) ).
cnf(c236,axiom,
a119 = product(a118,a70),
file('theBenchmark.p',knot_119) ).
cnf(c237,plain,
product(a118,a70) = a119,
inference(equational,[status(thm)],[c236]) ).
cnf(c238,axiom,
a120 = product(a119,a13),
file('theBenchmark.p',knot_120) ).
cnf(c239,plain,
product(a119,a13) = a120,
inference(equational,[status(thm)],[c238]) ).
cnf(c240,axiom,
a121 = product(a120,a32),
file('theBenchmark.p',knot_121) ).
cnf(c241,plain,
product(a120,a32) = a121,
inference(equational,[status(thm)],[c240]) ).
cnf(c242,axiom,
a122 = product(a121,a68),
file('theBenchmark.p',knot_122) ).
cnf(c243,plain,
product(a121,a68) = a122,
inference(equational,[status(thm)],[c242]) ).
cnf(c244,axiom,
a123 = product(a122,a115),
file('theBenchmark.p',knot_123) ).
cnf(c245,plain,
product(a122,a115) = a123,
inference(equational,[status(thm)],[c244]) ).
cnf(c246,axiom,
a124 = product(a123,a75),
file('theBenchmark.p',knot_124) ).
cnf(c247,plain,
product(a123,a75) = a124,
inference(equational,[status(thm)],[c246]) ).
cnf(c248,axiom,
a125 = product(a124,a2),
file('theBenchmark.p',knot_125) ).
cnf(c249,plain,
product(a124,a2) = a125,
inference(equational,[status(thm)],[c248]) ).
cnf(c250,axiom,
a126 = product(a125,a65),
file('theBenchmark.p',knot_126) ).
cnf(c251,plain,
product(a125,a65) = a126,
inference(equational,[status(thm)],[c250]) ).
cnf(c252,axiom,
a127 = product(a126,a41),
file('theBenchmark.p',knot_127) ).
cnf(c253,plain,
product(a126,a41) = a127,
inference(equational,[status(thm)],[c252]) ).
cnf(c254,axiom,
a128 = product(a127,a96),
file('theBenchmark.p',knot_128) ).
cnf(c255,plain,
product(a127,a96) = a128,
inference(equational,[status(thm)],[c254]) ).
cnf(c256,axiom,
a129 = product(a128,a62),
file('theBenchmark.p',knot_129) ).
cnf(c257,plain,
product(a128,a62) = a129,
inference(equational,[status(thm)],[c256]) ).
cnf(c258,axiom,
a130 = product(a129,a1),
file('theBenchmark.p',knot_130) ).
cnf(c259,plain,
product(a129,a1) = a130,
inference(equational,[status(thm)],[c258]) ).
cnf(c260,axiom,
a131 = product(a130,a13),
file('theBenchmark.p',knot_131) ).
cnf(c261,plain,
product(a130,a13) = a131,
inference(equational,[status(thm)],[c260]) ).
cnf(c262,axiom,
a132 = product(a131,a138),
file('theBenchmark.p',knot_132) ).
cnf(c263,plain,
product(a131,a138) = a132,
inference(equational,[status(thm)],[c262]) ).
cnf(c264,axiom,
a133 = product(a132,a58),
file('theBenchmark.p',knot_133) ).
cnf(c265,plain,
product(a132,a58) = a133,
inference(equational,[status(thm)],[c264]) ).
cnf(c266,axiom,
a134 = product(a133,a26),
file('theBenchmark.p',knot_134) ).
cnf(c267,plain,
product(a133,a26) = a134,
inference(equational,[status(thm)],[c266]) ).
cnf(c268,axiom,
a135 = product(a134,a37),
file('theBenchmark.p',knot_135) ).
cnf(c269,plain,
product(a134,a37) = a135,
inference(equational,[status(thm)],[c268]) ).
cnf(c270,axiom,
a136 = product(a135,a29),
file('theBenchmark.p',knot_136) ).
cnf(c271,plain,
product(a135,a29) = a136,
inference(equational,[status(thm)],[c270]) ).
cnf(c272,axiom,
a137 = product(a136,a39),
file('theBenchmark.p',knot_137) ).
cnf(c273,plain,
product(a136,a39) = a137,
inference(equational,[status(thm)],[c272]) ).
cnf(c274,axiom,
a138 = product(a137,a51),
file('theBenchmark.p',knot_138) ).
cnf(c275,plain,
product(a137,a51) = a138,
inference(equational,[status(thm)],[c274]) ).
cnf(c276,axiom,
a139 = product(a138,a20),
file('theBenchmark.p',knot_139) ).
cnf(c277,plain,
product(a138,a20) = a139,
inference(equational,[status(thm)],[c276]) ).
cnf(c278,axiom,
a140 = product(a139,a47),
file('theBenchmark.p',knot_140) ).
cnf(c279,plain,
product(a139,a47) = a140,
inference(equational,[status(thm)],[c278]) ).
cnf(c280,axiom,
a141 = product(a140,a11),
file('theBenchmark.p',knot_141) ).
cnf(c281,plain,
product(a140,a11) = a141,
inference(equational,[status(thm)],[c280]) ).
cnf(c282,axiom,
a1 = product(a141,a23),
file('theBenchmark.p',knot_142) ).
cnf(c283,plain,
product(a141,a23) = a1,
inference(equational,[status(thm)],[c282]) ).
cnf(c284,axiom,
product(product(X,Y),Y) = X,
file('theBenchmark.p',involutory_quandle_01) ).
cnf(c285,plain,
product(a2,a42) = a1,
inference(equational,[status(thm)],[c3,c284]) ).
cnf(c287,plain,
product(a101,a14) = a100,
inference(equational,[status(thm)],[c201,c284]) ).
cnf(c288,plain,
product(a102,a40) = a101,
inference(equational,[status(thm)],[c203,c284]) ).
cnf(c289,plain,
product(a103,a4) = a102,
inference(equational,[status(thm)],[c205,c284]) ).
cnf(c290,plain,
product(a104,a87) = a103,
inference(equational,[status(thm)],[c207,c284]) ).
cnf(c291,plain,
product(a105,a30) = a104,
inference(equational,[status(thm)],[c209,c284]) ).
cnf(c292,plain,
product(a106,a5) = a105,
inference(equational,[status(thm)],[c211,c284]) ).
cnf(c293,plain,
product(a107,a84) = a106,
inference(equational,[status(thm)],[c213,c284]) ).
cnf(c294,plain,
product(a108,a39) = a107,
inference(equational,[status(thm)],[c215,c284]) ).
cnf(c295,plain,
product(a109,a118) = a108,
inference(equational,[status(thm)],[c217,c284]) ).
cnf(c296,plain,
product(a110,a70) = a109,
inference(equational,[status(thm)],[c219,c284]) ).
cnf(c297,plain,
product(a12,a21) = a11,
inference(equational,[status(thm)],[c23,c284]) ).
cnf(c298,plain,
product(a111,a119) = a110,
inference(equational,[status(thm)],[c221,c284]) ).
cnf(c299,plain,
product(a112,a79) = a111,
inference(equational,[status(thm)],[c223,c284]) ).
cnf(c300,plain,
product(a113,a33) = a112,
inference(equational,[status(thm)],[c225,c284]) ).
cnf(c301,plain,
product(a114,a13) = a113,
inference(equational,[status(thm)],[c227,c284]) ).
cnf(c302,plain,
product(a115,a68) = a114,
inference(equational,[status(thm)],[c229,c284]) ).
cnf(c303,plain,
product(a116,a14) = a115,
inference(equational,[status(thm)],[c231,c284]) ).
cnf(c304,plain,
product(a117,a74) = a116,
inference(equational,[status(thm)],[c233,c284]) ).
cnf(c305,plain,
product(a118,a32) = a117,
inference(equational,[status(thm)],[c235,c284]) ).
cnf(c306,plain,
product(a119,a70) = a118,
inference(equational,[status(thm)],[c237,c284]) ).
cnf(c307,plain,
product(a120,a13) = a119,
inference(equational,[status(thm)],[c239,c284]) ).
cnf(c309,plain,
product(a121,a32) = a120,
inference(equational,[status(thm)],[c241,c284]) ).
cnf(c310,plain,
product(a122,a68) = a121,
inference(equational,[status(thm)],[c243,c284]) ).
cnf(c311,plain,
product(a123,a115) = a122,
inference(equational,[status(thm)],[c245,c284]) ).
cnf(c312,plain,
product(a124,a75) = a123,
inference(equational,[status(thm)],[c247,c284]) ).
cnf(c313,plain,
product(a125,a2) = a124,
inference(equational,[status(thm)],[c249,c284]) ).
cnf(c314,plain,
product(a126,a65) = a125,
inference(equational,[status(thm)],[c251,c284]) ).
cnf(c315,plain,
product(a127,a41) = a126,
inference(equational,[status(thm)],[c253,c284]) ).
cnf(c316,plain,
product(a128,a96) = a127,
inference(equational,[status(thm)],[c255,c284]) ).
cnf(c317,plain,
product(a129,a62) = a128,
inference(equational,[status(thm)],[c257,c284]) ).
cnf(c319,plain,
product(a14,a32) = a13,
inference(equational,[status(thm)],[c27,c284]) ).
cnf(c320,plain,
product(a131,a13) = a130,
inference(equational,[status(thm)],[c261,c284]) ).
cnf(c321,plain,
product(a132,a138) = a131,
inference(equational,[status(thm)],[c263,c284]) ).
cnf(c322,plain,
product(a133,a58) = a132,
inference(equational,[status(thm)],[c265,c284]) ).
cnf(c323,plain,
product(a134,a26) = a133,
inference(equational,[status(thm)],[c267,c284]) ).
cnf(c324,plain,
product(a135,a37) = a134,
inference(equational,[status(thm)],[c269,c284]) ).
cnf(c325,plain,
product(a136,a29) = a135,
inference(equational,[status(thm)],[c271,c284]) ).
cnf(c326,plain,
product(a137,a39) = a136,
inference(equational,[status(thm)],[c273,c284]) ).
cnf(c327,plain,
product(a138,a51) = a137,
inference(equational,[status(thm)],[c275,c284]) ).
cnf(c328,plain,
product(a139,a20) = a138,
inference(equational,[status(thm)],[c277,c284]) ).
cnf(c329,plain,
product(a140,a47) = a139,
inference(equational,[status(thm)],[c279,c284]) ).
cnf(c330,plain,
product(a15,a53) = a14,
inference(equational,[status(thm)],[c29,c284]) ).
cnf(c331,plain,
product(a141,a11) = a140,
inference(equational,[status(thm)],[c281,c284]) ).
cnf(c333,plain,
product(a16,a136) = a15,
inference(equational,[status(thm)],[c31,c284]) ).
cnf(c334,plain,
product(a17,a29) = a16,
inference(equational,[status(thm)],[c33,c284]) ).
cnf(c335,plain,
product(a18,a133) = a17,
inference(equational,[status(thm)],[c35,c284]) ).
cnf(c336,plain,
product(a19,a58) = a18,
inference(equational,[status(thm)],[c37,c284]) ).
cnf(c337,plain,
product(a20,a26) = a19,
inference(equational,[status(thm)],[c39,c284]) ).
cnf(c338,plain,
product(a3,a41) = a2,
inference(equational,[status(thm)],[c5,c284]) ).
cnf(c339,plain,
product(a21,a35) = a20,
inference(equational,[status(thm)],[c41,c284]) ).
cnf(c340,plain,
product(a22,a141) = a21,
inference(equational,[status(thm)],[c43,c284]) ).
cnf(c341,plain,
product(a23,a45) = a22,
inference(equational,[status(thm)],[c45,c284]) ).
cnf(c342,plain,
product(a24,a35) = a23,
inference(equational,[status(thm)],[c47,c284]) ).
cnf(c343,plain,
product(a25,a49) = a24,
inference(equational,[status(thm)],[c49,c284]) ).
cnf(c344,plain,
product(a26,a138) = a25,
inference(equational,[status(thm)],[c51,c284]) ).
cnf(c345,plain,
product(a27,a8) = a26,
inference(equational,[status(thm)],[c53,c284]) ).
cnf(c346,plain,
product(a28,a37) = a27,
inference(equational,[status(thm)],[c55,c284]) ).
cnf(c347,plain,
product(a29,a17) = a28,
inference(equational,[status(thm)],[c57,c284]) ).
cnf(c348,plain,
product(a30,a14) = a29,
inference(equational,[status(thm)],[c59,c284]) ).
cnf(c349,plain,
product(a4,a14) = a3,
inference(equational,[status(thm)],[c7,c284]) ).
cnf(c350,plain,
product(a31,a5) = a30,
inference(equational,[status(thm)],[c61,c284]) ).
cnf(c351,plain,
product(a32,a39) = a31,
inference(equational,[status(thm)],[c63,c284]) ).
cnf(c352,plain,
product(a33,a13) = a32,
inference(equational,[status(thm)],[c65,c284]) ).
cnf(c356,plain,
product(a37,a47) = a36,
inference(equational,[status(thm)],[c73,c284]) ).
cnf(c357,plain,
product(a38,a17) = a37,
inference(equational,[status(thm)],[c75,c284]) ).
cnf(c358,plain,
product(a39,a7) = a38,
inference(equational,[status(thm)],[c77,c284]) ).
cnf(c359,plain,
product(a40,a4) = a39,
inference(equational,[status(thm)],[c79,c284]) ).
cnf(c360,plain,
product(a5,a39) = a4,
inference(equational,[status(thm)],[c9,c284]) ).
cnf(c361,plain,
product(a41,a14) = a40,
inference(equational,[status(thm)],[c81,c284]) ).
cnf(c362,plain,
product(a42,a2) = a41,
inference(equational,[status(thm)],[c83,c284]) ).
cnf(c363,plain,
product(a43,a62) = a42,
inference(equational,[status(thm)],[c85,c284]) ).
cnf(c365,plain,
product(a45,a23) = a44,
inference(equational,[status(thm)],[c89,c284]) ).
cnf(c366,plain,
product(a46,a141) = a45,
inference(equational,[status(thm)],[c91,c284]) ).
cnf(c367,plain,
product(a47,a11) = a46,
inference(equational,[status(thm)],[c93,c284]) ).
cnf(c368,plain,
product(a48,a20) = a47,
inference(equational,[status(thm)],[c95,c284]) ).
cnf(c369,plain,
product(a49,a138) = a48,
inference(equational,[status(thm)],[c97,c284]) ).
cnf(c370,plain,
product(a50,a131) = a49,
inference(equational,[status(thm)],[c99,c284]) ).
cnf(c371,plain,
product(a6,a136) = a5,
inference(equational,[status(thm)],[c11,c284]) ).
cnf(c372,plain,
product(a51,a59) = a50,
inference(equational,[status(thm)],[c101,c284]) ).
cnf(c373,plain,
product(a52,a39) = a51,
inference(equational,[status(thm)],[c103,c284]) ).
cnf(c374,plain,
product(a53,a136) = a52,
inference(equational,[status(thm)],[c105,c284]) ).
cnf(c375,plain,
product(a54,a29) = a53,
inference(equational,[status(thm)],[c107,c284]) ).
cnf(c376,plain,
product(a55,a135) = a54,
inference(equational,[status(thm)],[c109,c284]) ).
cnf(c377,plain,
product(a56,a37) = a55,
inference(equational,[status(thm)],[c111,c284]) ).
cnf(c378,plain,
product(a57,a134) = a56,
inference(equational,[status(thm)],[c113,c284]) ).
cnf(c379,plain,
product(a58,a26) = a57,
inference(equational,[status(thm)],[c115,c284]) ).
cnf(c380,plain,
product(a59,a138) = a58,
inference(equational,[status(thm)],[c117,c284]) ).
cnf(c381,plain,
product(a60,a131) = a59,
inference(equational,[status(thm)],[c119,c284]) ).
cnf(c382,plain,
product(a7,a52) = a6,
inference(equational,[status(thm)],[c13,c284]) ).
cnf(c383,plain,
product(a61,a13) = a60,
inference(equational,[status(thm)],[c121,c284]) ).
cnf(c384,plain,
product(a62,a1) = a61,
inference(equational,[status(thm)],[c123,c284]) ).
cnf(c385,plain,
product(a63,a96) = a62,
inference(equational,[status(thm)],[c125,c284]) ).
cnf(c386,plain,
product(a64,a127) = a63,
inference(equational,[status(thm)],[c127,c284]) ).
cnf(c387,plain,
product(a65,a41) = a64,
inference(equational,[status(thm)],[c129,c284]) ).
cnf(c388,plain,
product(a66,a2) = a65,
inference(equational,[status(thm)],[c131,c284]) ).
cnf(c389,plain,
product(a67,a92) = a66,
inference(equational,[status(thm)],[c133,c284]) ).
cnf(c390,plain,
product(a68,a98) = a67,
inference(equational,[status(thm)],[c135,c284]) ).
cnf(c391,plain,
product(a69,a32) = a68,
inference(equational,[status(thm)],[c137,c284]) ).
cnf(c392,plain,
product(a70,a13) = a69,
inference(equational,[status(thm)],[c139,c284]) ).
cnf(c394,plain,
product(a71,a118) = a70,
inference(equational,[status(thm)],[c141,c284]) ).
cnf(c395,plain,
product(a72,a109) = a71,
inference(equational,[status(thm)],[c143,c284]) ).
cnf(c396,plain,
product(a73,a82) = a72,
inference(equational,[status(thm)],[c145,c284]) ).
cnf(c397,plain,
product(a74,a32) = a73,
inference(equational,[status(thm)],[c147,c284]) ).
cnf(c398,plain,
product(a75,a14) = a74,
inference(equational,[status(thm)],[c149,c284]) ).
cnf(c399,plain,
product(a76,a68) = a75,
inference(equational,[status(thm)],[c151,c284]) ).
cnf(c400,plain,
product(a77,a114) = a76,
inference(equational,[status(thm)],[c153,c284]) ).
cnf(c401,plain,
product(a78,a13) = a77,
inference(equational,[status(thm)],[c155,c284]) ).
cnf(c402,plain,
product(a79,a33) = a78,
inference(equational,[status(thm)],[c157,c284]) ).
cnf(c403,plain,
product(a80,a119) = a79,
inference(equational,[status(thm)],[c159,c284]) ).
cnf(c404,plain,
product(a9,a56) = a8,
inference(equational,[status(thm)],[c17,c284]) ).
cnf(c405,plain,
product(a81,a70) = a80,
inference(equational,[status(thm)],[c161,c284]) ).
cnf(c406,plain,
product(a82,a109) = a81,
inference(equational,[status(thm)],[c163,c284]) ).
cnf(c407,plain,
product(a83,a118) = a82,
inference(equational,[status(thm)],[c165,c284]) ).
cnf(c408,plain,
product(a84,a39) = a83,
inference(equational,[status(thm)],[c167,c284]) ).
cnf(c409,plain,
product(a85,a5) = a84,
inference(equational,[status(thm)],[c169,c284]) ).
cnf(c410,plain,
product(a86,a30) = a85,
inference(equational,[status(thm)],[c171,c284]) ).
cnf(c411,plain,
product(a87,a104) = a86,
inference(equational,[status(thm)],[c173,c284]) ).
cnf(c412,plain,
product(a88,a4) = a87,
inference(equational,[status(thm)],[c175,c284]) ).
cnf(c413,plain,
product(a89,a14) = a88,
inference(equational,[status(thm)],[c177,c284]) ).
cnf(c414,plain,
product(a90,a41) = a89,
inference(equational,[status(thm)],[c179,c284]) ).
cnf(c415,plain,
product(a10,a134) = a9,
inference(equational,[status(thm)],[c19,c284]) ).
cnf(c416,plain,
product(a91,a100) = a90,
inference(equational,[status(thm)],[c181,c284]) ).
cnf(c417,plain,
product(a92,a124) = a91,
inference(equational,[status(thm)],[c183,c284]) ).
cnf(c418,plain,
product(a93,a2) = a92,
inference(equational,[status(thm)],[c185,c284]) ).
cnf(c419,plain,
product(a94,a41) = a93,
inference(equational,[status(thm)],[c187,c284]) ).
cnf(c420,plain,
product(a95,a127) = a94,
inference(equational,[status(thm)],[c189,c284]) ).
cnf(c421,plain,
product(a96,a64) = a95,
inference(equational,[status(thm)],[c191,c284]) ).
cnf(c422,plain,
product(a97,a42) = a96,
inference(equational,[status(thm)],[c193,c284]) ).
cnf(c423,plain,
product(a98,a1) = a97,
inference(equational,[status(thm)],[c195,c284]) ).
cnf(c424,plain,
product(a99,a92) = a98,
inference(equational,[status(thm)],[c197,c284]) ).
cnf(c425,plain,
product(a100,a124) = a99,
inference(equational,[status(thm)],[c199,c284]) ).
cnf(c426,axiom,
product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)),
file('theBenchmark.p',involutory_quandle_02) ).
cnf(c427,plain,
product(product(X,Y),product(Z,Y)) = product(product(X,Z),Y),
inference(equational,[status(thm)],[c426]) ).
cnf(c428,plain,
product(product(X,Y),X) = product(X,product(Y,X)),
inference(equational,[status(thm)],[c1,c427]) ).
cnf(c429,plain,
product(a3,a2) = a1,
inference(equational,[status(thm)],[c5,c83,c285,c428]) ).
cnf(c430,plain,
product(a1,a2) = a3,
inference(equational,[status(thm)],[c5,c285,c362,c428]) ).
cnf(c432,plain,
product(a29,a16) = product(a28,a29),
inference(equational,[status(thm)],[c334,c347,c428]) ).
cnf(c434,plain,
product(a39,a5) = product(a40,a39),
inference(equational,[status(thm)],[c9,c79,c428]) ).
cnf(c435,plain,
product(a5,a4) = product(a4,a40),
inference(equational,[status(thm)],[c9,c79,c428]) ).
cnf(c436,plain,
product(a41,a3) = product(a42,a41),
inference(equational,[status(thm)],[c5,c83,c428]) ).
cnf(c438,plain,
product(a45,a22) = product(a44,a45),
inference(equational,[status(thm)],[c341,c365,c428]) ).
cnf(c439,plain,
product(a70,a119) = product(a71,a70),
inference(equational,[status(thm)],[c141,c237,c428]) ).
cnf(c440,plain,
product(a87,a103) = product(a86,a87),
inference(equational,[status(thm)],[c290,c411,c428]) ).
cnf(c441,plain,
product(a17,a28) = product(a16,a17),
inference(equational,[status(thm)],[c334,c347,c428]) ).
cnf(c444,plain,
product(a104,a86) = product(a103,a104),
inference(equational,[status(thm)],[c290,c411,c428]) ).
cnf(c445,plain,
product(product(a1,X),a42) = product(a2,product(X,a42)),
inference(equational,[status(thm)],[c3,c427]) ).
cnf(c446,plain,
product(a2,a1) = product(a3,a42),
inference(equational,[status(thm)],[c285,c430,c445]) ).
cnf(c447,plain,
product(product(a10,X),a37) = product(a11,product(X,a37)),
inference(equational,[status(thm)],[c21,c427]) ).
cnf(c448,plain,
product(a11,a135) = product(a9,a37),
inference(equational,[status(thm)],[c269,c415,c447]) ).
cnf(c453,plain,
product(product(a103,X),a87) = product(a104,product(X,a87)),
inference(equational,[status(thm)],[c207,c427]) ).
cnf(c454,plain,
product(product(a104,X),a30) = product(a105,product(X,a30)),
inference(equational,[status(thm)],[c209,c427]) ).
cnf(c455,plain,
product(product(a105,X),a5) = product(a106,product(X,a5)),
inference(equational,[status(thm)],[c211,c427]) ).
cnf(c456,plain,
product(a104,a5) = product(a106,a31),
inference(equational,[status(thm)],[c61,c291,c455]) ).
cnf(c458,plain,
product(product(a107,X),a39) = product(a108,product(X,a39)),
inference(equational,[status(thm)],[c215,c427]) ).
cnf(c459,plain,
product(a108,a83) = product(a106,a39),
inference(equational,[status(thm)],[c293,c408,c458]) ).
cnf(c460,plain,
product(product(a108,X),a118) = product(a109,product(X,a118)),
inference(equational,[status(thm)],[c217,c427]) ).
cnf(c461,plain,
product(product(a109,X),a70) = product(a110,product(X,a70)),
inference(equational,[status(thm)],[c219,c427]) ).
cnf(c462,plain,
product(a108,a70) = a111,
inference(equational,[status(thm)],[c221,c237,c295,c461]) ).
cnf(c463,plain,
product(a111,a70) = a108,
inference(equational,[status(thm)],[c284,c462]) ).
cnf(c464,plain,
product(a109,a71) = product(a111,a118),
inference(equational,[status(thm)],[c141,c460,c462]) ).
cnf(c466,plain,
product(product(a110,X),a119) = product(a111,product(X,a119)),
inference(equational,[status(thm)],[c221,c427]) ).
cnf(c467,plain,
product(product(a111,X),a79) = product(a112,product(X,a79)),
inference(equational,[status(thm)],[c223,c427]) ).
cnf(c468,plain,
product(product(a112,X),a33) = product(a113,product(X,a33)),
inference(equational,[status(thm)],[c225,c427]) ).
cnf(c469,plain,
product(a113,a78) = product(a111,a33),
inference(equational,[status(thm)],[c299,c402,c468]) ).
cnf(c470,plain,
product(product(a113,X),a13) = product(a114,product(X,a13)),
inference(equational,[status(thm)],[c227,c427]) ).
cnf(c471,plain,
product(a114,a32) = product(a112,a13),
inference(equational,[status(thm)],[c300,c352,c470]) ).
cnf(c472,plain,
product(product(a114,X),a68) = product(a115,product(X,a68)),
inference(equational,[status(thm)],[c229,c427]) ).
cnf(c474,plain,
product(product(a116,X),a74) = product(a117,product(X,a74)),
inference(equational,[status(thm)],[c233,c427]) ).
cnf(c475,plain,
product(product(a117,X),a32) = product(a118,product(X,a32)),
inference(equational,[status(thm)],[c235,c427]) ).
cnf(c476,plain,
product(a118,a73) = product(a116,a32),
inference(equational,[status(thm)],[c304,c397,c475]) ).
cnf(c477,plain,
product(product(a118,X),a70) = product(a119,product(X,a70)),
inference(equational,[status(thm)],[c237,c427]) ).
cnf(c478,plain,
product(product(a119,X),a13) = product(a120,product(X,a13)),
inference(equational,[status(thm)],[c239,c427]) ).
cnf(c479,plain,
product(a118,a13) = product(a120,a69),
inference(equational,[status(thm)],[c306,c392,c478]) ).
cnf(c481,plain,
product(product(a120,X),a32) = product(a121,product(X,a32)),
inference(equational,[status(thm)],[c241,c427]) ).
cnf(c483,plain,
product(product(a121,X),a68) = product(a122,product(X,a68)),
inference(equational,[status(thm)],[c243,c427]) ).
cnf(c484,plain,
product(product(a122,X),a115) = product(a123,product(X,a115)),
inference(equational,[status(thm)],[c245,c427]) ).
cnf(c485,plain,
product(product(a123,X),a75) = product(a124,product(X,a75)),
inference(equational,[status(thm)],[c247,c427]) ).
cnf(c486,plain,
product(product(a124,X),a2) = product(a125,product(X,a2)),
inference(equational,[status(thm)],[c249,c427]) ).
cnf(c488,plain,
product(product(a126,X),a41) = product(a127,product(X,a41)),
inference(equational,[status(thm)],[c253,c427]) ).
cnf(c489,plain,
product(a127,a64) = product(a125,a41),
inference(equational,[status(thm)],[c314,c387,c488]) ).
cnf(c492,plain,
product(product(a129,X),a1) = product(a130,product(X,a1)),
inference(equational,[status(thm)],[c259,c427]) ).
cnf(c493,plain,
product(a128,a1) = product(a130,a61),
inference(equational,[status(thm)],[c317,c384,c492]) ).
cnf(c495,plain,
product(product(a130,X),a13) = product(a131,product(X,a13)),
inference(equational,[status(thm)],[c261,c427]) ).
cnf(c496,plain,
product(product(a131,X),a138) = product(a132,product(X,a138)),
inference(equational,[status(thm)],[c263,c427]) ).
cnf(c498,plain,
product(product(a133,X),a26) = product(a134,product(X,a26)),
inference(equational,[status(thm)],[c267,c427]) ).
cnf(c499,plain,
product(a134,a57) = product(a132,a26),
inference(equational,[status(thm)],[c322,c379,c498]) ).
cnf(c500,plain,
product(product(a134,X),a37) = product(a135,product(X,a37)),
inference(equational,[status(thm)],[c269,c427]) ).
cnf(c504,plain,
product(product(a138,X),a20) = product(a139,product(X,a20)),
inference(equational,[status(thm)],[c277,c427]) ).
cnf(c507,plain,
product(product(a140,X),a11) = product(a141,product(X,a11)),
inference(equational,[status(thm)],[c281,c427]) ).
cnf(c508,plain,
product(a141,a46) = product(a139,a11),
inference(equational,[status(thm)],[c329,c367,c507]) ).
cnf(c509,plain,
product(product(a141,X),a23) = product(a1,product(X,a23)),
inference(equational,[status(thm)],[c283,c427]) ).
cnf(c510,plain,
product(product(a15,X),a136) = product(a16,product(X,a136)),
inference(equational,[status(thm)],[c31,c427]) ).
cnf(c511,plain,
product(a14,a136) = product(a16,a52),
inference(equational,[status(thm)],[c330,c374,c510]) ).
cnf(c517,plain,
product(product(a19,X),a26) = product(a20,product(X,a26)),
inference(equational,[status(thm)],[c39,c427]) ).
cnf(c518,plain,
product(a20,a57) = product(a18,a26),
inference(equational,[status(thm)],[c336,c379,c517]) ).
cnf(c519,plain,
product(product(a2,X),a41) = product(a3,product(X,a41)),
inference(equational,[status(thm)],[c5,c427]) ).
cnf(c524,plain,
product(product(a24,X),a49) = product(a25,product(X,a49)),
inference(equational,[status(thm)],[c49,c427]) ).
cnf(c525,plain,
product(product(a25,X),a138) = product(a26,product(X,a138)),
inference(equational,[status(thm)],[c51,c427]) ).
cnf(c526,plain,
product(a26,a48) = product(a24,a138),
inference(equational,[status(thm)],[c343,c369,c525]) ).
cnf(c528,plain,
product(product(a27,X),a37) = product(a28,product(X,a37)),
inference(equational,[status(thm)],[c55,c427]) ).
cnf(c529,plain,
product(product(a28,X),a17) = product(a29,product(X,a17)),
inference(equational,[status(thm)],[c57,c427]) ).
cnf(c530,plain,
product(a29,a38) = product(a27,a17),
inference(equational,[status(thm)],[c75,c346,c529]) ).
cnf(c532,plain,
product(product(a3,X),a14) = product(a4,product(X,a14)),
inference(equational,[status(thm)],[c7,c427]) ).
cnf(c533,plain,
product(a2,a14) = product(a4,a40),
inference(equational,[status(thm)],[c338,c361,c532]) ).
cnf(c535,plain,
product(product(a31,X),a39) = product(a32,product(X,a39)),
inference(equational,[status(thm)],[c63,c427]) ).
cnf(c536,plain,
product(a32,a4) = product(a30,a39),
inference(equational,[status(thm)],[c350,c360,c535]) ).
cnf(c538,plain,
product(product(a33,X),a131) = product(a34,product(X,a131)),
inference(equational,[status(thm)],[c67,c427]) ).
cnf(c539,plain,
product(product(a34,X),a60) = product(a35,product(X,a60)),
inference(equational,[status(thm)],[c69,c427]) ).
cnf(c540,plain,
product(product(a35,X),a139) = product(a36,product(X,a139)),
inference(equational,[status(thm)],[c71,c427]) ).
cnf(c541,plain,
product(product(a36,X),a47) = product(a37,product(X,a47)),
inference(equational,[status(thm)],[c73,c427]) ).
cnf(c546,plain,
product(product(a4,X),a39) = product(a5,product(X,a39)),
inference(equational,[status(thm)],[c9,c427]) ).
cnf(c547,plain,
product(product(a40,X),a14) = product(a41,product(X,a14)),
inference(equational,[status(thm)],[c81,c427]) ).
cnf(c548,plain,
product(a39,a14) = product(a42,a41),
inference(equational,[status(thm)],[c349,c359,c436,c547]) ).
cnf(c551,plain,
product(product(a43,X),a128) = product(a44,product(X,a128)),
inference(equational,[status(thm)],[c87,c427]) ).
cnf(c554,plain,
product(product(a46,X),a11) = product(a47,product(X,a11)),
inference(equational,[status(thm)],[c93,c427]) ).
cnf(c555,plain,
product(a47,a140) = product(a45,a11),
inference(equational,[status(thm)],[c331,c366,c554]) ).
cnf(c556,plain,
product(product(a47,X),a20) = product(a48,product(X,a20)),
inference(equational,[status(thm)],[c95,c427]) ).
cnf(c557,plain,
product(product(a48,X),a138) = product(a49,product(X,a138)),
inference(equational,[status(thm)],[c97,c427]) ).
cnf(c563,plain,
product(product(a53,X),a29) = product(a54,product(X,a29)),
inference(equational,[status(thm)],[c107,c427]) ).
cnf(c564,plain,
product(a52,a29) = a55,
inference(equational,[status(thm)],[c109,c325,c374,c563]) ).
cnf(c565,plain,
product(a55,a29) = a52,
inference(equational,[status(thm)],[c284,c564]) ).
cnf(c567,plain,
product(product(a55,X),a37) = product(a56,product(X,a37)),
inference(equational,[status(thm)],[c111,c427]) ).
cnf(c568,plain,
product(a54,a37) = a57,
inference(equational,[status(thm)],[c113,c324,c376,c567]) ).
cnf(c569,plain,
product(a57,a37) = a54,
inference(equational,[status(thm)],[c284,c568]) ).
cnf(c571,plain,
product(product(a57,X),a26) = product(a58,product(X,a26)),
inference(equational,[status(thm)],[c115,c427]) ).
cnf(c572,plain,
product(a58,a133) = product(a56,a26),
inference(equational,[status(thm)],[c323,c378,c571]) ).
cnf(c573,plain,
product(product(a58,X),a138) = product(a59,product(X,a138)),
inference(equational,[status(thm)],[c117,c427]) ).
cnf(c574,plain,
product(a59,a25) = product(a57,a138),
inference(equational,[status(thm)],[c344,c379,c573]) ).
cnf(c575,plain,
product(product(a59,X),a131) = product(a60,product(X,a131)),
inference(equational,[status(thm)],[c119,c427]) ).
cnf(c581,plain,
product(product(a63,X),a127) = product(a64,product(X,a127)),
inference(equational,[status(thm)],[c127,c427]) ).
cnf(c582,plain,
product(product(a64,X),a41) = product(a65,product(X,a41)),
inference(equational,[status(thm)],[c129,c427]) ).
cnf(c583,plain,
product(a65,a126) = product(a63,a41),
inference(equational,[status(thm)],[c315,c386,c582]) ).
cnf(c584,plain,
product(product(a65,X),a2) = product(a66,product(X,a2)),
inference(equational,[status(thm)],[c131,c427]) ).
cnf(c585,plain,
product(a64,a2) = product(a66,a42),
inference(equational,[status(thm)],[c83,c387,c584]) ).
cnf(c586,plain,
product(product(a66,X),a92) = product(a67,product(X,a92)),
inference(equational,[status(thm)],[c133,c427]) ).
cnf(c588,plain,
product(product(a68,X),a32) = product(a69,product(X,a32)),
inference(equational,[status(thm)],[c137,c427]) ).
cnf(c592,plain,
product(product(a70,X),a118) = product(a71,product(X,a118)),
inference(equational,[status(thm)],[c141,c427]) ).
cnf(c593,plain,
product(product(a71,X),a109) = product(a72,product(X,a109)),
inference(equational,[status(thm)],[c143,c427]) ).
cnf(c594,plain,
product(product(a72,X),a82) = product(a73,product(X,a82)),
inference(equational,[status(thm)],[c145,c427]) ).
cnf(c595,plain,
product(product(a73,X),a32) = product(a74,product(X,a32)),
inference(equational,[status(thm)],[c147,c427]) ).
cnf(c596,plain,
product(product(a74,X),a14) = product(a75,product(X,a14)),
inference(equational,[status(thm)],[c149,c427]) ).
cnf(c597,plain,
product(product(a75,X),a68) = product(a76,product(X,a68)),
inference(equational,[status(thm)],[c151,c427]) ).
cnf(c598,plain,
product(product(a76,X),a114) = product(a77,product(X,a114)),
inference(equational,[status(thm)],[c153,c427]) ).
cnf(c599,plain,
product(product(a77,X),a13) = product(a78,product(X,a13)),
inference(equational,[status(thm)],[c155,c427]) ).
cnf(c600,plain,
product(a78,a113) = product(a76,a13),
inference(equational,[status(thm)],[c301,c400,c599]) ).
cnf(c602,plain,
product(product(a79,X),a119) = product(a80,product(X,a119)),
inference(equational,[status(thm)],[c159,c427]) ).
cnf(c604,plain,
product(product(a80,X),a70) = product(a81,product(X,a70)),
inference(equational,[status(thm)],[c161,c427]) ).
cnf(c605,plain,
product(a79,a70) = product(a81,a118),
inference(equational,[status(thm)],[c306,c403,c604]) ).
cnf(c606,plain,
product(product(a81,X),a109) = product(a82,product(X,a109)),
inference(equational,[status(thm)],[c163,c427]) ).
cnf(c607,plain,
product(product(a82,X),a118) = product(a83,product(X,a118)),
inference(equational,[status(thm)],[c165,c427]) ).
cnf(c608,plain,
product(a83,a108) = product(a81,a118),
inference(equational,[status(thm)],[c295,c406,c607]) ).
cnf(c613,plain,
product(product(a87,X),a4) = product(a88,product(X,a4)),
inference(equational,[status(thm)],[c175,c427]) ).
cnf(c614,plain,
product(product(a88,X),a14) = product(a89,product(X,a14)),
inference(equational,[status(thm)],[c177,c427]) ).
cnf(c615,plain,
product(a87,a14) = product(a89,a3),
inference(equational,[status(thm)],[c349,c412,c614]) ).
cnf(c617,plain,
product(product(a9,X),a134) = product(a10,product(X,a134)),
inference(equational,[status(thm)],[c19,c427]) ).
cnf(c618,plain,
product(a8,a134) = product(a10,a57),
inference(equational,[status(thm)],[c113,c404,c617]) ).
cnf(c619,plain,
product(product(a90,X),a100) = product(a91,product(X,a100)),
inference(equational,[status(thm)],[c181,c427]) ).
cnf(c620,plain,
product(product(a91,X),a124) = product(a92,product(X,a124)),
inference(equational,[status(thm)],[c183,c427]) ).
cnf(c621,plain,
product(a92,a99) = product(a90,a124),
inference(equational,[status(thm)],[c416,c425,c620]) ).
cnf(c622,plain,
product(product(a92,X),a2) = product(a93,product(X,a2)),
inference(equational,[status(thm)],[c185,c427]) ).
cnf(c623,plain,
product(a93,a125) = product(a91,a2),
inference(equational,[status(thm)],[c249,c417,c622]) ).
cnf(c624,plain,
product(product(a93,X),a41) = product(a94,product(X,a41)),
inference(equational,[status(thm)],[c187,c427]) ).
cnf(c625,plain,
product(a92,a41) = product(a94,a3),
inference(equational,[status(thm)],[c5,c418,c624]) ).
cnf(c627,plain,
product(product(a95,X),a64) = product(a96,product(X,a64)),
inference(equational,[status(thm)],[c191,c427]) ).
cnf(c628,plain,
product(product(a96,X),a42) = product(a97,product(X,a42)),
inference(equational,[status(thm)],[c193,c427]) ).
cnf(c629,plain,
product(product(a97,X),a1) = product(a98,product(X,a1)),
inference(equational,[status(thm)],[c195,c427]) ).
cnf(c630,plain,
product(product(a98,X),a92) = product(a99,product(X,a92)),
inference(equational,[status(thm)],[c197,c427]) ).
cnf(c631,plain,
product(product(a99,X),a124) = product(a100,product(X,a124)),
inference(equational,[status(thm)],[c199,c427]) ).
cnf(c632,plain,
product(a98,a124) = product(a100,a91),
inference(equational,[status(thm)],[c417,c424,c631]) ).
cnf(c633,plain,
product(product(X,a42),a2) = product(product(X,a1),a42),
inference(equational,[status(thm)],[c3,c427]) ).
cnf(c634,plain,
product(a96,a2) = product(a98,a42),
inference(equational,[status(thm)],[c195,c422,c633]) ).
cnf(c635,plain,
product(product(a92,a1),a42) = a94,
inference(equational,[status(thm)],[c187,c362,c622,c633]) ).
cnf(c637,plain,
product(a92,a1) = product(a94,a42),
inference(equational,[status(thm)],[c284,c635]) ).
cnf(c638,plain,
product(product(X,a37),a11) = product(product(X,a10),a37),
inference(equational,[status(thm)],[c21,c427]) ).
cnf(c643,plain,
product(product(X,a30),a105) = product(product(X,a104),a30),
inference(equational,[status(thm)],[c209,c427]) ).
cnf(c644,plain,
product(a87,a30) = product(a85,a105),
inference(equational,[status(thm)],[c173,c410,c643]) ).
cnf(c645,plain,
product(product(X,a5),a106) = product(product(X,a105),a5),
inference(equational,[status(thm)],[c211,c427]) ).
cnf(c647,plain,
product(product(X,a39),a108) = product(product(X,a107),a39),
inference(equational,[status(thm)],[c215,c427]) ).
cnf(c648,plain,
product(product(X,a118),a109) = product(product(X,a108),a118),
inference(equational,[status(thm)],[c217,c427]) ).
cnf(c649,plain,
product(product(X,a70),a110) = product(product(X,a109),a70),
inference(equational,[status(thm)],[c219,c427]) ).
cnf(c650,plain,
product(a82,a70) = product(a80,a110),
inference(equational,[status(thm)],[c163,c405,c649]) ).
cnf(c652,plain,
product(product(X,a119),a111) = product(product(X,a110),a119),
inference(equational,[status(thm)],[c221,c427]) ).
cnf(c653,plain,
product(product(X,a79),a112) = product(product(X,a111),a79),
inference(equational,[status(thm)],[c223,c427]) ).
cnf(c654,plain,
product(product(X,a33),a113) = product(product(X,a112),a33),
inference(equational,[status(thm)],[c225,c427]) ).
cnf(c656,plain,
product(product(X,a68),a115) = product(product(X,a114),a68),
inference(equational,[status(thm)],[c229,c427]) ).
cnf(c657,plain,
product(a75,a115) = product(a77,a68),
inference(equational,[status(thm)],[c153,c399,c656]) ).
cnf(c658,plain,
product(product(X,a14),a116) = product(product(X,a115),a14),
inference(equational,[status(thm)],[c231,c427]) ).
cnf(c659,plain,
product(product(X,a74),a117) = product(product(X,a116),a74),
inference(equational,[status(thm)],[c233,c427]) ).
cnf(c660,plain,
product(product(X,a32),a118) = product(product(X,a117),a32),
inference(equational,[status(thm)],[c235,c427]) ).
cnf(c661,plain,
product(product(X,a70),a119) = product(product(X,a118),a70),
inference(equational,[status(thm)],[c237,c427]) ).
cnf(c662,plain,
product(product(a81,a118),a70) = a79,
inference(equational,[status(thm)],[c403,c405,c661]) ).
cnf(c663,plain,
product(product(X,a13),a120) = product(product(X,a119),a13),
inference(equational,[status(thm)],[c239,c427]) ).
cnf(c665,plain,
product(product(X,a32),a121) = product(product(X,a120),a32),
inference(equational,[status(thm)],[c241,c427]) ).
cnf(c666,plain,
product(product(X,a68),a122) = product(product(X,a121),a68),
inference(equational,[status(thm)],[c243,c427]) ).
cnf(c667,plain,
product(product(X,a115),a123) = product(product(X,a122),a115),
inference(equational,[status(thm)],[c245,c427]) ).
cnf(c668,plain,
product(product(X,a75),a124) = product(product(X,a123),a75),
inference(equational,[status(thm)],[c247,c427]) ).
cnf(c669,plain,
product(product(X,a2),a125) = product(product(X,a124),a2),
inference(equational,[status(thm)],[c249,c427]) ).
cnf(c672,plain,
product(product(X,a96),a128) = product(product(X,a127),a96),
inference(equational,[status(thm)],[c255,c427]) ).
cnf(c673,plain,
product(a62,a128) = product(a64,a96),
inference(equational,[status(thm)],[c127,c385,c672]) ).
cnf(c677,plain,
product(product(X,a13),a32) = product(product(X,a32),a14),
inference(equational,[status(thm)],[c27,c427]) ).
cnf(c678,plain,
product(a70,a32) = product(a68,a14),
inference(equational,[status(thm)],[c139,c391,c677]) ).
cnf(c679,plain,
product(a117,a14) = a122,
inference(equational,[status(thm)],[c243,c305,c391,c479,c481,c677]) ).
cnf(c680,plain,
product(a122,a14) = a117,
inference(equational,[status(thm)],[c284,c679]) ).
cnf(c681,plain,
product(a122,a32) = product(a120,a69),
inference(equational,[status(thm)],[c319,c475,c479,c679]) ).
cnf(c682,plain,
product(product(a33,a32),a14) = a32,
inference(equational,[status(thm)],[c1,c352,c677]) ).
cnf(c683,plain,
product(a123,a14) = product(a117,a116),
inference(equational,[status(thm)],[c245,c658,c680]) ).
cnf(c684,plain,
product(product(X,a13),a131) = product(product(X,a130),a13),
inference(equational,[status(thm)],[c261,c427]) ).
cnf(c685,plain,
product(product(a61,a130),a13) = a59,
inference(equational,[status(thm)],[c381,c383,c684]) ).
cnf(c686,plain,
product(product(X,a138),a132) = product(product(X,a131),a138),
inference(equational,[status(thm)],[c263,c427]) ).
cnf(c688,plain,
product(a58,a132) = product(a60,a138),
inference(equational,[status(thm)],[c119,c380,c686]) ).
cnf(c689,plain,
product(product(X,a58),a133) = product(product(X,a132),a58),
inference(equational,[status(thm)],[c265,c427]) ).
cnf(c690,plain,
product(product(a19,a132),a58) = a17,
inference(equational,[status(thm)],[c335,c336,c689]) ).
cnf(c691,plain,
product(product(X,a26),a134) = product(product(X,a133),a26),
inference(equational,[status(thm)],[c267,c427]) ).
cnf(c694,plain,
product(product(X,a39),a137) = product(product(X,a136),a39),
inference(equational,[status(thm)],[c273,c427]) ).
cnf(c696,plain,
product(a53,a39) = product(a51,a137),
inference(equational,[status(thm)],[c105,c373,c694]) ).
cnf(c697,plain,
product(product(X,a51),a138) = product(product(X,a137),a51),
inference(equational,[status(thm)],[c275,c427]) ).
cnf(c698,plain,
product(product(X,a138),a20) = product(product(X,a20),a139),
inference(equational,[status(thm)],[c277,c427]) ).
cnf(c699,plain,
product(a47,a139) = product(a49,a20),
inference(equational,[status(thm)],[c97,c368,c698]) ).
cnf(c701,plain,
product(product(X,a47),a140) = product(product(X,a139),a47),
inference(equational,[status(thm)],[c279,c427]) ).
cnf(c702,plain,
product(product(X,a14),a53) = product(product(X,a53),a15),
inference(equational,[status(thm)],[c29,c427]) ).
cnf(c704,plain,
product(product(X,a23),a1) = product(product(X,a141),a23),
inference(equational,[status(thm)],[c283,c427]) ).
cnf(c705,plain,
product(a46,a23) = product(a44,a1),
inference(equational,[status(thm)],[c91,c365,c704]) ).
cnf(c707,plain,
product(product(X,a29),a17) = product(product(X,a16),a29),
inference(equational,[status(thm)],[c33,c427]) ).
cnf(c711,plain,
product(product(X,a41),a3) = product(product(X,a2),a41),
inference(equational,[status(thm)],[c5,c427]) ).
cnf(c712,plain,
product(a2,a3) = product(a1,a41),
inference(equational,[status(thm)],[c338,c429,c711]) ).
cnf(c714,plain,
product(product(X,a20),a35) = product(product(X,a35),a21),
inference(equational,[status(thm)],[c41,c427]) ).
cnf(c715,plain,
product(product(X,a21),a141) = product(product(X,a141),a22),
inference(equational,[status(thm)],[c43,c427]) ).
cnf(c716,plain,
product(product(X,a45),a23) = product(product(X,a22),a45),
inference(equational,[status(thm)],[c45,c427]) ).
cnf(c717,plain,
product(product(X,a23),a35) = product(product(X,a35),a24),
inference(equational,[status(thm)],[c47,c427]) ).
cnf(c719,plain,
product(product(X,a138),a26) = product(product(X,a25),a138),
inference(equational,[status(thm)],[c51,c427]) ).
cnf(c720,plain,
product(product(X,a26),a8) = product(product(X,a8),a27),
inference(equational,[status(thm)],[c53,c427]) ).
cnf(c722,plain,
product(product(X,a17),a29) = product(product(X,a28),a17),
inference(equational,[status(thm)],[c57,c427]) ).
cnf(c724,plain,
product(product(X,a14),a4) = product(product(X,a3),a14),
inference(equational,[status(thm)],[c7,c427]) ).
cnf(c725,plain,
product(product(a42,a41),a14) = a39,
inference(equational,[status(thm)],[c359,c361,c436,c724]) ).
cnf(c726,plain,
product(product(a89,a3),a14) = a87,
inference(equational,[status(thm)],[c412,c413,c724]) ).
cnf(c727,plain,
product(product(X,a5),a31) = product(product(X,a30),a5),
inference(equational,[status(thm)],[c61,c427]) ).
cnf(c728,plain,
product(a84,a31) = product(a86,a5),
inference(equational,[status(thm)],[c171,c409,c727]) ).
cnf(c729,plain,
product(product(X,a39),a32) = product(product(X,a31),a39),
inference(equational,[status(thm)],[c63,c427]) ).
cnf(c730,plain,
product(product(X,a13),a33) = product(product(X,a32),a13),
inference(equational,[status(thm)],[c65,c427]) ).
cnf(c731,plain,
product(a119,a33) = product(a121,a13),
inference(equational,[status(thm)],[c241,c307,c730]) ).
cnf(c736,plain,
product(product(X,a37),a17) = product(product(X,a17),a38),
inference(equational,[status(thm)],[c75,c427]) ).
cnf(c739,plain,
product(product(X,a39),a4) = product(product(X,a4),a40),
inference(equational,[status(thm)],[c79,c427]) ).
cnf(c740,plain,
product(product(X,a39),a5) = product(product(X,a4),a39),
inference(equational,[status(thm)],[c9,c427]) ).
cnf(c741,plain,
product(product(X,a14),a41) = product(product(X,a40),a14),
inference(equational,[status(thm)],[c81,c427]) ).
cnf(c742,plain,
product(a100,a41) = product(a102,a14),
inference(equational,[status(thm)],[c203,c287,c741]) ).
cnf(c743,plain,
product(product(a4,a40),a14) = a2,
inference(equational,[status(thm)],[c338,c349,c741]) ).
cnf(c744,plain,
product(product(X,a41),a2) = product(product(X,a2),a42),
inference(equational,[status(thm)],[c83,c427]) ).
cnf(c752,plain,
product(product(X,a20),a48) = product(product(X,a47),a20),
inference(equational,[status(thm)],[c95,c427]) ).
cnf(c753,plain,
product(a138,a48) = product(a140,a20),
inference(equational,[status(thm)],[c279,c328,c752]) ).
cnf(c754,plain,
product(product(X,a138),a49) = product(product(X,a48),a138),
inference(equational,[status(thm)],[c97,c427]) ).
cnf(c757,plain,
product(product(X,a59),a51) = product(product(X,a50),a59),
inference(equational,[status(thm)],[c101,c427]) ).
cnf(c758,plain,
product(product(X,a39),a52) = product(product(X,a51),a39),
inference(equational,[status(thm)],[c103,c427]) ).
cnf(c759,plain,
product(a138,a39) = product(a136,a52),
inference(equational,[status(thm)],[c275,c326,c758]) ).
cnf(c760,plain,
product(product(X,a136),a53) = product(product(X,a52),a136),
inference(equational,[status(thm)],[c105,c427]) ).
cnf(c762,plain,
product(product(a16,a52),a136) = a14,
inference(equational,[status(thm)],[c330,c333,c760]) ).
cnf(c763,plain,
product(product(X,a29),a54) = product(product(X,a53),a29),
inference(equational,[status(thm)],[c107,c427]) ).
cnf(c764,plain,
product(product(X,a135),a55) = product(product(X,a54),a135),
inference(equational,[status(thm)],[c109,c427]) ).
cnf(c765,plain,
product(product(X,a37),a56) = product(product(X,a55),a37),
inference(equational,[status(thm)],[c111,c427]) ).
cnf(c767,plain,
product(product(X,a26),a58) = product(product(X,a57),a26),
inference(equational,[status(thm)],[c115,c427]) ).
cnf(c768,plain,
product(product(X,a138),a59) = product(product(X,a58),a138),
inference(equational,[status(thm)],[c117,c427]) ).
cnf(c773,plain,
product(product(X,a13),a61) = product(product(X,a60),a13),
inference(equational,[status(thm)],[c121,c427]) ).
cnf(c776,plain,
product(product(X,a96),a63) = product(product(X,a62),a96),
inference(equational,[status(thm)],[c125,c427]) ).
cnf(c777,plain,
product(a127,a63) = product(a129,a96),
inference(equational,[status(thm)],[c257,c316,c776]) ).
cnf(c778,plain,
product(product(X,a127),a64) = product(product(X,a63),a127),
inference(equational,[status(thm)],[c127,c427]) ).
cnf(c779,plain,
product(product(X,a41),a65) = product(product(X,a64),a41),
inference(equational,[status(thm)],[c129,c427]) ).
cnf(c780,plain,
product(product(X,a2),a66) = product(product(X,a65),a2),
inference(equational,[status(thm)],[c131,c427]) ).
cnf(c783,plain,
product(product(X,a98),a68) = product(product(X,a67),a98),
inference(equational,[status(thm)],[c135,c427]) ).
cnf(c784,plain,
product(product(X,a32),a69) = product(product(X,a68),a32),
inference(equational,[status(thm)],[c137,c427]) ).
cnf(c785,plain,
product(product(X,a13),a70) = product(product(X,a69),a13),
inference(equational,[status(thm)],[c139,c427]) ).
cnf(c786,plain,
product(product(a120,a69),a13) = a118,
inference(equational,[status(thm)],[c306,c307,c785]) ).
cnf(c788,plain,
product(product(X,a17),a8) = product(product(X,a7),a17),
inference(equational,[status(thm)],[c15,c427]) ).
cnf(c790,plain,
product(product(X,a70),a118) = product(product(X,a118),a71),
inference(equational,[status(thm)],[c141,c427]) ).
cnf(c791,plain,
product(a110,a118) = product(a108,a71),
inference(equational,[status(thm)],[c219,c295,c790]) ).
cnf(c792,plain,
product(a79,a118) = product(a81,a71),
inference(equational,[status(thm)],[c284,c662,c790]) ).
cnf(c793,plain,
product(product(a119,a118),a71) = a118,
inference(equational,[status(thm)],[c1,c306,c790]) ).
cnf(c794,plain,
product(product(X,a109),a72) = product(product(X,a71),a109),
inference(equational,[status(thm)],[c143,c427]) ).
cnf(c795,plain,
product(product(X,a82),a73) = product(product(X,a72),a82),
inference(equational,[status(thm)],[c145,c427]) ).
cnf(c796,plain,
product(product(X,a32),a74) = product(product(X,a73),a32),
inference(equational,[status(thm)],[c147,c427]) ).
cnf(c797,plain,
product(product(X,a14),a75) = product(product(X,a74),a14),
inference(equational,[status(thm)],[c149,c427]) ).
cnf(c798,plain,
product(a115,a75) = a122,
inference(equational,[status(thm)],[c233,c303,c679,c797]) ).
cnf(c799,plain,
product(a122,a75) = a115,
inference(equational,[status(thm)],[c284,c798]) ).
cnf(c800,plain,
product(product(X,a68),a76) = product(product(X,a75),a68),
inference(equational,[status(thm)],[c151,c427]) ).
cnf(c801,plain,
product(a114,a76) = a121,
inference(equational,[status(thm)],[c302,c310,c798,c800]) ).
cnf(c802,plain,
product(a121,a76) = a114,
inference(equational,[status(thm)],[c302,c310,c799,c800]) ).
cnf(c803,plain,
product(a114,a77) = product(a121,a114),
inference(equational,[status(thm)],[c153,c428,c801]) ).
cnf(c804,plain,
product(product(X,a114),a77) = product(product(X,a76),a114),
inference(equational,[status(thm)],[c153,c427]) ).
cnf(c805,plain,
product(product(X,a13),a78) = product(product(X,a77),a13),
inference(equational,[status(thm)],[c155,c427]) ).
cnf(c807,plain,
product(product(X,a119),a80) = product(product(X,a79),a119),
inference(equational,[status(thm)],[c159,c427]) ).
cnf(c808,plain,
product(a112,a119) = product(a110,a80),
inference(equational,[status(thm)],[c223,c298,c807]) ).
cnf(c810,plain,
product(product(X,a70),a81) = product(product(X,a80),a70),
inference(equational,[status(thm)],[c161,c427]) ).
cnf(c811,plain,
product(product(X,a109),a82) = product(product(X,a81),a109),
inference(equational,[status(thm)],[c163,c427]) ).
cnf(c812,plain,
product(product(X,a118),a83) = product(product(X,a82),a118),
inference(equational,[status(thm)],[c165,c427]) ).
cnf(c814,plain,
product(product(X,a5),a85) = product(product(X,a84),a5),
inference(equational,[status(thm)],[c169,c427]) ).
cnf(c815,plain,
product(a107,a5) = product(a105,a85),
inference(equational,[status(thm)],[c213,c292,c814]) ).
cnf(c816,plain,
product(product(X,a30),a86) = product(product(X,a85),a30),
inference(equational,[status(thm)],[c171,c427]) ).
cnf(c817,plain,
product(product(X,a104),a87) = product(product(X,a86),a104),
inference(equational,[status(thm)],[c173,c427]) ).
cnf(c818,plain,
product(product(X,a4),a88) = product(product(X,a87),a4),
inference(equational,[status(thm)],[c175,c427]) ).
cnf(c819,plain,
product(a104,a4) = product(a102,a88),
inference(equational,[status(thm)],[c207,c289,c818]) ).
cnf(c820,plain,
product(product(X,a14),a89) = product(product(X,a88),a14),
inference(equational,[status(thm)],[c177,c427]) ).
cnf(c823,plain,
product(product(X,a100),a91) = product(product(X,a90),a100),
inference(equational,[status(thm)],[c181,c427]) ).
cnf(c824,plain,
product(product(X,a124),a92) = product(product(X,a91),a124),
inference(equational,[status(thm)],[c183,c427]) ).
cnf(c825,plain,
product(product(a100,a91),a124) = a98,
inference(equational,[status(thm)],[c424,c425,c824]) ).
cnf(c826,plain,
product(product(X,a2),a93) = product(product(X,a92),a2),
inference(equational,[status(thm)],[c185,c427]) ).
cnf(c827,plain,
product(a65,a93) = product(a67,a2),
inference(equational,[status(thm)],[c133,c388,c826]) ).
cnf(c833,plain,
product(product(X,a92),a99) = product(product(X,a98),a92),
inference(equational,[status(thm)],[c197,c427]) ).
cnf(c834,plain,
product(a68,a92) = product(a66,a99),
inference(equational,[status(thm)],[c135,c389,c833]) ).
cnf(c835,plain,
product(product(X,a124),a100) = product(product(X,a99),a124),
inference(equational,[status(thm)],[c199,c427]) ).
cnf(c857,plain,
product(product(a91,a90),a100) = product(a90,a91),
inference(equational,[status(thm)],[c416,c823]) ).
cnf(c869,plain,
product(product(a41,a88),a14) = product(a40,a89),
inference(equational,[status(thm)],[c361,c820]) ).
cnf(c872,plain,
product(product(a103,a86),a104) = product(a104,a103),
inference(equational,[status(thm)],[c290,c453,c817]) ).
cnf(c877,plain,
product(product(a105,a85),a30) = product(a103,a104),
inference(equational,[status(thm)],[c291,c444,c816]) ).
cnf(c879,plain,
product(product(a71,a82),a118) = product(a70,a83),
inference(equational,[status(thm)],[c394,c812]) ).
cnf(c883,plain,
product(product(a109,a82),a118) = product(a106,a39),
inference(equational,[status(thm)],[c295,c459,c812]) ).
cnf(c891,plain,
product(product(a82,a81),a109) = product(a81,a82),
inference(equational,[status(thm)],[c406,c811]) ).
cnf(c894,plain,
product(product(a119,a80),a70) = product(a118,a81),
inference(equational,[status(thm)],[c306,c810]) ).
cnf(c895,plain,
product(product(a110,a80),a70) = product(a109,a81),
inference(equational,[status(thm)],[c296,c810]) ).
cnf(c919,plain,
product(product(a29,a7),a17) = product(a28,a8),
inference(equational,[status(thm)],[c347,c788]) ).
cnf(c921,plain,
product(product(a111,a108),a118) = product(a109,a72),
inference(equational,[status(thm)],[c1,c464,c648,c794]) ).
cnf(c922,plain,
product(product(a82,a71),a109) = product(a81,a72),
inference(equational,[status(thm)],[c406,c794]) ).
cnf(c923,plain,
product(product(a72,a71),a109) = product(a71,a72),
inference(equational,[status(thm)],[c395,c794]) ).
cnf(c935,plain,
product(product(a68,a67),a98) = product(a67,a68),
inference(equational,[status(thm)],[c390,c783]) ).
cnf(c940,plain,
product(product(a93,a65),a2) = product(a92,a66),
inference(equational,[status(thm)],[c418,c780]) ).
cnf(c941,plain,
product(product(a114,a60),a13) = product(a113,a61),
inference(equational,[status(thm)],[c301,c773]) ).
cnf(c947,plain,
product(product(a94,a64),a41) = product(a93,a65),
inference(equational,[status(thm)],[c419,c779]) ).
cnf(c949,plain,
product(product(a129,a96),a127) = product(a125,a41),
inference(equational,[status(thm)],[c1,c489,c777,c778]) ).
cnf(c979,plain,
product(product(a32,a51),a39) = product(a31,a52),
inference(equational,[status(thm)],[c351,c758]) ).
cnf(c1015,plain,
product(a5,product(a40,a39)) = product(a4,a5),
inference(equational,[status(thm)],[c360,c435,c546,c740]) ).
cnf(c1019,plain,
product(product(a108,a4),a39) = product(a105,a85),
inference(equational,[status(thm)],[c294,c740,c815]) ).
cnf(c1050,plain,
product(product(a86,a5),a39) = product(a83,a32),
inference(equational,[status(thm)],[c408,c728,c729]) ).
cnf(c1099,plain,
product(product(a141,a22),a45) = product(a1,a44),
inference(equational,[status(thm)],[c365,c509,c716]) ).
cnf(c1111,plain,
product(product(a90,a2),a41) = product(a89,a3),
inference(equational,[status(thm)],[c414,c711]) ).
cnf(c1113,plain,
product(product(a94,a2),a41) = product(a93,a3),
inference(equational,[status(thm)],[c419,c711]) ).
cnf(c1151,plain,
product(product(a49,a20),a47) = product(a45,a11),
inference(equational,[status(thm)],[c1,c555,c699,c701]) ).
cnf(c1152,plain,
product(product(a140,a139),a47) = product(a139,a140),
inference(equational,[status(thm)],[c329,c701]) ).
cnf(c1202,plain,
product(product(a115,a121),a68) = product(a114,a122),
inference(equational,[status(thm)],[c302,c666]) ).
cnf(c1203,plain,
product(product(a76,a121),a68) = product(a75,a122),
inference(equational,[status(thm)],[c399,c666]) ).
cnf(c1204,plain,
product(product(a122,a121),a68) = product(a121,a122),
inference(equational,[status(thm)],[c310,c666]) ).
cnf(c1206,plain,
product(product(a117,a116),a74) = product(a116,a117),
inference(equational,[status(thm)],[c304,c659]) ).
cnf(c1215,plain,
product(product(a69,a120),a32) = product(a68,a121),
inference(equational,[status(thm)],[c391,c665]) ).
cnf(c1217,plain,
product(product(a74,a117),a32) = product(a73,a118),
inference(equational,[status(thm)],[c397,c660]) ).
cnf(c1222,plain,
product(product(a71,a70),a13) = product(a69,a120),
inference(equational,[status(thm)],[c392,c439,c663]) ).
cnf(c1227,plain,
product(product(a108,a71),a70) = product(a109,a119),
inference(equational,[status(thm)],[c296,c661,c791]) ).
cnf(c1237,plain,
product(product(a112,a111),a79) = product(a111,a112),
inference(equational,[status(thm)],[c299,c653]) ).
cnf(c1240,plain,
product(product(a115,a114),a68) = product(a114,a115),
inference(equational,[status(thm)],[c302,c656]) ).
cnf(c1241,plain,
product(product(a122,a114),a68) = product(a121,a115),
inference(equational,[status(thm)],[c310,c656]) ).
cnf(c1243,plain,
product(product(a79,a112),a33) = product(a76,a13),
inference(equational,[status(thm)],[c402,c600,c654]) ).
cnf(c1248,plain,
product(product(a80,a110),a119) = product(a79,a111),
inference(equational,[status(thm)],[c403,c652]) ).
cnf(c1254,plain,
product(product(a119,a109),a70) = product(a118,a110),
inference(equational,[status(thm)],[c306,c649]) ).
cnf(c1255,plain,
product(product(a110,a109),a70) = product(a109,a110),
inference(equational,[status(thm)],[c296,c649]) ).
cnf(c1260,plain,
product(product(a84,a107),a39) = product(a81,a118),
inference(equational,[status(thm)],[c408,c608,c647]) ).
cnf(c1262,plain,
product(product(a71,a108),a118) = product(a70,a109),
inference(equational,[status(thm)],[c394,c648]) ).
cnf(c1266,plain,
product(product(a85,a105),a5) = product(a84,a106),
inference(equational,[status(thm)],[c409,c645]) ).
cnf(c1290,plain,
product(a97,product(a64,a42)) = product(a95,a42),
inference(equational,[status(thm)],[c421,c628]) ).
cnf(c1293,plain,
product(a96,product(a125,a41)) = product(a94,a64),
inference(equational,[status(thm)],[c420,c489,c627]) ).
cnf(c1301,plain,
product(a82,product(a70,a109)) = product(a80,a109),
inference(equational,[status(thm)],[c405,c606]) ).
cnf(c1309,plain,
product(a73,product(a109,a82)) = product(a71,a82),
inference(equational,[status(thm)],[c395,c594]) ).
cnf(c1310,plain,
product(a72,product(a118,a109)) = product(a70,a109),
inference(equational,[status(thm)],[c394,c593]) ).
cnf(c1346,plain,
product(a28,product(a8,a37)) = product(a26,a37),
inference(equational,[status(thm)],[c345,c528]) ).
cnf(c1371,plain,
product(a124,a122) = a115,
inference(equational,[status(thm)],[c311,c485,c798,c799]) ).
cnf(c1372,plain,
product(a115,a122) = a124,
inference(equational,[status(thm)],[c284,c1371]) ).
cnf(c1374,plain,
product(a124,a115) = product(a115,a123),
inference(equational,[status(thm)],[c245,c428,c1372]) ).
cnf(c1380,plain,
product(a111,product(a71,a70)) = product(a109,a119),
inference(equational,[status(thm)],[c296,c439,c466]) ).
cnf(c1386,plain,
product(a105,product(a85,a105)) = product(a103,a30),
inference(equational,[status(thm)],[c290,c454,c644]) ).
cnf(c1398,plain,
product(a99,product(a90,a124)) = product(a98,a99),
inference(equational,[status(thm)],[c424,c428,c621]) ).
cnf(c1399,plain,
product(a86,product(a103,a104)) = product(a87,a86),
inference(equational,[status(thm)],[c173,c428,c444]) ).
cnf(c1404,plain,
product(a90,product(a100,a90)) = product(a91,a90),
inference(equational,[status(thm)],[c181,c428]) ).
cnf(c1426,plain,
product(a81,product(a109,a81)) = product(a82,a81),
inference(equational,[status(thm)],[c163,c428]) ).
cnf(c1427,plain,
product(a82,product(a109,a82)) = product(a81,a82),
inference(equational,[status(thm)],[c406,c428]) ).
cnf(c1437,plain,
product(a76,product(a68,a76)) = product(a75,a76),
inference(equational,[status(thm)],[c399,c428]) ).
cnf(c1438,plain,
product(a77,a76) = product(a76,a121),
inference(equational,[status(thm)],[c153,c428,c801]) ).
cnf(c1439,plain,
product(a77,product(a121,a114)) = product(a76,a77),
inference(equational,[status(thm)],[c400,c428,c803]) ).
cnf(c1443,plain,
product(a79,product(a119,a79)) = product(a80,a79),
inference(equational,[status(thm)],[c159,c428]) ).
cnf(c1455,plain,
product(a71,product(a111,a118)) = product(a72,a71),
inference(equational,[status(thm)],[c143,c428,c464]) ).
cnf(c1482,plain,
product(a140,product(a45,a11)) = product(a139,a140),
inference(equational,[status(thm)],[c329,c428,c555]) ).
cnf(c1488,plain,
product(a57,product(a132,a26)) = product(a56,a57),
inference(equational,[status(thm)],[c378,c428,c499]) ).
cnf(c1495,plain,
product(a106,product(a84,a106)) = product(a107,a106),
inference(equational,[status(thm)],[c213,c428]) ).
cnf(c1499,plain,
product(a107,product(a84,a107)) = product(a106,a107),
inference(equational,[status(thm)],[c293,c428]) ).
cnf(c1506,plain,
product(a109,product(a70,a109)) = product(a110,a109),
inference(equational,[status(thm)],[c219,c428]) ).
cnf(c1509,plain,
product(a111,product(a119,a111)) = product(a110,a111),
inference(equational,[status(thm)],[c298,c428]) ).
cnf(c1531,plain,
product(a123,a122) = product(a122,a124),
inference(equational,[status(thm)],[c245,c428,c1372]) ).
cnf(c1533,plain,
product(a122,product(a68,a122)) = product(a121,a122),
inference(equational,[status(thm)],[c310,c428]) ).
cnf(c1535,plain,
product(a123,product(a115,a123)) = product(a122,a123),
inference(equational,[status(thm)],[c311,c428]) ).
cnf(c1536,plain,
product(a123,product(a75,a123)) = product(a124,a123),
inference(equational,[status(thm)],[c247,c428]) ).
cnf(c1555,plain,
product(a139,product(a49,a20)) = product(a140,a139),
inference(equational,[status(thm)],[c279,c428,c699]) ).
cnf(c1569,plain,
product(a111,product(a79,a111)) = product(a112,a111),
inference(equational,[status(thm)],[c223,c428]) ).
cnf(c1572,plain,
product(a116,product(a74,a116)) = product(a117,a116),
inference(equational,[status(thm)],[c233,c428]) ).
cnf(c1575,plain,
product(a117,product(a74,a117)) = product(a116,a117),
inference(equational,[status(thm)],[c304,c428]) ).
cnf(c1579,plain,
product(a112,product(a79,a112)) = product(a111,a112),
inference(equational,[status(thm)],[c299,c428]) ).
cnf(c1584,plain,
product(a119,product(a71,a70)) = product(a118,a119),
inference(equational,[status(thm)],[c306,c428,c439]) ).
cnf(c1588,plain,
product(a40,product(a4,a40)) = product(a39,a40),
inference(equational,[status(thm)],[c359,c428]) ).
cnf(c1615,plain,
product(a48,product(a140,a20)) = product(a49,a48),
inference(equational,[status(thm)],[c97,c428,c753]) ).
cnf(c1620,plain,
product(a49,product(a131,a49)) = product(a50,a49),
inference(equational,[status(thm)],[c99,c428]) ).
cnf(c1653,plain,
product(a22,product(a141,a22)) = product(a21,a22),
inference(equational,[status(thm)],[c340,c428]) ).
cnf(c1657,plain,
product(product(a16,a17),a28) = a17,
inference(equational,[status(thm)],[c284,c441]) ).
cnf(c1658,plain,
product(product(a39,a40),a14) = a42,
inference(equational,[status(thm)],[c83,c547,c743,c1588]) ).
cnf(c1659,plain,
product(a39,a40) = product(a42,a14),
inference(equational,[status(thm)],[c284,c1658]) ).
cnf(c1660,plain,
product(product(a86,a87),a103) = a87,
inference(equational,[status(thm)],[c284,c440]) ).
cnf(c1673,plain,
product(product(a24,a138),a48) = a26,
inference(equational,[status(thm)],[c284,c526]) ).
cnf(c1674,plain,
product(product(a18,a26),a57) = a20,
inference(equational,[status(thm)],[c284,c518]) ).
cnf(c1678,plain,
product(product(a1,a41),a14) = a5,
inference(equational,[status(thm)],[c9,c359,c428,c533,c712,c724]) ).
cnf(c1680,plain,
product(product(a30,a4),a40) = a32,
inference(equational,[status(thm)],[c284,c536,c739]) ).
cnf(c1686,plain,
product(product(a10,a57),a134) = a8,
inference(equational,[status(thm)],[c284,c618]) ).
cnf(c1690,plain,
product(product(a63,a41),a126) = a65,
inference(equational,[status(thm)],[c284,c583]) ).
cnf(c1691,plain,
product(product(a66,a1),a42) = a64,
inference(equational,[status(thm)],[c284,c585,c633]) ).
cnf(c1692,plain,
product(a64,a42) = product(a66,a1),
inference(equational,[status(thm)],[c284,c1691]) ).
cnf(c1693,plain,
product(a115,product(a77,a68)) = a123,
inference(equational,[status(thm)],[c245,c428,c657,c798]) ).
cnf(c1699,plain,
product(product(X,a47),a139) = product(product(X,a140),a47),
inference(equational,[status(thm)],[c329,c427]) ).
cnf(c1700,plain,
product(product(X,a14),a32) = product(product(X,a32),a13),
inference(equational,[status(thm)],[c319,c427]) ).
cnf(c1703,plain,
product(product(X,a2),a42) = product(product(X,a42),a1),
inference(equational,[status(thm)],[c285,c427]) ).
cnf(c1705,plain,
product(product(X,a26),a19) = product(product(X,a20),a26),
inference(equational,[status(thm)],[c337,c427]) ).
cnf(c1709,plain,
product(product(X,a29),a16) = product(product(X,a28),a17),
inference(equational,[status(thm)],[c334,c427,c722]) ).
cnf(c1715,plain,
product(product(X,a118),a82) = product(product(X,a83),a118),
inference(equational,[status(thm)],[c407,c427]) ).
cnf(c1716,plain,
product(product(X,a58),a132) = product(product(X,a133),a58),
inference(equational,[status(thm)],[c322,c427]) ).
cnf(c1718,plain,
product(product(X,a13),a130) = product(product(X,a131),a13),
inference(equational,[status(thm)],[c320,c427]) ).
cnf(c1719,plain,
product(a32,a130) = product(a34,a13),
inference(equational,[status(thm)],[c67,c352,c1718]) ).
cnf(c1724,plain,
product(product(X,a2),a65) = product(product(X,a66),a2),
inference(equational,[status(thm)],[c388,c427]) ).
cnf(c1728,plain,
product(product(X,a14),a40) = product(product(X,a41),a14),
inference(equational,[status(thm)],[c361,c427]) ).
cnf(c1729,plain,
product(a90,a14) = product(a88,a40),
inference(equational,[status(thm)],[c179,c413,c1728]) ).
cnf(c1730,plain,
product(a5,a40) = product(a1,a14),
inference(equational,[status(thm)],[c284,c1678,c1728]) ).
cnf(c1731,plain,
product(product(X,a14),a3) = product(product(X,a4),a14),
inference(equational,[status(thm)],[c349,c427]) ).
cnf(c1732,plain,
product(product(a98,X),a1) = product(a97,product(X,a1)),
inference(equational,[status(thm)],[c423,c427]) ).
cnf(c1734,plain,
product(product(X,a68),a98) = product(product(X,a98),a67),
inference(equational,[status(thm)],[c390,c427]) ).
cnf(c1736,plain,
product(product(X,a118),a70) = product(product(X,a71),a118),
inference(equational,[status(thm)],[c394,c427]) ).
cnf(c1737,plain,
product(product(a81,a71),a118) = a79,
inference(equational,[status(thm)],[c662,c1736]) ).
cnf(c1741,plain,
product(product(X,a32),a14) = product(product(X,a33),a13),
inference(equational,[status(thm)],[c352,c427,c677]) ).
cnf(c1745,plain,
product(product(X,a42),a1) = product(product(X,a3),a41),
inference(equational,[status(thm)],[c338,c427,c744,c1703]) ).
cnf(c1749,plain,
product(product(X,a39),a31) = product(product(X,a32),a39),
inference(equational,[status(thm)],[c351,c427]) ).
cnf(c1750,plain,
product(product(X,a5),a30) = product(product(X,a31),a5),
inference(equational,[status(thm)],[c350,c427]) ).
cnf(c1752,plain,
product(product(X,a109),a81) = product(product(X,a82),a109),
inference(equational,[status(thm)],[c406,c427]) ).
cnf(c1753,plain,
product(a73,a109) = product(a71,a81),
inference(equational,[status(thm)],[c145,c395,c1752]) ).
cnf(c1754,plain,
product(product(X,a70),a80) = product(product(X,a81),a70),
inference(equational,[status(thm)],[c405,c427]) ).
cnf(c1756,plain,
product(product(X,a119),a79) = product(product(X,a80),a119),
inference(equational,[status(thm)],[c403,c427]) ).
cnf(c1757,plain,
product(product(X,a68),a75) = product(product(X,a76),a68),
inference(equational,[status(thm)],[c399,c427]) ).
cnf(c1758,plain,
product(product(X,a114),a76) = product(product(X,a77),a114),
inference(equational,[status(thm)],[c400,c427]) ).
cnf(c1759,plain,
product(product(X,a32),a73) = product(product(X,a74),a32),
inference(equational,[status(thm)],[c397,c427]) ).
cnf(c1760,plain,
product(product(X,a13),a77) = product(product(X,a78),a13),
inference(equational,[status(thm)],[c401,c427]) ).
cnf(c1761,plain,
product(product(X,a82),a72) = product(product(X,a73),a82),
inference(equational,[status(thm)],[c396,c427]) ).
cnf(c1762,plain,
product(product(X,a13),a69) = product(product(X,a70),a13),
inference(equational,[status(thm)],[c392,c427]) ).
cnf(c1764,plain,
product(product(X,a33),a78) = product(product(X,a79),a33),
inference(equational,[status(thm)],[c402,c427]) ).
cnf(c1773,plain,
product(product(X,a1),a97) = product(product(X,a98),a1),
inference(equational,[status(thm)],[c423,c427]) ).
cnf(c1774,plain,
product(product(X,a92),a98) = product(product(X,a99),a92),
inference(equational,[status(thm)],[c424,c427]) ).
cnf(c1777,plain,
product(product(X,a100),a90) = product(product(X,a91),a100),
inference(equational,[status(thm)],[c416,c427]) ).
cnf(c1782,plain,
product(product(X,a92),a124) = product(product(X,a124),a91),
inference(equational,[status(thm)],[c417,c427]) ).
cnf(c1786,plain,
product(product(X,a138),a58) = product(product(X,a59),a138),
inference(equational,[status(thm)],[c380,c427]) ).
cnf(c1787,plain,
product(product(X,a134),a56) = product(product(X,a57),a134),
inference(equational,[status(thm)],[c378,c427]) ).
cnf(c1790,plain,
product(product(X,a37),a55) = product(product(X,a56),a37),
inference(equational,[status(thm)],[c377,c427]) ).
cnf(c1792,plain,
product(product(X,a127),a63) = product(product(X,a64),a127),
inference(equational,[status(thm)],[c386,c427]) ).
cnf(c1793,plain,
product(a96,a127) = product(a94,a63),
inference(equational,[status(thm)],[c191,c420,c1792]) ).
cnf(c1795,plain,
product(product(X,a2),a41) = product(product(X,a1),a42),
inference(equational,[status(thm)],[c362,c427,c633]) ).
cnf(c1796,plain,
product(product(X,a4),a39) = product(product(X,a40),a4),
inference(equational,[status(thm)],[c359,c427]) ).
cnf(c1805,plain,
product(product(X,a131),a49) = product(product(X,a50),a131),
inference(equational,[status(thm)],[c370,c427]) ).
cnf(c1806,plain,
product(product(X,a39),a51) = product(product(X,a52),a39),
inference(equational,[status(thm)],[c373,c427]) ).
cnf(c1808,plain,
product(product(X,a138),a48) = product(product(X,a49),a138),
inference(equational,[status(thm)],[c369,c427]) ).
cnf(c1809,plain,
product(product(X,a20),a47) = product(product(X,a48),a20),
inference(equational,[status(thm)],[c368,c427]) ).
cnf(c1811,plain,
product(product(X,a5),a39) = product(product(X,a4),a40),
inference(equational,[status(thm)],[c360,c427,c739]) ).
cnf(c1817,plain,
product(product(a97,X),a42) = product(a96,product(X,a42)),
inference(equational,[status(thm)],[c422,c427]) ).
cnf(c1819,plain,
product(product(X,a79),a111) = product(product(X,a112),a79),
inference(equational,[status(thm)],[c299,c427]) ).
cnf(c1820,plain,
product(product(X,a119),a110) = product(product(X,a111),a119),
inference(equational,[status(thm)],[c298,c427]) ).
cnf(c1822,plain,
product(product(X,a14),a100) = product(product(X,a101),a14),
inference(equational,[status(thm)],[c287,c427]) ).
cnf(c1823,plain,
product(product(X,a124),a99) = product(product(X,a100),a124),
inference(equational,[status(thm)],[c425,c427]) ).
cnf(c1825,plain,
product(product(X,a118),a108) = product(product(X,a109),a118),
inference(equational,[status(thm)],[c295,c427]) ).
cnf(c1826,plain,
product(a70,a108) = product(a72,a118),
inference(equational,[status(thm)],[c143,c394,c1825]) ).
cnf(c1830,plain,
product(product(a63,X),a96) = product(a62,product(X,a96)),
inference(equational,[status(thm)],[c385,c427]) ).
cnf(c1834,plain,
product(product(a69,X),a32) = product(a68,product(X,a32)),
inference(equational,[status(thm)],[c391,c427]) ).
cnf(c1835,plain,
product(product(X,a68),a114) = product(product(X,a115),a68),
inference(equational,[status(thm)],[c302,c427]) ).
cnf(c1836,plain,
product(a123,a68) = product(a121,a114),
inference(equational,[status(thm)],[c245,c310,c1835]) ).
cnf(c1837,plain,
product(product(X,a14),a115) = product(product(X,a116),a14),
inference(equational,[status(thm)],[c303,c427]) ).
cnf(c1838,plain,
product(product(X,a32),a117) = product(product(X,a118),a32),
inference(equational,[status(thm)],[c305,c427]) ).
cnf(c1842,plain,
product(product(X,a70),a109) = product(product(X,a110),a70),
inference(equational,[status(thm)],[c296,c427]) ).
cnf(c1854,plain,
product(product(X,a96),a127) = product(product(X,a128),a96),
inference(equational,[status(thm)],[c316,c427]) ).
cnf(c1856,plain,
product(product(X,a115),a122) = product(product(X,a123),a115),
inference(equational,[status(thm)],[c311,c427]) ).
cnf(c1861,plain,
product(product(X,a118),a71) = product(product(X,a119),a70),
inference(equational,[status(thm)],[c306,c427,c790]) ).
cnf(c1862,plain,
product(product(X,a32),a120) = product(product(X,a121),a32),
inference(equational,[status(thm)],[c309,c427]) ).
cnf(c1863,plain,
product(product(X,a124),a75) = product(product(X,a75),a123),
inference(equational,[status(thm)],[c312,c427]) ).
cnf(c1864,plain,
product(product(X,a68),a121) = product(product(X,a122),a68),
inference(equational,[status(thm)],[c310,c427]) ).
cnf(c1865,plain,
product(a124,a68) = product(a114,a121),
inference(equational,[status(thm)],[c302,c1372,c1864]) ).
cnf(c1867,plain,
product(product(a84,X),a39) = product(a83,product(X,a39)),
inference(equational,[status(thm)],[c408,c427]) ).
cnf(c1868,plain,
product(product(a81,X),a70) = product(a80,product(X,a70)),
inference(equational,[status(thm)],[c405,c427]) ).
cnf(c1873,plain,
product(product(a62,X),a1) = product(a61,product(X,a1)),
inference(equational,[status(thm)],[c384,c427]) ).
cnf(c1876,plain,
product(product(a71,X),a118) = product(a70,product(X,a118)),
inference(equational,[status(thm)],[c394,c427]) ).
cnf(c1877,plain,
product(product(a72,X),a109) = product(a71,product(X,a109)),
inference(equational,[status(thm)],[c395,c427]) ).
cnf(c1878,plain,
product(product(a80,X),a119) = product(a79,product(X,a119)),
inference(equational,[status(thm)],[c403,c427]) ).
cnf(c1879,plain,
product(product(a82,X),a109) = product(a81,product(X,a109)),
inference(equational,[status(thm)],[c406,c427]) ).
cnf(c1881,plain,
product(product(a79,X),a33) = product(a78,product(X,a33)),
inference(equational,[status(thm)],[c402,c427]) ).
cnf(c1882,plain,
product(product(a83,X),a118) = product(a82,product(X,a118)),
inference(equational,[status(thm)],[c407,c427]) ).
cnf(c1883,plain,
product(product(a78,X),a13) = product(a77,product(X,a13)),
inference(equational,[status(thm)],[c401,c427]) ).
cnf(c1887,plain,
product(product(a92,X),a124) = product(a91,product(X,a124)),
inference(equational,[status(thm)],[c417,c427]) ).
cnf(c1888,plain,
product(product(a76,X),a68) = product(a75,product(X,a68)),
inference(equational,[status(thm)],[c399,c427]) ).
cnf(c1889,plain,
product(product(a77,X),a114) = product(a76,product(X,a114)),
inference(equational,[status(thm)],[c400,c427]) ).
cnf(c1890,plain,
product(product(a73,X),a82) = product(a72,product(X,a82)),
inference(equational,[status(thm)],[c396,c427]) ).
cnf(c1891,plain,
product(product(a75,X),a14) = product(a74,product(X,a14)),
inference(equational,[status(thm)],[c398,c427]) ).
cnf(c1892,plain,
product(product(a74,X),a32) = product(a73,product(X,a32)),
inference(equational,[status(thm)],[c397,c427]) ).
cnf(c1896,plain,
product(product(a48,X),a20) = product(a47,product(X,a20)),
inference(equational,[status(thm)],[c368,c427]) ).
cnf(c1897,plain,
product(product(a49,X),a138) = product(a48,product(X,a138)),
inference(equational,[status(thm)],[c369,c427]) ).
cnf(c1900,plain,
product(product(a88,X),a4) = product(a87,product(X,a4)),
inference(equational,[status(thm)],[c412,c427]) ).
cnf(c1903,plain,
product(product(a43,X),a62) = product(a42,product(X,a62)),
inference(equational,[status(thm)],[c363,c427]) ).
cnf(c1908,plain,
product(product(a51,X),a59) = product(a50,product(X,a59)),
inference(equational,[status(thm)],[c372,c427]) ).
cnf(c1911,plain,
product(product(a47,X),a11) = product(a46,product(X,a11)),
inference(equational,[status(thm)],[c367,c427]) ).
cnf(c1912,plain,
product(product(a57,X),a134) = product(a56,product(X,a134)),
inference(equational,[status(thm)],[c378,c427]) ).
cnf(c1916,plain,
product(product(a38,X),a17) = product(a37,product(X,a17)),
inference(equational,[status(thm)],[c357,c427]) ).
cnf(c1923,plain,
product(product(a58,X),a26) = product(a57,product(X,a26)),
inference(equational,[status(thm)],[c379,c427]) ).
cnf(c1926,plain,
product(product(a59,X),a138) = product(a58,product(X,a138)),
inference(equational,[status(thm)],[c380,c427]) ).
cnf(c1934,plain,
product(product(a26,X),a138) = product(a25,product(X,a138)),
inference(equational,[status(thm)],[c344,c427]) ).
cnf(c1943,plain,
product(product(a22,X),a141) = product(a21,product(X,a141)),
inference(equational,[status(thm)],[c340,c427]) ).
cnf(c1944,plain,
product(product(a25,X),a49) = product(a24,product(X,a49)),
inference(equational,[status(thm)],[c343,c427]) ).
cnf(c1953,plain,
product(product(a138,X),a51) = product(a137,product(X,a51)),
inference(equational,[status(thm)],[c327,c427]) ).
cnf(c1954,plain,
product(product(a139,X),a20) = product(a138,product(X,a20)),
inference(equational,[status(thm)],[c328,c427]) ).
cnf(c1955,plain,
product(product(a140,X),a47) = product(a139,product(X,a47)),
inference(equational,[status(thm)],[c329,c427]) ).
cnf(c1956,plain,
product(product(a112,X),a79) = product(a111,product(X,a79)),
inference(equational,[status(thm)],[c299,c427]) ).
cnf(c1957,plain,
product(product(a109,X),a118) = product(a108,product(X,a118)),
inference(equational,[status(thm)],[c295,c427]) ).
cnf(c1958,plain,
product(product(a113,X),a33) = product(a112,product(X,a33)),
inference(equational,[status(thm)],[c300,c427]) ).
cnf(c1959,plain,
product(product(a110,X),a70) = product(a109,product(X,a70)),
inference(equational,[status(thm)],[c296,c427]) ).
cnf(c1960,plain,
product(product(a114,X),a13) = product(a113,product(X,a13)),
inference(equational,[status(thm)],[c301,c427]) ).
cnf(c1962,plain,
product(product(a118,X),a32) = product(a117,product(X,a32)),
inference(equational,[status(thm)],[c305,c427]) ).
cnf(c1963,plain,
product(product(a124,X),a75) = product(a123,product(X,a75)),
inference(equational,[status(thm)],[c312,c427]) ).
cnf(c1965,plain,
product(product(a123,X),a115) = product(a122,product(X,a115)),
inference(equational,[status(thm)],[c311,c427]) ).
cnf(c1966,plain,
product(product(a119,X),a70) = product(a118,product(X,a70)),
inference(equational,[status(thm)],[c306,c427]) ).
cnf(c1968,plain,
product(product(a122,X),a68) = product(a121,product(X,a68)),
inference(equational,[status(thm)],[c310,c427]) ).
cnf(c1969,plain,
product(product(a116,X),a14) = product(a115,product(X,a14)),
inference(equational,[status(thm)],[c303,c427]) ).
cnf(c1971,plain,
product(product(a115,X),a68) = product(a114,product(X,a68)),
inference(equational,[status(thm)],[c302,c427]) ).
cnf(c1972,plain,
product(product(a111,X),a119) = product(a110,product(X,a119)),
inference(equational,[status(thm)],[c298,c427]) ).
cnf(c1973,plain,
product(product(a117,X),a74) = product(a116,product(X,a74)),
inference(equational,[status(thm)],[c304,c427]) ).
cnf(c1978,plain,
product(product(a125,X),a2) = product(a124,product(X,a2)),
inference(equational,[status(thm)],[c313,c427]) ).
cnf(c1980,plain,
product(product(a101,X),a14) = product(a100,product(X,a14)),
inference(equational,[status(thm)],[c287,c427]) ).
cnf(c1981,plain,
product(product(a103,X),a4) = product(a102,product(X,a4)),
inference(equational,[status(thm)],[c289,c427]) ).
cnf(c1991,plain,
product(product(a100,X),a124) = product(a99,product(X,a124)),
inference(equational,[status(thm)],[c425,c427]) ).
cnf(c1992,plain,
product(product(a102,X),a40) = product(a101,product(X,a40)),
inference(equational,[status(thm)],[c288,c427]) ).
cnf(c2023,plain,
product(product(a116,a73),a32) = product(a117,product(a32,a74)),
inference(equational,[status(thm)],[c474,c796]) ).
cnf(c2052,plain,
product(product(a57,a25),a138) = product(a58,product(a138,a26)),
inference(equational,[status(thm)],[c571,c719]) ).
cnf(c2097,plain,
product(product(a66,a91),a124) = product(a67,product(a124,a92)),
inference(equational,[status(thm)],[c586,c824]) ).
cnf(c2115,plain,
product(product(a132,a133),a26) = product(a134,a56),
inference(equational,[status(thm)],[c1,c499,c691,c1787]) ).
cnf(c2126,plain,
product(product(a52,a53),a29) = product(a55,a54),
inference(equational,[status(thm)],[c564,c763]) ).
cnf(c2134,plain,
product(product(a1,a3),a14) = product(a4,a5),
inference(equational,[status(thm)],[c435,c546,c724,c1015,c1730,c1796]) ).
cnf(c2139,plain,
product(product(a90,a1),a42) = product(a89,a3),
inference(equational,[status(thm)],[c1111,c1795]) ).
cnf(c2142,plain,
product(product(a94,a1),a42) = product(a93,a3),
inference(equational,[status(thm)],[c1113,c1795]) ).
cnf(c2145,plain,
product(product(a125,a1),a42) = product(a124,a41),
inference(equational,[status(thm)],[c313,c1795]) ).
cnf(c2146,plain,
product(product(a98,a42),a41) = product(a97,a2),
inference(equational,[status(thm)],[c3,c628,c634,c1795]) ).
cnf(c2151,plain,
product(product(a108,a40),a4) = product(a105,a85),
inference(equational,[status(thm)],[c1019,c1796]) ).
cnf(c2161,plain,
product(a118,product(a32,a73)) = product(a116,a73),
inference(equational,[status(thm)],[c284,c397,c428,c475,c2023]) ).
cnf(c2166,plain,
product(product(a106,a39),a118) = product(a109,a82),
inference(equational,[status(thm)],[c217,c459,c1715]) ).
cnf(c2167,plain,
product(product(a56,a57),a26) = product(a60,a138),
inference(equational,[status(thm)],[c1,c572,c688,c767,c1716]) ).
cnf(c2184,plain,
product(a97,product(a94,a42)) = product(a99,a1),
inference(equational,[status(thm)],[c197,c637,c1732]) ).
cnf(c2226,plain,
product(product(a76,a32),a13) = product(a79,a112),
inference(equational,[status(thm)],[c284,c730,c1243]) ).
cnf(c2228,plain,
product(product(a53,a52),a39) = product(a51,a138),
inference(equational,[status(thm)],[c275,c428,c696,c1806]) ).
cnf(c2231,plain,
product(product(a108,a109),a70) = product(a111,a110),
inference(equational,[status(thm)],[c462,c649]) ).
cnf(c2234,plain,
product(product(a49,a48),a20) = product(a45,a11),
inference(equational,[status(thm)],[c1151,c1809]) ).
cnf(c2243,plain,
product(a104,product(a103,a104)) = product(a103,a86),
inference(equational,[status(thm)],[c284,c428,c872]) ).
cnf(c2252,plain,
product(a59,product(a138,a25)) = product(a57,a25),
inference(equational,[status(thm)],[c284,c344,c428,c573,c2052]) ).
cnf(c2255,plain,
product(a69,product(a120,a69)) = product(a71,a13),
inference(equational,[status(thm)],[c284,c428,c1222,c1762]) ).
cnf(c2258,plain,
product(product(a111,a33),a13) = product(a121,a114),
inference(equational,[status(thm)],[c227,c469,c803,c1760]) ).
cnf(c2259,plain,
product(product(a108,a81),a70) = product(a111,a80),
inference(equational,[status(thm)],[c462,c1754]) ).
cnf(c2262,plain,
product(product(a115,a123),a75) = product(a122,a124),
inference(equational,[status(thm)],[c668,c798]) ).
cnf(c2263,plain,
product(a121,product(a76,a121)) = product(a114,a121),
inference(equational,[status(thm)],[c428,c802]) ).
cnf(c2266,plain,
product(product(a107,a31),a5) = product(a103,a104),
inference(equational,[status(thm)],[c815,c877,c1750]) ).
cnf(c2268,plain,
product(product(a86,a4),a40) = product(a83,a32),
inference(equational,[status(thm)],[c1050,c1811]) ).
cnf(c2293,plain,
product(product(a38,a16),a29) = product(a37,a28),
inference(equational,[status(thm)],[c347,c707,c1916]) ).
cnf(c2296,plain,
product(a4,product(a4,a40)) = product(a1,a14),
inference(equational,[status(thm)],[c429,c532,c533]) ).
cnf(c2313,plain,
product(a122,product(a77,a68)) = product(a115,a123),
inference(equational,[status(thm)],[c247,c657,c1374,c1965]) ).
cnf(c2315,plain,
product(a124,product(a122,a124)) = product(a115,a124),
inference(equational,[status(thm)],[c428,c1371]) ).
cnf(c2317,plain,
product(a113,product(a76,a13)) = product(a121,a13),
inference(equational,[status(thm)],[c801,c1960]) ).
cnf(c2318,plain,
product(a111,a112) = a119,
inference(equational,[status(thm)],[c307,c309,c730,c1579,c1958,c2226,c2317]) ).
cnf(c2319,plain,
product(a119,a112) = a111,
inference(equational,[status(thm)],[c284,c2318]) ).
cnf(c2320,plain,
product(a119,a79) = product(a112,a111),
inference(equational,[status(thm)],[c299,c467,c2318]) ).
cnf(c2340,plain,
product(a108,product(a119,a118)) = product(a110,a71),
inference(equational,[status(thm)],[c219,c394,c460,c790,c1227,c1957]) ).
cnf(c2352,plain,
product(a101,product(a4,a40)) = product(a103,a40),
inference(equational,[status(thm)],[c205,c1992]) ).
cnf(c2358,plain,
product(a81,product(a118,a109)) = product(a83,a109),
inference(equational,[status(thm)],[c165,c1879]) ).
cnf(c2369,plain,
product(product(a60,a25),a138) = product(a56,a57),
inference(equational,[status(thm)],[c688,c719,c1488,c1923]) ).
cnf(c2374,plain,
product(a74,product(a68,a14)) = product(a76,a14),
inference(equational,[status(thm)],[c151,c1891]) ).
cnf(c2375,plain,
product(a79,a112) = product(a73,a70),
inference(equational,[status(thm)],[c139,c319,c588,c1700,c1892,c2226,c2374]) ).
cnf(c2421,plain,
product(a78,product(a121,a13)) = product(a80,a33),
inference(equational,[status(thm)],[c159,c731,c1881]) ).
cnf(c2422,plain,
product(product(a72,a71),a118) = product(a70,a111),
inference(equational,[status(thm)],[c284,c1455,c1876]) ).
cnf(c2425,plain,
product(product(a71,a119),a70) = product(a70,a71),
inference(equational,[status(thm)],[c394,c1861]) ).
cnf(c2427,plain,
product(product(a82,a119),a70) = product(a83,a71),
inference(equational,[status(thm)],[c165,c1861]) ).
cnf(c2428,plain,
product(product(a83,a119),a70) = product(a82,a71),
inference(equational,[status(thm)],[c407,c1861]) ).
cnf(c2429,plain,
product(product(a100,a75),a123) = product(a99,a75),
inference(equational,[status(thm)],[c425,c1863]) ).
cnf(c2434,plain,
product(a79,a111) = product(a83,a70),
inference(equational,[status(thm)],[c165,c650,c661,c1248]) ).
cnf(c2457,plain,
product(product(a115,a32),a13) = product(a116,a32),
inference(equational,[status(thm)],[c231,c1700]) ).
cnf(c2460,plain,
product(product(a100,a32),a13) = product(a101,a32),
inference(equational,[status(thm)],[c201,c1700]) ).
cnf(c2470,plain,
product(a64,product(a94,a63)) = product(a62,a127),
inference(equational,[status(thm)],[c316,c581,c1793,c1830,c1854]) ).
cnf(c2472,plain,
product(product(a83,a70),a111) = a79,
inference(equational,[status(thm)],[c284,c2434]) ).
cnf(c2473,plain,
product(product(a116,a32),a70) = a112,
inference(equational,[status(thm)],[c284,c302,c471,c784,c785,c2457]) ).
cnf(c2474,plain,
product(a116,a32) = product(a112,a70),
inference(equational,[status(thm)],[c284,c2473]) ).
cnf(c2476,plain,
product(a123,product(a77,a68)) = a115,
inference(equational,[status(thm)],[c284,c1693]) ).
cnf(c2477,plain,
product(a122,product(a75,a122)) = a124,
inference(equational,[status(thm)],[c243,c472,c483,c1203,c1372,c2263]) ).
cnf(c2478,plain,
product(product(a115,X),a75) = product(a122,product(X,a75)),
inference(equational,[status(thm)],[c427,c798]) ).
cnf(c2479,plain,
product(product(X,a75),a122) = product(product(X,a115),a75),
inference(equational,[status(thm)],[c427,c798]) ).
cnf(c2480,plain,
product(product(a124,X),a122) = product(a115,product(X,a122)),
inference(equational,[status(thm)],[c427,c1371]) ).
cnf(c2481,plain,
product(product(X,a124),a122) = product(product(X,a122),a115),
inference(equational,[status(thm)],[c427,c1371]) ).
cnf(c2482,plain,
product(product(a121,X),a76) = product(a114,product(X,a76)),
inference(equational,[status(thm)],[c427,c802]) ).
cnf(c2483,plain,
product(product(a114,X),a76) = product(a121,product(X,a76)),
inference(equational,[status(thm)],[c427,c801]) ).
cnf(c2484,plain,
product(product(X,a77),a114) = product(product(X,a76),a121),
inference(equational,[status(thm)],[c427,c801,c1758]) ).
cnf(c2485,plain,
product(product(X,a76),a114) = product(product(X,a121),a76),
inference(equational,[status(thm)],[c427,c802]) ).
cnf(c2486,plain,
product(product(X,a70),a111) = product(product(X,a108),a70),
inference(equational,[status(thm)],[c427,c462]) ).
cnf(c2487,plain,
product(product(a108,X),a70) = product(a111,product(X,a70)),
inference(equational,[status(thm)],[c427,c462]) ).
cnf(c2490,plain,
product(product(X,a37),a57) = product(product(X,a54),a37),
inference(equational,[status(thm)],[c427,c568]) ).
cnf(c2492,plain,
product(product(X,a2),a3) = product(product(X,a1),a2),
inference(equational,[status(thm)],[c427,c430]) ).
cnf(c2493,plain,
product(product(a3,X),a2) = product(a1,product(X,a2)),
inference(equational,[status(thm)],[c427,c429]) ).
cnf(c2494,plain,
product(product(X,a2),a1) = product(product(X,a3),a2),
inference(equational,[status(thm)],[c427,c429]) ).
cnf(c2505,plain,
product(product(a81,a82),a118) = product(a83,product(a106,a39)),
inference(equational,[status(thm)],[c607,c883,c1427]) ).
cnf(c2510,plain,
product(product(a122,a124),a123) = product(a123,product(a122,a123)),
inference(equational,[status(thm)],[c428,c1531]) ).
cnf(c2512,plain,
product(product(a116,a117),a32) = product(a118,product(a73,a118)),
inference(equational,[status(thm)],[c475,c1217,c1575]) ).
cnf(c2529,plain,
product(product(a114,a121),a32) = product(product(a110,a80),a13),
inference(equational,[status(thm)],[c471,c663,c808,c1862]) ).
cnf(c2535,plain,
product(product(a112,a111),a119) = product(a110,product(a80,a110)),
inference(equational,[status(thm)],[c428,c808,c1820]) ).
cnf(c2539,plain,
product(product(a82,a110),a70) = product(product(a80,a110),a109),
inference(equational,[status(thm)],[c650,c1842]) ).
cnf(c2590,plain,
product(a118,product(a73,a118)) = product(a109,a81),
inference(equational,[status(thm)],[c428,c476,c790,c808,c895,c1861,c2474]) ).
cnf(c2603,plain,
product(product(a110,a109),a118) = product(a108,product(a71,a108)),
inference(equational,[status(thm)],[c295,c592,c1506,c1957]) ).
cnf(c2605,plain,
product(product(a112,a80),a119) = product(a111,product(a112,a111)),
inference(equational,[status(thm)],[c1756,c1956,c2320]) ).
cnf(c2609,plain,
product(product(a140,a48),a20) = product(a139,product(a20,a47)),
inference(equational,[status(thm)],[c1809,c1955]) ).
cnf(c2611,plain,
product(product(a76,a121),a77) = product(a77,product(a76,a77)),
inference(equational,[status(thm)],[c428,c1438]) ).
cnf(c2622,plain,
product(product(a64,a96),a1) = product(a61,product(a130,a61)),
inference(equational,[status(thm)],[c493,c673,c1873]) ).
cnf(c2630,plain,
product(product(a75,a123),a115) = product(product(a77,a121),a68),
inference(equational,[status(thm)],[c657,c666,c1856]) ).
cnf(c2639,plain,
product(product(a91,a1),a42) = product(a94,product(a125,a41)),
inference(equational,[status(thm)],[c623,c624,c1795]) ).
cnf(c2685,plain,
product(product(a139,a11),a23) = product(a1,product(a44,a1)),
inference(equational,[status(thm)],[c508,c509,c705]) ).
cnf(c2714,plain,
product(product(a106,a107),a39) = product(a108,product(a81,a118)),
inference(equational,[status(thm)],[c458,c1260,c1499]) ).
cnf(c2746,plain,
product(product(a51,a58),a138) = product(a50,product(a138,a59)),
inference(equational,[status(thm)],[c768,c1908]) ).
cnf(c2749,plain,
product(product(a50,a49),a138) = product(a48,product(a132,a48)),
inference(equational,[status(thm)],[c369,c496,c1620,c1897]) ).
cnf(c2753,plain,
product(product(a77,a115),a68) = product(a76,product(a68,a114)),
inference(equational,[status(thm)],[c1835,c1889]) ).
cnf(c2766,plain,
product(product(a73,a81),a109) = product(a72,product(a109,a82)),
inference(equational,[status(thm)],[c811,c1890]) ).
cnf(c2772,plain,
product(product(a47,a10),a37) = product(a46,product(a37,a11)),
inference(equational,[status(thm)],[c638,c1911]) ).
cnf(c2779,plain,
product(product(a80,a110),a109) = product(a81,product(a70,a109)),
inference(equational,[status(thm)],[c1842,c1879,c2539]) ).
cnf(c2796,plain,
product(product(a80,a109),a118) = product(a83,product(a71,a108)),
inference(equational,[status(thm)],[c295,c592,c607,c1301]) ).
cnf(c2847,plain,
product(product(a46,a35),a24) = product(product(a44,a1),a35),
inference(equational,[status(thm)],[c705,c717]) ).
cnf(c2851,plain,
product(product(a70,a110),a119) = product(product(a71,a108),a70),
inference(equational,[status(thm)],[c439,c652,c2486]) ).
cnf(c2859,plain,
product(product(a110,a108),a118) = product(product(a108,a71),a109),
inference(equational,[status(thm)],[c648,c791]) ).
cnf(c2888,plain,
product(product(a45,a11),a20) = product(a49,a48),
inference(equational,[status(thm)],[c555,c556,c1615]) ).
cnf(c2913,plain,
product(product(a111,a71),a118) = product(a110,product(a71,a70)),
inference(equational,[status(thm)],[c439,c661,c1736,c1972]) ).
cnf(c2936,plain,
product(product(a123,a114),a68) = product(a122,product(a68,a115)),
inference(equational,[status(thm)],[c656,c1965]) ).
cnf(c2951,plain,
product(product(a103,a30),a5) = product(a107,a106),
inference(equational,[status(thm)],[c455,c1266,c1386,c1495]) ).
cnf(c3005,plain,
product(product(a100,a1),a42) = product(a103,a14),
inference(equational,[status(thm)],[c205,c711,c742,c1731,c1795]) ).
cnf(c3012,plain,
product(product(a123,a76),a68) = product(a124,product(a68,a75)),
inference(equational,[status(thm)],[c485,c1757]) ).
cnf(c3021,plain,
product(product(a110,a80),a112) = product(a112,a111),
inference(equational,[status(thm)],[c428,c808,c2319]) ).
cnf(c3022,plain,
product(product(a112,a110),a119) = product(product(a110,a80),a111),
inference(equational,[status(thm)],[c652,c808]) ).
cnf(c3024,plain,
product(product(a82,a80),a70) = product(product(a80,a110),a81),
inference(equational,[status(thm)],[c650,c810]) ).
cnf(c3058,plain,
product(product(a25,a50),a131) = product(a24,product(a131,a49)),
inference(equational,[status(thm)],[c1805,c1944]) ).
cnf(c3069,plain,
product(product(a106,a31),a39) = product(a101,product(a88,a40)),
inference(equational,[status(thm)],[c456,c819,c1811,c1992]) ).
cnf(c3085,plain,
product(product(a87,a53),a15) = product(product(a89,a3),a53),
inference(equational,[status(thm)],[c615,c702]) ).
cnf(c3117,plain,
product(product(a11,a54),a135) = product(a8,a37),
inference(equational,[status(thm)],[c404,c448,c764,c1790]) ).
cnf(c3159,plain,
product(product(a121,a77),a13) = product(a113,product(a111,a33)),
inference(equational,[status(thm)],[c468,c731,c805,c1764,c2320]) ).
cnf(c3211,plain,
product(product(a35,a140),a47) = product(a36,product(a49,a20)),
inference(equational,[status(thm)],[c540,c699,c1699]) ).
cnf(c3212,plain,
product(a37,product(a45,a11)) = product(a35,a140),
inference(equational,[status(thm)],[c284,c541,c1151,c3211]) ).
cnf(c3217,plain,
product(product(a99,a1),a42) = product(a96,a94),
inference(equational,[status(thm)],[c284,c1817,c2184]) ).
cnf(c3219,plain,
product(product(a111,a80),a70) = product(a108,a81),
inference(equational,[status(thm)],[c284,c2259]) ).
cnf(c3224,plain,
product(a114,product(a121,a114)) = product(a121,a77),
inference(equational,[status(thm)],[c284,c470,c2258,c3159]) ).
cnf(c3240,plain,
product(product(a111,a110),a70) = product(a108,a109),
inference(equational,[status(thm)],[c284,c2231]) ).
cnf(c3244,plain,
product(a110,product(a71,a70)) = product(a108,a119),
inference(equational,[status(thm)],[c439,c463,c1972]) ).
cnf(c3269,plain,
product(product(a71,a33),a13) = product(a68,a122),
inference(equational,[status(thm)],[c243,c391,c481,c677,c1741,c1834,c2255]) ).
cnf(c3281,plain,
product(a96,a41) = product(a98,a2),
inference(equational,[status(thm)],[c195,c422,c423,c633,c711,c2146,c2492]) ).
cnf(c3287,plain,
product(a108,product(a81,a118)) = product(a112,a70),
inference(equational,[status(thm)],[c284,c428,c476,c1957,c2474,c2590]) ).
cnf(c3292,plain,
product(product(a83,a70),a79) = product(a73,a70),
inference(equational,[status(thm)],[c223,c428,c2375,c2434]) ).
cnf(c3293,plain,
product(a111,product(a83,a70)) = product(a112,a111),
inference(equational,[status(thm)],[c1569,c2434]) ).
cnf(c3297,plain,
product(product(a57,a54),a37) = product(a54,a57),
inference(equational,[status(thm)],[c569,c2490]) ).
cnf(c3304,plain,
product(product(a109,a81),a13) = product(a124,a32),
inference(equational,[status(thm)],[c243,c472,c784,c895,c1372,c1762,c2529]) ).
cnf(c3314,plain,
product(product(a80,a33),a13) = product(a77,a121),
inference(equational,[status(thm)],[c284,c1883,c2421]) ).
cnf(c3317,plain,
product(a138,product(a20,a48)) = product(a140,a48),
inference(equational,[status(thm)],[c95,c284,c428,c1954,c2609]) ).
cnf(c3318,plain,
product(a76,product(a76,a121)) = product(a77,a121),
inference(equational,[status(thm)],[c153,c400,c428,c598,c802,c1438,c1889,c2484,c2611]) ).
cnf(c3330,plain,
product(product(a82,a71),a70) = product(a83,a119),
inference(equational,[status(thm)],[c284,c2428]) ).
cnf(c3332,plain,
product(a70,product(a71,a70)) = product(a71,a119),
inference(equational,[status(thm)],[c284,c428,c2425]) ).
cnf(c3334,plain,
product(product(a79,a108),a118) = product(a82,a72),
inference(equational,[status(thm)],[c143,c606,c648,c792]) ).
cnf(c3337,plain,
product(product(a122,a123),a75) = product(a115,a124),
inference(equational,[status(thm)],[c668,c799]) ).
cnf(c3340,plain,
product(a108,product(a106,a39)) = product(a101,a32),
inference(equational,[status(thm)],[c458,c1680,c1811,c1981,c1992,c2951]) ).
cnf(c3347,plain,
product(product(a124,a123),a115) = product(a115,a124),
inference(equational,[status(thm)],[c1372,c1856,c2480]) ).
cnf(c3349,plain,
product(product(a100,a122),a115) = product(a99,a122),
inference(equational,[status(thm)],[c425,c2481]) ).
cnf(c3352,plain,
product(product(a103,a40),a14) = product(a100,a2),
inference(equational,[status(thm)],[c743,c1980,c2352]) ).
cnf(c3356,plain,
product(a121,product(a68,a114)) = product(a123,a114),
inference(equational,[status(thm)],[c284,c302,c428,c1968,c2936]) ).
cnf(c3358,plain,
product(a83,product(a72,a118)) = product(a79,a108),
inference(equational,[status(thm)],[c143,c606,c607,c1737,c1825]) ).
cnf(c3376,plain,
product(product(a37,a28),a29) = product(a38,a16),
inference(equational,[status(thm)],[c284,c2293]) ).
cnf(c3388,plain,
product(product(a73,a70),a112) = a79,
inference(equational,[status(thm)],[c284,c2375]) ).
cnf(c3390,plain,
product(a110,product(a110,a80)) = a119,
inference(equational,[status(thm)],[c1,c808,c1972,c2318]) ).
cnf(c3392,plain,
product(product(X,product(Y,Z)),Z) = product(product(X,Z),Y),
inference(equational,[status(thm)],[c284,c427]) ).
cnf(c3393,plain,
product(product(a100,a91),a2) = product(a93,a65),
inference(equational,[status(thm)],[c632,c669,c947,c1293,c3281,c3392]) ).
cnf(c3394,plain,
product(a92,a66) = product(a100,a91),
inference(equational,[status(thm)],[c284,c940,c3393]) ).
cnf(c3395,plain,
product(product(a112,a70),a32) = a116,
inference(equational,[status(thm)],[c284,c476,c2161,c2474,c3392]) ).
cnf(c3396,plain,
product(product(X,a70),a108) = product(product(X,a111),a70),
inference(equational,[status(thm)],[c462,c3392]) ).
cnf(c3397,plain,
product(product(X,a75),a115) = product(product(X,a122),a75),
inference(equational,[status(thm)],[c798,c3392]) ).
cnf(c3398,plain,
product(product(X,a123),a115) = product(product(X,a122),a124),
inference(equational,[status(thm)],[c1371,c1856,c3392]) ).
cnf(c3405,plain,
product(a122,product(a122,a124)) = product(a123,a124),
inference(equational,[status(thm)],[c1,c245,c311,c484,c1531,c1965,c2481,c2510,c3398]) ).
cnf(c3407,plain,
product(product(a100,a91),a66) = a92,
inference(equational,[status(thm)],[c284,c3394]) ).
cnf(c3408,plain,
product(product(product(X,Y),Z),Y) = product(X,product(Z,Y)),
inference(equational,[status(thm)],[c284,c427]) ).
cnf(c3413,plain,
product(a112,product(a83,a70)) = product(a119,a111),
inference(equational,[status(thm)],[c1237,c2318,c2434,c3408]) ).
cnf(c3414,plain,
product(product(a111,X),a70) = product(a108,product(X,a70)),
inference(equational,[status(thm)],[c462,c3408]) ).
cnf(c3415,plain,
product(product(a122,X),a75) = product(a115,product(X,a75)),
inference(equational,[status(thm)],[c798,c3408]) ).
cnf(c3416,plain,
product(product(a115,X),a122) = product(a124,product(X,a122)),
inference(equational,[status(thm)],[c1371,c3408]) ).
cnf(c3430,plain,
product(a117,product(a74,a116)) = product(a116,product(a117,a116)),
inference(equational,[status(thm)],[c428,c1206,c3408]) ).
cnf(c3431,plain,
product(a109,product(a110,a109)) = product(a110,product(a70,a109)),
inference(equational,[status(thm)],[c428,c1255,c3408]) ).
cnf(c3433,plain,
product(product(a109,a119),a71) = product(a108,product(a70,a71)),
inference(equational,[status(thm)],[c1227,c3408]) ).
cnf(c3443,plain,
product(a115,product(a68,a114)) = product(a114,product(a115,a114)),
inference(equational,[status(thm)],[c428,c1240,c3408]) ).
cnf(c3444,plain,
product(a122,product(a68,a121)) = product(a121,product(a122,a121)),
inference(equational,[status(thm)],[c428,c1204,c3408]) ).
cnf(c3542,plain,
product(product(a31,a52),a51) = product(a32,product(a39,a51)),
inference(equational,[status(thm)],[c979,c3408]) ).
cnf(c3601,plain,
product(product(a76,a13),a112) = product(a79,product(a33,a112)),
inference(equational,[status(thm)],[c1243,c3408]) ).
cnf(c3684,plain,
product(product(a106,a39),a82) = product(a109,product(a118,a82)),
inference(equational,[status(thm)],[c883,c3408]) ).
cnf(c3687,plain,
product(product(a70,a109),a108) = product(a71,product(a118,a108)),
inference(equational,[status(thm)],[c1262,c3408]) ).
cnf(c3691,plain,
product(product(a83,a109),a70) = product(a80,product(a119,a110)),
inference(equational,[status(thm)],[c649,c1248,c2434,c3408]) ).
cnf(c3700,plain,
product(product(a113,a61),a60) = product(a114,product(a13,a60)),
inference(equational,[status(thm)],[c941,c3408]) ).
cnf(c3753,plain,
product(a82,product(a109,a81)) = product(a81,product(a82,a81)),
inference(equational,[status(thm)],[c428,c891,c3408]) ).
cnf(c3758,plain,
product(product(a73,a70),a33) = product(a76,a13),
inference(equational,[status(thm)],[c284,c2375,c3392,c3601]) ).
cnf(c3763,plain,
product(a124,product(a68,a122)) = product(a114,a122),
inference(equational,[status(thm)],[c666,c1202,c3416]) ).
cnf(c3772,plain,
product(product(a112,a70),a83) = product(a118,a108),
inference(equational,[status(thm)],[c463,c1966,c3392,c3413]) ).
cnf(c3773,plain,
product(product(a112,a111),a70) = product(a106,a39),
inference(equational,[status(thm)],[c284,c459,c1569,c2434,c3414]) ).
cnf(c3776,plain,
product(a108,product(a112,a70)) = a118,
inference(equational,[status(thm)],[c306,c2318,c3414]) ).
cnf(c3777,plain,
product(a118,a108) = product(a101,a32),
inference(equational,[status(thm)],[c428,c3340,c3396,c3773,c3776]) ).
cnf(c3778,plain,
product(a83,product(a81,a118)) = a73,
inference(equational,[status(thm)],[c284,c605,c3292,c3408]) ).
cnf(c3779,plain,
product(a82,a81) = product(a73,a118),
inference(equational,[status(thm)],[c284,c1882,c3778]) ).
cnf(c3787,plain,
product(product(a129,a3),a2) = product(a130,product(a3,a42)),
inference(equational,[status(thm)],[c446,c492,c2494]) ).
cnf(c3803,plain,
product(product(a121,a114),a75) = product(a124,product(a68,a75)),
inference(equational,[status(thm)],[c1757,c1836,c3012]) ).
cnf(c3805,plain,
product(product(a123,a98),a67) = product(product(a121,a114),a98),
inference(equational,[status(thm)],[c1734,c1836]) ).
cnf(c3807,plain,
product(product(a121,a114),a115) = product(a122,product(a68,a115)),
inference(equational,[status(thm)],[c656,c1836,c2936]) ).
cnf(c3816,plain,
product(product(a79,a71),a118) = product(a80,product(a71,a70)),
inference(equational,[status(thm)],[c792,c1736,c1868]) ).
cnf(c3822,plain,
product(product(a83,a71),a110) = product(a80,product(a118,a110)),
inference(equational,[status(thm)],[c649,c1254,c1868,c1879,c2427]) ).
cnf(c3834,plain,
product(product(a114,a121),a75) = product(a123,product(a68,a75)),
inference(equational,[status(thm)],[c1865,c1963]) ).
cnf(c3837,plain,
product(product(a124,a114),a68) = product(product(a114,a121),a115),
inference(equational,[status(thm)],[c656,c1865]) ).
cnf(c3838,plain,
product(product(a114,a121),a2) = product(a125,product(a68,a2)),
inference(equational,[status(thm)],[c486,c1865]) ).
cnf(c3843,plain,
product(product(a82,a108),a70) = product(product(a80,a110),a111),
inference(equational,[status(thm)],[c650,c2486]) ).
cnf(c3847,plain,
product(product(a106,a39),a70) = product(a112,a111),
inference(equational,[status(thm)],[c459,c2487,c3293]) ).
cnf(c3922,plain,
product(product(a90,a32),a13) = product(product(a88,a40),a32),
inference(equational,[status(thm)],[c1700,c1729]) ).
cnf(c3926,plain,
product(product(a90,a3),a14) = product(a87,a39),
inference(equational,[status(thm)],[c359,c724,c1729,c1900]) ).
cnf(c3927,plain,
product(product(a90,a53),a15) = product(product(a88,a40),a53),
inference(equational,[status(thm)],[c702,c1729]) ).
cnf(c3940,plain,
product(a115,product(a75,a123)) = product(a123,product(a122,a123)),
inference(equational,[status(thm)],[c2262,c2510,c3408]) ).
cnf(c3941,plain,
product(product(a82,a71),a119) = product(a83,product(a71,a70)),
inference(equational,[status(thm)],[c439,c2428,c3408]) ).
cnf(c3943,plain,
product(product(a111,a110),a109) = product(a108,product(a70,a109)),
inference(equational,[status(thm)],[c2231,c3408]) ).
cnf(c4028,plain,
product(product(a112,a111),a80) = product(a110,product(a112,a80)),
inference(equational,[status(thm)],[c3021,c3408]) ).
cnf(c4049,plain,
product(a115,product(a114,a115)) = product(a114,product(a68,a115)),
inference(equational,[status(thm)],[c229,c428,c472,c1240,c1971,c3443]) ).
cnf(c4069,plain,
product(a82,product(a81,a82)) = product(a81,product(a109,a82)),
inference(equational,[status(thm)],[c163,c428,c606,c891,c1879,c3753]) ).
cnf(c4073,plain,
product(product(a80,a110),a111) = product(a79,product(a119,a111)),
inference(equational,[status(thm)],[c221,c295,c428,c661,c1878,c1882,c3691,c3843]) ).
cnf(c4109,plain,
product(a117,product(a116,a117)) = product(a116,product(a74,a117)),
inference(equational,[status(thm)],[c233,c428,c474,c1206,c1973,c3430]) ).
cnf(c4146,plain,
product(a122,product(a121,a122)) = product(a121,product(a68,a122)),
inference(equational,[status(thm)],[c243,c428,c483,c1204,c1968,c3444]) ).
cnf(c4198,plain,
product(product(a60,a138),a57) = product(a56,product(a26,a57)),
inference(equational,[status(thm)],[c2167,c3408]) ).
cnf(c4213,plain,
product(product(a71,a81),a82) = product(a72,product(a109,a82)),
inference(equational,[status(thm)],[c811,c1753,c2766]) ).
cnf(c4216,plain,
product(product(a79,a82),a118) = product(product(a81,a71),a83),
inference(equational,[status(thm)],[c792,c812]) ).
cnf(c4225,plain,
product(product(a75,a122),a124) = product(product(a77,a121),a68),
inference(equational,[status(thm)],[c2630,c3398]) ).
cnf(c4239,plain,
product(product(a73,a70),a79) = product(a83,a70),
inference(equational,[status(thm)],[c299,c428,c2375,c2434]) ).
cnf(c4244,plain,
product(product(a99,a122),a123) = product(a100,a115),
inference(equational,[status(thm)],[c284,c667,c3349]) ).
cnf(c4251,plain,
product(product(a96,a94),a2) = product(a99,a42),
inference(equational,[status(thm)],[c284,c633,c3217]) ).
cnf(c4252,plain,
product(product(a124,a32),a13) = product(a109,a81),
inference(equational,[status(thm)],[c284,c3304]) ).
cnf(c4254,plain,
product(product(a101,a32),a83) = product(a112,a70),
inference(equational,[status(thm)],[c284,c3772,c3777]) ).
cnf(c4256,plain,
product(product(a87,a39),a14) = product(a90,a3),
inference(equational,[status(thm)],[c284,c3926]) ).
cnf(c4263,plain,
product(a111,product(a112,a111)) = product(a119,a111),
inference(equational,[status(thm)],[c428,c2318]) ).
cnf(c4270,plain,
product(a97,product(a66,a1)) = product(a95,a42),
inference(equational,[status(thm)],[c1290,c1692]) ).
cnf(c4271,plain,
product(product(a112,a70),a73) = a118,
inference(equational,[status(thm)],[c233,c235,c1759,c2474]) ).
cnf(c4272,plain,
product(a119,product(a110,a80)) = a110,
inference(equational,[status(thm)],[c284,c3390]) ).
cnf(c4273,plain,
product(a109,product(a109,a81)) = a118,
inference(equational,[status(thm)],[c306,c895,c1959,c3390]) ).
cnf(c4274,plain,
product(a118,a81) = product(a109,a82),
inference(equational,[status(thm)],[c163,c428,c3392,c4273]) ).
cnf(c4275,plain,
product(a118,product(a112,a70)) = a108,
inference(equational,[status(thm)],[c284,c3776]) ).
cnf(c4276,plain,
product(a117,a116) = product(a108,a32),
inference(equational,[status(thm)],[c1962,c3395,c4275]) ).
cnf(c4277,plain,
product(a73,product(a81,a118)) = a83,
inference(equational,[status(thm)],[c284,c3778]) ).
cnf(c4278,plain,
product(a101,product(a83,a32)) = a116,
inference(equational,[status(thm)],[c3395,c3408,c4254]) ).
cnf(c4280,plain,
product(product(a108,a33),a13) = a123,
inference(equational,[status(thm)],[c284,c683,c1741,c4276]) ).
cnf(c4293,plain,
product(product(X,product(Y,X)),Y) = product(X,product(X,Y)),
inference(equational,[status(thm)],[c428,c3408]) ).
cnf(c4294,plain,
product(a119,a111) = product(a110,a112),
inference(equational,[status(thm)],[c808,c2319,c4272,c4293]) ).
cnf(c4295,plain,
product(product(a109,a82),a81) = a118,
inference(equational,[status(thm)],[c163,c4273,c4293]) ).
cnf(c4296,plain,
product(a79,product(a112,a111)) = product(a80,a79),
inference(equational,[status(thm)],[c403,c428,c1878,c2320,c4293]) ).
cnf(c4298,plain,
product(product(a73,a108),a118) = product(a81,a82),
inference(equational,[status(thm)],[c163,c648,c1426,c3779,c4293]) ).
cnf(c4299,plain,
product(product(a108,a73),a32) = product(a116,a117),
inference(equational,[status(thm)],[c233,c796,c1572,c4276,c4293]) ).
cnf(c4300,plain,
product(a109,a81) = product(a108,a73),
inference(equational,[status(thm)],[c284,c2512,c2590,c4299]) ).
cnf(c4302,plain,
product(a110,product(a80,a110)) = product(a119,a80),
inference(equational,[status(thm)],[c1237,c1443,c2318,c2320,c2535,c3392,c4293]) ).
cnf(c4307,plain,
product(product(a83,a70),a112) = product(a79,product(a73,a70)),
inference(equational,[status(thm)],[c299,c2375,c2434,c4293]) ).
cnf(c4345,plain,
product(a119,product(a119,a80)) = product(a110,product(a112,a80)),
inference(equational,[status(thm)],[c403,c2320,c4028,c4293]) ).
cnf(c4349,plain,
product(product(a118,a83),a82) = product(a118,product(a118,a82)),
inference(equational,[status(thm)],[c165,c4293]) ).
cnf(c4364,plain,
product(product(a100,a91),a90) = product(a100,product(a100,a90)),
inference(equational,[status(thm)],[c181,c4293]) ).
cnf(c4386,plain,
product(a77,product(a121,a77)) = product(a76,product(a76,a77)),
inference(equational,[status(thm)],[c428,c1438,c3318,c4293]) ).
cnf(c4389,plain,
product(product(a119,a80),a79) = product(a119,product(a112,a111)),
inference(equational,[status(thm)],[c159,c2320,c4293]) ).
cnf(c4402,plain,
product(product(a101,a32),a109) = product(a118,product(a118,a109)),
inference(equational,[status(thm)],[c295,c3777,c4293]) ).
cnf(c4460,plain,
product(product(a1,a14),a5) = product(a4,product(a4,a5)),
inference(equational,[status(thm)],[c435,c2296,c4293]) ).
cnf(c4469,plain,
product(a123,product(a124,a123)) = product(a122,product(a122,a123)),
inference(equational,[status(thm)],[c428,c1531,c3405,c4293]) ).
cnf(c4545,plain,
product(a83,product(a106,a39)) = product(a73,a108),
inference(equational,[status(thm)],[c284,c2505,c4298]) ).
cnf(c4547,plain,
product(a111,product(a110,a80)) = product(a119,a110),
inference(equational,[status(thm)],[c298,c428,c466,c808,c4294]) ).
cnf(c4548,plain,
product(a111,product(a110,a112)) = product(a110,a111),
inference(equational,[status(thm)],[c1509,c4294]) ).
cnf(c4550,plain,
product(a109,product(a81,a82)) = product(a118,a82),
inference(equational,[status(thm)],[c3408,c4295]) ).
cnf(c4555,plain,
product(product(a4,a5),a40) = product(a5,product(a4,a40)),
inference(equational,[status(thm)],[c360,c435,c546,c724,c1811,c2134,c4460]) ).
cnf(c4559,plain,
product(a123,product(a122,a124)) = product(a122,product(a115,a124)),
inference(equational,[status(thm)],[c311,c484,c1531,c1965,c3347,c4469]) ).
cnf(c4562,plain,
product(product(a81,a118),a73) = product(a83,product(a112,a70)),
inference(equational,[status(thm)],[c605,c3392,c3408,c4307]) ).
cnf(c4566,plain,
product(product(a80,a112),a79) = product(a79,product(a73,a70)),
inference(equational,[status(thm)],[c1819,c2434,c3392,c4296,c4307]) ).
cnf(c4568,plain,
product(a77,product(a76,a121)) = product(a76,product(a114,a121)),
inference(equational,[status(thm)],[c400,c598,c802,c1438,c1889,c2484,c4386]) ).
cnf(c4569,plain,
product(a119,product(a112,a111)) = product(a110,a111),
inference(equational,[status(thm)],[c403,c428,c466,c2320,c2605,c4263,c4294,c4345,c4548]) ).
cnf(c4579,plain,
product(a110,product(a112,a80)) = product(a111,a110),
inference(equational,[status(thm)],[c298,c428,c466,c2535,c4302,c4345,c4569]) ).
cnf(c4581,plain,
product(a79,product(a83,a70)) = product(a80,a112),
inference(equational,[status(thm)],[c284,c428,c4239,c4566]) ).
cnf(c4583,plain,
product(a108,product(a108,a73)) = product(a118,a109),
inference(equational,[status(thm)],[c296,c895,c1966,c3414,c4300,c4547]) ).
cnf(c4585,plain,
product(a108,product(a73,a108)) = product(a118,a83),
inference(equational,[status(thm)],[c165,c428,c1957,c2505,c4545,c4550]) ).
cnf(c4586,plain,
product(product(a108,a73),a109) = product(a109,a82),
inference(equational,[status(thm)],[c163,c428,c4300]) ).
cnf(c4587,plain,
product(a109,product(a73,a118)) = product(a112,a70),
inference(equational,[status(thm)],[c460,c1957,c3287,c4300]) ).
cnf(c4613,plain,
product(product(product(X,a4),a40),a39) = product(X,a5),
inference(equational,[status(thm)],[c9,c739,c3408]) ).
cnf(c4616,plain,
product(product(a88,a40),a39) = product(a87,a5),
inference(equational,[status(thm)],[c175,c4613]) ).
cnf(c4645,plain,
product(product(product(X,a122),a124),a115) = product(X,a123),
inference(equational,[status(thm)],[c284,c667,c1856,c3398]) ).
cnf(c4646,plain,
product(product(X,a115),a124) = product(product(X,a123),a122),
inference(equational,[status(thm)],[c284,c1856,c2481,c3398,c4645]) ).
cnf(c4647,plain,
product(product(X,a124),a115) = product(product(X,a122),a123),
inference(equational,[status(thm)],[c284,c4645]) ).
cnf(c4649,plain,
product(product(a98,a122),a123) = product(product(a100,a91),a115),
inference(equational,[status(thm)],[c632,c4647]) ).
cnf(c4651,plain,
product(product(a91,a123),a122) = product(a92,product(a115,a124)),
inference(equational,[status(thm)],[c620,c4646]) ).
cnf(c4652,plain,
product(a124,product(a115,a124)) = product(a115,product(a122,a124)),
inference(equational,[status(thm)],[c428,c1531,c2480,c4646]) ).
cnf(c4654,plain,
product(product(a99,a123),a122) = product(a100,product(a115,a124)),
inference(equational,[status(thm)],[c631,c4646]) ).
cnf(c4656,plain,
product(product(a75,a123),a122) = product(product(a77,a68),a124),
inference(equational,[status(thm)],[c657,c4646]) ).
cnf(c4657,plain,
product(product(product(X,a76),a121),a114) = product(X,a77),
inference(equational,[status(thm)],[c284,c804,c1758,c2484]) ).
cnf(c4658,plain,
product(product(X,a114),a121) = product(product(X,a77),a76),
inference(equational,[status(thm)],[c802,c1758,c2484,c3408,c4657]) ).
cnf(c4659,plain,
product(product(X,a76),a77) = product(product(X,a121),a114),
inference(equational,[status(thm)],[c284,c4657]) ).
cnf(c4660,plain,
product(a77,product(a76,a77)) = product(a76,product(a121,a114)),
inference(equational,[status(thm)],[c428,c1889,c4659]) ).
cnf(c4663,plain,
product(product(a119,X),a112) = product(a111,product(X,a112)),
inference(equational,[status(thm)],[c2318,c3408]) ).
cnf(c4664,plain,
product(product(X,a112),a119) = product(product(X,a111),a112),
inference(equational,[status(thm)],[c427,c2318]) ).
cnf(c4665,plain,
product(product(a111,X),a112) = product(a119,product(X,a112)),
inference(equational,[status(thm)],[c427,c2318]) ).
cnf(c4666,plain,
product(product(X,a119),a112) = product(product(X,a112),a111),
inference(equational,[status(thm)],[c2318,c3392]) ).
cnf(c4681,plain,
product(product(a4,a5),product(a40,a39)) = a5,
inference(equational,[status(thm)],[c284,c1015]) ).
cnf(c4688,plain,
product(product(a98,a99),product(a90,a124)) = a99,
inference(equational,[status(thm)],[c284,c1398]) ).
cnf(c4689,plain,
product(product(a87,a86),product(a103,a104)) = a86,
inference(equational,[status(thm)],[c284,c1399]) ).
cnf(c4704,plain,
product(product(a122,product(X,a68)),X) = product(a121,product(a68,X)),
inference(equational,[status(thm)],[c483,c3408]) ).
cnf(c4709,plain,
product(product(a115,product(X,a68)),X) = product(a114,product(a68,X)),
inference(equational,[status(thm)],[c472,c3408]) ).
cnf(c4710,plain,
product(a114,product(a68,a121)) = product(a124,a121),
inference(equational,[status(thm)],[c243,c1372,c4709]) ).
cnf(c4711,plain,
product(a124,product(a121,a122)) = product(a114,product(a68,a122)),
inference(equational,[status(thm)],[c310,c3416,c4709]) ).
cnf(c4769,plain,
product(product(a77,product(X,a114)),X) = product(a76,product(a114,X)),
inference(equational,[status(thm)],[c598,c3408]) ).
cnf(c4770,plain,
product(product(a123,product(X,a115)),X) = product(a122,product(a115,X)),
inference(equational,[status(thm)],[c484,c3408]) ).
cnf(c4771,plain,
product(product(a115,a124),a123) = product(a115,product(a122,a123)),
inference(equational,[status(thm)],[c312,c1374,c1535,c1863,c2478,c3337,c3415,c4770]) ).
cnf(c4772,plain,
product(product(a115,a123),a124) = product(a115,product(a122,a124)),
inference(equational,[status(thm)],[c311,c428,c484,c1371,c1374,c1531,c3398,c3416,c4771]) ).
cnf(c4790,plain,
product(product(a34,product(X,a131)),X) = product(a33,product(a131,X)),
inference(equational,[status(thm)],[c538,c3408]) ).
cnf(c4794,plain,
product(product(a34,a49),a50) = product(a33,product(a131,a50)),
inference(equational,[status(thm)],[c370,c4790]) ).
cnf(c4838,plain,
product(product(a71,product(X,a118)),X) = product(a70,product(a118,X)),
inference(equational,[status(thm)],[c592,c3408]) ).
cnf(c4841,plain,
product(product(a71,a83),a82) = product(a70,product(a118,a82)),
inference(equational,[status(thm)],[c165,c4838]) ).
cnf(c4849,plain,
product(product(a109,product(X,a118)),X) = product(a108,product(a118,X)),
inference(equational,[status(thm)],[c460,c3408]) ).
cnf(c4852,plain,
product(product(a109,a82),a83) = product(a108,product(a118,a83)),
inference(equational,[status(thm)],[c407,c4849]) ).
cnf(c4956,plain,
product(product(a76,product(X,a68)),X) = product(a75,product(a68,X)),
inference(equational,[status(thm)],[c597,c3408]) ).
cnf(c4959,plain,
product(product(a76,a121),a122) = product(a75,product(a68,a122)),
inference(equational,[status(thm)],[c310,c4956]) ).
cnf(c5072,plain,
product(product(a82,product(X,a109)),X) = product(a81,product(a109,X)),
inference(equational,[status(thm)],[c606,c3408]) ).
cnf(c5073,plain,
product(a83,product(a101,a32)) = product(a81,a108),
inference(equational,[status(thm)],[c295,c428,c607,c3777,c5072]) ).
cnf(c5077,plain,
product(a81,product(a109,a82)) = product(a72,product(a118,a82)),
inference(equational,[status(thm)],[c406,c1890,c3779,c5072]) ).
cnf(c5098,plain,
product(product(a132,product(X,a138)),X) = product(a131,product(a138,X)),
inference(equational,[status(thm)],[c496,c3408]) ).
cnf(c5101,plain,
product(product(a132,a26),a25) = product(a131,product(a138,a25)),
inference(equational,[status(thm)],[c51,c5098]) ).
cnf(c5139,plain,
product(product(a44,product(X,a128)),X) = product(a43,product(a128,X)),
inference(equational,[status(thm)],[c551,c3408]) ).
cnf(c5155,plain,
product(product(a110,product(X,a70)),X) = product(a109,product(a70,X)),
inference(equational,[status(thm)],[c461,c3408]) ).
cnf(c5227,plain,
product(product(a5,product(X,a39)),X) = product(a4,product(a39,X)),
inference(equational,[status(thm)],[c546,c3408]) ).
cnf(c5230,plain,
product(a5,product(a4,a40)) = product(a4,product(a42,a14)),
inference(equational,[status(thm)],[c1015,c1659,c4555,c5227]) ).
cnf(c5277,plain,
product(product(a88,product(X,a4)),X) = product(a87,product(a4,X)),
inference(equational,[status(thm)],[c613,c3408]) ).
cnf(c5394,plain,
product(product(a119,product(X,a70)),X) = product(a118,product(a70,X)),
inference(equational,[status(thm)],[c477,c3408]) ).
cnf(c5396,plain,
product(product(a110,a112),a108) = product(a118,product(a72,a118)),
inference(equational,[status(thm)],[c462,c1826,c4294,c5394]) ).
cnf(c5397,plain,
product(product(a119,a110),a109) = product(a118,product(a70,a109)),
inference(equational,[status(thm)],[c219,c5394]) ).
cnf(c5405,plain,
product(product(a91,product(X,a100)),X) = product(a90,product(a100,X)),
inference(equational,[status(thm)],[c619,c3408]) ).
cnf(c5406,plain,
product(product(a98,product(X,a1)),X) = product(a97,product(a1,X)),
inference(equational,[status(thm)],[c629,c3408]) ).
cnf(c5436,plain,
product(product(a72,product(X,a109)),X) = product(a71,product(a109,X)),
inference(equational,[status(thm)],[c593,c3408]) ).
cnf(c5456,plain,
product(product(a117,product(X,a74)),X) = product(a116,product(a74,X)),
inference(equational,[status(thm)],[c474,c3408]) ).
cnf(c5457,plain,
product(a116,product(a74,a117)) = product(a109,a32),
inference(equational,[status(thm)],[c217,c304,c1838,c4276,c5456]) ).
cnf(c5459,plain,
product(product(a109,a73),a32) = product(a116,product(a108,a32)),
inference(equational,[status(thm)],[c304,c428,c474,c796,c3430,c4276,c5457]) ).
cnf(c5460,plain,
product(a109,a73) = product(a106,a39),
inference(equational,[status(thm)],[c284,c2474,c3392,c3396,c3773,c5459]) ).
cnf(c5464,plain,
product(product(a124,product(X,a75)),X) = product(a123,product(a75,X)),
inference(equational,[status(thm)],[c485,c3408]) ).
cnf(c5465,plain,
product(a123,product(a75,a122)) = product(a115,a124),
inference(equational,[status(thm)],[c799,c1372,c2480,c5464]) ).
cnf(c5466,plain,
product(a124,product(a77,a68)) = product(a122,a123),
inference(equational,[status(thm)],[c312,c428,c485,c657,c799,c2478,c5465]) ).
cnf(c5467,plain,
product(product(a112,product(X,a79)),X) = product(a111,product(a79,X)),
inference(equational,[status(thm)],[c467,c3408]) ).
cnf(c5468,plain,
product(product(a111,a80),a110) = a112,
inference(equational,[status(thm)],[c159,c223,c403,c428,c466,c808,c1820,c2318,c2320,c3392,c5467]) ).
cnf(c5469,plain,
product(a119,a110) = product(a112,a80),
inference(equational,[status(thm)],[c3408,c4547,c5468]) ).
cnf(c5470,plain,
product(a112,a110) = product(a111,a80),
inference(equational,[status(thm)],[c284,c5468]) ).
cnf(c5472,plain,
product(product(a112,a80),a70) = product(a118,a109),
inference(equational,[status(thm)],[c296,c1966,c5469]) ).
cnf(c5473,plain,
product(product(a110,a80),a111) = product(a110,a79),
inference(equational,[status(thm)],[c403,c1972,c3022,c5470]) ).
cnf(c5474,plain,
product(product(a80,product(X,a119)),X) = product(a79,product(a119,X)),
inference(equational,[status(thm)],[c602,c3408]) ).
cnf(c5476,plain,
product(product(a80,a111),a110) = product(a79,product(a112,a80)),
inference(equational,[status(thm)],[c221,c5469,c5474]) ).
cnf(c5480,plain,
product(product(a111,product(X,a119)),X) = product(a110,product(a119,X)),
inference(equational,[status(thm)],[c466,c3408]) ).
cnf(c5482,plain,
product(a110,product(a119,a80)) = product(a112,a80),
inference(equational,[status(thm)],[c223,c403,c5480]) ).
cnf(c5486,plain,
product(product(a83,product(X,a118)),X) = product(a82,product(a118,X)),
inference(equational,[status(thm)],[c607,c3408]) ).
cnf(c5487,plain,
product(a81,a82) = product(a73,a81),
inference(equational,[status(thm)],[c1427,c3778,c4274,c5486]) ).
cnf(c5494,plain,
product(product(a100,product(X,a124)),X) = product(a99,product(a124,X)),
inference(equational,[status(thm)],[c631,c3408]) ).
cnf(c5498,plain,
product(product(a73,product(X,a82)),X) = product(a72,product(a82,X)),
inference(equational,[status(thm)],[c594,c3408]) ).
cnf(c5530,plain,
product(a115,product(a122,a123)) = product(a122,product(a75,a123)),
inference(equational,[status(thm)],[c3337,c3408,c4771]) ).
cnf(c5531,plain,
product(a115,product(a122,a124)) = product(a122,product(a75,a124)),
inference(equational,[status(thm)],[c247,c428,c485,c2478,c3337,c3940,c4652]) ).
cnf(c5558,plain,
product(product(a76,a69),a13) = product(a73,product(a33,a70)),
inference(equational,[status(thm)],[c785,c3408,c3758]) ).
cnf(c5563,plain,
product(product(a79,a108),a83) = product(a83,product(a73,a118)),
inference(equational,[status(thm)],[c145,c428,c812,c3358]) ).
cnf(c5592,plain,
product(a124,product(a115,a123)) = product(a122,product(a75,a123)),
inference(equational,[status(thm)],[c428,c484,c1374,c1535,c4293,c4652,c5530]) ).
cnf(c5636,plain,
product(product(a83,a111),a119) = product(a80,product(a72,a70)),
inference(equational,[status(thm)],[c649,c922,c1820,c1868,c3330]) ).
cnf(c5737,plain,
product(product(a101,a32),a108) = a118,
inference(equational,[status(thm)],[c428,c647,c2714,c3287,c3340,c3776]) ).
cnf(c5738,plain,
product(a101,product(a108,a32)) = a117,
inference(equational,[status(thm)],[c305,c3408,c5737]) ).
cnf(c5739,plain,
product(a100,a123) = a122,
inference(equational,[status(thm)],[c679,c1741,c1980,c4280,c5738]) ).
cnf(c5740,plain,
product(a122,a123) = a100,
inference(equational,[status(thm)],[c284,c5739]) ).
cnf(c5741,plain,
product(a115,a124) = product(a100,a75),
inference(equational,[status(thm)],[c3337,c5740]) ).
cnf(c5742,plain,
product(a100,a115) = product(a122,a124),
inference(equational,[status(thm)],[c311,c484,c1531,c5740]) ).
cnf(c5743,plain,
product(a100,a122) = product(a123,a124),
inference(equational,[status(thm)],[c428,c1531,c3405,c5740]) ).
cnf(c5745,plain,
product(a112,product(a112,a111)) = product(a110,a79),
inference(equational,[status(thm)],[c808,c2318,c4293,c5473]) ).
cnf(c5759,plain,
product(product(a118,a82),a109) = product(a112,a70),
inference(equational,[status(thm)],[c406,c428,c606,c3779,c4550,c4587]) ).
cnf(c5760,plain,
product(a118,a82) = product(a108,a81),
inference(equational,[status(thm)],[c284,c1842,c3219,c5470,c5759]) ).
cnf(c5762,plain,
product(a122,product(a75,a123)) = product(a115,a100),
inference(equational,[status(thm)],[c312,c485,c2478,c3415,c4559,c5592,c5740]) ).
cnf(c5772,plain,
product(product(a109,a82),a71) = product(product(a112,a111),a118),
inference(equational,[status(thm)],[c790,c2166,c3847]) ).
cnf(c5776,plain,
product(product(a118,a83),a108) = product(a108,a73),
inference(equational,[status(thm)],[c284,c428,c4585]) ).
cnf(c5777,plain,
product(product(a118,a83),a73) = product(a118,a109),
inference(equational,[status(thm)],[c4293,c4583,c4585]) ).
cnf(c5779,plain,
product(product(a115,a100),a123) = product(a100,a75),
inference(equational,[status(thm)],[c3392,c5740,c5762]) ).
cnf(c5780,plain,
product(a115,a100) = product(a99,a75),
inference(equational,[status(thm)],[c284,c2429,c5779]) ).
cnf(c5783,plain,
product(product(a111,a110),a80) = product(a112,a111),
inference(equational,[status(thm)],[c3021,c3392,c4579]) ).
cnf(c5791,plain,
product(a100,product(a66,a91)) = product(a92,a91),
inference(equational,[status(thm)],[c3407,c3408]) ).
cnf(c5792,plain,
product(product(X,product(Y,Z)),Y) = product(product(X,Z),product(Z,Y)),
inference(equational,[status(thm)],[c3408]) ).
cnf(c5793,plain,
product(a72,product(a109,a82)) = product(a73,a118),
inference(equational,[status(thm)],[c1,c406,c1427,c2766,c3779,c5487,c5792]) ).
cnf(c5805,plain,
product(product(a80,a111),a79) = product(a80,a110),
inference(equational,[status(thm)],[c407,c650,c653,c661,c2318,c2434,c4296,c5792]) ).
cnf(c5808,plain,
product(a72,product(a108,a81)) = product(a71,a81),
inference(equational,[status(thm)],[c284,c594,c1753,c1890,c5760,c5793]) ).
cnf(c5809,plain,
product(product(a72,a81),a108) = a71,
inference(equational,[status(thm)],[c284,c3392,c5808]) ).
cnf(c5810,plain,
product(a72,a81) = product(a71,a108),
inference(equational,[status(thm)],[c284,c5809]) ).
cnf(c5819,plain,
product(a82,product(a73,a81)) = product(a71,a81),
inference(equational,[status(thm)],[c163,c606,c648,c1890,c3753,c3779,c4298,c5487,c5760,c5792,c5808]) ).
cnf(c5820,plain,
product(a81,product(a73,a118)) = a73,
inference(equational,[status(thm)],[c145,c163,c593,c1879,c2766,c5793,c5819]) ).
cnf(c5821,plain,
product(a73,product(a112,a70)) = a71,
inference(equational,[status(thm)],[c284,c428,c476,c2474,c3392,c3779,c5819]) ).
cnf(c5822,plain,
product(a71,a70) = a79,
inference(equational,[status(thm)],[c3388,c3392,c5821]) ).
cnf(c5823,plain,
a70 = a80,
inference(equational,[status(thm)],[c1,c159,c394,c661,c5822]) ).
cnf(c5824,plain,
a81 = a80,
inference(equational,[status(thm)],[c1,c161,c5823]) ).
cnf(c5825,plain,
product(a74,a116) = product(a71,a32),
inference(equational,[status(thm)],[c595,c3395,c5821]) ).
cnf(c5826,plain,
product(a73,a118) = product(a71,a73),
inference(equational,[status(thm)],[c428,c4271,c5821]) ).
cnf(c5827,plain,
product(a80,a118) = a71,
inference(equational,[status(thm)],[c284,c605,c5822,c5824]) ).
cnf(c5828,plain,
product(a109,a119) = a112,
inference(equational,[status(thm)],[c223,c1380,c5822]) ).
cnf(c5829,plain,
product(a79,a110) = product(a72,a80),
inference(equational,[status(thm)],[c143,c649,c5822,c5823]) ).
cnf(c5830,plain,
product(a118,a119) = product(a112,a111),
inference(equational,[status(thm)],[c1584,c2320,c5822]) ).
cnf(c5831,plain,
product(a80,a79) = product(a71,a119),
inference(equational,[status(thm)],[c3332,c5822,c5823]) ).
cnf(c5832,plain,
product(a110,a79) = product(a108,a119),
inference(equational,[status(thm)],[c3244,c5822]) ).
cnf(c5834,plain,
product(a68,a122) = product(a77,a68),
inference(equational,[status(thm)],[c303,c596,c657,c1741,c3269,c5825]) ).
cnf(c5835,plain,
product(a114,a122) = a100,
inference(equational,[status(thm)],[c3763,c5466,c5740,c5834]) ).
cnf(c5836,plain,
product(a68,a121) = a77,
inference(equational,[status(thm)],[c284,c310,c428,c5834]) ).
cnf(c5838,plain,
product(a111,a80) = a108,
inference(equational,[status(thm)],[c463,c5823]) ).
cnf(c5839,plain,
product(a71,a80) = a79,
inference(equational,[status(thm)],[c403,c439,c5823]) ).
cnf(c5840,plain,
product(a108,a80) = a111,
inference(equational,[status(thm)],[c462,c5823]) ).
cnf(c5841,plain,
product(a108,a73) = a110,
inference(equational,[status(thm)],[c284,c895,c4300,c5823]) ).
cnf(c5842,plain,
product(a109,a82) = a119,
inference(equational,[status(thm)],[c284,c894,c4274,c5823]) ).
cnf(c5844,plain,
product(a119,a80) = a118,
inference(equational,[status(thm)],[c284,c2535,c4302,c5830]) ).
cnf(c5845,plain,
product(a118,a109) = a112,
inference(equational,[status(thm)],[c284,c5472,c5823]) ).
cnf(c5846,plain,
product(a110,a80) = a109,
inference(equational,[status(thm)],[c284,c808,c5828]) ).
cnf(c5847,plain,
product(a109,a80) = a110,
inference(equational,[status(thm)],[c219,c5823]) ).
cnf(c5849,plain,
product(product(a71,a73),a80) = a82,
inference(equational,[status(thm)],[c284,c427,c5819,c5824]) ).
cnf(c5850,plain,
product(a82,a80) = product(a71,a73),
inference(equational,[status(thm)],[c284,c5849]) ).
cnf(c5851,plain,
product(a80,a109) = a82,
inference(equational,[status(thm)],[c428,c3024,c5823,c5824,c5846,c5849,c5850]) ).
cnf(c5852,plain,
product(a109,a110) = a118,
inference(equational,[status(thm)],[c4293,c5842,c5844,c5847,c5851]) ).
cnf(c5853,plain,
product(a82,a119) = product(a73,a80),
inference(equational,[status(thm)],[c1878,c2375,c5823,c5828,c5851]) ).
cnf(c5854,plain,
product(a80,a110) = product(a71,a73),
inference(equational,[status(thm)],[c1,c5072,c5824,c5847,c5850,c5851]) ).
cnf(c5855,plain,
product(a73,a80) = product(a71,a110),
inference(equational,[status(thm)],[c145,c5436,c5847,c5851]) ).
cnf(c5856,plain,
product(a122,a121) = product(a121,a77),
inference(equational,[status(thm)],[c310,c1836,c1971,c2313,c3224,c4293,c5834]) ).
cnf(c5857,plain,
product(a115,a123) = product(a121,a122),
inference(equational,[status(thm)],[c1533,c2313,c5834]) ).
cnf(c5859,plain,
product(a111,a110) = product(a106,a39),
inference(equational,[status(thm)],[c3773,c4028,c4579,c5823]) ).
cnf(c5860,plain,
product(a112,a111) = product(a108,a109),
inference(equational,[status(thm)],[c3240,c5783,c5823]) ).
cnf(c5861,plain,
product(a68,a14) = product(a80,a32),
inference(equational,[status(thm)],[c678,c5823]) ).
cnf(c5862,plain,
product(a112,a118) = product(a110,a71),
inference(equational,[status(thm)],[c1957,c2340,c5828]) ).
cnf(c5863,plain,
product(a80,a108) = product(a72,a118),
inference(equational,[status(thm)],[c1826,c5823]) ).
cnf(c5864,plain,
product(a77,a121) = a68,
inference(equational,[status(thm)],[c284,c1741,c3314,c5861]) ).
cnf(c5865,plain,
product(a112,a109) = a118,
inference(equational,[status(thm)],[c284,c5845]) ).
cnf(c5866,plain,
product(a119,a109) = a110,
inference(equational,[status(thm)],[c4272,c5846]) ).
cnf(c5867,plain,
product(a110,a109) = a119,
inference(equational,[status(thm)],[c3390,c5846]) ).
cnf(c5868,plain,
product(a110,a82) = a112,
inference(equational,[status(thm)],[c428,c3431,c5823,c5845,c5851,c5852]) ).
cnf(c5869,plain,
product(a118,a110) = a109,
inference(equational,[status(thm)],[c284,c5852]) ).
cnf(c5870,plain,
product(a83,a71) = a73,
inference(equational,[status(thm)],[c284,c2427,c5823,c5853]) ).
cnf(c5871,plain,
product(a110,a73) = a108,
inference(equational,[status(thm)],[c284,c5841]) ).
cnf(c5872,plain,
product(a100,a75) = a121,
inference(equational,[status(thm)],[c284,c1531,c2315,c3416,c5741,c5857]) ).
cnf(c5873,plain,
product(a108,a110) = a112,
inference(equational,[status(thm)],[c5468,c5838]) ).
cnf(c5875,plain,
product(a72,a111) = a79,
inference(equational,[status(thm)],[c403,c5077,c5760,c5824,c5840,c5842]) ).
cnf(c5876,plain,
product(a123,a124) = a114,
inference(equational,[status(thm)],[c284,c5743,c5835]) ).
cnf(c5880,plain,
product(product(a122,a100),a124) = product(a123,a114),
inference(equational,[status(thm)],[c1,c4469,c5740,c5792,c5876]) ).
cnf(c5881,plain,
product(a116,product(a108,a32)) = product(a101,product(a88,a40)),
inference(equational,[status(thm)],[c304,c428,c729,c796,c3069,c4276,c5457,c5460,c5792]) ).
cnf(c5882,plain,
product(a100,a90) = product(a121,a122),
inference(equational,[status(thm)],[c81,c179,c614,c1741,c1969,c1980,c4280,c5857,c5881]) ).
cnf(c5897,plain,
product(product(a123,a114),a99) = product(a122,a124),
inference(equational,[status(thm)],[c284,c1823,c5880]) ).
cnf(c5899,plain,
product(product(a71,a73),a112) = product(a71,a119),
inference(equational,[status(thm)],[c284,c653,c5805,c5831,c5854]) ).
cnf(c5900,plain,
product(product(a71,a73),a79) = product(a80,a111),
inference(equational,[status(thm)],[c284,c5805,c5854]) ).
cnf(c5903,plain,
product(a73,product(a71,a73)) = a80,
inference(equational,[status(thm)],[c284,c5820,c5824,c5826]) ).
cnf(c5905,plain,
product(a112,a80) = product(a111,a109),
inference(equational,[status(thm)],[c4547,c5469,c5846]) ).
cnf(c5906,plain,
product(a109,a112) = product(a108,a109),
inference(equational,[status(thm)],[c3021,c5846,c5860]) ).
cnf(c5907,plain,
product(a114,a123) = product(a99,a115),
inference(equational,[status(thm)],[c425,c4645,c5835]) ).
cnf(c5908,plain,
product(a115,a121) = product(a100,a68),
inference(equational,[status(thm)],[c310,c472,c5835]) ).
cnf(c5909,plain,
product(a80,a82) = product(a71,a110),
inference(equational,[status(thm)],[c5487,c5824,c5855]) ).
cnf(c5911,plain,
product(a83,a109) = product(a80,a112),
inference(equational,[status(thm)],[c2358,c5824,c5845]) ).
cnf(c5912,plain,
product(a72,a112) = a82,
inference(equational,[status(thm)],[c1310,c5823,c5845,c5851]) ).
cnf(c5914,plain,
product(a72,a80) = product(a71,a108),
inference(equational,[status(thm)],[c5810,c5824]) ).
cnf(c5915,plain,
product(a72,a79) = product(a71,a110),
inference(equational,[status(thm)],[c593,c1753,c2779,c5823,c5824,c5839,c5851,c5854,c5909]) ).
cnf(c5916,plain,
product(a72,a119) = product(a71,a73),
inference(equational,[status(thm)],[c5793,c5826,c5842]) ).
cnf(c5919,plain,
product(a118,a83) = product(a110,a108),
inference(equational,[status(thm)],[c428,c4585,c5841]) ).
cnf(c5920,plain,
product(a109,a111) = product(a108,a119),
inference(equational,[status(thm)],[c5473,c5832,c5846]) ).
cnf(c5921,plain,
product(a110,a71) = product(a101,a32),
inference(equational,[status(thm)],[c295,c428,c3777,c5845,c5862]) ).
cnf(c5922,plain,
product(a111,a109) = product(a108,a71),
inference(equational,[status(thm)],[c791,c5482,c5844,c5905]) ).
cnf(c5923,plain,
product(a118,a79) = product(a110,a111),
inference(equational,[status(thm)],[c4389,c4569,c5844]) ).
cnf(c5924,plain,
product(a119,a118) = product(a106,a39),
inference(equational,[status(thm)],[c4345,c4579,c5844,c5859]) ).
cnf(c5925,plain,
product(a124,a121) = product(a121,a114),
inference(equational,[status(thm)],[c803,c4710,c5836]) ).
cnf(c5926,plain,
product(a73,a119) = product(a71,a82),
inference(equational,[status(thm)],[c1309,c5842]) ).
cnf(c5929,plain,
product(a83,a80) = a72,
inference(equational,[status(thm)],[c284,c2434,c5823,c5875]) ).
cnf(c5930,plain,
product(a114,a124) = a123,
inference(equational,[status(thm)],[c284,c5876]) ).
cnf(c5931,plain,
product(a73,a71) = a83,
inference(equational,[status(thm)],[c284,c5870]) ).
cnf(c5932,plain,
product(a73,a110) = a82,
inference(equational,[status(thm)],[c3822,c5851,c5869,c5870]) ).
cnf(c5934,plain,
product(a121,a75) = a100,
inference(equational,[status(thm)],[c284,c5872]) ).
cnf(c5935,plain,
product(a82,a112) = a72,
inference(equational,[status(thm)],[c284,c5912]) ).
cnf(c5936,plain,
product(a112,a82) = a110,
inference(equational,[status(thm)],[c284,c5868]) ).
cnf(c5937,plain,
product(a82,product(a71,a73)) = a71,
inference(equational,[status(thm)],[c1,c284,c3392,c3779,c4069,c5077,c5760,c5792,c5824,c5826,c5914]) ).
cnf(c5938,plain,
product(a80,product(a71,a110)) = a72,
inference(equational,[status(thm)],[c143,c593,c1753,c1879,c5824,c5839,c5915,c5937]) ).
cnf(c5939,plain,
product(a72,a110) = product(a71,a83),
inference(equational,[status(thm)],[c428,c3392,c5854,c5931,c5938]) ).
cnf(c5940,plain,
product(a80,a111) = product(a73,a112),
inference(equational,[status(thm)],[c594,c4841,c5760,c5823,c5824,c5840,c5868,c5939]) ).
cnf(c5941,plain,
product(a71,product(a71,a73)) = a82,
inference(equational,[status(thm)],[c284,c5937]) ).
cnf(c5942,plain,
product(a82,a73) = product(a71,a83),
inference(equational,[status(thm)],[c428,c3392,c5931,c5941]) ).
cnf(c5943,plain,
product(a82,a72) = product(a73,a112),
inference(equational,[status(thm)],[c396,c428,c4841,c5760,c5823,c5824,c5840,c5940,c5942]) ).
cnf(c5952,plain,
product(a79,product(a110,a112)) = product(a80,a72),
inference(equational,[status(thm)],[c2434,c3408,c4073,c4294,c5805,c5823,c5929]) ).
cnf(c5953,plain,
product(product(a80,a72),a112) = a71,
inference(equational,[status(thm)],[c284,c2375,c3392,c5823,c5855,c5952]) ).
cnf(c5954,plain,
product(a80,a72) = product(a71,a112),
inference(equational,[status(thm)],[c284,c5953]) ).
cnf(c5957,plain,
product(a122,product(a75,a124)) = product(a121,a114),
inference(equational,[status(thm)],[c247,c485,c3940,c4772,c5531,c5740,c5792,c5872,c5925]) ).
cnf(c5958,plain,
product(product(a109,a32),a116) = product(a117,product(a108,a32)),
inference(equational,[status(thm)],[c1,c4109,c4276,c5457,c5792]) ).
cnf(c5969,plain,
product(a124,product(a68,a75)) = product(a123,a100),
inference(equational,[status(thm)],[c1,c1863,c3415,c3803,c3940,c5740,c5957]) ).
cnf(c5970,plain,
product(product(a121,a114),a124) = product(a121,a122),
inference(equational,[status(thm)],[c312,c3392,c3415,c5857,c5957]) ).
cnf(c5974,plain,
product(product(a110,a111),a79) = a118,
inference(equational,[status(thm)],[c653,c2318,c2535,c4302,c5745,c5792,c5844]) ).
cnf(c5975,plain,
product(a118,a111) = product(a110,a72),
inference(equational,[status(thm)],[c2434,c3408,c5823,c5929,c5974]) ).
cnf(c5976,plain,
product(a118,a112) = product(a108,a119),
inference(equational,[status(thm)],[c284,c653,c5832,c5974]) ).
cnf(c5977,plain,
product(a109,product(a108,a71)) = product(a101,a32),
inference(equational,[status(thm)],[c284,c475,c2474,c3408,c3777,c5823,c5905,c5922,c5958]) ).
cnf(c5978,plain,
product(product(a121,a122),a124) = product(a98,a99),
inference(equational,[status(thm)],[c1398,c1991,c5882]) ).
cnf(c5979,plain,
product(a90,product(a121,a122)) = product(a91,a90),
inference(equational,[status(thm)],[c1404,c5882]) ).
cnf(c5981,plain,
product(a83,product(a108,a71)) = product(a71,a73),
inference(equational,[status(thm)],[c3392,c4562,c5820,c5823,c5826,c5905,c5922]) ).
cnf(c5982,plain,
product(a73,a108) = product(a71,a83),
inference(equational,[status(thm)],[c428,c3392,c5870,c5931,c5981]) ).
cnf(c5983,plain,
product(product(a121,a122),a100) = product(a100,a91),
inference(equational,[status(thm)],[c181,c428,c5882]) ).
cnf(c5988,plain,
product(a80,product(a108,a71)) = product(a71,a83),
inference(equational,[status(thm)],[c604,c605,c812,c2505,c3392,c4545,c4581,c5823,c5824,c5905,c5922,c5982]) ).
cnf(c5989,plain,
product(a79,product(a73,a112)) = product(a83,a111),
inference(equational,[status(thm)],[c284,c661,c1736,c1878,c2422,c5636,c5823,c5940]) ).
cnf(c5992,plain,
product(a108,product(a71,a73)) = a119,
inference(equational,[status(thm)],[c1957,c2166,c5460,c5826,c5842]) ).
cnf(c5993,plain,
product(a119,a73) = product(a101,a32),
inference(equational,[status(thm)],[c3392,c5841,c5921,c5992]) ).
cnf(c6012,plain,
product(product(product(X,a123),a122),a115) = product(X,product(a121,a122)),
inference(equational,[status(thm)],[c667,c3408,c5857]) ).
cnf(c6013,plain,
product(a121,product(a77,a68)) = product(a114,a115),
inference(equational,[status(thm)],[c428,c1531,c3405,c4146,c5834,c5876,c6012]) ).
cnf(c6014,plain,
product(a115,a114) = product(a122,a77),
inference(equational,[status(thm)],[c284,c302,c472,c483,c6013]) ).
cnf(c6015,plain,
product(product(X,a100),a115) = product(product(X,a122),a121),
inference(equational,[status(thm)],[c1856,c3392,c3408,c5740,c6012]) ).
cnf(c6016,plain,
product(a114,a121) = product(a122,a124),
inference(equational,[status(thm)],[c1,c5742,c5743,c5876,c6015]) ).
cnf(c6017,plain,
product(product(a122,a124),a121) = a114,
inference(equational,[status(thm)],[c1531,c1965,c3405,c5742,c5876,c6015]) ).
cnf(c6018,plain,
product(product(X,a123),a124) = product(product(X,a122),a121),
inference(equational,[status(thm)],[c1372,c3392,c3408,c6012]) ).
cnf(c6019,plain,
product(a99,a114) = product(a122,a124),
inference(equational,[status(thm)],[c1991,c5743,c5876,c6016,c6018]) ).
cnf(c6020,plain,
product(a124,a114) = product(a100,a68),
inference(equational,[status(thm)],[c428,c1371,c5876,c5908,c6018]) ).
cnf(c6021,plain,
product(a99,a121) = a122,
inference(equational,[status(thm)],[c284,c4244,c5742,c6018]) ).
cnf(c6022,plain,
product(a121,a77) = a99,
inference(equational,[status(thm)],[c284,c5856,c6021]) ).
cnf(c6024,plain,
product(a114,product(a77,a68)) = product(a122,product(a68,a115)),
inference(equational,[status(thm)],[c1,c247,c1531,c1536,c2480,c3807,c4711,c5464,c5531,c5834,c5957,c6012]) ).
cnf(c6025,plain,
product(a115,a77) = product(a123,a114),
inference(equational,[status(thm)],[c284,c302,c428,c472,c1968,c3356,c6024]) ).
cnf(c6026,plain,
product(a100,product(a122,a124)) = product(a123,a121),
inference(equational,[status(thm)],[c1,c245,c311,c631,c1531,c1856,c2481,c3398,c4146,c4646,c4770,c5834,c5857,c5907,c6013,c6018]) ).
cnf(c6027,plain,
product(product(a123,a100),a124) = product(a123,a121),
inference(equational,[status(thm)],[c1,c245,c2481,c2510,c5740,c6018]) ).
cnf(c6029,plain,
product(product(a99,a122),a121) = product(a100,a114),
inference(equational,[status(thm)],[c631,c5876,c6018]) ).
cnf(c6031,plain,
product(product(a91,a122),a121) = product(a92,a114),
inference(equational,[status(thm)],[c620,c5876,c6018]) ).
cnf(c6032,plain,
product(a115,product(a121,a122)) = product(a121,a115),
inference(equational,[status(thm)],[c1531,c2315,c3416,c5741,c5872,c6012]) ).
cnf(c6033,plain,
product(a98,a99) = product(a121,a114),
inference(equational,[status(thm)],[c284,c1856,c3398,c3416,c5925,c5978,c6032]) ).
cnf(c6034,plain,
product(a114,a99) = product(a122,a114),
inference(equational,[status(thm)],[c302,c310,c483,c1971,c5856,c6022,c6032]) ).
cnf(c6035,plain,
product(product(a90,a122),a121) = product(a91,a115),
inference(equational,[status(thm)],[c1,c181,c416,c5405,c6015]) ).
cnf(c6036,plain,
product(a92,a114) = product(a90,a115),
inference(equational,[status(thm)],[c416,c6015,c6031]) ).
cnf(c6039,plain,
product(a121,product(a122,a124)) = a124,
inference(equational,[status(thm)],[c284,c1835,c1865,c1968,c5742,c6016,c6020]) ).
cnf(c6040,plain,
product(product(a123,a121),a99) = a114,
inference(equational,[status(thm)],[c284,c1823,c5876,c6027]) ).
cnf(c6041,plain,
product(a123,a121) = product(a122,a114),
inference(equational,[status(thm)],[c284,c6034,c6040]) ).
cnf(c6042,plain,
product(product(a124,a76),a121) = a122,
inference(equational,[status(thm)],[c243,c800,c1758,c2484,c5872,c6020]) ).
cnf(c6043,plain,
product(a124,a76) = a99,
inference(equational,[status(thm)],[c284,c5856,c6022,c6042]) ).
cnf(c6044,plain,
product(a124,a77) = product(a122,a114),
inference(equational,[status(thm)],[c4657,c6042]) ).
cnf(c6045,plain,
product(a100,a68) = product(a122,a76),
inference(equational,[status(thm)],[c802,c3408,c6020,c6042]) ).
cnf(c6046,plain,
product(a99,a76) = a124,
inference(equational,[status(thm)],[c1835,c1865,c1968,c2485,c5742,c5856,c6016,c6022,c6039,c6045]) ).
cnf(c6047,plain,
product(product(a122,a76),a121) = a115,
inference(equational,[status(thm)],[c229,c1758,c1864,c2484,c4658,c5743,c5876,c6020,c6044]) ).
cnf(c6048,plain,
product(a115,a76) = product(a122,a114),
inference(equational,[status(thm)],[c802,c3408,c6047]) ).
cnf(c6049,plain,
product(a114,a75) = product(a121,a115),
inference(equational,[status(thm)],[c399,c1241,c1971,c6048]) ).
cnf(c6050,plain,
product(product(a122,a77),a76) = a123,
inference(equational,[status(thm)],[c284,c2484,c4658,c6025,c6048]) ).
cnf(c6051,plain,
product(a123,a76) = product(a122,a77),
inference(equational,[status(thm)],[c284,c6050]) ).
cnf(c6052,plain,
product(a114,a115) = product(a123,a100),
inference(equational,[status(thm)],[c1968,c3012,c5969,c6013,c6051]) ).
cnf(c6054,plain,
product(a123,product(a121,a122)) = a100,
inference(equational,[status(thm)],[c284,c484,c1374,c3837,c5857,c6016,c6020]) ).
cnf(c6055,plain,
product(a100,a121) = product(a123,a114),
inference(equational,[status(thm)],[c1531,c1823,c5792,c5856,c5880,c6022,c6054]) ).
cnf(c6057,plain,
product(a99,a68) = product(a121,a122),
inference(equational,[status(thm)],[c483,c2313,c5857,c6022]) ).
cnf(c6058,plain,
product(a100,product(a75,a124)) = product(a121,a99),
inference(equational,[status(thm)],[c428,c631,c4771,c5740,c5741,c5780,c5856,c5872,c6018,c6022]) ).
cnf(c6060,plain,
product(a75,product(a121,a122)) = product(a68,a123),
inference(equational,[status(thm)],[c1,c666,c4647,c4656,c5864,c6012]) ).
cnf(c6062,plain,
product(product(a121,a99),a75) = product(a99,a123),
inference(equational,[status(thm)],[c312,c5494,c6058]) ).
cnf(c6063,plain,
product(product(a122,a124),a76) = product(a121,a114),
inference(equational,[status(thm)],[c802,c2483,c6016]) ).
cnf(c6065,plain,
product(a123,product(a68,a75)) = product(a121,a122),
inference(equational,[status(thm)],[c312,c3415,c3834,c5857,c6016]) ).
cnf(c6071,plain,
product(product(a122,a114),a124) = product(a99,a122),
inference(equational,[status(thm)],[c284,c1991,c6026,c6041]) ).
cnf(c6072,plain,
product(product(a90,a123),a122) = product(a91,a123),
inference(equational,[status(thm)],[c1887,c4646,c5930,c6036]) ).
cnf(c6073,plain,
product(a92,a121) = product(a90,a123),
inference(equational,[status(thm)],[c284,c4651,c5741,c5872,c6072]) ).
cnf(c6076,plain,
product(product(a91,a115),a121) = product(a90,a122),
inference(equational,[status(thm)],[c284,c6035]) ).
cnf(c6077,plain,
product(a92,product(a122,a124)) = product(a91,a90),
inference(equational,[status(thm)],[c620,c1856,c3398,c3408,c5979,c6035]) ).
cnf(c6078,plain,
product(a121,product(a122,a76)) = product(a124,a99),
inference(equational,[status(thm)],[c428,c1372,c5792,c5856,c5908,c6022,c6032,c6045]) ).
cnf(c6079,plain,
product(a99,a122) = product(a123,a100),
inference(equational,[status(thm)],[c284,c6027,c6041,c6071]) ).
cnf(c6081,plain,
product(a99,product(a122,a114)) = product(a123,a114),
inference(equational,[status(thm)],[c428,c1823,c5880,c6019,c6034]) ).
cnf(c6082,plain,
product(product(a124,a99),a76) = a100,
inference(equational,[status(thm)],[c284,c2482,c5835,c6078]) ).
cnf(c6083,plain,
product(a124,a99) = product(a100,a76),
inference(equational,[status(thm)],[c284,c6082]) ).
cnf(c6084,plain,
product(product(a123,a100),a122) = a99,
inference(equational,[status(thm)],[c284,c6079]) ).
cnf(c6087,plain,
product(a100,product(a121,a122)) = a123,
inference(equational,[status(thm)],[c284,c6054]) ).
cnf(c6090,plain,
product(product(a121,a114),a99) = a98,
inference(equational,[status(thm)],[c284,c6033]) ).
cnf(c6091,plain,
product(a98,a114) = a124,
inference(equational,[status(thm)],[c3408,c6019,c6039,c6090]) ).
cnf(c6092,plain,
product(a122,a76) = a98,
inference(equational,[status(thm)],[c284,c6020,c6045,c6091]) ).
cnf(c6093,plain,
product(a98,a121) = a115,
inference(equational,[status(thm)],[c6047,c6092]) ).
cnf(c6094,plain,
product(a98,a68) = a100,
inference(equational,[status(thm)],[c399,c1968,c5934,c6092]) ).
cnf(c6095,plain,
product(a98,a76) = a122,
inference(equational,[status(thm)],[c284,c6092]) ).
cnf(c6098,plain,
product(product(a121,a122),a115) = a124,
inference(equational,[status(thm)],[c1203,c1438,c1757,c1965,c2477,c3397,c5834,c6065]) ).
cnf(c6099,plain,
product(a124,a123) = product(a121,a115),
inference(equational,[status(thm)],[c284,c667,c6098]) ).
cnf(c6100,plain,
product(a100,a76) = product(a121,a98),
inference(equational,[status(thm)],[c6078,c6083,c6092]) ).
cnf(c6107,plain,
product(a99,product(a121,a122)) = product(a122,product(a123,a100)),
inference(equational,[status(thm)],[c1965,c4654,c5741,c5872,c6012,c6052,c6055]) ).
cnf(c6113,plain,
product(a115,product(a77,a75)) = product(a122,product(a121,a115)),
inference(equational,[status(thm)],[c2478,c3415,c6014,c6049]) ).
cnf(c6115,plain,
product(a114,product(a68,a115)) = product(a123,product(a77,a115)),
inference(equational,[status(thm)],[c428,c484,c4049,c6014]) ).
cnf(c6119,plain,
product(product(a100,a114),a122) = product(a122,product(a123,a100)),
inference(equational,[status(thm)],[c3408,c6029,c6107]) ).
cnf(c6120,plain,
product(a100,a114) = product(a122,a99),
inference(equational,[status(thm)],[c284,c428,c6084,c6119]) ).
cnf(c6121,plain,
product(product(a100,a91),a123) = a124,
inference(equational,[status(thm)],[c427,c1372,c1856,c3398,c4645,c4649,c6012,c6093]) ).
cnf(c6122,plain,
product(a100,a91) = product(a121,a115),
inference(equational,[status(thm)],[c284,c6099,c6121]) ).
cnf(c6134,plain,
product(a100,product(a123,a91)) = product(a124,a91),
inference(equational,[status(thm)],[c3408,c6121]) ).
cnf(c6137,plain,
product(product(a123,a100),a121) = product(a122,a99),
inference(equational,[status(thm)],[c6029,c6079,c6120]) ).
cnf(c6144,plain,
product(a122,product(a76,a124)) = product(a121,a122),
inference(equational,[status(thm)],[c3408,c5970,c6063]) ).
cnf(c6145,plain,
product(a114,a98) = product(a123,a114),
inference(equational,[status(thm)],[c1823,c2482,c5792,c5880,c6043,c6092,c6144]) ).
cnf(c6150,plain,
product(product(a121,a114),a92) = product(a99,a98),
inference(equational,[status(thm)],[c424,c630,c6033]) ).
cnf(c6152,plain,
product(product(a123,a100),a68) = product(a122,a77),
inference(equational,[status(thm)],[c284,c1965,c3392,c6052,c6115]) ).
cnf(c6157,plain,
product(product(product(X,a122),a121),a68) = product(X,product(a77,a68)),
inference(equational,[status(thm)],[c666,c3408,c5834]) ).
cnf(c6158,plain,
product(product(X,a68),a77) = product(product(X,a122),a121),
inference(equational,[status(thm)],[c284,c3392,c6157]) ).
cnf(c6159,plain,
product(a122,a77) = product(a121,a99),
inference(equational,[status(thm)],[c243,c428,c5856,c6022,c6158]) ).
cnf(c6160,plain,
product(product(X,a77),a68) = product(product(X,a121),a122),
inference(equational,[status(thm)],[c284,c427,c666,c1864,c6157]) ).
cnf(c6162,plain,
product(a75,a123) = product(a76,a122),
inference(equational,[status(thm)],[c229,c245,c284,c483,c1888,c2611,c4660,c6160]) ).
cnf(c6163,plain,
product(a68,a123) = product(a76,a115),
inference(equational,[status(thm)],[c284,c6012,c6060,c6162]) ).
cnf(c6165,plain,
product(a99,product(a77,a68)) = product(a121,product(a121,a122)),
inference(equational,[status(thm)],[c310,c1968,c4704,c5834,c5856,c6013,c6022,c6052,c6057,c6137,c6157]) ).
cnf(c6166,plain,
product(product(a121,a122),a77) = product(a122,a99),
inference(equational,[status(thm)],[c310,c483,c3392,c5856,c6022,c6057,c6165]) ).
cnf(c6171,plain,
product(product(a77,a122),a68) = product(a68,a77),
inference(equational,[status(thm)],[c1,c1864,c5834,c6158]) ).
cnf(c6172,plain,
product(product(a121,a99),a114) = a115,
inference(equational,[status(thm)],[c2484,c6092,c6093,c6159]) ).
cnf(c6174,plain,
product(product(a76,a122),a115) = a68,
inference(equational,[status(thm)],[c1,c3398,c4225,c5864,c6162]) ).
cnf(c6175,plain,
product(a77,a68) = product(a76,a124),
inference(equational,[status(thm)],[c1372,c3408,c5834,c6174]) ).
cnf(c6176,plain,
product(a68,a115) = product(a76,a122),
inference(equational,[status(thm)],[c284,c6174]) ).
cnf(c6177,plain,
product(a68,a114) = product(a75,a121),
inference(equational,[status(thm)],[c302,c310,c428,c1888,c6176]) ).
cnf(c6178,plain,
product(product(a76,a122),a123) = a75,
inference(equational,[status(thm)],[c284,c6162]) ).
cnf(c6179,plain,
product(a75,a124) = product(a76,a121),
inference(equational,[status(thm)],[c284,c6018,c6178]) ).
cnf(c6188,plain,
product(a115,product(a76,a122)) = product(a123,a100),
inference(equational,[status(thm)],[c3940,c5740,c6162]) ).
cnf(c6192,plain,
product(a76,product(a121,a114)) = product(a75,a121),
inference(equational,[status(thm)],[c310,c597,c1836,c1888,c6162]) ).
cnf(c6193,plain,
product(product(a122,a99),a77) = product(a121,a122),
inference(equational,[status(thm)],[c284,c6166]) ).
cnf(c6194,plain,
product(product(a76,a122),a75) = product(a76,a121),
inference(equational,[status(thm)],[c247,c428,c6162,c6179]) ).
cnf(c6197,plain,
product(a122,product(a121,a115)) = product(a99,a123),
inference(equational,[status(thm)],[c3415,c6062,c6113,c6159]) ).
cnf(c6198,plain,
product(product(a75,a121),a114) = a68,
inference(equational,[status(thm)],[c153,c3392,c5864,c6192]) ).
cnf(c6199,plain,
product(a68,a77) = product(a75,a76),
inference(equational,[status(thm)],[c284,c804,c2485,c6198]) ).
cnf(c6202,plain,
product(a77,product(a122,a124)) = a75,
inference(equational,[status(thm)],[c153,c284,c5792,c6016,c6192]) ).
cnf(c6205,plain,
product(product(a123,a77),a76) = product(product(a122,a99),a114),
inference(equational,[status(thm)],[c2482,c2484,c4658,c6092,c6145,c6166]) ).
cnf(c6213,plain,
product(product(a91,a115),a68) = product(a90,product(a76,a124)),
inference(equational,[status(thm)],[c6035,c6157,c6175]) ).
cnf(c6223,plain,
product(product(a75,a76),a115) = product(a75,product(a121,a115)),
inference(equational,[status(thm)],[c656,c1241,c1888,c1889,c6171,c6199]) ).
cnf(c6231,plain,
product(product(a76,a124),a121) = product(a75,a76),
inference(equational,[status(thm)],[c284,c657,c3392,c6175,c6223]) ).
cnf(c6238,plain,
product(a76,product(a122,a124)) = product(a68,a124),
inference(equational,[status(thm)],[c1531,c3408,c4646,c6174]) ).
cnf(c6239,plain,
product(a68,a124) = product(a75,a122),
inference(equational,[status(thm)],[c1531,c3408,c6178,c6238]) ).
cnf(c6252,plain,
product(product(a121,a122),a114) = product(a123,a77),
inference(equational,[status(thm)],[c284,c1758,c6193,c6205]) ).
cnf(c6254,plain,
product(product(a76,a121),a115) = product(a76,a75),
inference(equational,[status(thm)],[c284,c3397,c6194]) ).
cnf(c6316,plain,
product(product(product(X,a138),a137),a51) = product(X,product(a51,a138)),
inference(equational,[status(thm)],[c697,c3408]) ).
cnf(c6323,plain,
product(product(product(X,a109),a108),a118) = product(X,a112),
inference(equational,[status(thm)],[c648,c3408,c5845]) ).
cnf(c6324,plain,
product(product(a108,a71),a109) = a111,
inference(equational,[status(thm)],[c1,c2318,c2319,c2859,c5480,c5828,c5866,c6323]) ).
cnf(c6326,plain,
product(product(a71,a82),a112) = a80,
inference(equational,[status(thm)],[c284,c394,c406,c5498,c5823,c5824,c5842,c5914,c5926,c6323]) ).
cnf(c6327,plain,
product(a80,a112) = product(a71,a82),
inference(equational,[status(thm)],[c284,c6326]) ).
cnf(c6328,plain,
product(product(a108,a71),a112) = product(a109,a72),
inference(equational,[status(thm)],[c921,c5394,c5469,c5760,c5823,c5824,c5840,c5847,c5851,c5905,c5922,c6323]) ).
cnf(c6330,plain,
product(product(X,a109),a112) = product(product(X,a108),a118),
inference(equational,[status(thm)],[c284,c6323]) ).
cnf(c6331,plain,
product(product(a108,a112),a111) = a118,
inference(equational,[status(thm)],[c1,c4402,c4666,c5737,c5845,c5976,c6330]) ).
cnf(c6332,plain,
product(a110,a72) = product(a108,a112),
inference(equational,[status(thm)],[c284,c5975,c6331]) ).
cnf(c6333,plain,
product(product(X,a109),a118) = product(product(X,a112),a109),
inference(equational,[status(thm)],[c284,c648,c6323]) ).
cnf(c6334,plain,
product(a71,a108) = a83,
inference(equational,[status(thm)],[c163,c165,c406,c593,c5824,c5914,c6327,c6333]) ).
cnf(c6335,plain,
product(product(X,a109),a108) = product(product(X,a112),a118),
inference(equational,[status(thm)],[c284,c6323]) ).
cnf(c6336,plain,
product(a82,a108) = product(a80,a83),
inference(equational,[status(thm)],[c163,c879,c5823,c5824,c6327,c6335]) ).
cnf(c6337,plain,
product(a111,a118) = product(a110,a108),
inference(equational,[status(thm)],[c1,c2318,c2319,c5480,c5828,c5866,c6335]) ).
cnf(c6338,plain,
product(product(X,a118),a112) = product(product(X,a108),a109),
inference(equational,[status(thm)],[c284,c648,c1825,c6323]) ).
cnf(c6339,plain,
product(a79,a109) = a73,
inference(equational,[status(thm)],[c284,c3334,c5943,c6338]) ).
cnf(c6341,plain,
product(product(a80,a83),a109) = product(a83,a112),
inference(equational,[status(thm)],[c1,c2796,c5851,c6334,c6336,c6338]) ).
cnf(c6343,plain,
product(product(a110,a108),a109) = product(a109,a72),
inference(equational,[status(thm)],[c791,c6328,c6338]) ).
cnf(c6344,plain,
product(product(a73,a112),a109) = product(a80,a71),
inference(equational,[status(thm)],[c792,c1753,c5824,c5839,c6333]) ).
cnf(c6345,plain,
product(product(a73,a112),a118) = product(a79,a108),
inference(equational,[status(thm)],[c1753,c5824,c5839,c6335]) ).
cnf(c6348,plain,
product(a71,product(a101,a32)) = product(a80,a83),
inference(equational,[status(thm)],[c879,c3687,c3777,c5823,c6327,c6335]) ).
cnf(c6349,plain,
product(product(a110,a112),a118) = product(a119,a108),
inference(equational,[status(thm)],[c1,c5155,c5823,c5842,c5847,c5851,c6335]) ).
cnf(c6350,plain,
product(product(a108,a112),a109) = product(a109,a108),
inference(equational,[status(thm)],[c295,c460,c6333]) ).
cnf(c6352,plain,
product(product(a83,a112),a109) = product(a80,a83),
inference(equational,[status(thm)],[c295,c1882,c6333,c6336]) ).
cnf(c6353,plain,
product(product(a110,a112),a109) = product(a106,a39),
inference(equational,[status(thm)],[c1,c5155,c5823,c5842,c5847,c5851,c5924,c6333]) ).
cnf(c6354,plain,
product(a108,product(a110,a108)) = product(a111,a71),
inference(equational,[status(thm)],[c464,c3408,c6324,c6337]) ).
cnf(c6355,plain,
product(product(a111,a71),a108) = a112,
inference(equational,[status(thm)],[c1,c3392,c5873,c6354]) ).
cnf(c6356,plain,
product(a112,a108) = product(a111,a71),
inference(equational,[status(thm)],[c284,c6355]) ).
cnf(c6359,plain,
product(product(a80,a83),a108) = a82,
inference(equational,[status(thm)],[c284,c407,c6335,c6352]) ).
cnf(c6360,plain,
product(product(a110,a108),a71) = a109,
inference(equational,[status(thm)],[c298,c1861,c5823,c5846,c6337]) ).
cnf(c6361,plain,
product(a109,a108) = product(a110,a83),
inference(equational,[status(thm)],[c3408,c6334,c6360]) ).
cnf(c6365,plain,
product(product(a108,a82),a112) = a110,
inference(equational,[status(thm)],[c394,c460,c647,c2714,c3943,c5823,c5824,c5827,c5847,c5851,c5859,c6330]) ).
cnf(c6366,plain,
product(a110,a112) = product(a108,a82),
inference(equational,[status(thm)],[c284,c6365]) ).
cnf(c6367,plain,
product(a119,a108) = product(a109,a83),
inference(equational,[status(thm)],[c165,c460,c6349,c6366]) ).
cnf(c6369,plain,
product(a71,product(a108,a71)) = a73,
inference(equational,[status(thm)],[c428,c5870,c6334]) ).
cnf(c6371,plain,
product(product(a71,a110),a108) = product(a80,product(a106,a39)),
inference(equational,[status(thm)],[c1876,c2779,c5823,c5824,c5851,c5854,c5899,c5909,c5924,c6335]) ).
cnf(c6374,plain,
product(product(a106,a39),a112) = product(a109,product(a71,a82)),
inference(equational,[status(thm)],[c428,c459,c2603,c5867,c5911,c6327,c6334,c6338,c6367]) ).
cnf(c6377,plain,
product(product(a108,a82),a109) = product(a106,a39),
inference(equational,[status(thm)],[c459,c2603,c6333,c6334,c6366]) ).
cnf(c6380,plain,
product(a79,product(a108,a71)) = product(a80,a83),
inference(equational,[status(thm)],[c5436,c5875,c5977,c6324,c6348]) ).
cnf(c6381,plain,
product(product(a79,a71),a83) = a82,
inference(equational,[status(thm)],[c5792,c6334,c6359,c6380]) ).
cnf(c6382,plain,
product(a82,a71) = product(a79,a73),
inference(equational,[status(thm)],[c3408,c5870,c6381]) ).
cnf(c6383,plain,
product(a82,a83) = product(a79,a71),
inference(equational,[status(thm)],[c284,c6381]) ).
cnf(c6384,plain,
product(a83,a82) = product(a71,a119),
inference(equational,[status(thm)],[c407,c607,c3816,c5823,c5831,c5839,c6383]) ).
cnf(c6385,plain,
product(a109,product(a71,a82)) = product(a118,a72),
inference(equational,[status(thm)],[c1,c428,c648,c3392,c5396,c5911,c6327,c6349,c6367]) ).
cnf(c6390,plain,
product(a72,product(a108,a109)) = product(a71,a82),
inference(equational,[status(thm)],[c593,c5911,c6327,c6334]) ).
cnf(c6393,plain,
product(product(a110,a108),a80) = product(a108,a119),
inference(equational,[status(thm)],[c1736,c2913,c5823,c5832,c5839,c6337]) ).
cnf(c6396,plain,
product(a83,product(a71,a73)) = product(a71,a110),
inference(equational,[status(thm)],[c407,c812,c1876,c1890,c5563,c5823,c5826,c5909,c5936,c5939,c6345]) ).
cnf(c6398,plain,
product(product(a71,a73),a111) = product(a71,a112),
inference(equational,[status(thm)],[c428,c3843,c5823,c5854,c5929,c5954,c6336]) ).
cnf(c6399,plain,
product(a72,product(a71,a82)) = product(a71,a119),
inference(equational,[status(thm)],[c428,c593,c1752,c1890,c5824,c5831,c5839,c5911,c5936,c5939,c6327,c6344]) ).
cnf(c6401,plain,
product(product(a80,a71),a108) = product(a71,a73),
inference(equational,[status(thm)],[c284,c5826,c6335,c6344]) ).
cnf(c6403,plain,
product(product(a83,a112),a82) = product(a72,a118),
inference(equational,[status(thm)],[c428,c593,c811,c5824,c5865,c5929,c5954,c6341]) ).
cnf(c6404,plain,
product(a83,a112) = product(a73,a111),
inference(equational,[status(thm)],[c284,c594,c5760,c5824,c5840,c6403]) ).
cnf(c6405,plain,
product(product(a73,a111),a109) = product(a80,a83),
inference(equational,[status(thm)],[c284,c6341,c6404]) ).
cnf(c6406,plain,
product(product(a73,a111),a112) = a83,
inference(equational,[status(thm)],[c165,c6323,c6359,c6405]) ).
cnf(c6407,plain,
product(a83,a119) = product(a73,a112),
inference(equational,[status(thm)],[c284,c4664,c6406]) ).
cnf(c6411,plain,
product(product(a71,a119),a82) = a83,
inference(equational,[status(thm)],[c284,c594,c5931,c6399]) ).
cnf(c6412,plain,
product(product(a71,a73),a82) = a79,
inference(equational,[status(thm)],[c428,c794,c1761,c5875,c6324,c6390]) ).
cnf(c6413,plain,
product(a79,a82) = product(a71,a73),
inference(equational,[status(thm)],[c284,c6412]) ).
cnf(c6414,plain,
product(product(a83,X),a108) = product(a71,product(X,a108)),
inference(equational,[status(thm)],[c3408,c6334]) ).
cnf(c6415,plain,
product(product(a71,a83),a108) = a73,
inference(equational,[status(thm)],[c647,c2714,c4545,c5824,c5827,c5982,c6369,c6414]) ).
cnf(c6416,plain,
product(product(X,a83),a108) = product(product(X,a108),a71),
inference(equational,[status(thm)],[c3392,c6334]) ).
cnf(c6417,plain,
product(product(a109,a83),a71) = a112,
inference(equational,[status(thm)],[c4852,c5842,c5919,c6354,c6355,c6367,c6416]) ).
cnf(c6418,plain,
product(a109,a83) = product(a112,a71),
inference(equational,[status(thm)],[c284,c6417]) ).
cnf(c6419,plain,
product(product(a71,X),a108) = product(a83,product(X,a108)),
inference(equational,[status(thm)],[c427,c6334]) ).
cnf(c6420,plain,
product(product(X,a71),a108) = product(product(X,a108),a83),
inference(equational,[status(thm)],[c427,c6334]) ).
cnf(c6423,plain,
product(product(a111,a71),a83) = a119,
inference(equational,[status(thm)],[c428,c3433,c5823,c5828,c5992,c6356,c6401,c6420]) ).
cnf(c6426,plain,
product(product(a112,a71),a83) = a109,
inference(equational,[status(thm)],[c295,c460,c5772,c5842,c5860,c6360,c6361,c6367,c6416,c6418,c6420]) ).
cnf(c6427,plain,
product(a112,a73) = product(a110,a108),
inference(equational,[status(thm)],[c464,c3408,c5870,c6337,c6426]) ).
cnf(c6430,plain,
product(product(a80,a83),a82) = product(a82,product(a108,a82)),
inference(equational,[status(thm)],[c428,c6336]) ).
cnf(c6444,plain,
product(a111,product(a108,a119)) = product(a110,product(a108,a109)),
inference(equational,[status(thm)],[c466,c1972,c5830,c5860,c6337]) ).
cnf(c6452,plain,
product(a110,product(a108,a109)) = product(a118,a72),
inference(equational,[status(thm)],[c3408,c5906,c6353,c6374,c6385]) ).
cnf(c6455,plain,
product(product(a80,a83),a71) = product(a71,a110),
inference(equational,[status(thm)],[c3392,c5563,c5826,c6380,c6396,c6420]) ).
cnf(c6457,plain,
product(a80,product(a106,a39)) = product(a79,a71),
inference(equational,[status(thm)],[c6359,c6371,c6383,c6420,c6455]) ).
cnf(c6466,plain,
product(product(a108,a79),a119) = product(a110,a108),
inference(equational,[status(thm)],[c284,c807,c6393]) ).
cnf(c6467,plain,
product(a118,a72) = product(a108,a79),
inference(equational,[status(thm)],[c284,c466,c6444,c6452,c6466]) ).
cnf(c6476,plain,
product(product(a112,a71),a118) = product(a108,a82),
inference(equational,[status(thm)],[c4586,c5841,c5842,c6323,c6366,c6367,c6418]) ).
cnf(c6498,plain,
product(product(product(X,a111),a110),a119) = product(X,product(a108,a82)),
inference(equational,[status(thm)],[c652,c3408,c4294,c6366]) ).
cnf(c6500,plain,
product(product(a106,a39),a119) = product(a111,product(a108,a82)),
inference(equational,[status(thm)],[c1,c5859,c6498]) ).
cnf(c6501,plain,
product(a80,product(a108,a82)) = product(a83,a111),
inference(equational,[status(thm)],[c1878,c5476,c5905,c5922,c5989,c6380,c6407,c6498]) ).
cnf(c6505,plain,
product(a72,product(a108,a82)) = product(a73,a112),
inference(equational,[status(thm)],[c2472,c5823,c5829,c5914,c5929,c6334,c6407,c6498]) ).
cnf(c6506,plain,
product(a71,product(a106,a39)) = product(a80,a71),
inference(equational,[status(thm)],[c1877,c6344,c6377,c6505]) ).
cnf(c6512,plain,
product(product(a108,a112),a79) = product(a108,a71),
inference(equational,[status(thm)],[c1819,c4665,c4666,c5469,c5905,c5922,c6365,c6374,c6385,c6467,c6500]) ).
cnf(c6513,plain,
product(a109,a72) = product(a110,a111),
inference(equational,[status(thm)],[c653,c5923,c6328,c6331,c6512]) ).
cnf(c6515,plain,
product(product(product(X,a110),a109),a80) = product(X,product(a71,a73)),
inference(equational,[status(thm)],[c649,c3408,c5823,c5854]) ).
cnf(c6516,plain,
product(a109,product(a71,a73)) = product(a108,a71),
inference(equational,[status(thm)],[c428,c5828,c5867,c5905,c5922,c6515]) ).
cnf(c6518,plain,
product(a109,product(a71,a110)) = a111,
inference(equational,[status(thm)],[c428,c593,c1753,c5824,c5839,c5915,c6324,c6516]) ).
cnf(c6519,plain,
product(a119,product(a71,a73)) = a108,
inference(equational,[status(thm)],[c5397,c5760,c5823,c5824,c5838,c5840,c5851,c6515]) ).
cnf(c6521,plain,
product(product(a71,a79),a119) = product(a72,product(a71,a73)),
inference(equational,[status(thm)],[c807,c1877,c5867,c6515]) ).
cnf(c6524,plain,
product(product(a101,a32),a71) = a110,
inference(equational,[status(thm)],[c3392,c5841,c5993,c6519]) ).
cnf(c6526,plain,
product(a108,product(a71,a83)) = product(a110,a108),
inference(equational,[status(thm)],[c791,c1876,c1957,c5823,c5988,c6337,c6518]) ).
cnf(c6528,plain,
product(product(a71,a83),a73) = a82,
inference(equational,[status(thm)],[c3392,c4293,c5932,c6415,c6526]) ).
cnf(c6536,plain,
product(a111,product(a71,a119)) = product(a108,a112),
inference(equational,[status(thm)],[c4663,c5899,c6519]) ).
cnf(c6537,plain,
product(product(product(X,a112),a111),a79) = product(X,product(a71,a110)),
inference(equational,[status(thm)],[c653,c2375,c3408,c5823,c5855]) ).
cnf(c6539,plain,
product(a82,product(a71,a110)) = a79,
inference(equational,[status(thm)],[c1,c5498,c5875,c5932,c5935,c5936,c6537]) ).
cnf(c6544,plain,
product(a79,product(a71,a110)) = a82,
inference(equational,[status(thm)],[c284,c6539]) ).
cnf(c6545,plain,
product(a79,a73) = product(a72,a118),
inference(equational,[status(thm)],[c5073,c5792,c5824,c5829,c5863,c5914,c5921,c6334,c6382,c6544]) ).
cnf(c6555,plain,
product(product(a72,a118),a73) = a79,
inference(equational,[status(thm)],[c284,c6545]) ).
cnf(c6567,plain,
product(product(product(X,a115),a114),a68) = product(X,product(a76,a122)),
inference(equational,[status(thm)],[c656,c3408,c6176]) ).
cnf(c6568,plain,
product(a121,product(a76,a124)) = product(a123,a100),
inference(equational,[status(thm)],[c1,c483,c4146,c5834,c6014,c6057,c6159,c6175,c6188,c6567]) ).
cnf(c6569,plain,
product(product(a77,a67),a98) = product(a75,product(a76,a122)),
inference(equational,[status(thm)],[c598,c657,c783,c6020,c6045,c6092,c6175,c6567]) ).
cnf(c6570,plain,
product(a76,product(a75,a121)) = product(a77,a98),
inference(equational,[status(thm)],[c284,c310,c597,c783,c1888,c6569]) ).
cnf(c6572,plain,
product(a121,product(a75,a76)) = product(a122,a99),
inference(equational,[status(thm)],[c428,c6137,c6231,c6568]) ).
cnf(c6574,plain,
product(product(a122,a99),a76) = product(a121,a115),
inference(equational,[status(thm)],[c284,c2482,c6049,c6572]) ).
cnf(c6583,plain,
product(product(a121,a98),a114) = product(a121,a122),
inference(equational,[status(thm)],[c428,c4657,c5908,c6045,c6092,c6193,c6574]) ).
cnf(c6584,plain,
product(a123,a77) = product(a121,a98),
inference(equational,[status(thm)],[c284,c6252,c6583]) ).
cnf(c6590,plain,
product(product(product(X,a119),a71),a118) = product(X,a79),
inference(equational,[status(thm)],[c439,c661,c1736,c3408,c5823,c5839]) ).
cnf(c6592,plain,
product(product(a71,a83),a79) = product(a83,a111),
inference(equational,[status(thm)],[c428,c1876,c5436,c5823,c5828,c5866,c5939,c6476,c6501,c6590]) ).
cnf(c6594,plain,
product(product(X,a119),a71) = product(product(X,a79),a118),
inference(equational,[status(thm)],[c284,c6590]) ).
cnf(c6595,plain,
product(product(X,a119),a118) = product(product(X,a79),a80),
inference(equational,[status(thm)],[c284,c1736,c5823,c6590]) ).
cnf(c6596,plain,
product(product(X,a80),a119) = product(product(X,a71),a118),
inference(equational,[status(thm)],[c284,c1756,c6590]) ).
cnf(c6597,plain,
product(product(a71,a110),a119) = a82,
inference(equational,[status(thm)],[c145,c407,c5436,c5847,c5851,c5931,c6596]) ).
cnf(c6598,plain,
product(a82,a111) = product(a71,a119),
inference(equational,[status(thm)],[c284,c652,c6597]) ).
cnf(c6599,plain,
product(product(a71,a73),a119) = a72,
inference(equational,[status(thm)],[c1,c284,c5072,c5824,c5847,c5851,c5854,c6382,c6545,c6596]) ).
cnf(c6600,plain,
product(a80,a83) = product(a72,a73),
inference(equational,[status(thm)],[c3408,c5993,c6348,c6599]) ).
cnf(c6601,plain,
product(a73,a111) = product(a71,a79),
inference(equational,[status(thm)],[c1753,c1877,c5824,c5839,c6341,c6404,c6600]) ).
cnf(c6604,plain,
product(a72,product(a71,a73)) = product(a80,a71),
inference(equational,[status(thm)],[c592,c807,c5823,c5831,c5924,c6506,c6521,c6595]) ).
cnf(c6605,plain,
product(product(a73,a112),a80) = product(a72,a118),
inference(equational,[status(thm)],[c2851,c5823,c5854,c5900,c5929,c5940,c6334,c6595]) ).
cnf(c6608,plain,
product(product(a83,a111),a79) = product(a71,a83),
inference(equational,[status(thm)],[c284,c6592]) ).
cnf(c6611,plain,
product(product(a72,a73),a83) = a80,
inference(equational,[status(thm)],[c284,c5792,c5931,c6604]) ).
cnf(c6614,plain,
product(product(X,a80),a79) = product(product(X,a71),a80),
inference(equational,[status(thm)],[c284,c807,c1861,c5823,c6590,c6595,c6596]) ).
cnf(c6618,plain,
product(a82,product(a110,a108)) = product(a71,product(a112,a71)),
inference(equational,[status(thm)],[c428,c1882,c5436,c5828,c5866,c5939,c6337,c6592,c6594]) ).
cnf(c6621,plain,
product(product(a72,a73),a110) = product(a73,a112),
inference(equational,[status(thm)],[c3392,c6336,c6356,c6407,c6419,c6420,c6423,c6600,c6618]) ).
cnf(c6623,plain,
product(product(a71,a83),a112) = product(a83,a79),
inference(equational,[status(thm)],[c284,c653,c6608]) ).
cnf(c6631,plain,
product(product(a72,a118),a80) = product(a73,a112),
inference(equational,[status(thm)],[c284,c6605]) ).
cnf(c6634,plain,
product(product(a112,a71),a80) = product(a108,a112),
inference(equational,[status(thm)],[c1956,c5831,c6536,c6614]) ).
cnf(c6638,plain,
product(product(a71,a111),a112) = product(a71,a83),
inference(equational,[status(thm)],[c1820,c4664,c5939,c6398,c6599]) ).
cnf(c6639,plain,
product(a83,a79) = product(a71,a111),
inference(equational,[status(thm)],[c284,c6623,c6638]) ).
cnf(c6641,plain,
product(product(a71,a111),a79) = a83,
inference(equational,[status(thm)],[c165,c653,c1861,c4664,c5823,c5849,c5916,c6596,c6601,c6631]) ).
cnf(c6642,plain,
product(a83,a111) = product(a71,a72),
inference(equational,[status(thm)],[c2434,c3408,c5823,c5929,c6641]) ).
cnf(c6657,plain,
product(product(a108,a112),a80) = product(a112,a71),
inference(equational,[status(thm)],[c284,c6634]) ).
cnf(c6660,plain,
product(a82,product(a108,a82)) = product(a73,a72),
inference(equational,[status(thm)],[c396,c594,c6430,c6600]) ).
cnf(c6661,plain,
product(a73,product(a110,a108)) = product(a72,a108),
inference(equational,[status(thm)],[c428,c3408,c5871,c6427,c6621]) ).
cnf(c6673,plain,
product(a73,a72) = product(a71,a111),
inference(equational,[status(thm)],[c284,c1820,c6498,c6598,c6660]) ).
cnf(c6687,plain,
product(product(product(X,a91),a90),a100) = product(X,product(a121,a115)),
inference(equational,[status(thm)],[c823,c3408,c6122]) ).
cnf(c6688,plain,
product(a91,product(a121,a115)) = product(a90,a91),
inference(equational,[status(thm)],[c1,c857,c6687]) ).
cnf(c6689,plain,
product(product(a90,a91),a115) = product(a90,a122),
inference(equational,[status(thm)],[c3392,c6076,c6688]) ).
cnf(c6690,plain,
product(a100,product(a121,a115)) = product(a123,a100),
inference(equational,[status(thm)],[c4364,c5882,c6087,c6687]) ).
cnf(c6692,plain,
product(product(a122,a124),a98) = product(a122,a99),
inference(equational,[status(thm)],[c5742,c5792,c5908,c6045,c6092,c6137,c6690]) ).
cnf(c6693,plain,
product(product(a90,a122),a115) = product(a90,a91),
inference(equational,[status(thm)],[c284,c6689]) ).
cnf(c6706,plain,
product(product(product(X,a83),a82),a118) = product(X,product(a110,a108)),
inference(equational,[status(thm)],[c812,c3408,c5919]) ).
cnf(c6707,plain,
product(a83,product(a79,a71)) = product(a71,product(a112,a71)),
inference(equational,[status(thm)],[c428,c607,c1876,c5823,c5924,c6384,c6457,c6618,c6706]) ).
cnf(c6708,plain,
product(a82,product(a71,a119)) = product(a71,a72),
inference(equational,[status(thm)],[c1876,c1882,c3816,c5823,c5831,c5839,c6476,c6501,c6642,c6707]) ).
cnf(c6714,plain,
product(product(a71,a72),a82) = product(a79,a71),
inference(equational,[status(thm)],[c428,c6383,c6411,c6708]) ).
cnf(c6721,plain,
product(product(product(X,a82),a80),a109) = product(X,a119),
inference(equational,[status(thm)],[c811,c3408,c5824,c5842]) ).
cnf(c6722,plain,
product(product(X,a82),a110) = product(product(X,a79),a119),
inference(equational,[status(thm)],[c807,c3408,c5847,c6721]) ).
cnf(c6723,plain,
product(product(X,a119),a82) = product(product(X,a82),a109),
inference(equational,[status(thm)],[c284,c811,c5824,c6721]) ).
cnf(c6726,plain,
product(product(X,a82),a119) = product(product(X,a80),a109),
inference(equational,[status(thm)],[c284,c6721]) ).
cnf(c6728,plain,
product(a111,product(a108,a82)) = product(a110,a111),
inference(equational,[status(thm)],[c807,c3684,c5760,c5824,c5840,c5920,c6343,c6466,c6500,c6513,c6721]) ).
cnf(c6729,plain,
product(product(a112,a71),a109) = product(a108,a79),
inference(equational,[status(thm)],[c466,c4349,c5760,c5824,c5840,c5919,c5975,c6332,c6444,c6452,c6467,c6657,c6721]) ).
cnf(c6733,plain,
product(product(a71,a73),a110) = a80,
inference(equational,[status(thm)],[c1,c159,c4213,c5824,c5839,c5842,c5916,c6722]) ).
cnf(c6734,plain,
product(product(a108,a79),a72) = a118,
inference(equational,[status(thm)],[c284,c794,c5865,c6729]) ).
cnf(c6738,plain,
product(a110,product(a108,a71)) = product(a106,a39),
inference(equational,[status(thm)],[c298,c466,c1972,c5840,c5859,c5922,c6726,c6728]) ).
cnf(c6739,plain,
product(product(a108,a79),a82) = product(a110,a83),
inference(equational,[status(thm)],[c811,c5824,c6350,c6361,c6634,c6729]) ).
cnf(c6742,plain,
product(product(a71,a111),a82) = product(a72,a73),
inference(equational,[status(thm)],[c593,c594,c3941,c5760,c5823,c5824,c5839,c5840,c6339,c6382,c6545,c6601,c6639,c6723]) ).
cnf(c6743,plain,
product(product(a110,a83),a73) = a111,
inference(equational,[status(thm)],[c795,c5760,c5824,c5840,c6734,c6739]) ).
cnf(c6764,plain,
product(product(product(X,a68),a67),a98) = product(X,a100),
inference(equational,[status(thm)],[c783,c3408,c6094]) ).
cnf(c6765,plain,
product(a68,a100) = product(a67,a68),
inference(equational,[status(thm)],[c1,c935,c6764]) ).
cnf(c6766,plain,
product(a98,a67) = product(a100,a98),
inference(equational,[status(thm)],[c3392,c4293,c6045,c6092,c6765]) ).
cnf(c6767,plain,
product(product(a100,a67),a98) = product(a98,a100),
inference(equational,[status(thm)],[c1202,c5835,c5908,c6045,c6092,c6764]) ).
cnf(c6770,plain,
product(product(X,a98),a67) = product(product(X,a100),a68),
inference(equational,[status(thm)],[c284,c783,c1734,c6764]) ).
cnf(c6771,plain,
product(product(X,a68),a100) = product(product(X,a67),a98),
inference(equational,[status(thm)],[c284,c6764]) ).
cnf(c6772,plain,
product(a100,product(a67,a68)) = product(a98,a100),
inference(equational,[status(thm)],[c428,c6765,c6767,c6771]) ).
cnf(c6774,plain,
product(product(a99,a67),a98) = product(a121,a115),
inference(equational,[status(thm)],[c1204,c5856,c5983,c6022,c6122,c6771]) ).
cnf(c6775,plain,
product(a99,a98) = product(a122,a114),
inference(equational,[status(thm)],[c284,c302,c483,c783,c6774]) ).
cnf(c6778,plain,
product(product(a77,a115),a100) = product(a76,a124),
inference(equational,[status(thm)],[c135,c2753,c3408,c6175,c6177,c6570,c6764]) ).
cnf(c6781,plain,
product(product(a67,a114),a68) = product(a75,a76),
inference(equational,[status(thm)],[c656,c5834,c6015,c6175,c6231,c6765]) ).
cnf(c6782,plain,
product(a76,a75) = product(a67,a114),
inference(equational,[status(thm)],[c284,c399,c597,c6781]) ).
cnf(c6801,plain,
product(product(a121,a114),a98) = product(a121,a99),
inference(equational,[status(thm)],[c3805,c6152,c6159,c6770]) ).
cnf(c6806,plain,
product(product(a76,a99),a124) = product(a77,a115),
inference(equational,[status(thm)],[c284,c835,c6778]) ).
cnf(c6807,plain,
product(a75,product(a121,a115)) = product(a67,a68),
inference(equational,[status(thm)],[c284,c656,c6223,c6781]) ).
cnf(c6808,plain,
product(a76,product(a122,a114)) = a67,
inference(equational,[status(thm)],[c284,c302,c483,c597,c6807]) ).
cnf(c6809,plain,
product(a76,a115) = product(a67,a76),
inference(equational,[status(thm)],[c428,c1758,c6159,c6172,c6808]) ).
cnf(c6814,plain,
product(product(a122,a114),a98) = a99,
inference(equational,[status(thm)],[c284,c6775]) ).
cnf(c6818,plain,
product(product(a100,a98),a1) = product(a97,product(a67,a1)),
inference(equational,[status(thm)],[c1732,c6766]) ).
cnf(c6824,plain,
product(product(a75,a121),a76) = product(a67,product(a75,a121)),
inference(equational,[status(thm)],[c2485,c3408,c6177,c6781]) ).
cnf(c6840,plain,
product(a97,product(a68,a1)) = product(a100,a1),
inference(equational,[status(thm)],[c135,c284,c428,c1773,c6818]) ).
cnf(c6855,plain,
product(product(product(X,a72),a71),a109) = product(X,product(a110,a111)),
inference(equational,[status(thm)],[c794,c3408,c6513]) ).
cnf(c6856,plain,
product(a72,product(a110,a111)) = product(a71,a72),
inference(equational,[status(thm)],[c1,c923,c6855]) ).
cnf(c6868,plain,
product(product(product(X,a80),a69),a13) = product(X,product(a13,a80)),
inference(equational,[status(thm)],[c785,c3408,c5823]) ).
cnf(c6870,plain,
product(product(X,a13),a80) = product(product(X,a69),a13),
inference(equational,[status(thm)],[c284,c427,c1754,c5823,c5824,c6868]) ).
cnf(c6884,plain,
product(product(a71,a110),a33) = product(a76,a13),
inference(equational,[status(thm)],[c284,c3392,c5558,c5823,c5855,c6870]) ).
cnf(c6885,plain,
product(product(product(X,a73),a72),a82) = product(X,product(a71,a83)),
inference(equational,[status(thm)],[c795,c3408,c5942]) ).
cnf(c6886,plain,
product(a73,product(a71,a83)) = product(a72,a73),
inference(equational,[status(thm)],[c1,c6673,c6742,c6885]) ).
cnf(c6887,plain,
product(product(a73,a83),a71) = a80,
inference(equational,[status(thm)],[c3392,c6611,c6886]) ).
cnf(c6888,plain,
product(a80,a71) = product(a73,a83),
inference(equational,[status(thm)],[c284,c6887]) ).
cnf(c6904,plain,
product(product(product(X,a77),a121),a76) = product(X,product(a121,a114)),
inference(equational,[status(thm)],[c803,c804,c2485,c3408]) ).
cnf(c6905,plain,
product(a68,a76) = product(a76,a77),
inference(equational,[status(thm)],[c1,c1439,c5864,c6904]) ).
cnf(c6906,plain,
product(a121,product(a121,a114)) = a98,
inference(equational,[status(thm)],[c243,c428,c5864,c6092,c6904]) ).
cnf(c6907,plain,
product(a98,product(a121,a114)) = a121,
inference(equational,[status(thm)],[c284,c6906]) ).
cnf(c6908,plain,
product(a123,a114) = product(a121,a92),
inference(equational,[status(thm)],[c630,c6081,c6150,c6775,c6907]) ).
cnf(c6911,plain,
product(a76,product(a76,a77)) = product(a75,a76),
inference(equational,[status(thm)],[c1437,c6905]) ).
cnf(c6919,plain,
product(a98,product(a121,a99)) = product(a121,a98),
inference(equational,[status(thm)],[c428,c6801,c6907]) ).
cnf(c6920,plain,
product(a67,product(a75,a121)) = product(a75,a122),
inference(equational,[status(thm)],[c400,c598,c1438,c2485,c4568,c6016,c6238,c6239,c6824,c6911]) ).
cnf(c6923,plain,
product(a121,product(a90,a123)) = a100,
inference(equational,[status(thm)],[c428,c2482,c4658,c5835,c6073,c6095,c6584,c6908]) ).
cnf(c6926,plain,
product(product(a121,a98),a99) = a124,
inference(equational,[status(thm)],[c3392,c4658,c6022,c6033,c6046,c6919]) ).
cnf(c6935,plain,
product(product(a121,a98),a92) = product(a122,a124),
inference(equational,[status(thm)],[c833,c5897,c6908]) ).
cnf(c6936,plain,
product(a124,a92) = product(a122,a99),
inference(equational,[status(thm)],[c1774,c6692,c6926,c6935]) ).
cnf(c6939,plain,
product(product(a67,a121),a100) = product(a76,a124),
inference(equational,[status(thm)],[c428,c657,c799,c5792,c5934,c6175,c6920]) ).
cnf(c6940,plain,
product(a67,a99) = a75,
inference(equational,[status(thm)],[c3408,c4647,c5856,c6015,c6022,c6178,c6939]) ).
cnf(c6964,plain,
product(product(product(X,a49),a48),a138) = product(X,product(a138,a49)),
inference(equational,[status(thm)],[c754,c3408]) ).
cnf(c6973,plain,
product(product(product(X,a56),a55),a37) = product(X,product(a37,a56)),
inference(equational,[status(thm)],[c765,c3408]) ).
cnf(c6984,plain,
product(product(product(X,a99),a98),a92) = product(X,product(a90,a124)),
inference(equational,[status(thm)],[c621,c833,c3408]) ).
cnf(c6985,plain,
product(a100,product(a90,a124)) = product(a123,a92),
inference(equational,[status(thm)],[c1,c199,c2482,c3392,c4658,c5494,c5930,c6046,c6083,c6100,c6159,c6775,c6984]) ).
cnf(c6986,plain,
product(a114,a91) = product(a99,a90),
inference(equational,[status(thm)],[c284,c1782,c1991,c5876,c6985]) ).
cnf(c6987,plain,
product(a75,product(a90,a124)) = product(a66,a99),
inference(equational,[status(thm)],[c135,c834,c4769,c6019,c6034,c6202,c6808,c6984]) ).
cnf(c6989,plain,
product(product(a99,a90),a91) = a114,
inference(equational,[status(thm)],[c284,c6986]) ).
cnf(c6994,plain,
product(a114,product(a90,a124)) = a98,
inference(equational,[status(thm)],[c424,c6034,c6814,c6984]) ).
cnf(c6995,plain,
product(a123,a90) = product(a121,a115),
inference(equational,[status(thm)],[c632,c3392,c5930,c6122,c6994]) ).
cnf(c7034,plain,
product(a100,product(a90,a123)) = a121,
inference(equational,[status(thm)],[c284,c6923]) ).
cnf(c7035,plain,
product(a99,a123) = product(a121,a90),
inference(equational,[status(thm)],[c5739,c5792,c6197,c6995,c7034]) ).
cnf(c7046,plain,
product(a116,product(a83,a32)) = a101,
inference(equational,[status(thm)],[c284,c4278]) ).
cnf(c7047,plain,
product(product(a71,a83),a110) = a72,
inference(equational,[status(thm)],[c284,c3392,c5982,c6661]) ).
cnf(c7057,plain,
product(product(a67,a76),a75) = a77,
inference(equational,[status(thm)],[c153,c428,c802,c1856,c2479,c3392,c3398,c4959,c5834,c6175,c6179,c6254,c6809]) ).
cnf(c7059,plain,
product(a123,product(a76,a124)) = a115,
inference(equational,[status(thm)],[c2476,c6175]) ).
cnf(c7067,plain,
product(product(a121,a115),a91) = a100,
inference(equational,[status(thm)],[c284,c427,c6099,c6134]) ).
cnf(c7068,plain,
product(product(a121,a115),a90) = a123,
inference(equational,[status(thm)],[c4364,c5882,c6087,c6122]) ).
cnf(c7079,plain,
product(product(product(X,a41),a1),a42) = product(X,a3),
inference(equational,[status(thm)],[c284,c744,c1703,c1745,c1795]) ).
cnf(c7100,plain,
product(product(product(X,a32),a33),a13) = product(X,a14),
inference(equational,[status(thm)],[c284,c1741]) ).
cnf(c7104,plain,
product(product(a69,a120),a14) = product(a78,a32),
inference(equational,[status(thm)],[c352,c599,c1215,c5836,c7100]) ).
cnf(c7121,plain,
product(product(a91,a90),a115) = product(a91,a123),
inference(equational,[status(thm)],[c620,c4645,c6077]) ).
cnf(c7212,plain,
product(product(product(a88,a40),a32),a39) = product(a84,a106),
inference(equational,[status(thm)],[c9,c79,c644,c727,c1266,c1749,c5277]) ).
cnf(c7213,plain,
product(product(a88,a40),a32) = product(a71,a83),
inference(equational,[status(thm)],[c284,c1867,c4545,c5982,c7212]) ).
cnf(c7257,plain,
product(product(product(a33,a32),a88),a14) = product(a32,a89),
inference(equational,[status(thm)],[c682,c820]) ).
cnf(c7267,plain,
product(product(a67,product(a122,a99)),a124) = product(a66,a91),
inference(equational,[status(thm)],[c284,c2097,c6936]) ).
cnf(c7268,plain,
product(product(a66,a91),a100) = a68,
inference(equational,[status(thm)],[c1,c835,c3392,c4225,c5864,c6940,c7267]) ).
cnf(c7269,plain,
product(a68,a90) = product(a66,a100),
inference(equational,[status(thm)],[c284,c1777,c7268]) ).
cnf(c7270,plain,
product(a67,a68) = product(a66,a91),
inference(equational,[status(thm)],[c284,c6765,c7268]) ).
cnf(c7271,plain,
product(a92,a91) = product(a98,a100),
inference(equational,[status(thm)],[c5791,c6772,c7270]) ).
cnf(c7342,plain,
product(product(a80,a33),product(a121,a13)) = a78,
inference(equational,[status(thm)],[c284,c2421]) ).
cnf(c7359,plain,
product(product(a62,a127),product(a94,a63)) = a64,
inference(equational,[status(thm)],[c284,c2470]) ).
cnf(c7362,plain,
product(product(a103,a86),product(a103,a104)) = a104,
inference(equational,[status(thm)],[c284,c2243]) ).
cnf(c7366,plain,
product(product(a66,a99),product(a90,a124)) = a75,
inference(equational,[status(thm)],[c284,c6987]) ).
cnf(c7385,plain,
product(product(a71,a72),product(a110,a111)) = a72,
inference(equational,[status(thm)],[c284,c6856]) ).
cnf(c7595,plain,
product(product(a67,a114),a122) = a77,
inference(equational,[status(thm)],[c2479,c6782,c6809,c7057]) ).
cnf(c7660,plain,
product(product(product(a120,X),a73),a32) = product(product(a121,product(X,a32)),a74),
inference(equational,[status(thm)],[c481,c796]) ).
cnf(c7703,plain,
product(product(product(a92,X),a98),a92) = product(product(a92,product(X,a92)),a99),
inference(equational,[status(thm)],[c428,c833]) ).
cnf(c7717,plain,
product(product(product(X,a124),a98),a92) = product(product(product(X,a91),a100),a124),
inference(equational,[status(thm)],[c824,c833,c1823]) ).
cnf(c7718,plain,
product(a90,a91) = product(a121,a115),
inference(equational,[status(thm)],[c284,c621,c632,c2481,c3392,c6122,c6693,c6936,c7271,c7703,c7717]) ).
cnf(c7719,plain,
a100 = a90,
inference(equational,[status(thm)],[c284,c7067,c7718]) ).
cnf(c7720,plain,
a90 = a123,
inference(equational,[status(thm)],[c1,c4364,c7068,c7718,c7719]) ).
cnf(c7721,plain,
a91 = a123,
inference(equational,[status(thm)],[c1,c181,c7719,c7720]) ).
cnf(c7722,plain,
a68 = a66,
inference(equational,[status(thm)],[c284,c7268,c7719,c7720,c7721]) ).
cnf(c7723,plain,
a123 = a122,
inference(equational,[status(thm)],[c1,c311,c7121,c7720,c7721]) ).
cnf(c7724,plain,
a114 = a121,
inference(equational,[status(thm)],[c284,c6989,c7035,c7720,c7721]) ).
cnf(c7725,plain,
a115 = a121,
inference(equational,[status(thm)],[c310,c311,c6213,c7059,c7720,c7721]) ).
cnf(c7726,plain,
a124 = a122,
inference(equational,[status(thm)],[c1,c6121,c7719,c7720,c7721,c7723]) ).
cnf(c7727,plain,
a122 = a121,
inference(equational,[status(thm)],[c311,c1531,c6017,c6031,c6036,c7720,c7721,c7724]) ).
cnf(c7728,plain,
a98 = a121,
inference(equational,[status(thm)],[c1,c825,c5876,c7719,c7720,c7721,c7724]) ).
cnf(c7729,plain,
a92 = a121,
inference(equational,[status(thm)],[c183,c5876,c7721,c7724]) ).
cnf(c7730,plain,
a99 = a121,
inference(equational,[status(thm)],[c284,c4688,c5876,c6033,c7720]) ).
cnf(c7731,plain,
a75 = a66,
inference(equational,[status(thm)],[c1,c284,c7366,c7720,c7723,c7726,c7727,c7730]) ).
cnf(c7732,plain,
a76 = a66,
inference(equational,[status(thm)],[c284,c5864,c6806,c7722,c7725,c7726,c7727,c7730]) ).
cnf(c7733,plain,
a77 = a67,
inference(equational,[status(thm)],[c284,c7595,c7724,c7727]) ).
cnf(c7734,plain,
a118 = a110,
inference(equational,[status(thm)],[c681,c786,c4252,c5824,c5847,c7726]) ).
cnf(c7735,plain,
a82 = a79,
inference(equational,[status(thm)],[c5939,c6528,c6555,c7734]) ).
cnf(c7736,plain,
a109 = a110,
inference(equational,[status(thm)],[c5776,c5841,c6360,c6416,c7734]) ).
cnf(c7737,plain,
a119 = a111,
inference(equational,[status(thm)],[c5777,c5867,c6743,c7734]) ).
cnf(c7738,plain,
a112 = a111,
inference(equational,[status(thm)],[c5760,c5824,c5840,c5868,c7734]) ).
cnf(c7739,plain,
a80 = a73,
inference(equational,[status(thm)],[c284,c4216,c5824,c6413,c6733,c6888,c7734]) ).
cnf(c7740,plain,
a83 = a73,
inference(equational,[status(thm)],[c4277,c5824,c5854,c5903,c7734,c7739]) ).
cnf(c7741,plain,
a111 = a110,
inference(equational,[status(thm)],[c4274,c5824,c5842,c5846,c7734,c7736,c7737]) ).
cnf(c7742,plain,
a110 = a108,
inference(equational,[status(thm)],[c284,c793,c5469,c5905,c5922,c7734]) ).
cnf(c7743,plain,
product(a102,a14) = a89,
inference(equational,[status(thm)],[c414,c742,c7719]) ).
cnf(c7744,plain,
a88 = a102,
inference(equational,[status(thm)],[c284,c413,c7743]) ).
cnf(c7745,plain,
a87 = a103,
inference(equational,[status(thm)],[c205,c412,c7744]) ).
cnf(c7746,plain,
a104 = a86,
inference(equational,[status(thm)],[c4689,c7362,c7745]) ).
cnf(c7747,plain,
a86 = a103,
inference(equational,[status(thm)],[c284,c1660,c7745]) ).
cnf(c7748,plain,
a85 = a105,
inference(equational,[status(thm)],[c209,c410,c7746]) ).
cnf(c7749,plain,
a74 = a101,
inference(equational,[status(thm)],[c147,c288,c289,c2268,c7740,c7747]) ).
cnf(c7750,plain,
a117 = a101,
inference(equational,[status(thm)],[c147,c233,c7046,c7740]) ).
cnf(c7751,plain,
a73 = a72,
inference(equational,[status(thm)],[c6733,c7047,c7739,c7740]) ).
cnf(c7752,plain,
a79 = a71,
inference(equational,[status(thm)],[c284,c6528,c7735,c7740]) ).
cnf(c7753,plain,
product(a89,a3) = product(a103,a14),
inference(equational,[status(thm)],[c2139,c3005,c7719]) ).
cnf(c7754,plain,
product(a71,a72) = product(a101,a32),
inference(equational,[status(thm)],[c2460,c3922,c7213,c7719,c7740,c7751]) ).
cnf(c7755,plain,
a72 = a108,
inference(equational,[status(thm)],[c1,c5737,c7385,c7734,c7741,c7742,c7754]) ).
cnf(c7756,plain,
a71 = a108,
inference(equational,[status(thm)],[c1,c6524,c6714,c7735,c7742,c7752,c7754]) ).
cnf(c7757,plain,
product(a121,a41) = a89,
inference(equational,[status(thm)],[c414,c7720,c7723,c7727]) ).
cnf(c7759,plain,
a116 = a101,
inference(equational,[status(thm)],[c1,c304,c7749,c7750]) ).
cnf(c7760,plain,
a84 = a106,
inference(equational,[status(thm)],[c211,c409,c7748]) ).
cnf(c7761,plain,
a66 = a121,
inference(equational,[status(thm)],[c149,c287,c7719,c7720,c7723,c7727,c7731,c7749]) ).
cnf(c7762,plain,
product(a67,a121) = a121,
inference(equational,[status(thm)],[c1,c6163,c6809,c7269,c7719,c7720,c7723,c7727,c7732,c7761]) ).
cnf(c7763,plain,
a67 = a121,
inference(equational,[status(thm)],[c1,c284,c7762]) ).
cnf(c7765,plain,
product(a93,a65) = product(a121,a2),
inference(equational,[status(thm)],[c1,c3393,c7719,c7720,c7721,c7723,c7727]) ).
cnf(c7766,plain,
product(a121,a2) = a93,
inference(equational,[status(thm)],[c1,c284,c1724,c7761,c7765]) ).
cnf(c7767,plain,
product(a121,a13) = a113,
inference(equational,[status(thm)],[c301,c7724]) ).
cnf(c7769,plain,
product(a106,a39) = a108,
inference(equational,[status(thm)],[c1,c6738,c7742,c7756]) ).
cnf(c7770,plain,
a107 = a106,
inference(equational,[status(thm)],[c284,c294,c7769]) ).
cnf(c7772,plain,
a93 = a126,
inference(equational,[status(thm)],[c1,c251,c388,c3838,c7722,c7724,c7766]) ).
cnf(c7773,plain,
a126 = a125,
inference(equational,[status(thm)],[c314,c7765,c7766,c7772]) ).
cnf(c7774,plain,
a127 = a94,
inference(equational,[status(thm)],[c187,c253,c7772]) ).
cnf(c7775,plain,
a95 = a94,
inference(equational,[status(thm)],[c1,c189,c7774]) ).
cnf(c7776,plain,
a69 = a120,
inference(equational,[status(thm)],[c137,c309,c7722,c7761]) ).
cnf(c7777,plain,
product(a121,a1) = a97,
inference(equational,[status(thm)],[c423,c7728]) ).
cnf(c7778,plain,
product(a108,a33) = a113,
inference(equational,[status(thm)],[c1,c6884,c7732,c7742,c7756,c7761,c7767]) ).
cnf(c7779,plain,
product(a94,a42) = a97,
inference(equational,[status(thm)],[c4270,c6840,c7719,c7720,c7722,c7723,c7727,c7775,c7777]) ).
cnf(c7780,plain,
a96 = a94,
inference(equational,[status(thm)],[c284,c422,c7779]) ).
cnf(c7781,plain,
a128 = a94,
inference(equational,[status(thm)],[c1,c255,c7774,c7780]) ).
cnf(c7785,plain,
product(a94,a3) = a89,
inference(equational,[status(thm)],[c625,c7729,c7757]) ).
cnf(c7786,plain,
product(a103,a14) = a94,
inference(equational,[status(thm)],[c284,c7753,c7785]) ).
cnf(c7787,plain,
product(a63,a41) = a125,
inference(equational,[status(thm)],[c583,c827,c7763,c7766,c7772,c7773]) ).
cnf(c7788,plain,
a65 = a125,
inference(equational,[status(thm)],[c1,c1690,c7773,c7787]) ).
cnf(c7789,plain,
a78 = a113,
inference(equational,[status(thm)],[c1,c654,c7342,c7738,c7739,c7741,c7742,c7751,c7755,c7767,c7778]) ).
cnf(c7792,plain,
product(a120,a14) = product(a113,a32),
inference(equational,[status(thm)],[c1,c7104,c7776,c7789]) ).
cnf(c7793,plain,
product(a97,a2) = product(a125,a3),
inference(equational,[status(thm)],[c633,c2142,c7772,c7773,c7779]) ).
cnf(c7796,plain,
product(a103,a30) = a105,
inference(equational,[status(thm)],[c1,c644,c7745,c7748]) ).
cnf(c7798,plain,
product(a63,a94) = a64,
inference(equational,[status(thm)],[c127,c7774]) ).
cnf(c7799,plain,
product(a94,a63) = a94,
inference(equational,[status(thm)],[c1,c1793,c7774,c7780]) ).
cnf(c7800,plain,
a62 = a64,
inference(equational,[status(thm)],[c284,c7359,c7774,c7799]) ).
cnf(c7801,plain,
product(a125,a41) = a129,
inference(equational,[status(thm)],[c284,c949,c7774,c7780]) ).
cnf(c7803,plain,
a63 = a129,
inference(equational,[status(thm)],[c284,c7787,c7801]) ).
cnf(c7804,plain,
product(a129,a3) = a89,
inference(equational,[status(thm)],[c2145,c7079,c7726,c7727,c7757,c7787,c7803]) ).
cnf(c7805,plain,
a94 = a129,
inference(equational,[status(thm)],[c284,c7753,c7786,c7804]) ).
cnf(c7806,plain,
a64 = a129,
inference(equational,[status(thm)],[c1,c7798,c7803,c7805]) ).
cnf(c7811,plain,
product(a129,a2) = product(a121,a42),
inference(equational,[status(thm)],[c1,c4251,c7730,c7780,c7805]) ).
cnf(c7812,plain,
product(a129,a41) = a125,
inference(equational,[status(thm)],[c1,c583,c7773,c7788,c7803]) ).
cnf(c7813,plain,
product(product(X,a14),a121) = product(product(X,a101),a14),
inference(equational,[status(thm)],[c1822,c7719,c7720,c7723,c7727]) ).
cnf(c7816,plain,
product(a43,a129) = a44,
inference(equational,[status(thm)],[c87,c7781,c7805]) ).
cnf(c7860,plain,
product(product(a103,a101),a14) = product(a129,a121),
inference(equational,[status(thm)],[c615,c7745,c7753,c7786,c7805,c7813]) ).
cnf(c7877,plain,
a61 = a130,
inference(equational,[status(thm)],[c259,c384,c7800,c7806]) ).
cnf(c7878,plain,
a131 = a59,
inference(equational,[status(thm)],[c1,c261,c685,c7877]) ).
cnf(c7879,plain,
a60 = a59,
inference(equational,[status(thm)],[c261,c383,c7877,c7878]) ).
cnf(c7880,plain,
a58 = a132,
inference(equational,[status(thm)],[c263,c380,c7878]) ).
cnf(c7881,plain,
a51 = a49,
inference(equational,[status(thm)],[c101,c370,c7878]) ).
cnf(c7882,plain,
a17 = a19,
inference(equational,[status(thm)],[c284,c690,c7880]) ).
cnf(c7883,plain,
a133 = a132,
inference(equational,[status(thm)],[c1,c265,c7880]) ).
cnf(c7884,plain,
a42 = a44,
inference(equational,[status(thm)],[c363,c7800,c7806,c7816]) ).
cnf(c7885,plain,
product(a129,a44) = a97,
inference(equational,[status(thm)],[c7779,c7805,c7884]) ).
cnf(c7895,plain,
product(a97,a44) = a129,
inference(equational,[status(thm)],[c1,c2639,c7721,c7723,c7727,c7777,c7801,c7805,c7884]) ).
cnf(c7921,plain,
product(product(a129,product(X,a41)),a2) = product(product(a121,product(X,a2)),a44),
inference(equational,[status(thm)],[c624,c744,c1978,c7726,c7727,c7772,c7773,c7805,c7884]) ).
cnf(c7922,plain,
product(product(a121,a44),a2) = a129,
inference(equational,[status(thm)],[c338,c429,c7777,c7811,c7884,c7895,c7921]) ).
cnf(c7924,plain,
product(a121,product(a1,a44)) = a125,
inference(equational,[status(thm)],[c1795,c3408,c7812,c7884,c7922]) ).
cnf(c7939,plain,
product(product(product(a129,X),a2),a44) = product(a121,product(product(X,a2),a44)),
inference(equational,[status(thm)],[c582,c584,c744,c7761,c7806,c7884]) ).
cnf(c7940,plain,
product(product(a130,a44),a3) = a125,
inference(equational,[status(thm)],[c429,c3392,c3787,c7884,c7924,c7939]) ).
cnf(c7942,plain,
product(a121,product(a44,product(a2,a44))) = a130,
inference(equational,[status(thm)],[c259,c284,c428,c633,c7884,c7939]) ).
cnf(c7946,plain,
product(a130,product(a3,a44)) = product(a125,a44),
inference(equational,[status(thm)],[c3408,c7940]) ).
cnf(c7947,plain,
product(product(a125,a3),a44) = a130,
inference(equational,[status(thm)],[c284,c427,c7946]) ).
cnf(c7949,plain,
product(a130,product(a44,product(a2,a44))) = a121,
inference(equational,[status(thm)],[c284,c7942]) ).
cnf(c7950,plain,
product(product(a2,product(X,a2)),a44) = product(a1,product(product(X,a2),a44)),
inference(equational,[status(thm)],[c428,c519,c744,c2493,c7884]) ).
cnf(c7951,plain,
product(a1,a44) = a2,
inference(equational,[status(thm)],[c1,c83,c284,c7884,c7950]) ).
cnf(c7952,plain,
product(a2,a44) = a1,
inference(equational,[status(thm)],[c284,c7951]) ).
cnf(c7960,plain,
product(a1,product(a44,a1)) = product(a3,a44),
inference(equational,[status(thm)],[c428,c446,c7884,c7951]) ).
cnf(c7966,plain,
product(a130,product(a44,a1)) = a121,
inference(equational,[status(thm)],[c7949,c7952]) ).
cnf(c7968,plain,
product(product(X,a2),a44) = product(product(X,a44),a1),
inference(equational,[status(thm)],[c3392,c7951]) ).
cnf(c7969,plain,
product(a41,a44) = product(a44,a1),
inference(equational,[status(thm)],[c1,c362,c7884,c7968]) ).
cnf(c7971,plain,
product(a44,a2) = a41,
inference(equational,[status(thm)],[c284,c428,c7951,c7969]) ).
cnf(c7973,plain,
product(product(X,a1),a44) = product(product(X,a44),a2),
inference(equational,[status(thm)],[c427,c7951]) ).
cnf(c8030,plain,
product(product(product(X,a49),a59),a138) = product(product(product(X,a137),a49),a132),
inference(equational,[status(thm)],[c686,c697,c7878,c7881]) ).
cnf(c8031,plain,
product(product(X,a49),a138) = product(product(X,a137),a49),
inference(equational,[status(thm)],[c284,c1786,c7880,c8030]) ).
cnf(c8032,plain,
product(a49,product(a137,a49)) = a48,
inference(equational,[status(thm)],[c1,c369,c428,c1897,c8031]) ).
cnf(c8033,plain,
product(a49,a137) = product(a48,a49),
inference(equational,[status(thm)],[c1,c3392,c8032]) ).
cnf(c8034,plain,
product(a25,product(a137,a49)) = a26,
inference(equational,[status(thm)],[c49,c51,c524,c8031]) ).
cnf(c8035,plain,
product(a26,a49) = product(a24,a137),
inference(equational,[status(thm)],[c284,c1944,c8034]) ).
cnf(c8036,plain,
product(X,product(a137,a49)) = product(X,a138),
inference(equational,[status(thm)],[c284,c3408,c8031]) ).
cnf(c8037,plain,
product(a138,a49) = a137,
inference(equational,[status(thm)],[c1,c284,c1953,c7881,c8036]) ).
cnf(c8039,plain,
product(a140,a139) = product(a137,a20),
inference(equational,[status(thm)],[c504,c1555,c8037]) ).
cnf(c8040,plain,
product(a140,a20) = product(a137,a138),
inference(equational,[status(thm)],[c369,c428,c753,c8037]) ).
cnf(c8042,plain,
product(product(a138,a137),a49) = product(a137,a138),
inference(equational,[status(thm)],[c369,c428,c753,c8031,c8040]) ).
cnf(c8044,plain,
product(product(a26,a137),a49) = product(a25,a48),
inference(equational,[status(thm)],[c369,c1934,c8031]) ).
cnf(c8046,plain,
product(product(a50,a137),a49) = product(a48,product(a132,a48)),
inference(equational,[status(thm)],[c2749,c8031]) ).
cnf(c8047,plain,
product(a49,a59) = a50,
inference(equational,[status(thm)],[c1,c284,c321,c557,c3392,c6964,c7878,c8037,c8046]) ).
cnf(c8050,plain,
product(product(a137,a48),a138) = product(a138,a137),
inference(equational,[status(thm)],[c284,c754,c8042]) ).
cnf(c8053,plain,
product(product(X,a49),a137) = product(product(X,a48),a138),
inference(equational,[status(thm)],[c754,c3392,c8036]) ).
cnf(c8054,plain,
product(product(X,a138),a137) = product(product(X,a48),a49),
inference(equational,[status(thm)],[c427,c5792,c8033,c8036]) ).
cnf(c8059,plain,
product(product(a25,a48),a137) = product(a26,product(a48,a49)),
inference(equational,[status(thm)],[c3408,c8033,c8044]) ).
cnf(c8062,plain,
product(product(a56,a57),a137) = product(a57,a137),
inference(equational,[status(thm)],[c284,c574,c1808,c2369,c7879,c8031,c8054]) ).
cnf(c8063,plain,
product(a56,a57) = a57,
inference(equational,[status(thm)],[c284,c8062]) ).
cnf(c8064,plain,
a56 = a57,
inference(equational,[status(thm)],[c1,c284,c8063]) ).
cnf(c8065,plain,
a55 = a54,
inference(equational,[status(thm)],[c377,c569,c8064]) ).
cnf(c8066,plain,
a53 = a52,
inference(equational,[status(thm)],[c375,c565,c8065]) ).
cnf(c8067,plain,
a49 = a48,
inference(equational,[status(thm)],[c1,c369,c373,c2228,c7881,c8066]) ).
cnf(c8068,plain,
product(a8,a57) = a9,
inference(equational,[status(thm)],[c17,c8064]) ).
cnf(c8072,plain,
product(product(a48,a50),a59) = product(a50,a48),
inference(equational,[status(thm)],[c757,c7881,c8047,c8067]) ).
cnf(c8073,plain,
product(a48,a59) = a50,
inference(equational,[status(thm)],[c284,c757,c7881,c8067,c8072]) ).
cnf(c8075,plain,
product(product(a24,a137),a138) = product(a25,a48),
inference(equational,[status(thm)],[c369,c1934,c8035]) ).
cnf(c8079,plain,
product(a138,a137) = product(a137,a48),
inference(equational,[status(thm)],[c1,c428,c8033,c8050,c8053,c8067]) ).
cnf(c8080,plain,
product(a137,a138) = a137,
inference(equational,[status(thm)],[c284,c8042,c8067,c8079]) ).
cnf(c8083,plain,
product(a48,a137) = a48,
inference(equational,[status(thm)],[c1,c369,c557,c1897,c8033,c8067,c8080]) ).
cnf(c8086,plain,
product(a47,product(a137,a20)) = a47,
inference(equational,[status(thm)],[c368,c1896,c8083]) ).
cnf(c8089,plain,
product(a137,a48) = a138,
inference(equational,[status(thm)],[c284,c428,c8079,c8083]) ).
cnf(c8090,plain,
product(product(a24,a137),a48) = a26,
inference(equational,[status(thm)],[c1,c97,c526,c1673,c6316,c7881,c8059,c8067,c8075]) ).
cnf(c8091,plain,
product(product(a138,X),a48) = product(a137,product(X,a48)),
inference(equational,[status(thm)],[c427,c8037,c8067]) ).
cnf(c8092,plain,
product(a137,a20) = a140,
inference(equational,[status(thm)],[c284,c3317,c8091]) ).
cnf(c8093,plain,
product(a45,a11) = a47,
inference(equational,[status(thm)],[c555,c8086,c8092]) ).
cnf(c8094,plain,
a45 = a46,
inference(equational,[status(thm)],[c284,c367,c8093]) ).
cnf(c8095,plain,
product(a35,a140) = a36,
inference(equational,[status(thm)],[c356,c3212,c8093]) ).
cnf(c8096,plain,
product(a139,a140) = a139,
inference(equational,[status(thm)],[c329,c1482,c8093]) ).
cnf(c8097,plain,
product(a36,a140) = a35,
inference(equational,[status(thm)],[c284,c8095]) ).
cnf(c8098,plain,
product(a44,a1) = a44,
inference(equational,[status(thm)],[c365,c705,c8094]) ).
cnf(c8099,plain,
a41 = a44,
inference(equational,[status(thm)],[c1,c7971,c7973,c8098]) ).
cnf(c8100,plain,
a1 = a3,
inference(equational,[status(thm)],[c430,c4293,c7951,c7952,c8098]) ).
cnf(c8101,plain,
a89 = a130,
inference(equational,[status(thm)],[c1,c2622,c7780,c7804,c7805,c7806,c7877,c8100]) ).
cnf(c8102,plain,
a97 = a125,
inference(equational,[status(thm)],[c129,c7788,c7806,c7885,c8099]) ).
cnf(c8103,plain,
product(a22,a46) = a23,
inference(equational,[status(thm)],[c45,c8094]) ).
cnf(c8106,plain,
product(a46,a22) = product(a44,a46),
inference(equational,[status(thm)],[c438,c8094]) ).
cnf(c8108,plain,
product(product(X,a48),a138) = product(product(X,a48),a137),
inference(equational,[status(thm)],[c427,c754,c8037,c8067]) ).
cnf(c8109,plain,
product(X,a138) = product(X,a137),
inference(equational,[status(thm)],[c753,c3408,c8040,c8080,c8089,c8108]) ).
cnf(c8110,plain,
product(a132,a137) = a59,
inference(equational,[status(thm)],[c321,c1926,c7878,c7880,c8079,c8080,c8089,c8109]) ).
cnf(c8117,plain,
product(product(a48,X),a59) = product(a50,product(X,a59)),
inference(equational,[status(thm)],[c427,c8047,c8067]) ).
cnf(c8119,plain,
product(a50,product(a137,a59)) = a50,
inference(equational,[status(thm)],[c8073,c8083,c8117]) ).
cnf(c8123,plain,
product(a14,a52) = a15,
inference(equational,[status(thm)],[c29,c8066]) ).
cnf(c8124,plain,
product(a44,a3) = a44,
inference(equational,[status(thm)],[c284,c428,c705,c8100,c8103,c8106]) ).
cnf(c8126,plain,
product(a3,a44) = a2,
inference(equational,[status(thm)],[c7951,c7960,c8098]) ).
cnf(c8128,plain,
product(a125,a3) = a121,
inference(equational,[status(thm)],[c284,c5406,c7728,c7793,c7951,c8098]) ).
cnf(c8134,plain,
product(product(product(a102,X),a101),a14) = product(product(a130,product(X,a14)),a121),
inference(equational,[status(thm)],[c614,c797,c7731,c7744,c7749,c7761,c8101]) ).
cnf(c8135,plain,
product(product(a130,a101),a14) = product(a102,a121),
inference(equational,[status(thm)],[c1,c287,c3408,c7719,c7720,c7723,c7727,c7813,c8134]) ).
cnf(c8136,plain,
product(a130,a14) = a102,
inference(equational,[status(thm)],[c284,c1837,c7725,c7759,c8135]) ).
cnf(c8137,plain,
product(a59,a33) = product(a102,a32),
inference(equational,[status(thm)],[c65,c495,c1700,c7878,c8136]) ).
cnf(c8139,plain,
product(product(a130,a3),a121) = product(a129,a121),
inference(equational,[status(thm)],[c205,c349,c7860,c8134]) ).
cnf(c8140,plain,
product(a130,a3) = a129,
inference(equational,[status(thm)],[c284,c8139]) ).
cnf(c8160,plain,
product(product(X,a14),a130) = product(product(X,a102),a14),
inference(equational,[status(thm)],[c3392,c8136]) ).
cnf(c8161,plain,
product(a44,a14) = a40,
inference(equational,[status(thm)],[c284,c869,c7744,c8099,c8101,c8160]) ).
cnf(c8162,plain,
a39 = a40,
inference(equational,[status(thm)],[c359,c724,c8124,c8161]) ).
cnf(c8165,plain,
product(a4,a40) = a5,
inference(equational,[status(thm)],[c1,c4555,c4681,c5230,c7884,c8161,c8162]) ).
cnf(c8169,plain,
product(a121,a3) = a125,
inference(equational,[status(thm)],[c3352,c4256,c7719,c7720,c7723,c7727,c7745,c7766,c7772,c7773,c8162]) ).
cnf(c8170,plain,
product(a52,a40) = a48,
inference(equational,[status(thm)],[c1,c97,c2228,c7881,c8066,c8067,c8162]) ).
cnf(c8174,plain,
product(a40,a7) = a38,
inference(equational,[status(thm)],[c358,c8162]) ).
cnf(c8176,plain,
product(a136,a40) = a137,
inference(equational,[status(thm)],[c273,c8162]) ).
cnf(c8182,plain,
product(a138,a40) = product(a136,a52),
inference(equational,[status(thm)],[c759,c8162]) ).
cnf(c8183,plain,
product(product(a34,a59),a13) = a32,
inference(equational,[status(thm)],[c284,c682,c1718,c1719,c7257,c7744,c7878,c8101,c8160]) ).
cnf(c8184,plain,
product(a34,a59) = a33,
inference(equational,[status(thm)],[c65,c284,c8183]) ).
cnf(c8185,plain,
product(a33,a59) = a34,
inference(equational,[status(thm)],[c284,c8184]) ).
cnf(c8186,plain,
product(a35,a59) = a34,
inference(equational,[status(thm)],[c1,c539,c7879,c8184,c8185]) ).
cnf(c8187,plain,
a35 = a33,
inference(equational,[status(thm)],[c284,c8184,c8186]) ).
cnf(c8201,plain,
product(a24,a33) = a23,
inference(equational,[status(thm)],[c342,c8187]) ).
cnf(c8202,plain,
product(a21,a33) = a20,
inference(equational,[status(thm)],[c339,c8187]) ).
cnf(c8206,plain,
product(a33,a140) = a36,
inference(equational,[status(thm)],[c8095,c8187]) ).
cnf(c8256,plain,
product(product(a102,a32),a59) = product(a59,a34),
inference(equational,[status(thm)],[c575,c7878,c7879,c8137,c8185]) ).
cnf(c8286,plain,
product(product(product(a132,X),a8),a27) = product(product(a134,product(X,a26)),a8),
inference(equational,[status(thm)],[c498,c720,c7883]) ).
cnf(c8287,plain,
product(product(a132,X),a26) = product(a134,product(X,a26)),
inference(equational,[status(thm)],[c284,c345,c3408,c8286]) ).
cnf(c8288,plain,
product(product(a132,a26),X) = product(a134,X),
inference(equational,[status(thm)],[c284,c3392,c8287]) ).
cnf(c8292,plain,
product(a134,a25) = product(a57,a25),
inference(equational,[status(thm)],[c2252,c5101,c7878,c8288]) ).
cnf(c8293,plain,
a134 = a57,
inference(equational,[status(thm)],[c284,c8292]) ).
cnf(c8294,plain,
a8 = a10,
inference(equational,[status(thm)],[c284,c1686,c8293]) ).
cnf(c8295,plain,
a135 = a54,
inference(equational,[status(thm)],[c269,c569,c8293]) ).
cnf(c8296,plain,
a136 = a52,
inference(equational,[status(thm)],[c271,c375,c8066,c8295]) ).
cnf(c8297,plain,
a48 = a137,
inference(equational,[status(thm)],[c8170,c8176,c8296]) ).
cnf(c8298,plain,
a14 = a16,
inference(equational,[status(thm)],[c284,c762,c8296]) ).
cnf(c8299,plain,
a5 = a7,
inference(equational,[status(thm)],[c13,c371,c8296]) ).
cnf(c8300,plain,
a40 = a38,
inference(equational,[status(thm)],[c1,c434,c8162,c8174,c8299]) ).
cnf(c8301,plain,
a26 = a24,
inference(equational,[status(thm)],[c284,c8090,c8297]) ).
cnf(c8302,plain,
a138 = a137,
inference(equational,[status(thm)],[c1,c8089,c8297]) ).
cnf(c8303,plain,
a47 = a140,
inference(equational,[status(thm)],[c1,c93,c2234,c8067,c8092,c8094,c8297]) ).
cnf(c8304,plain,
product(a10,a57) = a9,
inference(equational,[status(thm)],[c618,c8068,c8293]) ).
cnf(c8305,plain,
a139 = a140,
inference(equational,[status(thm)],[c1,c1152,c8039,c8092,c8096,c8303]) ).
cnf(c8306,plain,
a141 = a46,
inference(equational,[status(thm)],[c281,c367,c8303]) ).
cnf(c8307,plain,
a37 = a33,
inference(equational,[status(thm)],[c73,c8097,c8187,c8303]) ).
cnf(c8311,plain,
product(a27,a10) = a24,
inference(equational,[status(thm)],[c345,c8294,c8301]) ).
cnf(c8312,plain,
product(a57,product(a132,a24)) = product(a132,a24),
inference(equational,[status(thm)],[c499,c2115,c7883,c8064,c8287,c8293,c8301]) ).
cnf(c8313,plain,
product(a132,a24) = a57,
inference(equational,[status(thm)],[c1,c284,c427,c8312]) ).
cnf(c8314,plain,
product(a57,a24) = a132,
inference(equational,[status(thm)],[c284,c8313]) ).
cnf(c8320,plain,
a2 = a3,
inference(equational,[status(thm)],[c281,c283,c2685,c8100,c8124,c8126,c8305]) ).
cnf(c8321,plain,
a44 = a3,
inference(equational,[status(thm)],[c284,c1099,c8094,c8100,c8106,c8126,c8306,c8320]) ).
cnf(c8322,plain,
a23 = a21,
inference(equational,[status(thm)],[c340,c8103,c8306]) ).
cnf(c8324,plain,
product(a28,a11) = a21,
inference(equational,[status(thm)],[c21,c1346,c8201,c8294,c8301,c8307,c8322]) ).
cnf(c8327,plain,
product(a16,a52) = a15,
inference(equational,[status(thm)],[c511,c8123,c8296]) ).
cnf(c8331,plain,
product(a57,product(a33,a57)) = product(a54,a57),
inference(equational,[status(thm)],[c499,c500,c568,c6973,c8064,c8065,c8288,c8293,c8295,c8307]) ).
cnf(c8332,plain,
product(a57,a33) = a54,
inference(equational,[status(thm)],[c284,c1912,c8064,c8293,c8331]) ).
cnf(c8336,plain,
product(product(a57,a19),a38) = product(a54,a19),
inference(equational,[status(thm)],[c269,c337,c736,c1705,c7882,c8287,c8288,c8293,c8295]) ).
cnf(c8339,plain,
a129 = a121,
inference(equational,[status(thm)],[c1,c7966,c8100,c8140,c8321]) ).
cnf(c8340,plain,
a130 = a125,
inference(equational,[status(thm)],[c7947,c8128,c8169,c8321]) ).
cnf(c8341,plain,
a20 = a24,
inference(equational,[status(thm)],[c47,c8187,c8202,c8322]) ).
cnf(c8342,plain,
a13 = a11,
inference(equational,[status(thm)],[c25,c297,c8322]) ).
cnf(c8349,plain,
product(a7,a38) = a4,
inference(equational,[status(thm)],[c360,c8162,c8299,c8300]) ).
cnf(c8354,plain,
product(a101,a16) = a121,
inference(equational,[status(thm)],[c303,c7725,c7759,c8298]) ).
cnf(c8359,plain,
product(a121,a16) = a101,
inference(equational,[status(thm)],[c680,c7727,c7750,c8298]) ).
cnf(c8360,plain,
a103 = a101,
inference(equational,[status(thm)],[c726,c7745,c8101,c8140,c8298,c8339,c8359]) ).
cnf(c8361,plain,
product(a3,a16) = a38,
inference(equational,[status(thm)],[c1,c725,c7884,c8099,c8162,c8298,c8300,c8321]) ).
cnf(c8362,plain,
product(a38,a16) = a3,
inference(equational,[status(thm)],[c1,c548,c7884,c8099,c8162,c8298,c8300,c8321]) ).
cnf(c8363,plain,
a7 = a38,
inference(equational,[status(thm)],[c533,c8165,c8298,c8299,c8320,c8361]) ).
cnf(c8364,plain,
a4 = a38,
inference(equational,[status(thm)],[c1,c8349,c8363]) ).
cnf(c8365,plain,
a108 = a105,
inference(equational,[status(thm)],[c1,c284,c2151,c7748,c8300,c8364]) ).
cnf(c8366,plain,
a32 = a30,
inference(equational,[status(thm)],[c284,c1680,c8300,c8364]) ).
cnf(c8368,plain,
product(a30,a16) = a29,
inference(equational,[status(thm)],[c348,c8298]) ).
cnf(c8369,plain,
product(a16,a30) = a11,
inference(equational,[status(thm)],[c319,c8298,c8342,c8366]) ).
cnf(c8370,plain,
product(a28,a29) = a30,
inference(equational,[status(thm)],[c59,c432,c8298]) ).
cnf(c8376,plain,
product(a54,a21) = product(a132,a33),
inference(equational,[status(thm)],[c714,c8187,c8288,c8293,c8314,c8332,c8341]) ).
cnf(c8435,plain,
product(product(a54,a19),a38) = product(a57,a19),
inference(equational,[status(thm)],[c284,c8336]) ).
cnf(c8443,plain,
product(a54,product(a38,a19)) = a57,
inference(equational,[status(thm)],[c284,c3408,c8435]) ).
cnf(c8444,plain,
a24 = a19,
inference(equational,[status(thm)],[c1,c337,c8301,c8341]) ).
cnf(c8449,plain,
product(a120,a16) = product(a113,a30),
inference(equational,[status(thm)],[c7792,c8298,c8366]) ).
cnf(c8463,plain,
product(a28,a19) = a29,
inference(equational,[status(thm)],[c1,c1709,c7882,c8368,c8370]) ).
cnf(c8471,plain,
product(a38,a52) = a6,
inference(equational,[status(thm)],[c382,c8363]) ).
cnf(c8472,plain,
product(a38,a19) = a10,
inference(equational,[status(thm)],[c15,c7882,c8294,c8363]) ).
cnf(c8475,plain,
product(a28,a10) = a27,
inference(equational,[status(thm)],[c284,c530,c919,c7882,c8294,c8363]) ).
cnf(c8476,plain,
a28 = a19,
inference(equational,[status(thm)],[c284,c8311,c8444,c8475]) ).
cnf(c8477,plain,
a29 = a19,
inference(equational,[status(thm)],[c1,c8463,c8476]) ).
cnf(c8478,plain,
a19 = a16,
inference(equational,[status(thm)],[c284,c1657,c7882,c8476]) ).
cnf(c8479,plain,
a3 = a10,
inference(equational,[status(thm)],[c8362,c8472,c8478]) ).
cnf(c8480,plain,
a30 = a16,
inference(equational,[status(thm)],[c1,c8370,c8476,c8477,c8478]) ).
cnf(c8481,plain,
a33 = a10,
inference(equational,[status(thm)],[c284,c3376,c8307,c8362,c8476,c8477,c8479]) ).
cnf(c8483,plain,
a121 = a105,
inference(equational,[status(thm)],[c7796,c8354,c8360,c8480]) ).
cnf(c8485,plain,
product(a11,a16) = a16,
inference(equational,[status(thm)],[c33,c428,c7882,c8368,c8369,c8478]) ).
cnf(c8486,plain,
a11 = a16,
inference(equational,[status(thm)],[c1,c284,c8485]) ).
cnf(c8487,plain,
a21 = a16,
inference(equational,[status(thm)],[c1,c8324,c8476,c8478,c8486]) ).
cnf(c8488,plain,
a16 = a10,
inference(equational,[status(thm)],[c1,c284,c3117,c8294,c8295,c8307,c8481,c8486]) ).
cnf(c8489,plain,
a46 = a137,
inference(equational,[status(thm)],[c1,c284,c2888,c8067,c8094,c8297,c8341,c8444,c8478,c8486]) ).
cnf(c8490,plain,
a137 = a10,
inference(equational,[status(thm)],[c1,c284,c2847,c8100,c8187,c8321,c8444,c8478,c8479,c8481,c8488,c8489]) ).
cnf(c8491,plain,
a38 = a10,
inference(equational,[status(thm)],[c1,c8361,c8479,c8488]) ).
cnf(c8492,plain,
a12 = a10,
inference(equational,[status(thm)],[c1,c23,c8486,c8487,c8488]) ).
cnf(c8493,plain,
a52 = a10,
inference(equational,[status(thm)],[c1,c8182,c8296,c8300,c8302,c8490,c8491]) ).
cnf(c8494,plain,
a6 = a10,
inference(equational,[status(thm)],[c1,c8471,c8491,c8493]) ).
cnf(c8495,plain,
a15 = a10,
inference(equational,[status(thm)],[c1,c8327,c8488,c8493]) ).
cnf(c8496,plain,
a31 = a10,
inference(equational,[status(thm)],[c1,c284,c3542,c7881,c8067,c8162,c8297,c8300,c8366,c8480,c8488,c8490,c8491,c8493]) ).
cnf(c8497,plain,
a54 = a10,
inference(equational,[status(thm)],[c1,c2126,c8065,c8066,c8477,c8478,c8488,c8493]) ).
cnf(c8498,plain,
a57 = a10,
inference(equational,[status(thm)],[c1,c8443,c8478,c8488,c8491,c8497]) ).
cnf(c8499,plain,
a9 = a10,
inference(equational,[status(thm)],[c284,c3297,c8304,c8307,c8481,c8497,c8498]) ).
cnf(c8500,plain,
a125 = a101,
inference(equational,[status(thm)],[c284,c3085,c7745,c8066,c8101,c8340,c8360,c8479,c8493,c8495]) ).
cnf(c8501,plain,
a105 = a102,
inference(equational,[status(thm)],[c284,c3927,c7720,c7723,c7727,c7744,c8066,c8300,c8483,c8491,c8493,c8495]) ).
cnf(c8502,plain,
a106 = a101,
inference(equational,[status(thm)],[c1,c284,c2266,c7746,c7747,c7770,c8299,c8360,c8363,c8491,c8496]) ).
cnf(c8503,plain,
a132 = a10,
inference(equational,[status(thm)],[c1,c8314,c8444,c8478,c8488,c8498]) ).
cnf(c8504,plain,
a59 = a10,
inference(equational,[status(thm)],[c1,c284,c4198,c7879,c8064,c8301,c8302,c8444,c8478,c8488,c8490,c8498]) ).
cnf(c8505,plain,
a18 = a10,
inference(equational,[status(thm)],[c284,c1674,c8301,c8341,c8444,c8478,c8488,c8498]) ).
cnf(c8506,plain,
a50 = a10,
inference(equational,[status(thm)],[c1,c428,c2746,c7880,c7881,c8067,c8110,c8119,c8297,c8302,c8490,c8504]) ).
cnf(c8507,plain,
a34 = a10,
inference(equational,[status(thm)],[c1,c284,c4794,c7878,c8067,c8297,c8481,c8490,c8504,c8506]) ).
cnf(c8508,plain,
a25 = a10,
inference(equational,[status(thm)],[c1,c284,c3058,c7878,c8067,c8297,c8444,c8478,c8488,c8490,c8504,c8506]) ).
cnf(c8509,plain,
product(a102,a10) = a101,
inference(equational,[status(thm)],[c284,c8354,c8483,c8488,c8501]) ).
cnf(c8510,plain,
product(a101,a10) = a102,
inference(equational,[status(thm)],[c284,c4616,c7744,c7745,c8162,c8299,c8300,c8360,c8363,c8491]) ).
cnf(c8511,plain,
a27 = a10,
inference(equational,[status(thm)],[c1,c53,c8294,c8301,c8444,c8478,c8488]) ).
cnf(c8512,plain,
a113 = a101,
inference(equational,[status(thm)],[c284,c481,c8366,c8369,c8449,c8483,c8486,c8488,c8501,c8509]) ).
cnf(c8513,plain,
a102 = a101,
inference(equational,[status(thm)],[c1,c3700,c7724,c7877,c7879,c8340,c8342,c8483,c8486,c8488,c8500,c8501,c8504,c8509,c8510,c8512]) ).
cnf(c8514,plain,
a101 = a10,
inference(equational,[status(thm)],[c1,c8256,c8366,c8480,c8488,c8504,c8507,c8510,c8513]) ).
cnf(c8515,plain,
product(a10,a22) = a10,
inference(equational,[status(thm)],[c1,c715,c8306,c8376,c8481,c8489,c8490,c8497,c8503]) ).
cnf(c8517,plain,
product(a22,product(a22,a10)) = a22,
inference(equational,[status(thm)],[c284,c4293,c8515]) ).
cnf(c8518,plain,
product(a22,a10) = a10,
inference(equational,[status(thm)],[c284,c1943,c8306,c8487,c8488,c8489,c8490,c8515,c8517]) ).
cnf(c8519,plain,
a10 = a22,
inference(equational,[status(thm)],[c8517,c8518]) ).
cnf(c8520,plain,
a140 = a22,
inference(equational,[status(thm)],[c1,c284,c2772,c8303,c8307,c8481,c8486,c8488,c8489,c8490,c8519]) ).
cnf(c8521,plain,
a36 = a22,
inference(equational,[status(thm)],[c1,c8206,c8481,c8519,c8520]) ).
cnf(c8522,plain,
product(product(a22,product(X,a22)),a120) = product(a22,X),
inference(equational,[status(thm)],[c1,c428,c470,c663,c3392,c7724,c7737,c7741,c7742,c8342,c8365,c8483,c8486,c8488,c8501,c8512,c8513,c8514,c8519]) ).
cnf(c8523,plain,
product(a22,a120) = a22,
inference(equational,[status(thm)],[c1,c1653,c8306,c8487,c8488,c8489,c8490,c8519,c8522]) ).
cnf(c8524,plain,
product(a22,a43) = a22,
inference(equational,[status(thm)],[c1,c5139,c7781,c7805,c8321,c8339,c8479,c8483,c8501,c8513,c8514,c8519,c8522]) ).
cnf(c8527,plain,
product(a43,product(a43,a22)) = a43,
inference(equational,[status(thm)],[c284,c4293,c8524]) ).
cnf(c8528,plain,
product(a43,a22) = a22,
inference(equational,[status(thm)],[c284,c1903,c7800,c7806,c7884,c8321,c8339,c8479,c8483,c8501,c8513,c8514,c8519,c8524,c8527]) ).
cnf(c8529,plain,
a43 = a22,
inference(equational,[status(thm)],[c8527,c8528]) ).
cnf(c8530,plain,
product(a120,product(a120,a22)) = a120,
inference(equational,[status(thm)],[c284,c4293,c8523]) ).
cnf(c8531,plain,
a120 = a22,
inference(equational,[status(thm)],[c1,c284,c7660,c7749,c7751,c7755,c8365,c8366,c8480,c8483,c8488,c8501,c8513,c8514,c8519,c8523,c8530]) ).
cnf(g1,plain,
tuple(a1,a2,a41,a42,a3,a40,a4,a13,a14,a5,a38,a39,a6,a135,a136,a7,a52,a51,a8,a16,a17,a9,a55,a56,a10,a133,a134,a11,a36,a37,a12,a21,a20,a23,a31,a32,a15,a53,a28,a29,a18,a132,a19,a58,a57,a20,a25,a26,a34,a35,a140,a44,a45,a24,a48,a49,a138,a137,a27,a30,a33,a130,a131,a59,a60,a139,a46,a47,a43,a61,a62,a127,a128,a50,a54,a63,a95,a96,a64,a126,a65,a66,a67,a91,a92,a68,a97,a98,a69,a70,a71,a118,a117,a72,a108,a109,a73,a81,a82,a74,a75,a76,a77,a113,a114,a78,a79,a80,a119,a83,a84,a85,a86,a87,a103,a104,a88,a89,a90,a99,a100,a123,a124,a93,a94,a101,a102,a105,a106,a107,a110,a111,a112,a115,a116,a120,a121,a122,a125,a129) = tuple(a2,a3,a42,a43,a4,a41,a5,a14,a15,a6,a39,a40,a7,a136,a137,a8,a53,a52,a9,a17,a18,a10,a56,a57,a11,a134,a135,a12,a37,a38,a13,a23,a21,a24,a32,a33,a16,a54,a29,a30,a19,a133,a20,a59,a58,a22,a26,a27,a35,a36,a141,a45,a46,a25,a49,a50,a139,a138,a28,a31,a34,a131,a132,a60,a61,a140,a47,a48,a44,a62,a63,a128,a129,a51,a55,a64,a96,a97,a65,a127,a66,a67,a68,a92,a93,a69,a98,a99,a70,a71,a72,a119,a118,a73,a109,a110,a74,a82,a83,a75,a76,a77,a78,a114,a115,a79,a80,a81,a120,a84,a85,a86,a87,a88,a104,a105,a89,a90,a91,a100,a101,a124,a125,a94,a95,a102,a103,a106,a107,a108,a111,a112,a113,a116,a117,a121,a122,a123,a126,a130),
inference(equational,[status(thm)],[c5823,c5824,c7719,c7720,c7721,c7722,c7723,c7724,c7725,c7726,c7727,c7728,c7729,c7730,c7731,c7732,c7733,c7734,c7735,c7736,c7737,c7738,c7739,c7740,c7741,c7742,c7744,c7745,c7746,c7747,c7748,c7749,c7750,c7751,c7752,c7755,c7756,c7759,c7760,c7761,c7763,c7770,c7772,c7773,c7774,c7775,c7776,c7780,c7781,c7788,c7789,c7800,c7803,c7805,c7806,c7877,c7878,c7879,c7880,c7881,c7882,c7883,c7884,c8064,c8065,c8066,c8067,c8094,c8099,c8100,c8101,c8102,c8162,c8187,c8293,c8294,c8295,c8296,c8297,c8298,c8299,c8300,c8301,c8302,c8303,c8305,c8306,c8307,c8320,c8321,c8322,c8339,c8340,c8341,c8342,c8360,c8363,c8364,c8365,c8366,c8444,c8476,c8477,c8478,c8479,c8480,c8481,c8483,c8486,c8487,c8488,c8489,c8490,c8491,c8492,c8493,c8494,c8495,c8496,c8497,c8498,c8499,c8500,c8501,c8502,c8503,c8504,c8505,c8506,c8507,c8508,c8511,c8512,c8513,c8514,c8519,c8520,c8521,c8529,c8531]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : TOP052-1 : TPTP v9.0.0. Released v8.1.0.
% 0.06/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n002.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Jul 14 23:31:19 EDT 2025
% 0.11/0.32 % CPUTime :
% 74.16/74.33 % SZS status Unsatisfiable
% 74.16/74.33 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------