TSTP Solution File: TOP052-1 by SNARK---20120808r022

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : TOP052-1 : TPTP v8.1.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n018.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Thu Jul 21 21:34:38 EDT 2022

% Result   : Unsatisfiable 19.07s 19.29s
% Output   : Refutation 19.45s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)

% Comments : 
%------------------------------------------------------------------------------
cnf(involutory_quandle,axiom,
    product(X,X) = X,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutory_quandle) ).

cnf(involutory_quandle_01,axiom,
    product(product(X,Y),Y) = X,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutory_quandle_01) ).

cnf(involutory_quandle_02,axiom,
    product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutory_quandle_02) ).

cnf(knot,axiom,
    a2 = product(a1,a42),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot) ).

cnf(knot_03,axiom,
    a3 = product(a2,a41),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_03) ).

cnf(knot_04,axiom,
    a4 = product(a3,a14),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_04) ).

cnf(knot_05,axiom,
    a5 = product(a4,a39),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_05) ).

cnf(knot_06,axiom,
    a6 = product(a5,a136),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_06) ).

cnf(knot_07,axiom,
    a7 = product(a6,a52),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_07) ).

cnf(knot_08,axiom,
    a8 = product(a7,a17),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_08) ).

cnf(knot_09,axiom,
    a9 = product(a8,a56),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_09) ).

cnf(knot_10,axiom,
    a10 = product(a9,a134),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_10) ).

cnf(knot_11,axiom,
    a11 = product(a10,a37),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_11) ).

cnf(knot_12,axiom,
    a12 = product(a11,a21),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_12) ).

cnf(knot_13,axiom,
    a13 = product(a12,a23),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_13) ).

cnf(knot_14,axiom,
    a14 = product(a13,a32),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_14) ).

cnf(knot_15,axiom,
    a15 = product(a14,a53),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_15) ).

cnf(knot_16,axiom,
    a16 = product(a15,a136),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_16) ).

cnf(knot_17,axiom,
    a17 = product(a16,a29),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_17) ).

cnf(knot_18,axiom,
    a18 = product(a17,a133),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_18) ).

cnf(knot_19,axiom,
    a19 = product(a18,a58),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_19) ).

cnf(knot_20,axiom,
    a20 = product(a19,a26),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_20) ).

cnf(knot_21,axiom,
    a21 = product(a20,a35),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_21) ).

cnf(knot_22,axiom,
    a22 = product(a21,a141),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_22) ).

cnf(knot_23,axiom,
    a23 = product(a22,a45),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_23) ).

cnf(knot_24,axiom,
    a24 = product(a23,a35),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_24) ).

cnf(knot_25,axiom,
    a25 = product(a24,a49),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_25) ).

cnf(knot_26,axiom,
    a26 = product(a25,a138),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_26) ).

cnf(knot_27,axiom,
    a27 = product(a26,a8),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_27) ).

cnf(knot_28,axiom,
    a28 = product(a27,a37),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_28) ).

cnf(knot_29,axiom,
    a29 = product(a28,a17),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_29) ).

cnf(knot_30,axiom,
    a30 = product(a29,a14),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_30) ).

cnf(knot_31,axiom,
    a31 = product(a30,a5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_31) ).

cnf(knot_32,axiom,
    a32 = product(a31,a39),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_32) ).

cnf(knot_33,axiom,
    a33 = product(a32,a13),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_33) ).

cnf(knot_34,axiom,
    a34 = product(a33,a131),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_34) ).

cnf(knot_35,axiom,
    a35 = product(a34,a60),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_35) ).

cnf(knot_36,axiom,
    a36 = product(a35,a139),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_36) ).

cnf(knot_37,axiom,
    a37 = product(a36,a47),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_37) ).

cnf(knot_38,axiom,
    a38 = product(a37,a17),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_38) ).

cnf(knot_39,axiom,
    a39 = product(a38,a7),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_39) ).

cnf(knot_40,axiom,
    a40 = product(a39,a4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_40) ).

cnf(knot_41,axiom,
    a41 = product(a40,a14),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_41) ).

cnf(knot_42,axiom,
    a42 = product(a41,a2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_42) ).

cnf(knot_43,axiom,
    a43 = product(a42,a62),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_43) ).

cnf(knot_44,axiom,
    a44 = product(a43,a128),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_44) ).

cnf(knot_45,axiom,
    a45 = product(a44,a23),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_45) ).

cnf(knot_46,axiom,
    a46 = product(a45,a141),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_46) ).

cnf(knot_47,axiom,
    a47 = product(a46,a11),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_47) ).

cnf(knot_48,axiom,
    a48 = product(a47,a20),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_48) ).

cnf(knot_49,axiom,
    a49 = product(a48,a138),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_49) ).

cnf(knot_50,axiom,
    a50 = product(a49,a131),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_50) ).

cnf(knot_51,axiom,
    a51 = product(a50,a59),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_51) ).

cnf(knot_52,axiom,
    a52 = product(a51,a39),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_52) ).

cnf(knot_53,axiom,
    a53 = product(a52,a136),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_53) ).

cnf(knot_54,axiom,
    a54 = product(a53,a29),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_54) ).

cnf(knot_55,axiom,
    a55 = product(a54,a135),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_55) ).

cnf(knot_56,axiom,
    a56 = product(a55,a37),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_56) ).

cnf(knot_57,axiom,
    a57 = product(a56,a134),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_57) ).

cnf(knot_58,axiom,
    a58 = product(a57,a26),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_58) ).

cnf(knot_59,axiom,
    a59 = product(a58,a138),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_59) ).

cnf(knot_60,axiom,
    a60 = product(a59,a131),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_60) ).

cnf(knot_61,axiom,
    a61 = product(a60,a13),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_61) ).

cnf(knot_62,axiom,
    a62 = product(a61,a1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_62) ).

cnf(knot_63,axiom,
    a63 = product(a62,a96),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_63) ).

cnf(knot_64,axiom,
    a64 = product(a63,a127),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_64) ).

cnf(knot_65,axiom,
    a65 = product(a64,a41),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_65) ).

cnf(knot_66,axiom,
    a66 = product(a65,a2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_66) ).

cnf(knot_67,axiom,
    a67 = product(a66,a92),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_67) ).

cnf(knot_68,axiom,
    a68 = product(a67,a98),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_68) ).

cnf(knot_69,axiom,
    a69 = product(a68,a32),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_69) ).

cnf(knot_70,axiom,
    a70 = product(a69,a13),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_70) ).

cnf(knot_71,axiom,
    a71 = product(a70,a118),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_71) ).

cnf(knot_72,axiom,
    a72 = product(a71,a109),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_72) ).

cnf(knot_73,axiom,
    a73 = product(a72,a82),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_73) ).

cnf(knot_74,axiom,
    a74 = product(a73,a32),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_74) ).

cnf(knot_75,axiom,
    a75 = product(a74,a14),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_75) ).

cnf(knot_76,axiom,
    a76 = product(a75,a68),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_76) ).

cnf(knot_77,axiom,
    a77 = product(a76,a114),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_77) ).

cnf(knot_78,axiom,
    a78 = product(a77,a13),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_78) ).

cnf(knot_79,axiom,
    a79 = product(a78,a33),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_79) ).

cnf(knot_80,axiom,
    a80 = product(a79,a119),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_80) ).

cnf(knot_81,axiom,
    a81 = product(a80,a70),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_81) ).

cnf(knot_82,axiom,
    a82 = product(a81,a109),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_82) ).

cnf(knot_83,axiom,
    a83 = product(a82,a118),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_83) ).

cnf(knot_84,axiom,
    a84 = product(a83,a39),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_84) ).

cnf(knot_85,axiom,
    a85 = product(a84,a5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_85) ).

cnf(knot_86,axiom,
    a86 = product(a85,a30),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_86) ).

cnf(knot_87,axiom,
    a87 = product(a86,a104),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_87) ).

cnf(knot_88,axiom,
    a88 = product(a87,a4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_88) ).

cnf(knot_89,axiom,
    a89 = product(a88,a14),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_89) ).

cnf(knot_90,axiom,
    a90 = product(a89,a41),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_90) ).

cnf(knot_91,axiom,
    a91 = product(a90,a100),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_91) ).

cnf(knot_92,axiom,
    a92 = product(a91,a124),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_92) ).

cnf(knot_93,axiom,
    a93 = product(a92,a2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_93) ).

cnf(knot_94,axiom,
    a94 = product(a93,a41),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_94) ).

cnf(knot_95,axiom,
    a95 = product(a94,a127),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_95) ).

cnf(knot_96,axiom,
    a96 = product(a95,a64),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_96) ).

cnf(knot_97,axiom,
    a97 = product(a96,a42),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_97) ).

cnf(knot_98,axiom,
    a98 = product(a97,a1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_98) ).

cnf(knot_99,axiom,
    a99 = product(a98,a92),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_99) ).

cnf(knot_100,axiom,
    a100 = product(a99,a124),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_100) ).

cnf(knot_101,axiom,
    a101 = product(a100,a14),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_101) ).

cnf(knot_102,axiom,
    a102 = product(a101,a40),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_102) ).

cnf(knot_103,axiom,
    a103 = product(a102,a4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_103) ).

cnf(knot_104,axiom,
    a104 = product(a103,a87),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_104) ).

cnf(knot_105,axiom,
    a105 = product(a104,a30),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_105) ).

cnf(knot_106,axiom,
    a106 = product(a105,a5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_106) ).

cnf(knot_107,axiom,
    a107 = product(a106,a84),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_107) ).

cnf(knot_108,axiom,
    a108 = product(a107,a39),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_108) ).

cnf(knot_109,axiom,
    a109 = product(a108,a118),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_109) ).

cnf(knot_110,axiom,
    a110 = product(a109,a70),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_110) ).

cnf(knot_111,axiom,
    a111 = product(a110,a119),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_111) ).

cnf(knot_112,axiom,
    a112 = product(a111,a79),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_112) ).

cnf(knot_113,axiom,
    a113 = product(a112,a33),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_113) ).

cnf(knot_114,axiom,
    a114 = product(a113,a13),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_114) ).

cnf(knot_115,axiom,
    a115 = product(a114,a68),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_115) ).

cnf(knot_116,axiom,
    a116 = product(a115,a14),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_116) ).

cnf(knot_117,axiom,
    a117 = product(a116,a74),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_117) ).

cnf(knot_118,axiom,
    a118 = product(a117,a32),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_118) ).

cnf(knot_119,axiom,
    a119 = product(a118,a70),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_119) ).

cnf(knot_120,axiom,
    a120 = product(a119,a13),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_120) ).

cnf(knot_121,axiom,
    a121 = product(a120,a32),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_121) ).

cnf(knot_122,axiom,
    a122 = product(a121,a68),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_122) ).

cnf(knot_123,axiom,
    a123 = product(a122,a115),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_123) ).

cnf(knot_124,axiom,
    a124 = product(a123,a75),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_124) ).

cnf(knot_125,axiom,
    a125 = product(a124,a2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_125) ).

cnf(knot_126,axiom,
    a126 = product(a125,a65),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_126) ).

cnf(knot_127,axiom,
    a127 = product(a126,a41),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_127) ).

cnf(knot_128,axiom,
    a128 = product(a127,a96),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_128) ).

cnf(knot_129,axiom,
    a129 = product(a128,a62),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_129) ).

cnf(knot_130,axiom,
    a130 = product(a129,a1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_130) ).

cnf(knot_131,axiom,
    a131 = product(a130,a13),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_131) ).

cnf(knot_132,axiom,
    a132 = product(a131,a138),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_132) ).

cnf(knot_133,axiom,
    a133 = product(a132,a58),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_133) ).

cnf(knot_134,axiom,
    a134 = product(a133,a26),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_134) ).

cnf(knot_135,axiom,
    a135 = product(a134,a37),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_135) ).

cnf(knot_136,axiom,
    a136 = product(a135,a29),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_136) ).

cnf(knot_137,axiom,
    a137 = product(a136,a39),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_137) ).

cnf(knot_138,axiom,
    a138 = product(a137,a51),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_138) ).

cnf(knot_139,axiom,
    a139 = product(a138,a20),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_139) ).

cnf(knot_140,axiom,
    a140 = product(a139,a47),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_140) ).

cnf(knot_141,axiom,
    a141 = product(a140,a11),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_141) ).

cnf(knot_142,axiom,
    a1 = product(a141,a23),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_142) ).

cnf(goal,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('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).

cnf(146,plain,
    product(a123,a115) = a122,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_123,theory(equality)]) ).

cnf(147,plain,
    product(a92,a124) = a91,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_92,theory(equality)]) ).

cnf(148,plain,
    product(a100,a124) = a99,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_100,theory(equality)]) ).

cnf(149,plain,
    product(a91,a100) = a90,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_91,theory(equality)]) ).

cnf(150,plain,
    product(a87,a104) = a86,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_87,theory(equality)]) ).

cnf(151,plain,
    product(a104,a87) = a103,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_104,theory(equality)]) ).

cnf(152,plain,
    product(a107,a84) = a106,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_107,theory(equality)]) ).

cnf(153,plain,
    product(a80,a119) = a79,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_80,theory(equality)]) ).

cnf(154,plain,
    product(a111,a119) = a110,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_111,theory(equality)]) ).

cnf(155,plain,
    product(a112,a79) = a111,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_112,theory(equality)]) ).

cnf(156,plain,
    product(a77,a114) = a76,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_77,theory(equality)]) ).

cnf(157,plain,
    product(a124,a75) = a123,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_124,theory(equality)]) ).

cnf(158,plain,
    product(a117,a74) = a116,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_117,theory(equality)]) ).

cnf(159,plain,
    product(a73,a82) = a72,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_73,theory(equality)]) ).

cnf(160,plain,
    product(a72,a109) = a71,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_72,theory(equality)]) ).

cnf(161,plain,
    product(a82,a109) = a81,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_82,theory(equality)]) ).

cnf(162,plain,
    product(a71,a118) = a70,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_71,theory(equality)]) ).

cnf(163,plain,
    product(a83,a118) = a82,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_83,theory(equality)]) ).

cnf(164,plain,
    product(a109,a118) = a108,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_109,theory(equality)]) ).

cnf(165,plain,
    product(a81,a70) = a80,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_81,theory(equality)]) ).

cnf(166,plain,
    product(a110,a70) = a109,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_110,theory(equality)]) ).

cnf(167,plain,
    product(a119,a70) = a118,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_119,theory(equality)]) ).

cnf(168,plain,
    product(a68,a98) = a67,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_68,theory(equality)]) ).

cnf(169,plain,
    product(a76,a68) = a75,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_76,theory(equality)]) ).

cnf(170,plain,
    product(a115,a68) = a114,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_115,theory(equality)]) ).

cnf(171,plain,
    product(a122,a68) = a121,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_122,theory(equality)]) ).

cnf(172,plain,
    product(a67,a92) = a66,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_67,theory(equality)]) ).

cnf(173,plain,
    product(a99,a92) = a98,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_99,theory(equality)]) ).

cnf(174,plain,
    product(a126,a65) = a125,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_126,theory(equality)]) ).

cnf(175,plain,
    product(a64,a127) = a63,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_64,theory(equality)]) ).

cnf(176,plain,
    product(a95,a127) = a94,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_95,theory(equality)]) ).

cnf(177,plain,
    product(a96,a64) = a95,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_96,theory(equality)]) ).

cnf(178,plain,
    product(a63,a96) = a62,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_63,theory(equality)]) ).

cnf(179,plain,
    product(a128,a96) = a127,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_128,theory(equality)]) ).

cnf(180,plain,
    product(a55,a135) = a54,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_55,theory(equality)]) ).

cnf(182,plain,
    product(a138,a51) = a137,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_138,theory(equality)]) ).

cnf(184,plain,
    product(a43,a62) = a42,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_43,theory(equality)]) ).

cnf(185,plain,
    product(a129,a62) = a128,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_129,theory(equality)]) ).

cnf(186,plain,
    product(a102,a40) = a101,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_102,theory(equality)]) ).

cnf(187,plain,
    product(a37,a47) = a36,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_37,theory(equality)]) ).

cnf(188,plain,
    product(a140,a47) = a139,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_140,theory(equality)]) ).

cnf(189,plain,
    product(a36,a139) = a35,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_36,theory(equality)]) ).

cnf(191,plain,
    product(a34,a131) = a33,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_34,theory(equality)]) ).

cnf(192,plain,
    product(a50,a131) = a49,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_50,theory(equality)]) ).

cnf(193,plain,
    product(a60,a131) = a59,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_60,theory(equality)]) ).

cnf(194,plain,
    product(a79,a33) = a78,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_79,theory(equality)]) ).

cnf(195,plain,
    product(a113,a33) = a112,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_113,theory(equality)]) ).

cnf(196,plain,
    product(a86,a30) = a85,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_86,theory(equality)]) ).

cnf(197,plain,
    product(a105,a30) = a104,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_105,theory(equality)]) ).

cnf(198,plain,
    product(a26,a138) = a25,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_26,theory(equality)]) ).

cnf(199,plain,
    product(a49,a138) = a48,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_49,theory(equality)]) ).

cnf(200,plain,
    product(a59,a138) = a58,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_59,theory(equality)]) ).

cnf(201,plain,
    product(a132,a138) = a131,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_132,theory(equality)]) ).

cnf(202,plain,
    product(a25,a49) = a24,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_25,theory(equality)]) ).

cnf(204,plain,
    product(a22,a141) = a21,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_22,theory(equality)]) ).

cnf(206,plain,
    product(a21,a35) = a20,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_21,theory(equality)]) ).

cnf(208,plain,
    product(a20,a26) = a19,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_20,theory(equality)]) ).

cnf(209,plain,
    product(a58,a26) = a57,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_58,theory(equality)]) ).

cnf(210,plain,
    product(a134,a26) = a133,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_134,theory(equality)]) ).

cnf(211,plain,
    product(a48,a20) = a47,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_48,theory(equality)]) ).

cnf(212,plain,
    product(a139,a20) = a138,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_139,theory(equality)]) ).

cnf(215,plain,
    product(a18,a133) = a17,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_18,theory(equality)]) ).

cnf(216,plain,
    product(a17,a29) = a16,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_17,theory(equality)]) ).

cnf(217,plain,
    product(a54,a29) = a53,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_54,theory(equality)]) ).

cnf(219,plain,
    product(a15,a53) = a14,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_15,theory(equality)]) ).

cnf(220,plain,
    product(a14,a32) = a13,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_14,theory(equality)]) ).

cnf(221,plain,
    product(a69,a32) = a68,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_69,theory(equality)]) ).

cnf(222,plain,
    product(a74,a32) = a73,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_74,theory(equality)]) ).

cnf(223,plain,
    product(a118,a32) = a117,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_118,theory(equality)]) ).

cnf(224,plain,
    product(a121,a32) = a120,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_121,theory(equality)]) ).

cnf(226,plain,
    product(a45,a23) = a44,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_45,theory(equality)]) ).

cnf(227,plain,
    product(a1,a23) = a141,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_142,theory(equality)]) ).

cnf(228,plain,
    product(a33,a13) = a32,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_33,theory(equality)]) ).

cnf(229,plain,
    product(a61,a13) = a60,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_61,theory(equality)]) ).

cnf(230,plain,
    product(a70,a13) = a69,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_70,theory(equality)]) ).

cnf(231,plain,
    product(a78,a13) = a77,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_78,theory(equality)]) ).

cnf(232,plain,
    product(a114,a13) = a113,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_114,theory(equality)]) ).

cnf(233,plain,
    product(a120,a13) = a119,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_120,theory(equality)]) ).

cnf(234,plain,
    product(a131,a13) = a130,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_131,theory(equality)]) ).

cnf(235,plain,
    product(a12,a21) = a11,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_12,theory(equality)]) ).

cnf(236,plain,
    product(a11,a37) = a10,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_11,theory(equality)]) ).

cnf(237,plain,
    product(a28,a37) = a27,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_28,theory(equality)]) ).

cnf(238,plain,
    product(a56,a37) = a55,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_56,theory(equality)]) ).

cnf(239,plain,
    product(a135,a37) = a134,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_135,theory(equality)]) ).

cnf(240,plain,
    product(a47,a11) = a46,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_47,theory(equality)]) ).

cnf(241,plain,
    product(a141,a11) = a140,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_141,theory(equality)]) ).

cnf(242,plain,
    product(a10,a134) = a9,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_10,theory(equality)]) ).

cnf(243,plain,
    product(a57,a134) = a56,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_57,theory(equality)]) ).

cnf(246,plain,
    product(a29,a17) = a28,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_29,theory(equality)]) ).

cnf(247,plain,
    product(a38,a17) = a37,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_38,theory(equality)]) ).

cnf(248,plain,
    product(a27,a8) = a26,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_27,theory(equality)]) ).

cnf(249,plain,
    product(a7,a52) = a6,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_07,theory(equality)]) ).

cnf(250,plain,
    product(a39,a7) = a38,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_39,theory(equality)]) ).

cnf(251,plain,
    product(a6,a136) = a5,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_06,theory(equality)]) ).

cnf(252,plain,
    product(a16,a136) = a15,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_16,theory(equality)]) ).

cnf(253,plain,
    product(a53,a136) = a52,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_53,theory(equality)]) ).

cnf(254,plain,
    product(a5,a39) = a4,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_05,theory(equality)]) ).

cnf(255,plain,
    product(a32,a39) = a31,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_32,theory(equality)]) ).

cnf(256,plain,
    product(a52,a39) = a51,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_52,theory(equality)]) ).

cnf(257,plain,
    product(a84,a39) = a83,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_84,theory(equality)]) ).

cnf(258,plain,
    product(a108,a39) = a107,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_108,theory(equality)]) ).

cnf(259,plain,
    product(a137,a39) = a136,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_137,theory(equality)]) ).

cnf(260,plain,
    product(a31,a5) = a30,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_31,theory(equality)]) ).

cnf(261,plain,
    product(a85,a5) = a84,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_85,theory(equality)]) ).

cnf(262,plain,
    product(a106,a5) = a105,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_106,theory(equality)]) ).

cnf(263,plain,
    product(a4,a14) = a3,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_04,theory(equality)]) ).

cnf(264,plain,
    product(a30,a14) = a29,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_30,theory(equality)]) ).

cnf(265,plain,
    product(a41,a14) = a40,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_41,theory(equality)]) ).

cnf(266,plain,
    product(a75,a14) = a74,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_75,theory(equality)]) ).

cnf(267,plain,
    product(a89,a14) = a88,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_89,theory(equality)]) ).

cnf(268,plain,
    product(a101,a14) = a100,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_101,theory(equality)]) ).

cnf(269,plain,
    product(a116,a14) = a115,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_116,theory(equality)]) ).

cnf(270,plain,
    product(a40,a4) = a39,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_40,theory(equality)]) ).

cnf(272,plain,
    product(a103,a4) = a102,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_103,theory(equality)]) ).

cnf(273,plain,
    product(a3,a41) = a2,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_03,theory(equality)]) ).

cnf(274,plain,
    product(a65,a41) = a64,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_65,theory(equality)]) ).

cnf(275,plain,
    product(a90,a41) = a89,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_90,theory(equality)]) ).

cnf(276,plain,
    product(a94,a41) = a93,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_94,theory(equality)]) ).

cnf(277,plain,
    product(a127,a41) = a126,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_127,theory(equality)]) ).

cnf(278,plain,
    product(a2,a42) = a1,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot,theory(equality)]) ).

cnf(279,plain,
    product(a97,a42) = a96,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_97,theory(equality)]) ).

cnf(280,plain,
    product(a62,a1) = a61,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_62,theory(equality)]) ).

cnf(281,plain,
    product(a98,a1) = a97,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_98,theory(equality)]) ).

cnf(282,plain,
    product(a130,a1) = a129,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_130,theory(equality)]) ).

cnf(283,plain,
    product(a42,a2) = a41,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_42,theory(equality)]) ).

cnf(284,plain,
    product(a66,a2) = a65,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_66,theory(equality)]) ).

cnf(285,plain,
    product(a93,a2) = a92,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_93,theory(equality)]) ).

cnf(286,plain,
    product(a125,a2) = a124,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_125,theory(equality)]) ).

cnf(287,plain,
    product(a123,X) = product(product(a122,X),product(a115,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_123,theory(equality)]) ).

cnf(288,plain,
    product(a92,X) = product(product(a91,X),product(a124,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_92,theory(equality)]) ).

cnf(289,plain,
    product(a100,X) = product(product(a99,X),product(a124,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_100,theory(equality)]) ).

cnf(290,plain,
    product(a91,X) = product(product(a90,X),product(a100,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_91,theory(equality)]) ).

cnf(291,plain,
    product(a87,X) = product(product(a86,X),product(a104,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_87,theory(equality)]) ).

cnf(292,plain,
    product(a104,X) = product(product(a103,X),product(a87,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_104,theory(equality)]) ).

cnf(293,plain,
    product(a107,X) = product(product(a106,X),product(a84,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_107,theory(equality)]) ).

cnf(294,plain,
    product(a80,X) = product(product(a79,X),product(a119,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_80,theory(equality)]) ).

cnf(295,plain,
    product(a111,X) = product(product(a110,X),product(a119,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_111,theory(equality)]) ).

cnf(296,plain,
    product(a112,X) = product(product(a111,X),product(a79,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_112,theory(equality)]) ).

cnf(297,plain,
    product(a77,X) = product(product(a76,X),product(a114,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_77,theory(equality)]) ).

cnf(298,plain,
    product(a124,X) = product(product(a123,X),product(a75,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_124,theory(equality)]) ).

cnf(299,plain,
    product(a117,X) = product(product(a116,X),product(a74,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_117,theory(equality)]) ).

cnf(300,plain,
    product(a73,X) = product(product(a72,X),product(a82,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_73,theory(equality)]) ).

cnf(301,plain,
    product(a72,X) = product(product(a71,X),product(a109,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_72,theory(equality)]) ).

cnf(302,plain,
    product(a82,X) = product(product(a81,X),product(a109,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_82,theory(equality)]) ).

cnf(303,plain,
    product(a71,X) = product(product(a70,X),product(a118,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_71,theory(equality)]) ).

cnf(304,plain,
    product(a83,X) = product(product(a82,X),product(a118,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_83,theory(equality)]) ).

cnf(305,plain,
    product(a109,X) = product(product(a108,X),product(a118,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_109,theory(equality)]) ).

cnf(306,plain,
    product(a81,X) = product(product(a80,X),product(a70,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_81,theory(equality)]) ).

cnf(307,plain,
    product(a110,X) = product(product(a109,X),product(a70,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_110,theory(equality)]) ).

cnf(308,plain,
    product(a119,X) = product(product(a118,X),product(a70,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_119,theory(equality)]) ).

cnf(309,plain,
    product(a68,X) = product(product(a67,X),product(a98,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_68,theory(equality)]) ).

cnf(310,plain,
    product(a76,X) = product(product(a75,X),product(a68,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_76,theory(equality)]) ).

cnf(311,plain,
    product(a115,X) = product(product(a114,X),product(a68,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_115,theory(equality)]) ).

cnf(312,plain,
    product(a122,X) = product(product(a121,X),product(a68,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_122,theory(equality)]) ).

cnf(313,plain,
    product(a67,X) = product(product(a66,X),product(a92,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_67,theory(equality)]) ).

cnf(314,plain,
    product(a99,X) = product(product(a98,X),product(a92,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_99,theory(equality)]) ).

cnf(315,plain,
    product(a126,X) = product(product(a125,X),product(a65,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_126,theory(equality)]) ).

cnf(316,plain,
    product(a64,X) = product(product(a63,X),product(a127,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_64,theory(equality)]) ).

cnf(317,plain,
    product(a95,X) = product(product(a94,X),product(a127,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_95,theory(equality)]) ).

cnf(318,plain,
    product(a96,X) = product(product(a95,X),product(a64,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_96,theory(equality)]) ).

cnf(319,plain,
    product(a63,X) = product(product(a62,X),product(a96,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_63,theory(equality)]) ).

cnf(321,plain,
    product(a55,X) = product(product(a54,X),product(a135,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_55,theory(equality)]) ).

cnf(324,plain,
    product(a44,X) = product(product(a43,X),product(a128,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_44,theory(equality)]) ).

cnf(326,plain,
    product(a129,X) = product(product(a128,X),product(a62,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_129,theory(equality)]) ).

cnf(327,plain,
    product(a102,X) = product(product(a101,X),product(a40,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_102,theory(equality)]) ).

cnf(329,plain,
    product(a140,X) = product(product(a139,X),product(a47,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_140,theory(equality)]) ).

cnf(330,plain,
    product(a36,X) = product(product(a35,X),product(a139,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_36,theory(equality)]) ).

cnf(335,plain,
    product(a79,X) = product(product(a78,X),product(a33,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_79,theory(equality)]) ).

cnf(336,plain,
    product(a113,X) = product(product(a112,X),product(a33,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_113,theory(equality)]) ).

cnf(340,plain,
    product(a49,X) = product(product(a48,X),product(a138,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_49,theory(equality)]) ).

cnf(342,plain,
    product(a132,X) = product(product(a131,X),product(a138,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_132,theory(equality)]) ).

cnf(344,plain,
    product(a23,X) = product(product(a22,X),product(a45,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_23,theory(equality)]) ).

cnf(345,plain,
    product(a22,X) = product(product(a21,X),product(a141,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_22,theory(equality)]) ).

cnf(346,plain,
    product(a46,X) = product(product(a45,X),product(a141,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_46,theory(equality)]) ).

cnf(347,plain,
    product(a21,X) = product(product(a20,X),product(a35,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_21,theory(equality)]) ).

cnf(349,plain,
    product(a20,X) = product(product(a19,X),product(a26,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_20,theory(equality)]) ).

cnf(353,plain,
    product(a139,X) = product(product(a138,X),product(a20,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_139,theory(equality)]) ).

cnf(354,plain,
    product(a19,X) = product(product(a18,X),product(a58,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_19,theory(equality)]) ).

cnf(355,plain,
    product(a133,X) = product(product(a132,X),product(a58,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_133,theory(equality)]) ).

cnf(357,plain,
    product(a17,X) = product(product(a16,X),product(a29,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_17,theory(equality)]) ).

cnf(359,plain,
    product(a136,X) = product(product(a135,X),product(a29,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_136,theory(equality)]) ).

cnf(361,plain,
    product(a14,X) = product(product(a13,X),product(a32,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_14,theory(equality)]) ).

cnf(362,plain,
    product(a69,X) = product(product(a68,X),product(a32,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_69,theory(equality)]) ).

cnf(365,plain,
    product(a121,X) = product(product(a120,X),product(a32,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_121,theory(equality)]) ).

cnf(368,plain,
    product(a1,X) = product(product(a141,X),product(a23,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_142,theory(equality)]) ).

cnf(369,plain,
    product(a33,X) = product(product(a32,X),product(a13,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_33,theory(equality)]) ).

cnf(371,plain,
    product(a70,X) = product(product(a69,X),product(a13,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_70,theory(equality)]) ).

cnf(374,plain,
    product(a120,X) = product(product(a119,X),product(a13,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_120,theory(equality)]) ).

cnf(375,plain,
    product(a131,X) = product(product(a130,X),product(a13,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_131,theory(equality)]) ).

cnf(377,plain,
    product(a11,X) = product(product(a10,X),product(a37,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_11,theory(equality)]) ).

cnf(378,plain,
    product(a28,X) = product(product(a27,X),product(a37,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_28,theory(equality)]) ).

cnf(382,plain,
    product(a141,X) = product(product(a140,X),product(a11,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_141,theory(equality)]) ).

cnf(385,plain,
    product(a9,X) = product(product(a8,X),product(a56,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_09,theory(equality)]) ).

cnf(387,plain,
    product(a29,X) = product(product(a28,X),product(a17,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_29,theory(equality)]) ).

cnf(388,plain,
    product(a38,X) = product(product(a37,X),product(a17,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_38,theory(equality)]) ).

cnf(391,plain,
    product(a39,X) = product(product(a38,X),product(a7,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_39,theory(equality)]) ).

cnf(395,plain,
    product(a5,X) = product(product(a4,X),product(a39,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_05,theory(equality)]) ).

cnf(396,plain,
    product(a32,X) = product(product(a31,X),product(a39,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_32,theory(equality)]) ).

cnf(399,plain,
    product(a108,X) = product(product(a107,X),product(a39,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_108,theory(equality)]) ).

cnf(401,plain,
    product(a31,X) = product(product(a30,X),product(a5,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_31,theory(equality)]) ).

cnf(402,plain,
    product(a85,X) = product(product(a84,X),product(a5,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_85,theory(equality)]) ).

cnf(403,plain,
    product(a106,X) = product(product(a105,X),product(a5,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_106,theory(equality)]) ).

cnf(404,plain,
    product(a4,X) = product(product(a3,X),product(a14,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_04,theory(equality)]) ).

cnf(405,plain,
    product(a30,X) = product(product(a29,X),product(a14,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_30,theory(equality)]) ).

cnf(406,plain,
    product(a41,X) = product(product(a40,X),product(a14,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_41,theory(equality)]) ).

cnf(407,plain,
    product(a75,X) = product(product(a74,X),product(a14,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_75,theory(equality)]) ).

cnf(409,plain,
    product(a101,X) = product(product(a100,X),product(a14,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_101,theory(equality)]) ).

cnf(410,plain,
    product(a116,X) = product(product(a115,X),product(a14,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_116,theory(equality)]) ).

cnf(411,plain,
    product(a40,X) = product(product(a39,X),product(a4,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_40,theory(equality)]) ).

cnf(412,plain,
    product(a88,X) = product(product(a87,X),product(a4,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_88,theory(equality)]) ).

cnf(413,plain,
    product(a103,X) = product(product(a102,X),product(a4,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_103,theory(equality)]) ).

cnf(414,plain,
    product(a3,X) = product(product(a2,X),product(a41,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_03,theory(equality)]) ).

cnf(415,plain,
    product(a65,X) = product(product(a64,X),product(a41,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_65,theory(equality)]) ).

cnf(416,plain,
    product(a90,X) = product(product(a89,X),product(a41,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_90,theory(equality)]) ).

cnf(417,plain,
    product(a94,X) = product(product(a93,X),product(a41,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_94,theory(equality)]) ).

cnf(418,plain,
    product(a127,X) = product(product(a126,X),product(a41,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_127,theory(equality)]) ).

cnf(419,plain,
    product(a2,X) = product(product(a1,X),product(a42,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot,theory(equality)]) ).

cnf(420,plain,
    product(a97,X) = product(product(a96,X),product(a42,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_97,theory(equality)]) ).

cnf(424,plain,
    product(a42,X) = product(product(a41,X),product(a2,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_42,theory(equality)]) ).

cnf(425,plain,
    product(a66,X) = product(product(a65,X),product(a2,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_66,theory(equality)]) ).

cnf(427,plain,
    product(a125,X) = product(product(a124,X),product(a2,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_125,theory(equality)]) ).

cnf(428,plain,
    product(product(a122,X),a115) = product(a123,product(X,a115)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_123,theory(equality)]) ).

cnf(429,plain,
    product(product(a91,X),a124) = product(a92,product(X,a124)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_92,theory(equality)]) ).

cnf(430,plain,
    product(product(a99,X),a124) = product(a100,product(X,a124)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_100,theory(equality)]) ).

cnf(432,plain,
    product(product(a86,X),a104) = product(a87,product(X,a104)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_87,theory(equality)]) ).

cnf(433,plain,
    product(product(a103,X),a87) = product(a104,product(X,a87)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_104,theory(equality)]) ).

cnf(434,plain,
    product(product(a106,X),a84) = product(a107,product(X,a84)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_107,theory(equality)]) ).

cnf(435,plain,
    product(product(a79,X),a119) = product(a80,product(X,a119)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_80,theory(equality)]) ).

cnf(436,plain,
    product(product(a110,X),a119) = product(a111,product(X,a119)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_111,theory(equality)]) ).

cnf(437,plain,
    product(product(a111,X),a79) = product(a112,product(X,a79)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_112,theory(equality)]) ).

cnf(438,plain,
    product(product(a76,X),a114) = product(a77,product(X,a114)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_77,theory(equality)]) ).

cnf(439,plain,
    product(product(a123,X),a75) = product(a124,product(X,a75)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_124,theory(equality)]) ).

cnf(441,plain,
    product(product(a72,X),a82) = product(a73,product(X,a82)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_73,theory(equality)]) ).

cnf(442,plain,
    product(product(a71,X),a109) = product(a72,product(X,a109)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_72,theory(equality)]) ).

cnf(443,plain,
    product(product(a81,X),a109) = product(a82,product(X,a109)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_82,theory(equality)]) ).

cnf(444,plain,
    product(product(a70,X),a118) = product(a71,product(X,a118)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_71,theory(equality)]) ).

cnf(445,plain,
    product(product(a82,X),a118) = product(a83,product(X,a118)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_83,theory(equality)]) ).

cnf(446,plain,
    product(product(a108,X),a118) = product(a109,product(X,a118)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_109,theory(equality)]) ).

cnf(447,plain,
    product(product(a80,X),a70) = product(a81,product(X,a70)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_81,theory(equality)]) ).

cnf(448,plain,
    product(product(a109,X),a70) = product(a110,product(X,a70)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_110,theory(equality)]) ).

cnf(449,plain,
    product(product(a118,X),a70) = product(a119,product(X,a70)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_119,theory(equality)]) ).

cnf(450,plain,
    product(product(a67,X),a98) = product(a68,product(X,a98)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_68,theory(equality)]) ).

cnf(451,plain,
    product(product(a75,X),a68) = product(a76,product(X,a68)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_76,theory(equality)]) ).

cnf(452,plain,
    product(product(a114,X),a68) = product(a115,product(X,a68)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_115,theory(equality)]) ).

cnf(453,plain,
    product(product(a121,X),a68) = product(a122,product(X,a68)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_122,theory(equality)]) ).

cnf(454,plain,
    product(product(a66,X),a92) = product(a67,product(X,a92)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_67,theory(equality)]) ).

cnf(455,plain,
    product(product(a98,X),a92) = product(a99,product(X,a92)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_99,theory(equality)]) ).

cnf(456,plain,
    product(product(a125,X),a65) = product(a126,product(X,a65)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_126,theory(equality)]) ).

cnf(457,plain,
    product(product(a63,X),a127) = product(a64,product(X,a127)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_64,theory(equality)]) ).

cnf(459,plain,
    product(product(a95,X),a64) = product(a96,product(X,a64)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_96,theory(equality)]) ).

cnf(460,plain,
    product(product(a62,X),a96) = product(a63,product(X,a96)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_63,theory(equality)]) ).

cnf(461,plain,
    product(product(a127,X),a96) = product(a128,product(X,a96)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_128,theory(equality)]) ).

cnf(466,plain,
    product(product(a42,X),a62) = product(a43,product(X,a62)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_43,theory(equality)]) ).

cnf(468,plain,
    product(product(a101,X),a40) = product(a102,product(X,a40)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_102,theory(equality)]) ).

cnf(470,plain,
    product(product(a139,X),a47) = product(a140,product(X,a47)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_140,theory(equality)]) ).

cnf(476,plain,
    product(product(a78,X),a33) = product(a79,product(X,a33)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_79,theory(equality)]) ).

cnf(477,plain,
    product(product(a112,X),a33) = product(a113,product(X,a33)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_113,theory(equality)]) ).

cnf(479,plain,
    product(product(a104,X),a30) = product(a105,product(X,a30)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_105,theory(equality)]) ).

cnf(490,plain,
    product(product(a19,X),a26) = product(a20,product(X,a26)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_20,theory(equality)]) ).

cnf(495,plain,
    product(product(a18,X),a58) = product(a19,product(X,a58)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_19,theory(equality)]) ).

cnf(498,plain,
    product(product(a16,X),a29) = product(a17,product(X,a29)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_17,theory(equality)]) ).

cnf(500,plain,
    product(product(a135,X),a29) = product(a136,product(X,a29)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_136,theory(equality)]) ).

cnf(503,plain,
    product(product(a68,X),a32) = product(a69,product(X,a32)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_69,theory(equality)]) ).

cnf(504,plain,
    product(product(a73,X),a32) = product(a74,product(X,a32)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_74,theory(equality)]) ).

cnf(505,plain,
    product(product(a117,X),a32) = product(a118,product(X,a32)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_118,theory(equality)]) ).

cnf(506,plain,
    product(product(a120,X),a32) = product(a121,product(X,a32)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_121,theory(equality)]) ).

cnf(509,plain,
    product(product(a141,X),a23) = product(a1,product(X,a23)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_142,theory(equality)]) ).

cnf(513,plain,
    product(product(a77,X),a13) = product(a78,product(X,a13)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_78,theory(equality)]) ).

cnf(514,plain,
    product(product(a113,X),a13) = product(a114,product(X,a13)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_114,theory(equality)]) ).

cnf(515,plain,
    product(product(a119,X),a13) = product(a120,product(X,a13)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_120,theory(equality)]) ).

cnf(517,plain,
    product(product(a11,X),a21) = product(a12,product(X,a21)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_12,theory(equality)]) ).

cnf(518,plain,
    product(product(a10,X),a37) = product(a11,product(X,a37)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_11,theory(equality)]) ).

cnf(521,plain,
    product(product(a134,X),a37) = product(a135,product(X,a37)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_135,theory(equality)]) ).

cnf(528,plain,
    product(product(a28,X),a17) = product(a29,product(X,a17)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_29,theory(equality)]) ).

cnf(532,plain,
    product(product(a38,X),a7) = product(a39,product(X,a7)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_39,theory(equality)]) ).

cnf(533,plain,
    product(product(a5,X),a136) = product(a6,product(X,a136)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_06,theory(equality)]) ).

cnf(536,plain,
    product(product(a4,X),a39) = product(a5,product(X,a39)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_05,theory(equality)]) ).

cnf(537,plain,
    product(product(a31,X),a39) = product(a32,product(X,a39)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_32,theory(equality)]) ).

cnf(539,plain,
    product(product(a83,X),a39) = product(a84,product(X,a39)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_84,theory(equality)]) ).

cnf(540,plain,
    product(product(a107,X),a39) = product(a108,product(X,a39)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_108,theory(equality)]) ).

cnf(543,plain,
    product(product(a84,X),a5) = product(a85,product(X,a5)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_85,theory(equality)]) ).

cnf(544,plain,
    product(product(a105,X),a5) = product(a106,product(X,a5)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_106,theory(equality)]) ).

cnf(545,plain,
    product(product(a3,X),a14) = product(a4,product(X,a14)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_04,theory(equality)]) ).

cnf(546,plain,
    product(product(a29,X),a14) = product(a30,product(X,a14)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_30,theory(equality)]) ).

cnf(547,plain,
    product(product(a40,X),a14) = product(a41,product(X,a14)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_41,theory(equality)]) ).

cnf(548,plain,
    product(product(a74,X),a14) = product(a75,product(X,a14)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_75,theory(equality)]) ).

cnf(549,plain,
    product(product(a88,X),a14) = product(a89,product(X,a14)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_89,theory(equality)]) ).

cnf(550,plain,
    product(product(a100,X),a14) = product(a101,product(X,a14)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_101,theory(equality)]) ).

cnf(551,plain,
    product(product(a115,X),a14) = product(a116,product(X,a14)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_116,theory(equality)]) ).

cnf(552,plain,
    product(product(a39,X),a4) = product(a40,product(X,a4)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_40,theory(equality)]) ).

cnf(553,plain,
    product(product(a87,X),a4) = product(a88,product(X,a4)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_88,theory(equality)]) ).

cnf(554,plain,
    product(product(a102,X),a4) = product(a103,product(X,a4)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_103,theory(equality)]) ).

cnf(555,plain,
    product(product(a2,X),a41) = product(a3,product(X,a41)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_03,theory(equality)]) ).

cnf(556,plain,
    product(product(a64,X),a41) = product(a65,product(X,a41)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_65,theory(equality)]) ).

cnf(561,plain,
    product(product(a96,X),a42) = product(a97,product(X,a42)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_97,theory(equality)]) ).

cnf(563,plain,
    product(product(a97,X),a1) = product(a98,product(X,a1)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_98,theory(equality)]) ).

cnf(565,plain,
    product(product(a41,X),a2) = product(a42,product(X,a2)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_42,theory(equality)]) ).

cnf(567,plain,
    product(product(a92,X),a2) = product(a93,product(X,a2)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_93,theory(equality)]) ).

cnf(569,plain,
    product(product(X,Y),X) = product(X,product(Y,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,involutory_quandle,theory(equality)]) ).

cnf(570,plain,
    product(product(X,a122),a115) = product(product(X,a115),a123),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_123,theory(equality)]) ).

cnf(572,plain,
    product(product(X,a99),a124) = product(product(X,a124),a100),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_100,theory(equality)]) ).

cnf(574,plain,
    product(product(X,a86),a104) = product(product(X,a104),a87),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_87,theory(equality)]) ).

cnf(575,plain,
    product(product(X,a103),a87) = product(product(X,a87),a104),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_104,theory(equality)]) ).

cnf(577,plain,
    product(product(X,a79),a119) = product(product(X,a119),a80),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_80,theory(equality)]) ).

cnf(578,plain,
    product(product(X,a110),a119) = product(product(X,a119),a111),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_111,theory(equality)]) ).

cnf(579,plain,
    product(product(X,a111),a79) = product(product(X,a79),a112),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_112,theory(equality)]) ).

cnf(580,plain,
    product(product(X,a76),a114) = product(product(X,a114),a77),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_77,theory(equality)]) ).

cnf(581,plain,
    product(product(X,a123),a75) = product(product(X,a75),a124),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_124,theory(equality)]) ).

cnf(583,plain,
    product(product(X,a72),a82) = product(product(X,a82),a73),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_73,theory(equality)]) ).

cnf(584,plain,
    product(product(X,a71),a109) = product(product(X,a109),a72),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_72,theory(equality)]) ).

cnf(585,plain,
    product(product(X,a81),a109) = product(product(X,a109),a82),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_82,theory(equality)]) ).

cnf(586,plain,
    product(product(X,a70),a118) = product(product(X,a118),a71),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_71,theory(equality)]) ).

cnf(587,plain,
    product(product(X,a82),a118) = product(product(X,a118),a83),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_83,theory(equality)]) ).

cnf(588,plain,
    product(product(X,a108),a118) = product(product(X,a118),a109),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_109,theory(equality)]) ).

cnf(589,plain,
    product(product(X,a80),a70) = product(product(X,a70),a81),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_81,theory(equality)]) ).

cnf(590,plain,
    product(product(X,a109),a70) = product(product(X,a70),a110),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_110,theory(equality)]) ).

cnf(591,plain,
    product(product(X,a118),a70) = product(product(X,a70),a119),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_119,theory(equality)]) ).

cnf(593,plain,
    product(product(X,a75),a68) = product(product(X,a68),a76),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_76,theory(equality)]) ).

cnf(594,plain,
    product(product(X,a114),a68) = product(product(X,a68),a115),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_115,theory(equality)]) ).

cnf(597,plain,
    product(product(X,a98),a92) = product(product(X,a92),a99),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_99,theory(equality)]) ).

cnf(598,plain,
    product(product(X,a125),a65) = product(product(X,a65),a126),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_126,theory(equality)]) ).

cnf(599,plain,
    product(product(X,a63),a127) = product(product(X,a127),a64),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_64,theory(equality)]) ).

cnf(602,plain,
    product(product(X,a62),a96) = product(product(X,a96),a63),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_63,theory(equality)]) ).

cnf(609,plain,
    product(product(X,a128),a62) = product(product(X,a62),a129),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_129,theory(equality)]) ).

cnf(613,plain,
    product(product(X,a35),a139) = product(product(X,a139),a36),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_36,theory(equality)]) ).

cnf(615,plain,
    product(product(X,a33),a131) = product(product(X,a131),a34),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_34,theory(equality)]) ).

cnf(619,plain,
    product(product(X,a112),a33) = product(product(X,a33),a113),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_113,theory(equality)]) ).

cnf(628,plain,
    product(product(X,a21),a141) = product(product(X,a141),a22),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_22,theory(equality)]) ).

cnf(634,plain,
    product(product(X,a133),a26) = product(product(X,a26),a134),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_134,theory(equality)]) ).

cnf(635,plain,
    product(product(X,a47),a20) = product(product(X,a20),a48),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_48,theory(equality)]) ).

cnf(636,plain,
    product(product(X,a138),a20) = product(product(X,a20),a139),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_139,theory(equality)]) ).

cnf(640,plain,
    product(product(X,a16),a29) = product(product(X,a29),a17),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_17,theory(equality)]) ).

cnf(642,plain,
    product(product(X,a135),a29) = product(product(X,a29),a136),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_136,theory(equality)]) ).

cnf(644,plain,
    product(product(X,a13),a32) = product(product(X,a32),a14),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_14,theory(equality)]) ).

cnf(645,plain,
    product(product(X,a68),a32) = product(product(X,a32),a69),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_69,theory(equality)]) ).

cnf(647,plain,
    product(product(X,a117),a32) = product(product(X,a32),a118),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_118,theory(equality)]) ).

cnf(648,plain,
    product(product(X,a120),a32) = product(product(X,a32),a121),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_121,theory(equality)]) ).

cnf(652,plain,
    product(product(X,a32),a13) = product(product(X,a13),a33),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_33,theory(equality)]) ).

cnf(654,plain,
    product(product(X,a69),a13) = product(product(X,a13),a70),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_70,theory(equality)]) ).

cnf(657,plain,
    product(product(X,a119),a13) = product(product(X,a13),a120),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_120,theory(equality)]) ).

cnf(663,plain,
    product(product(X,a134),a37) = product(product(X,a37),a135),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_135,theory(equality)]) ).

cnf(664,plain,
    product(product(X,a46),a11) = product(product(X,a11),a47),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_47,theory(equality)]) ).

cnf(670,plain,
    product(product(X,a28),a17) = product(product(X,a17),a29),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_29,theory(equality)]) ).

cnf(671,plain,
    product(product(X,a37),a17) = product(product(X,a17),a38),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_38,theory(equality)]) ).

cnf(674,plain,
    product(product(X,a38),a7) = product(product(X,a7),a39),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_39,theory(equality)]) ).

cnf(678,plain,
    product(product(X,a4),a39) = product(product(X,a39),a5),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_05,theory(equality)]) ).

cnf(681,plain,
    product(product(X,a83),a39) = product(product(X,a39),a84),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_84,theory(equality)]) ).

cnf(682,plain,
    product(product(X,a107),a39) = product(product(X,a39),a108),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_108,theory(equality)]) ).

cnf(684,plain,
    product(product(X,a30),a5) = product(product(X,a5),a31),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_31,theory(equality)]) ).

cnf(688,plain,
    product(product(X,a29),a14) = product(product(X,a14),a30),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_30,theory(equality)]) ).

cnf(689,plain,
    product(product(X,a40),a14) = product(product(X,a14),a41),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_41,theory(equality)]) ).

cnf(691,plain,
    product(product(X,a88),a14) = product(product(X,a14),a89),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_89,theory(equality)]) ).

cnf(693,plain,
    product(product(X,a115),a14) = product(product(X,a14),a116),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_116,theory(equality)]) ).

cnf(694,plain,
    product(product(X,a39),a4) = product(product(X,a4),a40),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_40,theory(equality)]) ).

cnf(697,plain,
    product(product(X,a2),a41) = product(product(X,a41),a3),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_03,theory(equality)]) ).

cnf(700,plain,
    product(product(X,a93),a41) = product(product(X,a41),a94),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_94,theory(equality)]) ).

cnf(701,plain,
    product(product(X,a126),a41) = product(product(X,a41),a127),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_127,theory(equality)]) ).

cnf(702,plain,
    product(product(X,a1),a42) = product(product(X,a42),a2),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot,theory(equality)]) ).

cnf(707,plain,
    product(product(X,a41),a2) = product(product(X,a2),a42),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_42,theory(equality)]) ).

cnf(708,plain,
    product(product(X,a65),a2) = product(product(X,a2),a66),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_66,theory(equality)]) ).

cnf(709,plain,
    product(product(X,a92),a2) = product(product(X,a2),a93),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_93,theory(equality)]) ).

cnf(711,plain,
    product(product(product(X,Y),Z),product(Y,Z)) = product(X,Z),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,involutory_quandle_02,theory(equality)]) ).

cnf(712,plain,
    product(product(product(X,Y),Z),Y) = product(X,product(Z,Y)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,involutory_quandle_01,theory(equality)]) ).

cnf(713,plain,
    product(product(X,product(Y,Z)),Z) = product(product(X,Z),Y),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,involutory_quandle_01,theory(equality)]) ).

cnf(715,plain,
    product(product(product(X,Y),Z),U) = product(product(product(X,U),product(Y,U)),product(Z,U)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,involutory_quandle_02,theory(equality)]) ).

cnf(716,plain,
    product(product(X,product(Y,Z)),U) = product(product(X,U),product(product(Y,U),product(Z,U))),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,involutory_quandle_02,theory(equality)]) ).

cnf(719,plain,
    product(product(X,product(Y,Z)),product(U,Z)) = product(product(X,product(U,Z)),product(product(Y,U),Z)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,involutory_quandle_02,theory(equality)]) ).

cnf(720,plain,
    product(a122,X) = product(product(a123,X),product(a115,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,146,theory(equality)]) ).

cnf(721,plain,
    product(product(a123,X),a115) = product(a122,product(X,a115)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,146,theory(equality)]) ).

cnf(722,plain,
    product(product(X,a123),a115) = product(product(X,a115),a122),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,146,theory(equality)]) ).

cnf(723,plain,
    product(a91,X) = product(product(a92,X),product(a124,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,147,theory(equality)]) ).

cnf(726,plain,
    product(a99,X) = product(product(a100,X),product(a124,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,148,theory(equality)]) ).

cnf(727,plain,
    product(product(a100,X),a124) = product(a99,product(X,a124)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,148,theory(equality)]) ).

cnf(728,plain,
    product(product(X,a100),a124) = product(product(X,a124),a99),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,148,theory(equality)]) ).

cnf(732,plain,
    product(a86,X) = product(product(a87,X),product(a104,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,150,theory(equality)]) ).

cnf(733,plain,
    product(product(a87,X),a104) = product(a86,product(X,a104)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,150,theory(equality)]) ).

cnf(736,plain,
    product(product(a104,X),a87) = product(a103,product(X,a87)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,151,theory(equality)]) ).

cnf(737,plain,
    product(product(X,a104),a87) = product(product(X,a87),a103),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,151,theory(equality)]) ).

cnf(740,plain,
    product(product(X,a107),a84) = product(product(X,a84),a106),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,152,theory(equality)]) ).

cnf(741,plain,
    product(a79,X) = product(product(a80,X),product(a119,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,153,theory(equality)]) ).

cnf(742,plain,
    product(product(a80,X),a119) = product(a79,product(X,a119)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,153,theory(equality)]) ).

cnf(743,plain,
    product(product(X,a80),a119) = product(product(X,a119),a79),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,153,theory(equality)]) ).

cnf(744,plain,
    product(a110,X) = product(product(a111,X),product(a119,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,154,theory(equality)]) ).

cnf(745,plain,
    product(product(a111,X),a119) = product(a110,product(X,a119)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,154,theory(equality)]) ).

cnf(746,plain,
    product(product(X,a111),a119) = product(product(X,a119),a110),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,154,theory(equality)]) ).

cnf(747,plain,
    product(a111,X) = product(product(a112,X),product(a79,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,155,theory(equality)]) ).

cnf(748,plain,
    product(product(a112,X),a79) = product(a111,product(X,a79)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,155,theory(equality)]) ).

cnf(749,plain,
    product(product(X,a112),a79) = product(product(X,a79),a111),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,155,theory(equality)]) ).

cnf(750,plain,
    product(a76,X) = product(product(a77,X),product(a114,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,156,theory(equality)]) ).

cnf(751,plain,
    product(product(a77,X),a114) = product(a76,product(X,a114)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,156,theory(equality)]) ).

cnf(754,plain,
    product(product(a124,X),a75) = product(a123,product(X,a75)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,157,theory(equality)]) ).

cnf(755,plain,
    product(product(X,a124),a75) = product(product(X,a75),a123),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,157,theory(equality)]) ).

cnf(756,plain,
    product(a116,X) = product(product(a117,X),product(a74,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,158,theory(equality)]) ).

cnf(759,plain,
    product(a72,X) = product(product(a73,X),product(a82,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,159,theory(equality)]) ).

cnf(760,plain,
    product(product(a73,X),a82) = product(a72,product(X,a82)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,159,theory(equality)]) ).

cnf(761,plain,
    product(product(X,a73),a82) = product(product(X,a82),a72),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,159,theory(equality)]) ).

cnf(762,plain,
    product(a71,X) = product(product(a72,X),product(a109,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,160,theory(equality)]) ).

cnf(763,plain,
    product(product(a72,X),a109) = product(a71,product(X,a109)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,160,theory(equality)]) ).

cnf(765,plain,
    product(a81,X) = product(product(a82,X),product(a109,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,161,theory(equality)]) ).

cnf(766,plain,
    product(product(a82,X),a109) = product(a81,product(X,a109)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,161,theory(equality)]) ).

cnf(767,plain,
    product(product(X,a82),a109) = product(product(X,a109),a81),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,161,theory(equality)]) ).

cnf(768,plain,
    product(a70,X) = product(product(a71,X),product(a118,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,162,theory(equality)]) ).

cnf(769,plain,
    product(product(a71,X),a118) = product(a70,product(X,a118)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,162,theory(equality)]) ).

cnf(771,plain,
    product(a82,X) = product(product(a83,X),product(a118,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,163,theory(equality)]) ).

cnf(772,plain,
    product(product(a83,X),a118) = product(a82,product(X,a118)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,163,theory(equality)]) ).

cnf(774,plain,
    product(a108,X) = product(product(a109,X),product(a118,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,164,theory(equality)]) ).

cnf(775,plain,
    product(product(a109,X),a118) = product(a108,product(X,a118)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,164,theory(equality)]) ).

cnf(776,plain,
    product(product(X,a109),a118) = product(product(X,a118),a108),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,164,theory(equality)]) ).

cnf(778,plain,
    product(product(a81,X),a70) = product(a80,product(X,a70)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,165,theory(equality)]) ).

cnf(779,plain,
    product(product(X,a81),a70) = product(product(X,a70),a80),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,165,theory(equality)]) ).

cnf(781,plain,
    product(product(a110,X),a70) = product(a109,product(X,a70)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,166,theory(equality)]) ).

cnf(782,plain,
    product(product(X,a110),a70) = product(product(X,a70),a109),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,166,theory(equality)]) ).

cnf(783,plain,
    product(a118,X) = product(product(a119,X),product(a70,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,167,theory(equality)]) ).

cnf(784,plain,
    product(product(a119,X),a70) = product(a118,product(X,a70)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,167,theory(equality)]) ).

cnf(785,plain,
    product(product(X,a119),a70) = product(product(X,a118),a71),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,167,theory(equality)]),586,theory(equality)]) ).

cnf(786,plain,
    product(a67,X) = product(product(a68,X),product(a98,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,168,theory(equality)]) ).

cnf(789,plain,
    product(a75,X) = product(product(a76,X),product(a68,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,169,theory(equality)]) ).

cnf(790,plain,
    product(product(a76,X),a68) = product(a75,product(X,a68)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,169,theory(equality)]) ).

cnf(791,plain,
    product(product(X,a76),a68) = product(product(X,a68),a75),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,169,theory(equality)]) ).

cnf(792,plain,
    product(a114,X) = product(product(a115,X),product(a68,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,170,theory(equality)]) ).

cnf(793,plain,
    product(product(a115,X),a68) = product(a114,product(X,a68)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,170,theory(equality)]) ).

cnf(794,plain,
    product(product(X,a115),a68) = product(product(X,a68),a114),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,170,theory(equality)]) ).

cnf(795,plain,
    product(a121,X) = product(product(a122,X),product(a68,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,171,theory(equality)]) ).

cnf(796,plain,
    product(product(a122,X),a68) = product(a121,product(X,a68)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,171,theory(equality)]) ).

cnf(797,plain,
    product(product(X,a122),a68) = product(product(X,a68),a121),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,171,theory(equality)]) ).

cnf(798,plain,
    product(a66,X) = product(product(a67,X),product(a92,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,172,theory(equality)]) ).

cnf(799,plain,
    product(product(a67,X),a92) = product(a66,product(X,a92)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,172,theory(equality)]) ).

cnf(800,plain,
    product(product(X,a67),a92) = product(product(X,a92),a66),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,172,theory(equality)]) ).

cnf(802,plain,
    product(product(a99,X),a92) = product(a98,product(X,a92)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,173,theory(equality)]) ).

cnf(806,plain,
    product(product(X,a126),a65) = product(product(X,a65),a125),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,174,theory(equality)]) ).

cnf(808,plain,
    product(product(a64,X),a127) = product(a63,product(X,a127)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,175,theory(equality)]) ).

cnf(813,plain,
    product(a95,X) = product(product(a96,X),product(a64,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,177,theory(equality)]) ).

cnf(815,plain,
    product(product(X,a96),a64) = product(product(X,a64),a95),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,177,theory(equality)]) ).

cnf(819,plain,
    product(a127,X) = product(product(a128,X),product(a96,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,179,theory(equality)]) ).

cnf(820,plain,
    product(product(a128,X),a96) = product(a127,product(X,a96)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,179,theory(equality)]) ).

cnf(838,plain,
    product(product(a129,X),a62) = product(a128,product(X,a62)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,185,theory(equality)]) ).

cnf(839,plain,
    product(product(X,a129),a62) = product(product(X,a62),a128),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,185,theory(equality)]) ).

cnf(847,plain,
    product(product(a140,X),a47) = product(a139,product(X,a47)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,188,theory(equality)]) ).

cnf(867,plain,
    product(a112,X) = product(product(a113,X),product(a33,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,195,theory(equality)]) ).

cnf(868,plain,
    product(product(a113,X),a33) = product(a112,product(X,a33)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,195,theory(equality)]) ).

cnf(878,plain,
    product(product(X,a26),a138) = product(product(X,a138),a25),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,198,theory(equality)]) ).

cnf(888,plain,
    product(a24,X) = product(product(a25,X),product(a49,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,202,theory(equality)]) ).

cnf(902,plain,
    product(product(X,a21),a35) = product(product(X,a35),a20),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,206,theory(equality)]) ).

cnf(906,plain,
    product(a19,X) = product(product(a20,X),product(a26,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,208,theory(equality)]) ).

cnf(911,plain,
    product(product(X,a58),a26) = product(product(X,a26),a57),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,209,theory(equality)]) ).

cnf(915,plain,
    product(a47,X) = product(product(a48,X),product(a20,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,211,theory(equality)]) ).

cnf(919,plain,
    product(product(a139,X),a20) = product(a138,product(X,a20)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,212,theory(equality)]) ).

cnf(920,plain,
    product(product(X,a139),a20) = product(product(X,a20),a138),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,212,theory(equality)]) ).

cnf(930,plain,
    product(a16,X) = product(product(a17,X),product(a29,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,216,theory(equality)]) ).

cnf(944,plain,
    product(product(X,a14),a32) = product(product(X,a13),a33),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,220,theory(equality)]),652,theory(equality)]) ).

cnf(946,plain,
    product(product(a69,X),a32) = product(a68,product(X,a32)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,221,theory(equality)]) ).

cnf(947,plain,
    product(product(X,a69),a32) = product(product(X,a32),a68),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,221,theory(equality)]) ).

cnf(950,plain,
    product(product(X,a74),a32) = product(product(X,a32),a73),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,222,theory(equality)]) ).

cnf(952,plain,
    product(product(a118,X),a32) = product(a117,product(X,a32)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,223,theory(equality)]) ).

cnf(956,plain,
    product(product(X,a121),a32) = product(product(X,a32),a120),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,224,theory(equality)]) ).

cnf(968,plain,
    product(product(X,a33),a13) = product(product(X,a13),a32),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,228,theory(equality)]) ).

cnf(973,plain,
    product(product(a70,X),a13) = product(a69,product(X,a13)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,230,theory(equality)]) ).

cnf(974,plain,
    product(product(X,a70),a13) = product(product(X,a13),a69),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,230,theory(equality)]) ).

cnf(979,plain,
    product(product(a114,X),a13) = product(a113,product(X,a13)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,232,theory(equality)]) ).

cnf(989,plain,
    product(product(X,a12),a21) = product(product(X,a21),a11),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,235,theory(equality)]) ).

cnf(992,plain,
    product(product(X,a11),a37) = product(product(X,a37),a10),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,236,theory(equality)]) ).

cnf(1002,plain,
    product(a46,X) = product(product(a47,X),product(a11,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,240,theory(equality)]) ).

cnf(1006,plain,
    product(product(a141,X),a11) = product(a140,product(X,a11)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,241,theory(equality)]) ).

cnf(1007,plain,
    product(product(X,a141),a11) = product(product(X,a11),a140),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,241,theory(equality)]) ).

cnf(1013,plain,
    product(product(X,a57),a134) = product(product(X,a134),a56),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,243,theory(equality)]) ).

cnf(1021,plain,
    product(product(a29,X),a17) = product(a28,product(X,a17)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,246,theory(equality)]) ).

cnf(1022,plain,
    product(product(X,a16),a29) = product(product(X,a17),a28),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,246,theory(equality)]),640,theory(equality)]) ).

cnf(1032,plain,
    product(a38,X) = product(product(a39,X),product(a7,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,250,theory(equality)]) ).

cnf(1034,plain,
    product(product(X,a39),a7) = product(product(X,a7),a38),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,250,theory(equality)]) ).

cnf(1040,plain,
    product(product(X,a16),a136) = product(product(X,a136),a15),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,252,theory(equality)]) ).

cnf(1045,plain,
    product(product(a5,X),a39) = product(a4,product(X,a39)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,254,theory(equality)]) ).

cnf(1046,plain,
    product(product(X,a5),a39) = product(product(X,a39),a4),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,254,theory(equality)]) ).

cnf(1048,plain,
    product(product(a32,X),a39) = product(a31,product(X,a39)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,255,theory(equality)]) ).

cnf(1049,plain,
    product(product(X,a32),a39) = product(product(X,a39),a31),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,255,theory(equality)]) ).

cnf(1055,plain,
    product(product(X,a84),a39) = product(product(X,a39),a83),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,257,theory(equality)]) ).

cnf(1057,plain,
    product(product(a108,X),a39) = product(a107,product(X,a39)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,258,theory(equality)]) ).

cnf(1060,plain,
    product(product(a137,X),a39) = product(a136,product(X,a39)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,259,theory(equality)]) ).

cnf(1064,plain,
    product(product(X,a31),a5) = product(product(X,a5),a30),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,260,theory(equality)]) ).

cnf(1070,plain,
    product(product(X,a106),a5) = product(product(X,a5),a105),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,262,theory(equality)]) ).

cnf(1073,plain,
    product(product(X,a4),a14) = product(product(X,a14),a3),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,263,theory(equality)]) ).

cnf(1075,plain,
    product(product(a30,X),a14) = product(a29,product(X,a14)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,264,theory(equality)]) ).

cnf(1078,plain,
    product(product(a41,X),a14) = product(a40,product(X,a14)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,265,theory(equality)]) ).

cnf(1079,plain,
    product(product(X,a41),a14) = product(product(X,a14),a40),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,265,theory(equality)]) ).

cnf(1081,plain,
    product(product(a75,X),a14) = product(a74,product(X,a14)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,266,theory(equality)]) ).

cnf(1082,plain,
    product(product(X,a75),a14) = product(product(X,a14),a74),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,266,theory(equality)]) ).

cnf(1087,plain,
    product(product(a101,X),a14) = product(a100,product(X,a14)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,268,theory(equality)]) ).

cnf(1092,plain,
    product(a39,X) = product(product(a40,X),product(a4,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,270,theory(equality)]) ).

cnf(1093,plain,
    product(product(a40,X),a4) = product(a39,product(X,a4)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,270,theory(equality)]) ).

cnf(1094,plain,
    product(product(X,a40),a4) = product(product(X,a39),a5),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,270,theory(equality)]),678,theory(equality)]) ).

cnf(1099,plain,
    product(product(a103,X),a4) = product(a102,product(X,a4)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,272,theory(equality)]) ).

cnf(1102,plain,
    product(product(a3,X),a41) = product(a2,product(X,a41)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,273,theory(equality)]) ).

cnf(1103,plain,
    product(product(X,a3),a41) = product(product(X,a2),a42),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,273,theory(equality)]),707,theory(equality)]) ).

cnf(1109,plain,
    product(product(X,a90),a41) = product(product(X,a41),a89),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,275,theory(equality)]) ).

cnf(1114,plain,
    product(product(a127,X),a41) = product(a126,product(X,a41)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,277,theory(equality)]) ).

cnf(1118,plain,
    product(product(X,a2),a42) = product(product(X,a42),a1),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,278,theory(equality)]) ).

cnf(1121,plain,
    product(product(X,a97),a42) = product(product(X,a42),a96),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,279,theory(equality)]) ).

cnf(1126,plain,
    product(product(a98,X),a1) = product(a97,product(X,a1)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,281,theory(equality)]) ).

cnf(1129,plain,
    product(product(a130,X),a1) = product(a129,product(X,a1)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,282,theory(equality)]) ).

cnf(1133,plain,
    product(product(X,a1),a42) = product(product(X,a2),a41),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,283,theory(equality)]),702,theory(equality)]) ).

cnf(1134,plain,
    product(product(X,a1),a42) = product(product(X,a41),a3),
    inference('REWRITE',[status(thm)],[697,1133,theory(equality)]) ).

cnf(1136,plain,
    product(product(a66,X),a2) = product(a65,product(X,a2)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,284,theory(equality)]) ).

cnf(1137,plain,
    product(product(X,a66),a2) = product(product(X,a2),a65),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,284,theory(equality)]) ).

cnf(1139,plain,
    product(product(a93,X),a2) = product(a92,product(X,a2)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,285,theory(equality)]) ).

cnf(1144,plain,
    product(a123,a68) = product(a121,a114),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[287,171,theory(equality)]),170,theory(equality)]) ).

cnf(1145,plain,
    product(a123,a122) = product(a122,product(a115,a122)),
    inference('PARAMODULATE',[status(thm)],[287,involutory_quandle,theory(equality)]) ).

cnf(1149,plain,
    product(product(a121,a114),a68) = a123,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1144,theory(equality)]) ).

cnf(1154,plain,
    product(product(product(a121,a114),X),a68) = product(a123,product(X,a68)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1149,theory(equality)]) ).

cnf(1157,plain,
    product(product(a123,a122),X) = product(product(a122,X),product(product(a115,a122),X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1145,theory(equality)]) ).

cnf(1158,plain,
    product(product(a122,X),product(a115,a122)) = product(product(a123,a122),product(X,product(a115,a122))),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1145,theory(equality)]) ).

cnf(1160,plain,
    product(a92,a100) = product(a90,product(a124,a100)),
    inference('PARAMODULATE',[status(thm)],[288,149,theory(equality)]) ).

cnf(1184,plain,
    product(a91,a41) = product(a89,product(a100,a41)),
    inference('PARAMODULATE',[status(thm)],[290,275,theory(equality)]) ).

cnf(1185,plain,
    product(a91,a90) = product(a90,product(a100,a90)),
    inference('PARAMODULATE',[status(thm)],[290,involutory_quandle,theory(equality)]) ).

cnf(1196,plain,
    product(a87,a30) = product(a85,a105),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[291,196,theory(equality)]),knot_105,theory(equality)]) ).

cnf(1197,plain,
    product(a87,a86) = product(a86,product(a104,a86)),
    inference('PARAMODULATE',[status(thm)],[291,involutory_quandle,theory(equality)]) ).

cnf(1208,plain,
    product(a104,a4) = product(a102,a88),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[292,272,theory(equality)]),knot_88,theory(equality)]) ).

cnf(1209,plain,
    product(a104,a103) = product(a103,product(a87,a103)),
    inference('PARAMODULATE',[status(thm)],[292,involutory_quandle,theory(equality)]) ).

cnf(1222,plain,
    product(a107,a5) = product(a105,a85),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[293,262,theory(equality)]),knot_85,theory(equality)]) ).

cnf(1223,plain,
    product(a107,a106) = product(a106,product(a84,a106)),
    inference('PARAMODULATE',[status(thm)],[293,involutory_quandle,theory(equality)]) ).

cnf(1224,plain,
    a108 = product(product(a106,a39),a83),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[293,257,theory(equality)]),knot_108,theory(equality)]) ).

cnf(1232,plain,
    product(a108,a83) = product(a106,a39),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1224,theory(equality)]) ).

cnf(1244,plain,
    product(a80,a79) = product(a79,product(a119,a79)),
    inference('PARAMODULATE',[status(thm)],[294,involutory_quandle,theory(equality)]) ).

cnf(1245,plain,
    a81 = product(product(a79,a118),a71),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[294,167,theory(equality)]),586,knot_81,theory(equality)]) ).

cnf(1249,plain,
    product(a81,a71) = product(a79,a118),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1245,theory(equality)]) ).

cnf(1263,plain,
    product(a111,a70) = a108,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[295,166,theory(equality)]),164,167,theory(equality)]) ).

cnf(1264,plain,
    product(a111,a110) = product(a110,product(a119,a110)),
    inference('PARAMODULATE',[status(thm)],[295,involutory_quandle,theory(equality)]) ).

cnf(1268,plain,
    product(a108,a70) = a111,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1263,theory(equality)]) ).

cnf(1270,plain,
    product(product(a111,X),a70) = product(a108,product(X,a70)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1263,theory(equality)]) ).

cnf(1271,plain,
    product(product(X,a111),a70) = product(product(X,a70),a108),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1263,theory(equality)]) ).

cnf(1273,plain,
    product(product(a108,X),a70) = product(a111,product(X,a70)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1268,theory(equality)]) ).

cnf(1274,plain,
    product(product(X,a108),a70) = product(product(X,a70),a111),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1268,theory(equality)]) ).

cnf(1276,plain,
    product(a112,a119) = product(a110,a80),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[296,154,theory(equality)]),knot_80,theory(equality)]) ).

cnf(1277,plain,
    product(a112,a111) = product(a111,product(a79,a111)),
    inference('PARAMODULATE',[status(thm)],[296,involutory_quandle,theory(equality)]) ).

cnf(1278,plain,
    a113 = product(product(a111,a33),a78),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[296,194,theory(equality)]),knot_113,theory(equality)]) ).

cnf(1288,plain,
    product(a113,a78) = product(a111,a33),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1278,theory(equality)]) ).

cnf(1299,plain,
    product(a77,a68) = product(a75,a115),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[297,169,theory(equality)]),knot_115,theory(equality)]) ).

cnf(1300,plain,
    product(a77,a76) = product(a76,product(a114,a76)),
    inference('PARAMODULATE',[status(thm)],[297,involutory_quandle,theory(equality)]) ).

cnf(1305,plain,
    product(product(a77,X),a68) = product(product(a75,a115),product(X,a68)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1299,theory(equality)]) ).

cnf(1311,plain,
    product(a124,a115) = product(a122,product(a75,a115)),
    inference('PARAMODULATE',[status(thm)],[298,146,theory(equality)]) ).

cnf(1312,plain,
    product(a124,a123) = product(a123,product(a75,a123)),
    inference('PARAMODULATE',[status(thm)],[298,involutory_quandle,theory(equality)]) ).

cnf(1313,plain,
    product(a124,a68) = product(product(a121,a114),a76),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[298,knot_76,theory(equality)]),1144,theory(equality)]) ).

cnf(1314,plain,
    product(a124,a14) = product(product(a123,a14),a74),
    inference('PARAMODULATE',[status(thm)],[298,266,theory(equality)]) ).

cnf(1324,plain,
    product(product(a124,a14),a74) = product(a123,a14),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1314,theory(equality)]) ).

cnf(1328,plain,
    product(a117,a14) = product(a115,a75),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[299,269,theory(equality)]),knot_75,theory(equality)]) ).

cnf(1329,plain,
    product(a117,a116) = product(a116,product(a74,a116)),
    inference('PARAMODULATE',[status(thm)],[299,involutory_quandle,theory(equality)]) ).

cnf(1330,plain,
    a118 = product(product(a116,a32),a73),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[299,222,theory(equality)]),knot_118,theory(equality)]) ).

cnf(1334,plain,
    product(product(a117,a14),a75) = a115,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1328,theory(equality)]) ).

cnf(1336,plain,
    product(product(a117,a14),X) = product(product(a115,X),product(a75,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1328,theory(equality)]) ).

cnf(1338,plain,
    product(product(X,a115),a75) = product(product(X,a75),product(a117,a14)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1328,theory(equality)]) ).

cnf(1339,plain,
    product(a118,a73) = product(a116,a32),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1330,theory(equality)]) ).

cnf(1342,plain,
    product(product(X,product(a116,a32)),a73) = product(product(X,a73),a118),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1330,theory(equality)]) ).

cnf(1345,plain,
    product(product(X,a118),a73) = product(product(X,a73),product(a116,a32)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1339,theory(equality)]) ).

cnf(1348,plain,
    product(product(X,product(a117,a14)),a75) = product(product(X,a75),a115),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1334,theory(equality)]) ).

cnf(1349,plain,
    product(product(a117,a116),X) = product(product(a116,X),product(product(a74,a116),X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1329,theory(equality)]) ).

cnf(1350,plain,
    product(a73,a109) = product(a71,a81),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[300,160,theory(equality)]),161,theory(equality)]) ).

cnf(1351,plain,
    product(a73,a72) = product(a72,product(a82,a72)),
    inference('PARAMODULATE',[status(thm)],[300,involutory_quandle,theory(equality)]) ).

cnf(1352,plain,
    product(a73,a118) = product(product(a72,a118),a83),
    inference('PARAMODULATE',[status(thm)],[300,knot_83,theory(equality)]) ).

cnf(1356,plain,
    product(product(a73,a109),a81) = a71,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1350,theory(equality)]) ).

cnf(1364,plain,
    product(product(a73,a118),a83) = product(a72,a118),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1352,theory(equality)]) ).

cnf(1368,plain,
    product(a72,a118) = product(a70,a108),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[301,162,theory(equality)]),164,theory(equality)]) ).

cnf(1369,plain,
    product(a73,a118) = product(product(a70,a108),a83),
    inference('REWRITE',[status(thm)],[1352,1368,theory(equality)]) ).

cnf(1370,plain,
    product(product(a73,a118),a83) = product(a70,a108),
    inference('REWRITE',[status(thm)],[1364,1368,theory(equality)]) ).

cnf(1379,plain,
    product(product(a72,X),a118) = product(product(a70,a108),product(X,a118)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1368,theory(equality)]) ).

cnf(1385,plain,
    product(a82,a70) = product(a80,a110),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[302,165,theory(equality)]),knot_110,theory(equality)]) ).

cnf(1386,plain,
    product(a82,a81) = product(a81,product(a109,a81)),
    inference('PARAMODULATE',[status(thm)],[302,involutory_quandle,theory(equality)]) ).

cnf(1387,plain,
    product(a82,a71) = product(product(a79,a118),product(a109,a71)),
    inference('PARAMODULATE',[status(thm)],[302,1249,theory(equality)]) ).

cnf(1391,plain,
    product(a73,a70) = product(product(a72,a70),product(a80,a110)),
    inference('PARAMODULATE',[status(thm)],[300,1385,theory(equality)]) ).

cnf(1393,plain,
    product(product(a82,X),a70) = product(product(a80,a110),product(X,a70)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1385,theory(equality)]) ).

cnf(1396,plain,
    product(product(a82,a81),X) = product(product(a81,X),product(product(a109,a81),X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1386,theory(equality)]) ).

cnf(1398,plain,
    product(product(X,a109),a81) = product(product(X,product(a109,a81)),product(a82,a81)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1386,theory(equality)]),involutory_quandle_02,theory(equality)]) ).

cnf(1399,plain,
    product(a71,a13) = product(a69,product(a118,a13)),
    inference('PARAMODULATE',[status(thm)],[303,230,theory(equality)]) ).

cnf(1400,plain,
    product(a71,a70) = product(a70,a119),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[303,involutory_quandle,theory(equality)]),knot_119,theory(equality)]) ).

cnf(1404,plain,
    product(a72,a70) = product(product(a70,a111),a119),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[301,1400,theory(equality)]),746,knot_110,theory(equality)]) ).

cnf(1406,plain,
    product(product(a71,X),a70) = product(product(a70,a119),product(X,a70)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1400,theory(equality)]) ).

cnf(1411,plain,
    product(a83,a109) = product(a81,product(a118,a109)),
    inference('PARAMODULATE',[status(thm)],[304,161,theory(equality)]) ).

cnf(1412,plain,
    product(a83,a82) = product(a82,product(a118,a82)),
    inference('PARAMODULATE',[status(thm)],[304,involutory_quandle,theory(equality)]) ).

cnf(1413,plain,
    product(a83,a70) = product(a79,a111),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[304,knot_119,theory(equality)]),knot_111,742,1385,theory(equality)]) ).

cnf(1417,plain,
    product(product(a79,a111),a70) = a83,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1413,theory(equality)]) ).

cnf(1419,plain,
    product(product(a83,X),a70) = product(product(a79,a111),product(X,a70)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1413,theory(equality)]) ).

cnf(1420,plain,
    product(product(X,a83),a70) = product(product(X,a70),product(a79,a111)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1413,theory(equality)]) ).

cnf(1422,plain,
    product(product(product(a79,a111),X),a70) = product(a83,product(X,a70)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1417,theory(equality)]) ).

cnf(1426,plain,
    product(product(a81,X),product(a118,a109)) = product(product(a83,a109),product(X,product(a118,a109))),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1411,theory(equality)]) ).

cnf(1433,plain,
    product(a109,a108) = product(a108,product(a118,a108)),
    inference('PARAMODULATE',[status(thm)],[305,involutory_quandle,theory(equality)]) ).

cnf(1437,plain,
    product(product(a109,a108),X) = product(product(a108,X),product(product(a118,a108),X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1433,theory(equality)]) ).

cnf(1438,plain,
    product(a81,a119) = product(a79,product(a70,a119)),
    inference('PARAMODULATE',[status(thm)],[306,153,theory(equality)]) ).

cnf(1440,plain,
    product(a81,a118) = product(product(a80,a118),a71),
    inference('PARAMODULATE',[status(thm)],[306,knot_71,theory(equality)]) ).

cnf(1441,plain,
    product(a81,a13) = product(product(a80,a13),a69),
    inference('PARAMODULATE',[status(thm)],[306,230,theory(equality)]) ).

cnf(1462,plain,
    product(a110,a118) = product(a108,a71),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[307,164,theory(equality)]),knot_71,theory(equality)]) ).

cnf(1463,plain,
    product(a110,a109) = product(a109,product(a70,a109)),
    inference('PARAMODULATE',[status(thm)],[307,involutory_quandle,theory(equality)]) ).

cnf(1464,plain,
    product(a110,a13) = product(product(a109,a13),a69),
    inference('PARAMODULATE',[status(thm)],[307,230,theory(equality)]) ).

cnf(1468,plain,
    product(product(a110,a118),a71) = a108,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1462,theory(equality)]) ).

cnf(1472,plain,
    product(product(X,a108),a71) = product(product(X,a71),product(a110,a118)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1462,theory(equality)]) ).

cnf(1474,plain,
    product(product(product(a110,a118),X),a71) = product(a108,product(X,a71)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1468,theory(equality)]) ).

cnf(1477,plain,
    product(product(a110,a13),a69) = product(a109,a13),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1464,theory(equality)]) ).

cnf(1481,plain,
    product(a119,a118) = product(a118,a71),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[308,involutory_quandle,theory(equality)]),knot_71,theory(equality)]) ).

cnf(1482,plain,
    a120 = product(product(a118,a13),a69),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[308,230,theory(equality)]),knot_120,theory(equality)]) ).

cnf(1486,plain,
    product(product(a119,a118),a71) = a118,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1481,theory(equality)]) ).

cnf(1488,plain,
    product(a109,a71) = product(a111,a118),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[305,1481,theory(equality)]),295,1462,theory(equality)]) ).

cnf(1493,plain,
    product(a82,a71) = product(product(a79,a111),a118),
    inference('REWRITE',[status(thm)],[1387,involutory_quandle_02,1488,theory(equality)]) ).

cnf(1497,plain,
    product(product(a118,X),a71) = product(product(a119,a118),product(X,a71)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1481,theory(equality)]) ).

cnf(1499,plain,
    product(a120,a69) = product(a118,a13),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1482,theory(equality)]) ).

cnf(1519,plain,
    product(a68,a92) = product(a66,a99),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[309,172,theory(equality)]),knot_99,theory(equality)]) ).

cnf(1521,plain,
    product(a68,a1) = product(product(a67,a1),a97),
    inference('PARAMODULATE',[status(thm)],[309,281,theory(equality)]) ).

cnf(1526,plain,
    product(product(a68,a92),a99) = a66,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1519,theory(equality)]) ).

cnf(1539,plain,
    product(a76,a75) = product(a75,product(a68,a75)),
    inference('PARAMODULATE',[status(thm)],[310,involutory_quandle,theory(equality)]) ).

cnf(1540,plain,
    product(a76,a32) = product(product(a75,a32),a69),
    inference('PARAMODULATE',[status(thm)],[310,knot_69,theory(equality)]) ).

cnf(1550,plain,
    product(product(a76,a75),X) = product(product(a75,X),product(product(a68,a75),X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1539,theory(equality)]) ).

cnf(1557,plain,
    product(a115,a114) = product(a114,product(a68,a114)),
    inference('PARAMODULATE',[status(thm)],[311,involutory_quandle,theory(equality)]) ).

cnf(1558,plain,
    product(a115,a32) = product(product(a114,a32),a69),
    inference('PARAMODULATE',[status(thm)],[311,knot_69,theory(equality)]) ).

cnf(1562,plain,
    product(product(a115,a114),X) = product(product(a114,X),product(product(a68,a114),X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1557,theory(equality)]) ).

cnf(1563,plain,
    product(product(a115,a32),a69) = product(a114,a32),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1558,theory(equality)]) ).

cnf(1566,plain,
    product(product(X,product(a114,a32)),a69) = product(product(X,a69),product(a115,a32)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1558,theory(equality)]) ).

cnf(1567,plain,
    product(a122,a32) = product(a118,a13),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[312,224,theory(equality)]),1499,knot_69,theory(equality)]) ).

cnf(1568,plain,
    product(a122,a121) = product(a121,product(a68,a121)),
    inference('PARAMODULATE',[status(thm)],[312,involutory_quandle,theory(equality)]) ).

cnf(1572,plain,
    product(product(a118,a13),a32) = a122,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1567,theory(equality)]) ).

cnf(1577,plain,
    a122 = product(a117,a14),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1572,theory(equality)]),knot_14,223,theory(equality)]) ).

cnf(1578,plain,
    a122 = product(a115,a75),
    inference('REWRITE',[status(thm)],[1328,1577,theory(equality)]) ).

cnf(1579,plain,
    product(a122,a75) = a115,
    inference('REWRITE',[status(thm)],[1334,1577,theory(equality)]) ).

cnf(1580,plain,
    product(a122,X) = product(product(a115,X),product(a75,X)),
    inference('REWRITE',[status(thm)],[1336,1577,theory(equality)]) ).

cnf(1582,plain,
    product(product(X,a115),a75) = product(product(X,a75),a122),
    inference('REWRITE',[status(thm)],[1338,1577,theory(equality)]) ).

cnf(1585,plain,
    product(product(X,a122),a75) = product(product(X,a75),a115),
    inference('REWRITE',[status(thm)],[1348,1577,theory(equality)]) ).

cnf(1589,plain,
    a124 = product(a115,a122),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[287,1578,theory(equality)]),1579,knot_124,theory(equality)]) ).

cnf(1590,plain,
    product(a123,a122) = product(a122,a124),
    inference('REWRITE',[status(thm)],[1145,1589,theory(equality)]) ).

cnf(1591,plain,
    product(product(a123,a122),X) = product(product(a122,X),product(a124,X)),
    inference('REWRITE',[status(thm)],[1157,1589,theory(equality)]) ).

cnf(1592,plain,
    product(product(a122,X),a124) = product(product(a123,a122),product(X,a124)),
    inference('REWRITE',[status(thm)],[1158,1589,theory(equality)]) ).

cnf(1594,plain,
    product(a124,a122) = a115,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1589,theory(equality)]) ).

cnf(1595,plain,
    product(a124,X) = product(product(a115,X),product(a122,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1589,theory(equality)]) ).

cnf(1596,plain,
    product(product(a115,X),a122) = product(a124,product(X,a122)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1589,theory(equality)]) ).

cnf(1597,plain,
    product(product(X,a115),a122) = product(product(X,a122),a124),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1589,theory(equality)]) ).

cnf(1598,plain,
    product(a122,a14) = a117,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1577,theory(equality)]) ).

cnf(1606,plain,
    product(product(X,a124),a122) = product(product(X,a115),a123),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1594,theory(equality)]),570,theory(equality)]) ).

cnf(1607,plain,
    product(a123,a14) = product(a117,a116),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[287,1598,theory(equality)]),knot_116,theory(equality)]) ).

cnf(1608,plain,
    product(a124,a14) = product(product(a117,a116),a74),
    inference('REWRITE',[status(thm)],[1314,1607,theory(equality)]) ).

cnf(1609,plain,
    product(product(a124,a14),a74) = product(a117,a116),
    inference('REWRITE',[status(thm)],[1324,1607,theory(equality)]) ).

cnf(1616,plain,
    product(product(X,a122),a14) = product(product(X,a14),a117),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1598,theory(equality)]) ).

cnf(1617,plain,
    product(product(a122,a121),X) = product(product(a121,X),product(product(a68,a121),X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1568,theory(equality)]) ).

cnf(1618,plain,
    product(a124,a14) = product(a116,a117),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1608,theory(equality)]),knot_117,158,theory(equality)]) ).

cnf(1619,plain,
    product(a116,a117) = product(product(a117,a116),a74),
    inference('REWRITE',[status(thm)],[1608,1618,theory(equality)]) ).

cnf(1620,plain,
    product(product(a116,a117),a74) = product(a117,a116),
    inference('REWRITE',[status(thm)],[1609,1618,theory(equality)]) ).

cnf(1624,plain,
    product(product(a116,a117),a14) = a124,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1618,theory(equality)]) ).

cnf(1633,plain,
    product(a67,a2) = product(a65,a93),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[313,284,theory(equality)]),knot_93,theory(equality)]) ).

cnf(1641,plain,
    product(product(a65,X),a93) = product(product(a67,a2),product(X,a93)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1633,theory(equality)]) ).

cnf(1652,plain,
    product(a99,a98) = product(a98,product(a92,a98)),
    inference('PARAMODULATE',[status(thm)],[314,involutory_quandle,theory(equality)]) ).

cnf(1654,plain,
    a100 = product(product(a98,a124),a91),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[314,147,theory(equality)]),knot_100,theory(equality)]) ).

cnf(1658,plain,
    product(a100,a91) = product(a98,a124),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1654,theory(equality)]) ).

cnf(1674,plain,
    product(a126,a2) = product(a124,a66),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[315,286,theory(equality)]),knot_66,theory(equality)]) ).

cnf(1675,plain,
    product(a126,a125) = product(a125,product(a65,a125)),
    inference('PARAMODULATE',[status(thm)],[315,involutory_quandle,theory(equality)]) ).

cnf(1676,plain,
    a127 = product(product(a125,a41),a64),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[315,274,theory(equality)]),knot_127,theory(equality)]) ).

cnf(1685,plain,
    product(product(X,a124),a66) = product(product(X,a66),product(a126,a2)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1674,theory(equality)]) ).

cnf(1686,plain,
    product(a127,a64) = product(a125,a41),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1676,theory(equality)]) ).

cnf(1688,plain,
    product(product(product(a125,a41),X),a64) = product(a127,product(X,a64)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1676,theory(equality)]) ).

cnf(1692,plain,
    product(product(X,a127),a64) = product(product(X,a64),product(a125,a41)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1686,theory(equality)]) ).

cnf(1697,plain,
    product(a64,a96) = product(a62,a128),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[316,178,theory(equality)]),knot_128,theory(equality)]) ).

cnf(1698,plain,
    product(a64,a63) = product(a63,product(a127,a63)),
    inference('PARAMODULATE',[status(thm)],[316,involutory_quandle,theory(equality)]) ).

cnf(1702,plain,
    product(product(a62,a128),a96) = a64,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1697,theory(equality)]) ).

cnf(1713,plain,
    product(a95,a41) = product(a93,a126),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[317,276,theory(equality)]),277,theory(equality)]) ).

cnf(1725,plain,
    product(a96,a127) = product(a94,a63),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[318,176,theory(equality)]),175,theory(equality)]) ).

cnf(1727,plain,
    product(a96,a41) = product(product(a93,a126),a65),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[318,knot_65,theory(equality)]),1713,theory(equality)]) ).

cnf(1732,plain,
    product(product(a96,X),a127) = product(product(a94,a63),product(X,a127)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1725,theory(equality)]) ).

cnf(1738,plain,
    product(product(a96,a41),a65) = product(a93,a126),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1727,theory(equality)]) ).

cnf(1745,plain,
    product(a63,a64) = product(product(a62,a64),a95),
    inference('PARAMODULATE',[status(thm)],[319,177,theory(equality)]) ).

cnf(1755,plain,
    product(product(a63,a64),a95) = product(a62,a64),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1745,theory(equality)]) ).

cnf(1757,plain,
    product(product(product(a62,a64),X),a95) = product(product(a63,a64),product(X,a95)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1745,theory(equality)]) ).

cnf(1779,plain,
    product(a55,a29) = a52,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[321,217,theory(equality)]),253,knot_136,theory(equality)]) ).

cnf(1787,plain,
    product(product(X,a55),a29) = product(product(X,a29),a52),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1779,theory(equality)]) ).

cnf(1826,plain,
    product(a44,a62) = product(a42,a129),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[324,184,theory(equality)]),knot_129,theory(equality)]) ).

cnf(1831,plain,
    product(product(a42,a129),a62) = a44,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1826,theory(equality)]) ).

cnf(1855,plain,
    product(a129,a96) = product(a127,a63),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[326,179,theory(equality)]),knot_63,theory(equality)]) ).

cnf(1856,plain,
    product(a129,a128) = product(a128,product(a62,a128)),
    inference('PARAMODULATE',[status(thm)],[326,involutory_quandle,theory(equality)]) ).

cnf(1861,plain,
    product(product(a127,a63),a96) = a129,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1855,theory(equality)]) ).

cnf(1872,plain,
    product(a129,X) = product(product(product(a127,a63),X),product(a96,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1861,theory(equality)]) ).

cnf(1873,plain,
    product(product(product(a127,a63),X),a96) = product(a129,product(X,a96)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1861,theory(equality)]) ).

cnf(1876,plain,
    product(a102,a14) = product(a100,a41),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[327,268,theory(equality)]),knot_41,theory(equality)]) ).

cnf(1877,plain,
    product(a91,a41) = product(a89,product(a102,a14)),
    inference('REWRITE',[status(thm)],[1184,1876,theory(equality)]) ).

cnf(1882,plain,
    a103 = product(product(a101,a39),a5),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[327,270,theory(equality)]),678,knot_103,theory(equality)]) ).

cnf(1886,plain,
    product(product(a102,a14),a41) = a100,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1876,theory(equality)]) ).

cnf(1890,plain,
    product(a103,a5) = product(a101,a39),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1882,theory(equality)]) ).

cnf(1919,plain,
    product(a140,a20) = product(a138,a48),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[329,212,theory(equality)]),knot_48,theory(equality)]) ).

cnf(1921,plain,
    a141 = product(product(a139,a11),a46),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[329,240,theory(equality)]),knot_141,theory(equality)]) ).

cnf(1925,plain,
    product(product(a140,a20),a48) = a138,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1919,theory(equality)]) ).

cnf(1927,plain,
    product(product(a138,X),a48) = product(product(a140,a20),product(X,a48)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1919,theory(equality)]) ).

cnf(1929,plain,
    product(a141,a46) = product(a139,a11),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1921,theory(equality)]) ).

cnf(1936,plain,
    product(a138,X) = product(product(product(a140,a20),X),product(a48,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1925,theory(equality)]) ).

cnf(1940,plain,
    product(a36,a35) = product(a35,product(a139,a35)),
    inference('PARAMODULATE',[status(thm)],[330,involutory_quandle,theory(equality)]) ).

cnf(2028,plain,
    product(a79,a13) = product(a77,a32),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[335,231,theory(equality)]),228,theory(equality)]) ).

cnf(2035,plain,
    product(a80,a13) = product(product(a77,a121),a32),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[294,2028,theory(equality)]),956,knot_120,theory(equality)]) ).

cnf(2048,plain,
    product(a113,a131) = product(product(a112,a131),a34),
    inference('PARAMODULATE',[status(thm)],[336,knot_34,theory(equality)]) ).

cnf(2049,plain,
    a114 = product(product(a112,a13),a32),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[336,228,theory(equality)]),knot_114,theory(equality)]) ).

cnf(2054,plain,
    product(a114,a32) = product(a112,a13),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,2049,theory(equality)]) ).

cnf(2055,plain,
    product(a115,a32) = product(product(a112,a13),a69),
    inference('REWRITE',[status(thm)],[1558,2054,theory(equality)]) ).

cnf(2056,plain,
    product(product(a115,a32),a69) = product(a112,a13),
    inference('REWRITE',[status(thm)],[1563,2054,theory(equality)]) ).

cnf(2059,plain,
    product(product(X,product(a112,a13)),a69) = product(product(X,a69),product(a115,a32)),
    inference('REWRITE',[status(thm)],[1566,2054,theory(equality)]) ).

cnf(2068,plain,
    product(product(a113,a131),a34) = product(a112,a131),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,2048,theory(equality)]) ).

cnf(2108,plain,
    product(a49,a20) = product(a47,a139),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[340,211,theory(equality)]),knot_139,theory(equality)]) ).

cnf(2133,plain,
    product(a132,a13) = product(a130,product(a138,a13)),
    inference('PARAMODULATE',[status(thm)],[342,234,theory(equality)]) ).

cnf(2160,plain,
    product(a23,a141) = product(a21,a46),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[344,204,theory(equality)]),knot_46,theory(equality)]) ).

cnf(2173,plain,
    product(a22,a21) = product(a21,product(a141,a21)),
    inference('PARAMODULATE',[status(thm)],[345,involutory_quandle,theory(equality)]) ).

cnf(2187,plain,
    product(a46,a23) = product(a44,a1),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[346,226,theory(equality)]),knot_142,theory(equality)]) ).

cnf(2189,plain,
    a47 = product(product(a45,a11),a140),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[346,241,theory(equality)]),knot_47,theory(equality)]) ).

cnf(2196,plain,
    product(a47,a140) = product(a45,a11),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,2189,theory(equality)]) ).

cnf(2215,plain,
    product(a21,a139) = product(product(a20,a139),a36),
    inference('PARAMODULATE',[status(thm)],[347,knot_36,theory(equality)]) ).

cnf(2236,plain,
    product(a20,a19) = product(a19,product(a26,a19)),
    inference('PARAMODULATE',[status(thm)],[349,involutory_quandle,theory(equality)]) ).

cnf(2237,plain,
    product(a20,a138) = product(product(a19,a138),a25),
    inference('PARAMODULATE',[status(thm)],[349,198,theory(equality)]) ).

cnf(2242,plain,
    product(product(a20,a138),a25) = product(a19,a138),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,2237,theory(equality)]) ).

cnf(2292,plain,
    product(a139,a138) = product(a138,product(a20,a138)),
    inference('PARAMODULATE',[status(thm)],[353,involutory_quandle,theory(equality)]) ).

cnf(2302,plain,
    a20 = product(product(a18,a26),a57),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[354,209,theory(equality)]),knot_20,theory(equality)]) ).

cnf(2307,plain,
    product(a20,a57) = product(a18,a26),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,2302,theory(equality)]) ).

cnf(2329,plain,
    a134 = product(product(a132,a26),a57),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[355,209,theory(equality)]),knot_134,theory(equality)]) ).

cnf(2344,plain,
    product(product(X,product(a132,a26)),a57) = product(product(X,a134),a56),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,2329,theory(equality)]),1013,theory(equality)]) ).

cnf(2363,plain,
    product(a17,a16) = product(a16,product(a29,a16)),
    inference('PARAMODULATE',[status(thm)],[357,involutory_quandle,theory(equality)]) ).

cnf(2393,plain,
    product(a136,a17) = product(product(a135,a16),a29),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[359,246,theory(equality)]),1022,theory(equality)]) ).

cnf(2426,plain,
    product(a14,a13) = product(a13,a33),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[361,involutory_quandle,theory(equality)]),knot_33,theory(equality)]) ).

cnf(2439,plain,
    a70 = product(product(a68,a13),a33),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[362,knot_33,theory(equality)]),knot_70,theory(equality)]) ).

cnf(2483,plain,
    product(a121,a13) = product(a119,a33),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[365,233,theory(equality)]),knot_33,theory(equality)]) ).

cnf(2493,plain,
    product(product(a121,a13),a33) = a119,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,2483,theory(equality)]) ).

cnf(2521,plain,
    product(a1,a11) = product(a140,product(a23,a11)),
    inference('PARAMODULATE',[status(thm)],[368,241,theory(equality)]) ).

cnf(2529,plain,
    product(a33,a32) = product(a32,a14),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[369,involutory_quandle,theory(equality)]),knot_14,theory(equality)]) ).

cnf(2555,plain,
    product(a70,a32) = product(a68,a14),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[371,221,theory(equality)]),knot_14,theory(equality)]) ).

cnf(2563,plain,
    product(a71,a32) = product(product(a68,a122),a14),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[303,2555,theory(equality)]),1616,223,theory(equality)]) ).

cnf(2601,plain,
    product(a120,a33) = product(product(a121,a14),a13),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[374,2483,theory(equality)]),involutory_quandle_02,2426,theory(equality)]) ).

cnf(2607,plain,
    product(a131,a1) = product(a129,product(a13,a1)),
    inference('PARAMODULATE',[status(thm)],[375,282,theory(equality)]) ).

cnf(2630,plain,
    product(a11,a10) = product(a10,product(a37,a10)),
    inference('PARAMODULATE',[status(thm)],[377,involutory_quandle,theory(equality)]) ).

cnf(2641,plain,
    a29 = product(product(a27,a17),a38),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[378,knot_38,theory(equality)]),knot_29,theory(equality)]) ).

cnf(2645,plain,
    product(a29,a38) = product(a27,a17),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,2641,theory(equality)]) ).

cnf(2700,plain,
    product(a141,a140) = product(a140,product(a11,a140)),
    inference('PARAMODULATE',[status(thm)],[382,involutory_quandle,theory(equality)]) ).

cnf(2707,plain,
    product(product(X,a11),a140) = product(product(X,product(a11,a140)),product(a141,a140)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,2700,theory(equality)]),involutory_quandle_02,theory(equality)]) ).

cnf(2741,plain,
    product(a9,a37) = product(product(a8,a37),a55),
    inference('PARAMODULATE',[status(thm)],[385,238,theory(equality)]) ).

cnf(2757,plain,
    product(product(a9,a37),a55) = product(a8,a37),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,2741,theory(equality)]) ).

cnf(2778,plain,
    product(a29,a28) = product(a28,product(a17,a28)),
    inference('PARAMODULATE',[status(thm)],[387,involutory_quandle,theory(equality)]) ).

cnf(2791,plain,
    product(a38,a37) = product(a37,product(a17,a37)),
    inference('PARAMODULATE',[status(thm)],[388,involutory_quandle,theory(equality)]) ).

cnf(2848,plain,
    product(a39,a38) = product(a38,product(a7,a38)),
    inference('PARAMODULATE',[status(thm)],[391,involutory_quandle,theory(equality)]) ).

cnf(2849,plain,
    product(a39,a52) = product(product(a38,a52),a6),
    inference('PARAMODULATE',[status(thm)],[391,249,theory(equality)]) ).

cnf(2867,plain,
    product(product(a39,a38),X) = product(product(a38,X),product(product(a7,a38),X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,2848,theory(equality)]) ).

cnf(2868,plain,
    product(product(a39,a52),a6) = product(a38,a52),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,2849,theory(equality)]) ).

cnf(2913,plain,
    product(a5,a14) = product(a3,product(a39,a14)),
    inference('PARAMODULATE',[status(thm)],[395,263,theory(equality)]) ).

cnf(2914,plain,
    product(a5,a4) = product(a4,a40),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[395,involutory_quandle,theory(equality)]),knot_40,theory(equality)]) ).

cnf(2966,plain,
    a32 = product(product(a30,a39),a4),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[401,254,theory(equality)]),knot_32,theory(equality)]) ).

cnf(2967,plain,
    product(a31,a4) = product(product(a30,a4),product(a4,a40)),
    inference('PARAMODULATE',[status(thm)],[401,2914,theory(equality)]) ).

cnf(2972,plain,
    product(a32,a4) = product(a30,a39),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,2966,theory(equality)]) ).

cnf(2992,plain,
    product(a85,a39) = product(a83,a4),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[402,257,theory(equality)]),254,theory(equality)]) ).

cnf(3001,plain,
    product(product(a85,X),a39) = product(product(a83,a4),product(X,a39)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,2992,theory(equality)]) ).

cnf(3013,plain,
    product(a106,a39) = product(product(a105,a39),a4),
    inference('PARAMODULATE',[status(thm)],[403,254,theory(equality)]) ).

cnf(3014,plain,
    product(a106,a4) = product(product(a105,a4),product(a4,a40)),
    inference('PARAMODULATE',[status(thm)],[403,2914,theory(equality)]) ).

cnf(3024,plain,
    product(product(a106,a39),a4) = product(a105,a39),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,3013,theory(equality)]) ).

cnf(3028,plain,
    product(a4,a3) = product(a3,product(a14,a3)),
    inference('PARAMODULATE',[status(thm)],[404,involutory_quandle,theory(equality)]) ).

cnf(3036,plain,
    product(product(X,a14),a3) = product(product(X,product(a14,a3)),product(a4,a3)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,3028,theory(equality)]),involutory_quandle_02,theory(equality)]) ).

cnf(3042,plain,
    product(a30,a29) = product(a29,product(a14,a29)),
    inference('PARAMODULATE',[status(thm)],[405,involutory_quandle,theory(equality)]) ).

cnf(3063,plain,
    product(a41,a40) = product(a40,product(a14,a40)),
    inference('PARAMODULATE',[status(thm)],[406,involutory_quandle,theory(equality)]) ).

cnf(3085,plain,
    product(a75,a32) = product(a73,a13),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[407,222,theory(equality)]),220,theory(equality)]) ).

cnf(3086,plain,
    product(a76,a32) = product(product(a73,a13),a69),
    inference('REWRITE',[status(thm)],[1540,3085,theory(equality)]) ).

cnf(3097,plain,
    product(product(a75,X),a32) = product(product(a73,a13),product(X,a32)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,3085,theory(equality)]) ).

cnf(3122,plain,
    product(a101,a32) = product(product(a100,a13),a33),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[409,220,theory(equality)]),652,theory(equality)]) ).

cnf(3128,plain,
    product(product(a101,a32),a33) = product(a100,a13),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,3122,theory(equality)]) ).

cnf(3133,plain,
    product(a116,a32) = product(product(a115,a13),a33),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[410,220,theory(equality)]),652,theory(equality)]) ).

cnf(3143,plain,
    product(a40,a39) = product(a39,a5),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[411,involutory_quandle,theory(equality)]),knot_05,theory(equality)]) ).

cnf(3144,plain,
    a41 = product(product(a39,a14),a3),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[411,263,theory(equality)]),knot_41,theory(equality)]) ).

cnf(3148,plain,
    product(product(a40,a39),a5) = a39,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,3143,theory(equality)]) ).

cnf(3154,plain,
    product(a32,a5) = product(a30,product(a40,a39)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[396,3143,theory(equality)]),260,theory(equality)]) ).

cnf(3157,plain,
    product(product(a39,X),a5) = product(product(a40,a39),product(X,a5)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,3143,theory(equality)]) ).

cnf(3159,plain,
    product(a41,a3) = product(a39,a14),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,3144,theory(equality)]) ).

cnf(3165,plain,
    product(product(X,a1),a42) = product(product(X,a3),product(a39,a14)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,3159,theory(equality)]),1134,theory(equality)]) ).

cnf(3169,plain,
    product(product(X,product(a40,a39)),a5) = product(product(X,a39),a4),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,3148,theory(equality)]),1046,theory(equality)]) ).

cnf(3173,plain,
    a89 = product(product(a87,a14),a3),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[412,263,theory(equality)]),knot_89,theory(equality)]) ).

cnf(3178,plain,
    product(a89,a3) = product(a87,a14),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,3173,theory(equality)]) ).

cnf(3198,plain,
    product(a103,a39) = product(product(a102,a39),a5),
    inference('PARAMODULATE',[status(thm)],[413,knot_05,theory(equality)]) ).

cnf(3199,plain,
    product(a103,a14) = product(product(a102,a14),a3),
    inference('PARAMODULATE',[status(thm)],[413,263,theory(equality)]) ).

cnf(3208,plain,
    product(product(a103,a14),a3) = product(a102,a14),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,3199,theory(equality)]) ).

cnf(3212,plain,
    product(a3,a2) = a1,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[414,involutory_quandle,theory(equality)]),278,knot_42,theory(equality)]) ).

cnf(3213,plain,
    a4 = product(product(a2,a14),a40),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[414,265,theory(equality)]),knot_04,theory(equality)]) ).

cnf(3214,plain,
    a3 = product(product(a2,a1),a42),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[414,3159,theory(equality)]),3165,involutory_quandle,theory(equality)]) ).

cnf(3218,plain,
    product(a1,a2) = a3,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,3212,theory(equality)]) ).

cnf(3219,plain,
    product(a4,a2) = product(a1,product(a14,a2)),
    inference('PARAMODULATE',[status(thm)],[404,3212,theory(equality)]) ).

cnf(3225,plain,
    product(product(X,a1),a2) = product(product(X,a2),a3),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,3218,theory(equality)]) ).

cnf(3226,plain,
    product(a4,a40) = product(a2,a14),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,3213,theory(equality)]) ).

cnf(3227,plain,
    product(a5,a4) = product(a2,a14),
    inference('REWRITE',[status(thm)],[2914,3226,theory(equality)]) ).

cnf(3232,plain,
    product(a31,a4) = product(product(a30,a4),product(a2,a14)),
    inference('REWRITE',[status(thm)],[2967,3226,theory(equality)]) ).

cnf(3234,plain,
    product(a106,a4) = product(product(a105,a4),product(a2,a14)),
    inference('REWRITE',[status(thm)],[3014,3226,theory(equality)]) ).

cnf(3237,plain,
    product(product(X,product(a2,a14)),a40) = product(product(X,a39),a5),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,3213,theory(equality)]),1094,theory(equality)]) ).

cnf(3238,plain,
    product(product(a2,a14),a4) = a5,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,3227,theory(equality)]) ).

cnf(3239,plain,
    product(a103,a40) = product(product(a100,a2),a14),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[413,3226,theory(equality)]),550,186,theory(equality)]) ).

cnf(3252,plain,
    product(product(X,product(a2,a1)),a42) = product(product(X,a42),a3),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,3214,theory(equality)]) ).

cnf(3259,plain,
    a66 = product(product(a64,a2),a42),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[415,knot_42,theory(equality)]),knot_66,theory(equality)]) ).

cnf(3260,plain,
    product(a65,a14) = product(product(a64,a14),a40),
    inference('PARAMODULATE',[status(thm)],[415,265,theory(equality)]) ).

cnf(3265,plain,
    product(a66,a42) = product(a64,a2),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,3259,theory(equality)]) ).

cnf(3266,plain,
    product(a66,X) = product(product(product(a64,a2),X),product(a42,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,3259,theory(equality)]) ).

cnf(3283,plain,
    product(product(a65,a14),a40) = product(a64,a14),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,3260,theory(equality)]) ).

cnf(3287,plain,
    product(a90,a14) = product(a88,a40),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[416,267,theory(equality)]),265,theory(equality)]) ).

cnf(3306,plain,
    product(a94,a2) = product(a92,a42),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[417,285,theory(equality)]),knot_42,theory(equality)]) ).

cnf(3313,plain,
    product(a95,a2) = product(product(a92,a42),product(a127,a2)),
    inference('PARAMODULATE',[status(thm)],[317,3306,theory(equality)]) ).

cnf(3326,plain,
    product(a127,a2) = product(product(a126,a2),a42),
    inference('PARAMODULATE',[status(thm)],[418,knot_42,theory(equality)]) ).

cnf(3336,plain,
    product(product(X,product(a126,a2)),a42) = product(product(X,a42),product(a127,a2)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,3326,theory(equality)]) ).

cnf(3341,plain,
    product(a2,a1) = product(a1,product(a42,a1)),
    inference('PARAMODULATE',[status(thm)],[419,involutory_quandle,theory(equality)]) ).

cnf(3400,plain,
    product(a42,a14) = product(a40,product(a2,a14)),
    inference('PARAMODULATE',[status(thm)],[424,265,theory(equality)]) ).

cnf(3401,plain,
    product(a42,a41) = product(a39,a14),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[424,involutory_quandle,theory(equality)]),3159,knot_03,theory(equality)]) ).

cnf(3406,plain,
    product(product(a39,a14),a41) = a42,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,3401,theory(equality)]) ).

cnf(3421,plain,
    product(a66,a41) = product(a64,a3),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[425,274,theory(equality)]),knot_03,theory(equality)]) ).

cnf(3459,plain,
    product(a125,a122) = product(a115,product(a2,a122)),
    inference('PARAMODULATE',[status(thm)],[427,1594,theory(equality)]) ).

cnf(3470,plain,
    product(a121,a115) = product(a123,product(a68,a115)),
    inference('PARAMODULATE',[status(thm)],[428,171,theory(equality)]) ).

cnf(3471,plain,
    a115 = product(a123,product(a75,a115)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[428,1579,theory(equality)]),involutory_quandle,theory(equality)]) ).

cnf(3482,plain,
    product(a115,product(a75,a115)) = a123,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,3471,theory(equality)]) ).

cnf(3487,plain,
    product(a90,a124) = product(a92,a99),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[429,149,theory(equality)]),148,theory(equality)]) ).

cnf(3515,plain,
    product(a86,a87) = product(a87,a103),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[432,1197,theory(equality)]),151,involutory_quandle,574,knot_87,733,theory(equality)]) ).

cnf(3519,plain,
    product(product(a87,a103),a87) = a86,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,3515,theory(equality)]) ).

cnf(3520,plain,
    product(a86,product(a103,a104)) = product(a87,a86),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[432,3515,theory(equality)]),150,733,theory(equality)]) ).

cnf(3532,plain,
    product(product(a103,a104),a87) = product(a104,a103),
    inference('PARAMODULATE',[status(thm)],[433,151,theory(equality)]) ).

cnf(3533,plain,
    product(product(a103,a86),a87) = product(a104,product(a87,a103)),
    inference('PARAMODULATE',[status(thm)],[433,3515,theory(equality)]) ).

cnf(3534,plain,
    product(product(a104,a103),a87) = product(a104,a86),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[433,3519,theory(equality)]),1209,theory(equality)]) ).

cnf(3541,plain,
    product(a104,a86) = product(a103,a104),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,3532,theory(equality)]),3534,theory(equality)]) ).

cnf(3548,plain,
    product(product(product(a103,a104),X),a87) = product(product(a104,a103),product(X,a87)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,3532,theory(equality)]) ).

cnf(3549,plain,
    product(product(X,product(a103,a104)),a87) = product(product(X,a87),product(a104,a103)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,3532,theory(equality)]) ).

cnf(3551,plain,
    product(product(a103,a104),X) = product(product(a104,X),product(a86,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,3541,theory(equality)]) ).

cnf(3554,plain,
    product(product(a106,a107),a84) = product(a107,a106),
    inference('PARAMODULATE',[status(thm)],[434,152,theory(equality)]) ).

cnf(3560,plain,
    product(product(a107,a106),a84) = product(a106,a107),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,3554,theory(equality)]) ).

cnf(3567,plain,
    product(a79,a80) = product(a80,product(a119,a80)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[435,1244,theory(equality)]),involutory_quandle,577,knot_80,742,theory(equality)]) ).

cnf(3575,plain,
    product(product(a110,a111),a119) = product(a111,a110),
    inference('PARAMODULATE',[status(thm)],[436,154,theory(equality)]) ).

cnf(3581,plain,
    product(product(a111,a110),a119) = product(a110,a111),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,3575,theory(equality)]) ).

cnf(3586,plain,
    product(product(a111,a112),a79) = product(a112,a111),
    inference('PARAMODULATE',[status(thm)],[437,155,theory(equality)]) ).

cnf(3595,plain,
    product(product(product(a111,a112),X),a79) = product(product(a112,a111),product(X,a79)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,3586,theory(equality)]) ).

cnf(3597,plain,
    product(a75,a114) = product(a77,product(a68,a114)),
    inference('PARAMODULATE',[status(thm)],[438,169,theory(equality)]) ).

cnf(3598,plain,
    product(a76,a77) = product(a77,product(a114,a77)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[438,1300,theory(equality)]),involutory_quandle,580,knot_77,751,theory(equality)]) ).

cnf(3606,plain,
    product(product(a123,a124),a75) = product(a124,a123),
    inference('PARAMODULATE',[status(thm)],[439,157,theory(equality)]) ).

cnf(3607,plain,
    product(product(a123,a122),a75) = product(a124,a115),
    inference('PARAMODULATE',[status(thm)],[439,1579,theory(equality)]) ).

cnf(3619,plain,
    product(product(X,product(a123,a124)),a75) = product(product(X,a75),product(a124,a123)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,3606,theory(equality)]) ).

cnf(3636,plain,
    product(a70,a109) = product(a72,product(a118,a109)),
    inference('PARAMODULATE',[status(thm)],[442,162,theory(equality)]) ).

cnf(3645,plain,
    product(product(X,a72),product(a118,a109)) = product(product(X,product(a118,a109)),product(a70,a109)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,3636,theory(equality)]) ).

cnf(3646,plain,
    product(a80,a109) = product(a82,product(a70,a109)),
    inference('PARAMODULATE',[status(thm)],[443,165,theory(equality)]) ).

cnf(3647,plain,
    product(product(a79,a108),a118) = product(a82,a72),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[443,1249,theory(equality)]),knot_72,588,theory(equality)]) ).

cnf(3648,plain,
    product(a81,a82) = product(a82,product(a109,a82)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[443,1386,theory(equality)]),involutory_quandle,585,knot_82,766,theory(equality)]) ).

cnf(3657,plain,
    product(a69,a118) = product(a71,product(a13,a118)),
    inference('PARAMODULATE',[status(thm)],[444,230,theory(equality)]) ).

cnf(3662,plain,
    product(product(X,product(a70,Y)),a118) = product(product(X,a118),product(a71,product(Y,a118))),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,444,theory(equality)]) ).

cnf(3668,plain,
    product(a81,a118) = product(a83,a108),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[445,161,theory(equality)]),164,theory(equality)]) ).

cnf(3669,plain,
    product(product(a80,a110),a118) = product(a83,a71),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[445,1385,theory(equality)]),knot_71,theory(equality)]) ).

cnf(3670,plain,
    product(a82,a83) = product(a83,product(a118,a83)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[445,1412,theory(equality)]),involutory_quandle,587,knot_83,772,theory(equality)]) ).

cnf(3680,plain,
    product(product(a106,a39),a118) = product(a109,a82),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[446,163,theory(equality)]),1232,theory(equality)]) ).

cnf(3681,plain,
    product(product(a108,a109),a118) = product(a109,a108),
    inference('PARAMODULATE',[status(thm)],[446,164,theory(equality)]) ).

cnf(3693,plain,
    product(product(a109,a108),a118) = product(a108,a109),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,3681,theory(equality)]) ).

cnf(3698,plain,
    product(a79,a70) = product(a81,a118),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[447,153,theory(equality)]),167,theory(equality)]) ).

cnf(3699,plain,
    product(a79,a70) = product(product(a80,a118),a71),
    inference('REWRITE',[status(thm)],[1440,3698,theory(equality)]) ).

cnf(3703,plain,
    product(a79,a70) = product(a83,a108),
    inference('REWRITE',[status(thm)],[3668,3698,theory(equality)]) ).

cnf(3714,plain,
    product(product(a79,a110),a70) = product(a82,product(a118,a109)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[443,3698,theory(equality)]),782,theory(equality)]) ).

cnf(3718,plain,
    product(product(X,a81),a118) = product(product(X,a118),product(a79,a70)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,3698,theory(equality)]) ).

cnf(3719,plain,
    product(product(a79,a70),a71) = product(a80,a118),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,3699,theory(equality)]) ).

cnf(3720,plain,
    product(product(a109,a110),a70) = product(a110,a109),
    inference('PARAMODULATE',[status(thm)],[448,166,theory(equality)]) ).

cnf(3721,plain,
    product(product(a109,a111),a70) = product(a110,a108),
    inference('PARAMODULATE',[status(thm)],[448,1263,theory(equality)]) ).

cnf(3723,plain,
    product(product(a111,a118),a70) = product(a108,a119),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[448,1400,theory(equality)]),1263,745,1488,theory(equality)]) ).

cnf(3734,plain,
    product(product(a118,a109),a70) = product(a119,a110),
    inference('PARAMODULATE',[status(thm)],[449,knot_110,theory(equality)]) ).

cnf(3735,plain,
    product(product(a118,a110),a70) = product(a119,a109),
    inference('PARAMODULATE',[status(thm)],[449,166,theory(equality)]) ).

cnf(3736,plain,
    product(product(a118,a111),a70) = product(a119,a108),
    inference('PARAMODULATE',[status(thm)],[449,1263,theory(equality)]) ).

cnf(3737,plain,
    product(product(a118,a108),a70) = product(a119,a111),
    inference('PARAMODULATE',[status(thm)],[449,1268,theory(equality)]) ).

cnf(3738,plain,
    product(product(a119,a118),a70) = product(a119,product(a70,a119)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[449,1400,theory(equality)]),1481,theory(equality)]) ).

cnf(3745,plain,
    product(product(a119,a110),a70) = product(a118,a109),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,3734,theory(equality)]) ).

cnf(3751,plain,
    product(product(a119,a109),a70) = product(a118,a110),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,3735,theory(equality)]) ).

cnf(3757,plain,
    product(product(a67,a68),a98) = product(a68,a67),
    inference('PARAMODULATE',[status(thm)],[450,168,theory(equality)]) ).

cnf(3766,plain,
    product(product(a68,a67),a98) = product(a67,a68),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,3757,theory(equality)]) ).

cnf(3773,plain,
    product(a75,a76) = product(a76,product(a68,a76)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[451,1539,theory(equality)]),involutory_quandle,593,knot_76,790,theory(equality)]) ).

cnf(3782,plain,
    product(product(a114,a121),a68) = a124,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[452,knot_122,theory(equality)]),1589,theory(equality)]) ).

cnf(3784,plain,
    product(product(a114,a122),a68) = product(a115,a121),
    inference('PARAMODULATE',[status(thm)],[452,171,theory(equality)]) ).

cnf(3792,plain,
    product(a124,a68) = product(a114,a121),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,3782,theory(equality)]) ).

cnf(3793,plain,
    product(a114,a121) = product(product(a121,a114),a76),
    inference('REWRITE',[status(thm)],[1313,3792,theory(equality)]) ).

cnf(3806,plain,
    product(product(a114,a124),a68) = product(a115,product(a114,a121)),
    inference('PARAMODULATE',[status(thm)],[452,3792,theory(equality)]) ).

cnf(3815,plain,
    product(product(a115,a121),a68) = product(a114,a122),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,3784,theory(equality)]) ).

cnf(3820,plain,
    product(product(a121,a115),a68) = product(a122,a114),
    inference('PARAMODULATE',[status(thm)],[453,170,theory(equality)]) ).

cnf(3821,plain,
    product(product(a121,a122),a68) = product(a122,a121),
    inference('PARAMODULATE',[status(thm)],[453,171,theory(equality)]) ).

cnf(3822,plain,
    product(product(a121,a123),a68) = product(a122,product(a121,a114)),
    inference('PARAMODULATE',[status(thm)],[453,1144,theory(equality)]) ).

cnf(3823,plain,
    product(product(a121,a124),a68) = product(a122,product(a114,a121)),
    inference('PARAMODULATE',[status(thm)],[453,3792,theory(equality)]) ).

cnf(3829,plain,
    product(product(a122,a114),a68) = product(a121,a115),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,3820,theory(equality)]) ).

cnf(3835,plain,
    product(product(a122,a121),a68) = product(a121,a122),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,3821,theory(equality)]) ).

cnf(3841,plain,
    product(product(a66,a67),a92) = product(a67,a66),
    inference('PARAMODULATE',[status(thm)],[454,172,theory(equality)]) ).

cnf(3849,plain,
    product(product(a67,a66),X) = product(product(product(a66,a67),X),product(a92,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,3841,theory(equality)]) ).

cnf(3855,plain,
    product(a98,a99) = product(product(a100,a90),a124),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[455,1652,theory(equality)]),727,3487,involutory_quandle,597,knot_99,802,theory(equality)]) ).

cnf(3865,plain,
    product(product(a125,a126),a65) = product(a126,a125),
    inference('PARAMODULATE',[status(thm)],[456,174,theory(equality)]) ).

cnf(3871,plain,
    product(product(a126,a125),a65) = product(a125,a126),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,3865,theory(equality)]) ).

cnf(3877,plain,
    product(a63,a64) = product(a64,product(a125,a41)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[457,1698,theory(equality)]),1686,involutory_quandle,599,knot_64,808,theory(equality)]) ).

cnf(3897,plain,
    product(a94,a64) = product(a96,product(a125,a41)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[459,176,theory(equality)]),1686,theory(equality)]) ).

cnf(3909,plain,
    product(product(a62,a127),a96) = product(a63,a128),
    inference('PARAMODULATE',[status(thm)],[460,knot_128,theory(equality)]) ).

cnf(3911,plain,
    product(product(a62,a64),a96) = product(a63,product(a62,a128)),
    inference('PARAMODULATE',[status(thm)],[460,1697,theory(equality)]) ).

cnf(3912,plain,
    product(product(a62,a129),a96) = product(a64,a63),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[460,1855,theory(equality)]),1698,theory(equality)]) ).

cnf(3929,plain,
    product(product(a127,a62),a96) = product(a128,a63),
    inference('PARAMODULATE',[status(thm)],[461,knot_63,theory(equality)]) ).

cnf(3930,plain,
    product(product(a127,a128),a96) = product(a128,a127),
    inference('PARAMODULATE',[status(thm)],[461,179,theory(equality)]) ).

cnf(3931,plain,
    product(product(a125,a41),a96) = product(a129,a128),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[461,1697,theory(equality)]),1856,1686,theory(equality)]) ).

cnf(3939,plain,
    product(product(a128,a63),a96) = product(a127,a62),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,3929,theory(equality)]) ).

cnf(3942,plain,
    product(product(a128,a63),X) = product(product(product(a127,a62),X),product(a96,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,3929,theory(equality)]) ).

cnf(3945,plain,
    product(product(a128,a127),a96) = product(a127,a128),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,3930,theory(equality)]) ).

cnf(3998,plain,
    product(product(a42,a128),a62) = product(a43,a129),
    inference('PARAMODULATE',[status(thm)],[466,knot_129,theory(equality)]) ).

cnf(4081,plain,
    product(product(a139,a36),a47) = product(a140,a37),
    inference('PARAMODULATE',[status(thm)],[470,knot_37,theory(equality)]) ).

cnf(4082,plain,
    product(product(a139,a37),a47) = product(a140,a36),
    inference('PARAMODULATE',[status(thm)],[470,187,theory(equality)]) ).

cnf(4096,plain,
    product(product(a140,a36),a47) = product(a139,a37),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,4082,theory(equality)]) ).

cnf(4198,plain,
    product(product(a103,a104),a30) = product(a107,a5),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[479,196,theory(equality)]),1222,3541,theory(equality)]) ).

cnf(4200,plain,
    product(a103,a30) = product(a105,product(a85,a105)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[479,1196,theory(equality)]),151,theory(equality)]) ).

cnf(4206,plain,
    product(product(a107,a31),a5) = product(a103,a104),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,4198,theory(equality)]),1064,theory(equality)]) ).

cnf(4341,plain,
    product(product(a19,a133),a26) = product(a20,a134),
    inference('PARAMODULATE',[status(thm)],[490,knot_134,theory(equality)]) ).

cnf(4342,plain,
    product(product(a19,a20),a26) = product(a20,a19),
    inference('PARAMODULATE',[status(thm)],[490,208,theory(equality)]) ).

cnf(4356,plain,
    product(product(a20,a19),a26) = product(a19,a20),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,4342,theory(equality)]) ).

cnf(4449,plain,
    product(product(a18,a132),a58) = product(a19,a133),
    inference('PARAMODULATE',[status(thm)],[495,knot_133,theory(equality)]) ).

cnf(4507,plain,
    product(product(a16,a17),a29) = product(a17,a16),
    inference('PARAMODULATE',[status(thm)],[498,216,theory(equality)]) ).

cnf(4539,plain,
    product(product(a17,a16),a29) = product(a16,a17),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,4507,theory(equality)]) ).

cnf(4550,plain,
    product(product(a135,a17),a29) = product(a136,a16),
    inference('PARAMODULATE',[status(thm)],[500,216,theory(equality)]) ).

cnf(4561,plain,
    product(product(a136,a16),a29) = product(a135,a17),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,4550,theory(equality)]) ).

cnf(4624,plain,
    product(a67,a32) = product(a69,product(a98,a32)),
    inference('PARAMODULATE',[status(thm)],[503,168,theory(equality)]) ).

cnf(4635,plain,
    product(a72,a32) = product(a74,product(a82,a32)),
    inference('PARAMODULATE',[status(thm)],[504,159,theory(equality)]) ).

cnf(4793,plain,
    product(product(a139,a11),a23) = product(a1,product(a44,a1)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[509,2187,theory(equality)]),1929,theory(equality)]) ).

cnf(4843,plain,
    product(a76,a13) = product(a78,a113),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[513,156,theory(equality)]),232,theory(equality)]) ).

cnf(4850,plain,
    product(product(a76,a13),a33) = product(a79,a112),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[476,4843,theory(equality)]),195,theory(equality)]) ).

cnf(4857,plain,
    product(product(a111,a13),a32) = product(a114,a77),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[514,231,theory(equality)]),968,1288,theory(equality)]) ).

cnf(4871,plain,
    product(product(a114,a77),a32) = product(a111,a13),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,4857,theory(equality)]) ).

cnf(4929,plain,
    product(product(a11,a12),a21) = product(a12,a11),
    inference('PARAMODULATE',[status(thm)],[517,235,theory(equality)]) ).

cnf(4941,plain,
    product(a9,a37) = product(a11,a135),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[518,knot_135,theory(equality)]),242,theory(equality)]) ).

cnf(4943,plain,
    product(product(a11,a135),a55) = product(a8,a37),
    inference('REWRITE',[status(thm)],[2757,4941,theory(equality)]) ).

cnf(4949,plain,
    product(product(a10,a135),a37) = product(a11,a134),
    inference('PARAMODULATE',[status(thm)],[518,239,theory(equality)]) ).

cnf(4957,plain,
    product(product(a11,a135),a37) = a9,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,4941,theory(equality)]) ).

cnf(4981,plain,
    product(product(a11,a134),a37) = product(a10,a135),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,4949,theory(equality)]) ).

cnf(5037,plain,
    product(product(a134,a28),a37) = product(a135,a27),
    inference('PARAMODULATE',[status(thm)],[521,237,theory(equality)]) ).

cnf(5128,plain,
    product(a28,a29) = product(a29,a16),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[528,2778,theory(equality)]),216,involutory_quandle,670,knot_29,1021,theory(equality)]) ).

cnf(5133,plain,
    product(product(a29,a16),a29) = a28,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,5128,theory(equality)]) ).

cnf(5141,plain,
    product(a16,a17) = product(a17,a28),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[498,5133,theory(equality)]),4539,2363,theory(equality)]) ).

cnf(5184,plain,
    product(product(a38,a39),a7) = product(a39,a38),
    inference('PARAMODULATE',[status(thm)],[532,250,theory(equality)]) ).

cnf(5200,plain,
    product(product(X,product(a38,a39)),a7) = product(product(X,a7),product(a39,a38)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,5184,theory(equality)]) ).

cnf(5201,plain,
    product(a4,a136) = product(a6,product(a39,a136)),
    inference('PARAMODULATE',[status(thm)],[533,254,theory(equality)]) ).

cnf(5231,plain,
    product(product(a2,a14),a39) = product(a5,product(a40,a39)),
    inference('PARAMODULATE',[status(thm)],[536,3226,theory(equality)]) ).

cnf(5299,plain,
    product(product(a79,a39),product(a70,a39)) = product(a84,a107),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[539,3703,theory(equality)]),258,involutory_quandle_02,theory(equality)]) ).

cnf(5432,plain,
    product(a104,a5) = product(a106,a31),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[544,knot_31,theory(equality)]),197,theory(equality)]) ).

cnf(5443,plain,
    product(product(a106,a31),a5) = a104,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,5432,theory(equality)]) ).

cnf(5466,plain,
    product(a1,a14) = product(a4,product(a2,a14)),
    inference('PARAMODULATE',[status(thm)],[545,3212,theory(equality)]) ).

cnf(5472,plain,
    product(a28,a14) = product(a30,product(a17,a14)),
    inference('PARAMODULATE',[status(thm)],[546,246,theory(equality)]) ).

cnf(5473,plain,
    product(product(a27,a14),product(a17,a14)) = product(a30,product(a38,a14)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[546,2645,theory(equality)]),involutory_quandle_02,theory(equality)]) ).

cnf(5474,plain,
    product(a29,a30) = product(a30,product(a14,a30)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[546,3042,theory(equality)]),involutory_quandle,688,knot_30,1075,theory(equality)]) ).

cnf(5484,plain,
    product(a40,a41) = product(a41,product(a14,a41)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[547,3063,theory(equality)]),involutory_quandle,689,knot_41,1078,theory(equality)]) ).

cnf(5490,plain,
    product(product(a72,a13),a32) = product(a75,product(product(a82,a13),a32)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[548,4635,theory(equality)]),644,theory(equality)]) ).

cnf(5504,plain,
    product(product(a100,a115),a14) = product(a101,a116),
    inference('PARAMODULATE',[status(thm)],[550,knot_116,theory(equality)]) ).

cnf(5508,plain,
    product(product(a100,a122),a14) = product(a101,a117),
    inference('PARAMODULATE',[status(thm)],[550,1598,theory(equality)]) ).

cnf(5515,plain,
    product(product(a101,a116),a14) = product(a100,a115),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,5504,theory(equality)]) ).

cnf(5534,plain,
    product(product(a115,a124),a14) = product(a116,product(a116,a117)),
    inference('PARAMODULATE',[status(thm)],[551,1618,theory(equality)]) ).

cnf(5560,plain,
    product(a39,a40) = product(a42,a14),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[552,3227,theory(equality)]),3400,knot_40,1093,3143,theory(equality)]) ).

cnf(5575,plain,
    product(a97,a14) = product(product(a96,a14),product(a39,a40)),
    inference('PARAMODULATE',[status(thm)],[420,5560,theory(equality)]) ).

cnf(5591,plain,
    product(a86,a4) = product(a88,product(a104,a4)),
    inference('PARAMODULATE',[status(thm)],[553,150,theory(equality)]) ).

cnf(5592,plain,
    product(product(a85,a105),a4) = product(a88,product(a30,a4)),
    inference('PARAMODULATE',[status(thm)],[553,1196,theory(equality)]) ).

cnf(5599,plain,
    product(product(a86,a14),a3) = product(a89,product(product(a104,a14),a3)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[549,5591,theory(equality)]),1073,theory(equality)]) ).

cnf(5604,plain,
    product(product(a102,a39),a4) = product(a103,a40),
    inference('PARAMODULATE',[status(thm)],[554,knot_40,theory(equality)]) ).

cnf(5638,plain,
    product(a1,a41) = product(a5,a14),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[555,3401,theory(equality)]),2913,278,theory(equality)]) ).

cnf(5651,plain,
    product(product(a1,a14),a40) = a5,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,5638,theory(equality)]),1079,theory(equality)]) ).

cnf(5678,plain,
    product(a5,a40) = product(a1,a14),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,5651,theory(equality)]) ).

cnf(5679,plain,
    product(product(product(a100,a1),a14),a40) = product(a102,a5),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[468,5651,theory(equality)]),550,theory(equality)]) ).

cnf(5683,plain,
    product(product(a1,a14),a136) = product(a6,product(a40,a136)),
    inference('PARAMODULATE',[status(thm)],[533,5678,theory(equality)]) ).

cnf(5692,plain,
    product(a63,a41) = product(a65,a126),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[556,175,theory(equality)]),277,theory(equality)]) ).

cnf(5702,plain,
    product(product(a63,a41),X) = product(product(a65,X),product(a126,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,5692,theory(equality)]) ).

cnf(5703,plain,
    product(product(a65,X),a126) = product(product(a63,a41),product(X,a126)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,5692,theory(equality)]) ).

cnf(5704,plain,
    product(product(X,a125),a65) = product(product(X,a126),product(a63,a41)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,5692,theory(equality)]),598,theory(equality)]) ).

cnf(5754,plain,
    product(a95,a42) = product(a97,product(a64,a42)),
    inference('PARAMODULATE',[status(thm)],[561,177,theory(equality)]) ).

cnf(5780,plain,
    product(product(a95,a2),a42) = product(a98,a66),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[563,5754,theory(equality)]),3259,1118,theory(equality)]) ).

cnf(5796,plain,
    product(a40,a2) = product(a42,product(a14,a2)),
    inference('PARAMODULATE',[status(thm)],[565,265,theory(equality)]) ).

cnf(5797,plain,
    product(product(a39,a14),a2) = product(a42,a1),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[565,3159,theory(equality)]),3212,theory(equality)]) ).

cnf(5811,plain,
    product(a91,a2) = product(a93,a125),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[567,147,theory(equality)]),knot_125,theory(equality)]) ).

cnf(5834,plain,
    product(a122,a123) = product(a123,product(a115,a123)),
    inference('PARAMODULATE',[status(thm)],[569,146,theory(equality)]) ).

cnf(5835,plain,
    product(a106,a107) = product(a107,product(a84,a107)),
    inference('PARAMODULATE',[status(thm)],[569,152,theory(equality)]) ).

cnf(5836,plain,
    product(a110,a111) = product(a111,product(a119,a111)),
    inference('PARAMODULATE',[status(thm)],[569,154,theory(equality)]) ).

cnf(5837,plain,
    product(a111,a112) = product(a112,product(a79,a112)),
    inference('PARAMODULATE',[status(thm)],[569,155,theory(equality)]) ).

cnf(5838,plain,
    product(a123,a124) = product(a124,product(a75,a124)),
    inference('PARAMODULATE',[status(thm)],[569,157,theory(equality)]) ).

cnf(5839,plain,
    product(a116,a117) = product(a117,product(a74,a117)),
    inference('PARAMODULATE',[status(thm)],[569,158,theory(equality)]) ).

cnf(5842,plain,
    product(a70,a71) = product(a71,product(a119,a118)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,162,theory(equality)]),1481,theory(equality)]) ).

cnf(5843,plain,
    product(a108,a109) = product(a109,product(a118,a109)),
    inference('PARAMODULATE',[status(thm)],[569,164,theory(equality)]) ).

cnf(5844,plain,
    product(a109,a110) = product(a110,product(a70,a110)),
    inference('PARAMODULATE',[status(thm)],[569,166,theory(equality)]) ).

cnf(5845,plain,
    product(a118,a119) = product(product(a119,a118),a70),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,167,theory(equality)]),3738,theory(equality)]) ).

cnf(5846,plain,
    product(a118,a119) = product(a119,product(a70,a119)),
    inference('REWRITE',[status(thm)],[3738,5845,theory(equality)]) ).

cnf(5847,plain,
    product(a67,a68) = product(a68,product(a98,a68)),
    inference('PARAMODULATE',[status(thm)],[569,168,theory(equality)]) ).

cnf(5848,plain,
    product(a114,a115) = product(a115,product(a68,a115)),
    inference('PARAMODULATE',[status(thm)],[569,170,theory(equality)]) ).

cnf(5849,plain,
    product(a121,a122) = product(a122,product(a68,a122)),
    inference('PARAMODULATE',[status(thm)],[569,171,theory(equality)]) ).

cnf(5850,plain,
    product(a66,a67) = product(a67,product(a92,a67)),
    inference('PARAMODULATE',[status(thm)],[569,172,theory(equality)]) ).

cnf(5851,plain,
    product(a125,a126) = product(product(a127,a63),a41),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,174,theory(equality)]),1114,5692,theory(equality)]) ).

cnf(5852,plain,
    product(a62,a63) = product(a63,product(a96,a63)),
    inference('PARAMODULATE',[status(thm)],[569,178,theory(equality)]) ).

cnf(5853,plain,
    product(a127,a128) = product(a128,product(a96,a128)),
    inference('PARAMODULATE',[status(thm)],[569,179,theory(equality)]) ).

cnf(5855,plain,
    product(a137,a138) = product(a138,product(a51,a138)),
    inference('PARAMODULATE',[status(thm)],[569,182,theory(equality)]) ).

cnf(5857,plain,
    product(a128,a129) = product(a129,product(a62,a129)),
    inference('PARAMODULATE',[status(thm)],[569,185,theory(equality)]) ).

cnf(5868,plain,
    product(a20,a21) = product(a21,product(a35,a21)),
    inference('PARAMODULATE',[status(thm)],[569,206,theory(equality)]) ).

cnf(5891,plain,
    product(a38,a39) = product(a39,product(a7,a39)),
    inference('PARAMODULATE',[status(thm)],[569,250,theory(equality)]) ).

cnf(5893,plain,
    product(a4,a5) = product(product(a2,a14),a39),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,254,theory(equality)]),5231,3143,theory(equality)]) ).

cnf(5894,plain,
    product(a4,a5) = product(a5,product(a40,a39)),
    inference('REWRITE',[status(thm)],[5231,5893,theory(equality)]) ).

cnf(5898,plain,
    product(a30,a31) = product(a31,product(a5,a31)),
    inference('PARAMODULATE',[status(thm)],[569,260,theory(equality)]) ).

cnf(5924,plain,
    product(a124,a115) = product(a115,a123),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,knot_123,theory(equality)]),1589,theory(equality)]) ).

cnf(5925,plain,
    product(a115,a123) = product(a122,product(a75,a115)),
    inference('REWRITE',[status(thm)],[1311,5924,theory(equality)]) ).

cnf(5927,plain,
    product(product(a123,a122),a75) = product(a115,a123),
    inference('REWRITE',[status(thm)],[3607,5924,theory(equality)]) ).

cnf(5931,plain,
    product(product(a119,a110),a119) = product(a119,a111),
    inference('PARAMODULATE',[status(thm)],[569,knot_111,theory(equality)]) ).

cnf(5932,plain,
    product(product(a119,a111),a119) = product(a119,a110),
    inference('PARAMODULATE',[status(thm)],[569,154,theory(equality)]) ).

cnf(5933,plain,
    product(product(a79,a111),a79) = product(a79,a112),
    inference('PARAMODULATE',[status(thm)],[569,knot_112,theory(equality)]) ).

cnf(5934,plain,
    product(product(a79,a112),a79) = product(a79,a111),
    inference('PARAMODULATE',[status(thm)],[569,155,theory(equality)]) ).

cnf(5936,plain,
    product(product(a75,a124),a75) = product(a75,a123),
    inference('PARAMODULATE',[status(thm)],[569,157,theory(equality)]) ).

cnf(5941,plain,
    product(product(a111,a108),a118) = product(a109,a72),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,knot_72,theory(equality)]),588,1488,theory(equality)]) ).

cnf(5942,plain,
    product(product(a118,a108),a118) = product(a118,a109),
    inference('PARAMODULATE',[status(thm)],[569,knot_109,theory(equality)]) ).

cnf(5943,plain,
    product(product(a118,a109),a118) = product(a118,a108),
    inference('PARAMODULATE',[status(thm)],[569,164,theory(equality)]) ).

cnf(5944,plain,
    product(product(a70,a109),a70) = product(a70,a110),
    inference('PARAMODULATE',[status(thm)],[569,knot_110,theory(equality)]) ).

cnf(5945,plain,
    product(product(a70,a110),a70) = product(a70,a109),
    inference('PARAMODULATE',[status(thm)],[569,166,theory(equality)]) ).

cnf(5948,plain,
    product(product(a68,a114),a68) = product(a68,a115),
    inference('PARAMODULATE',[status(thm)],[569,knot_115,theory(equality)]) ).

cnf(5949,plain,
    product(product(a68,a121),a68) = product(a68,a122),
    inference('PARAMODULATE',[status(thm)],[569,knot_122,theory(equality)]) ).

cnf(5954,plain,
    product(product(a90,a124),a92) = product(a92,a98),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,173,theory(equality)]),3487,theory(equality)]) ).

cnf(5955,plain,
    product(product(a65,a125),a65) = product(a63,a41),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,knot_126,theory(equality)]),5692,theory(equality)]) ).

cnf(5956,plain,
    product(product(a63,a41),a65) = product(a65,a125),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,174,theory(equality)]),5692,theory(equality)]) ).

cnf(5957,plain,
    product(product(a125,a126),a41) = product(a127,a63),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,175,theory(equality)]),701,1686,theory(equality)]) ).

cnf(5959,plain,
    product(product(a96,a62),a96) = product(a96,a63),
    inference('PARAMODULATE',[status(thm)],[569,knot_63,theory(equality)]) ).

cnf(5961,plain,
    product(product(a96,a63),a96) = product(a96,a62),
    inference('PARAMODULATE',[status(thm)],[569,178,theory(equality)]) ).

cnf(5967,plain,
    product(product(a62,a128),a62) = product(a62,a129),
    inference('PARAMODULATE',[status(thm)],[569,knot_129,theory(equality)]) ).

cnf(5985,plain,
    product(product(a138,a132),a138) = product(a138,a131),
    inference('PARAMODULATE',[status(thm)],[569,201,theory(equality)]) ).

cnf(5993,plain,
    product(product(a26,a19),a26) = product(a26,a20),
    inference('PARAMODULATE',[status(thm)],[569,knot_20,theory(equality)]) ).

cnf(5995,plain,
    product(product(a26,a20),a26) = product(a26,a19),
    inference('PARAMODULATE',[status(thm)],[569,208,theory(equality)]) ).

cnf(6023,plain,
    product(product(a37,a134),a37) = product(a37,a135),
    inference('PARAMODULATE',[status(thm)],[569,knot_135,theory(equality)]) ).

cnf(6055,plain,
    product(a108,a111) = product(a111,product(a70,a111)),
    inference('PARAMODULATE',[status(thm)],[569,1263,theory(equality)]) ).

cnf(6059,plain,
    product(product(a75,a115),a75) = product(a75,a122),
    inference('PARAMODULATE',[status(thm)],[569,1578,theory(equality)]) ).

cnf(6061,plain,
    a124 = product(a122,product(a75,a122)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,1579,theory(equality)]),1589,theory(equality)]) ).

cnf(6067,plain,
    product(product(a70,a108),a70) = product(a70,a111),
    inference('PARAMODULATE',[status(thm)],[569,1268,theory(equality)]) ).

cnf(6070,plain,
    product(a115,a124) = product(product(a115,a123),a122),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,1594,theory(equality)]),1596,1590,theory(equality)]) ).

cnf(6072,plain,
    product(product(a79,a70),a83) = product(a83,product(a106,a39)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,3703,theory(equality)]),1232,theory(equality)]) ).

cnf(6076,plain,
    product(product(a107,a106),a5) = product(a103,a30),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,1222,theory(equality)]),4200,1070,theory(equality)]) ).

cnf(6077,plain,
    product(product(a73,a109),a71) = product(a71,product(a79,a118)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,1350,theory(equality)]),1249,theory(equality)]) ).

cnf(6078,plain,
    product(product(a112,a111),a119) = product(a110,product(a80,a110)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,1276,theory(equality)]),746,theory(equality)]) ).

cnf(6080,plain,
    product(product(a79,a70),a81) = product(a81,product(a118,a81)),
    inference('PARAMODULATE',[status(thm)],[569,3698,theory(equality)]) ).

cnf(6083,plain,
    product(product(a70,a119),a71) = product(a71,product(a70,a71)),
    inference('PARAMODULATE',[status(thm)],[569,1400,theory(equality)]) ).

cnf(6084,plain,
    product(product(a79,a111),a83) = product(a83,product(a70,a83)),
    inference('PARAMODULATE',[status(thm)],[569,1413,theory(equality)]) ).

cnf(6085,plain,
    product(product(a121,a114),a123) = product(a123,product(a68,a123)),
    inference('PARAMODULATE',[status(thm)],[569,1144,theory(equality)]) ).

cnf(6116,plain,
    product(product(a2,a14),a5) = product(a5,product(a4,a5)),
    inference('PARAMODULATE',[status(thm)],[569,3227,theory(equality)]) ).

cnf(6125,plain,
    product(product(a111,a112),a33) = product(product(a114,a76),a13),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,4843,theory(equality)]),979,619,1288,theory(equality)]) ).

cnf(6126,plain,
    product(product(a106,a107),a39) = product(a112,a70),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,3703,theory(equality)]),knot_112,1270,682,1232,theory(equality)]) ).

cnf(6133,plain,
    product(product(a71,a108),a71) = product(a71,product(a110,a118)),
    inference('PARAMODULATE',[status(thm)],[569,1462,theory(equality)]) ).

cnf(6155,plain,
    product(product(a114,a121),a124) = product(a124,product(a68,a124)),
    inference('PARAMODULATE',[status(thm)],[569,3792,theory(equality)]) ).

cnf(6176,plain,
    product(product(a87,a86),a87) = product(a87,product(a87,a103)),
    inference('PARAMODULATE',[status(thm)],[569,3515,theory(equality)]) ).

cnf(6177,plain,
    product(product(a73,a118),a73) = product(a73,product(a116,a32)),
    inference('PARAMODULATE',[status(thm)],[569,1339,theory(equality)]) ).

cnf(6178,plain,
    product(product(a71,a13),a69) = product(a69,a120),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,1482,theory(equality)]),1399,theory(equality)]) ).

cnf(6179,plain,
    product(product(a69,a120),a69) = product(a71,a13),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,1499,theory(equality)]),1399,theory(equality)]) ).

cnf(6180,plain,
    product(product(a68,a124),a68) = product(a68,product(a114,a121)),
    inference('PARAMODULATE',[status(thm)],[569,3792,theory(equality)]) ).

cnf(6212,plain,
    product(product(a75,a114),a77) = product(a77,product(product(a68,a114),a77)),
    inference('PARAMODULATE',[status(thm)],[569,3597,theory(equality)]) ).

cnf(6213,plain,
    product(product(a83,a109),a81) = product(a81,product(product(a118,a109),a81)),
    inference('PARAMODULATE',[status(thm)],[569,1411,theory(equality)]) ).

cnf(6214,plain,
    product(product(a70,a109),a72) = product(a72,product(product(a118,a109),a72)),
    inference('PARAMODULATE',[status(thm)],[569,3636,theory(equality)]) ).

cnf(6217,plain,
    product(product(a69,a118),a71) = product(a71,product(product(a13,a118),a71)),
    inference('PARAMODULATE',[status(thm)],[569,3657,theory(equality)]) ).

cnf(6254,plain,
    product(product(a1,a11),a140) = product(a140,product(product(a23,a11),a140)),
    inference('PARAMODULATE',[status(thm)],[569,2521,theory(equality)]) ).

cnf(6266,plain,
    product(product(a4,a136),a6) = product(a6,product(product(a39,a136),a6)),
    inference('PARAMODULATE',[status(thm)],[569,5201,theory(equality)]) ).

cnf(6273,plain,
    product(product(a91,a41),a89) = product(a89,product(product(a102,a14),a89)),
    inference('PARAMODULATE',[status(thm)],[569,1877,theory(equality)]) ).

cnf(6427,plain,
    product(product(a117,a116),a32) = product(product(a116,a32),product(a73,product(a116,a32))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,1330,theory(equality)]),505,theory(equality)]) ).

cnf(6428,plain,
    product(a81,product(a79,a118)) = product(product(a79,a118),product(product(a73,a109),a71)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,1245,theory(equality)]),6077,theory(equality)]) ).

cnf(6506,plain,
    product(a71,product(X,a70)) = product(product(product(a70,X),a70),product(product(a119,X),a70)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[303,569,theory(equality)]),784,theory(equality)]) ).

cnf(6738,plain,
    product(a118,product(a119,a118)) = product(a119,a71),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,1486,theory(equality)]),knot_119,1497,5842,theory(equality)]) ).

cnf(6757,plain,
    product(a39,product(a40,a39)) = product(a40,a5),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,3148,theory(equality)]),knot_40,3157,5894,theory(equality)]) ).

cnf(6773,plain,
    product(a86,product(a87,a103)) = product(product(a87,a103),product(a87,product(a87,a103))),
    inference('PARAMODULATE',[status(thm)],[569,3519,theory(equality)]) ).

cnf(6778,plain,
    product(product(a112,a111),product(a111,a112)) = product(product(a111,a112),product(a79,product(a111,a112))),
    inference('PARAMODULATE',[status(thm)],[569,3586,theory(equality)]) ).

cnf(6856,plain,
    product(product(a20,a138),product(a19,a138)) = product(product(a19,a138),product(a25,product(a19,a138))),
    inference('PARAMODULATE',[status(thm)],[569,2237,theory(equality)]) ).

cnf(6989,plain,
    product(a65,product(a65,a125)) = product(product(a63,a125),product(a41,a125)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,1675,theory(equality)]),involutory_quandle_02,5702,involutory_quandle_01,theory(equality)]) ).

cnf(6990,plain,
    product(a75,product(a75,a123)) = product(product(a75,a123),product(a124,a123)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,1312,theory(equality)]),involutory_quandle_01,theory(equality)]) ).

cnf(6991,plain,
    product(a68,product(a68,a121)) = product(product(a68,a121),product(a122,a121)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,1568,theory(equality)]),involutory_quandle_01,theory(equality)]) ).

cnf(6994,plain,
    product(a74,product(a74,a116)) = product(product(a74,a116),product(a117,a116)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,1329,theory(equality)]),involutory_quandle_01,theory(equality)]) ).

cnf(6996,plain,
    product(product(product(a68,a115),a123),product(a68,a115)) = product(product(a68,a115),product(a121,a115)),
    inference('PARAMODULATE',[status(thm)],[569,3470,theory(equality)]) ).

cnf(6999,plain,
    product(a79,product(a79,a111)) = product(product(a79,a111),product(a112,a111)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,1277,theory(equality)]),involutory_quandle_01,theory(equality)]) ).

cnf(7000,plain,
    product(a119,product(a119,a110)) = product(product(a119,a110),product(a111,a110)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,1264,theory(equality)]),involutory_quandle_01,theory(equality)]) ).

cnf(7003,plain,
    product(a84,product(a84,a106)) = product(product(a84,a106),product(a107,a106)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,1223,theory(equality)]),involutory_quandle_01,theory(equality)]) ).

cnf(7005,plain,
    product(a87,product(a87,a103)) = product(a86,a103),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,1209,theory(equality)]),732,involutory_quandle_01,theory(equality)]) ).

cnf(7006,plain,
    product(product(a87,a86),a87) = product(a86,a103),
    inference('REWRITE',[status(thm)],[6176,7005,theory(equality)]) ).

cnf(7007,plain,
    product(a86,product(a87,a103)) = product(product(a87,a103),product(a86,a103)),
    inference('REWRITE',[status(thm)],[6773,7005,theory(equality)]) ).

cnf(7031,plain,
    product(a109,product(a109,a81)) = product(product(a109,a82),a81),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,1386,theory(equality)]),involutory_quandle_02,involutory_quandle_01,theory(equality)]) ).

cnf(7036,plain,
    product(a119,product(a119,a79)) = product(product(a119,a80),a79),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,1244,theory(equality)]),involutory_quandle_02,involutory_quandle_01,theory(equality)]) ).

cnf(7038,plain,
    product(a68,product(a68,a114)) = product(product(a68,a114),product(a115,a114)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,1557,theory(equality)]),involutory_quandle_01,theory(equality)]) ).

cnf(7048,plain,
    product(a70,product(a70,a109)) = product(product(a70,a109),product(a110,a109)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,1463,theory(equality)]),involutory_quandle_01,theory(equality)]) ).

cnf(7051,plain,
    product(a82,product(a82,a72)) = product(product(a82,a72),product(a73,a72)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,1351,theory(equality)]),involutory_quandle_01,theory(equality)]) ).

cnf(7088,plain,
    product(a7,product(a7,a38)) = product(product(a7,a38),product(a39,a38)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,2848,theory(equality)]),involutory_quandle_01,theory(equality)]) ).

cnf(7130,plain,
    product(a14,product(a14,a29)) = product(product(a14,a30),a29),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,3042,theory(equality)]),involutory_quandle_02,involutory_quandle_01,theory(equality)]) ).

cnf(7333,plain,
    product(product(a20,X),product(a19,X)) = product(product(a19,X),product(product(a26,X),product(a19,X))),
    inference('PARAMODULATE',[status(thm)],[569,349,theory(equality)]) ).

cnf(7560,plain,
    product(product(a115,a123),a124) = product(a124,product(a115,a124)),
    inference('PARAMODULATE',[status(thm)],[569,5924,theory(equality)]) ).

cnf(7563,plain,
    product(product(X,a124),a115) = product(product(X,a115),product(a115,a123)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,5924,theory(equality)]) ).

cnf(7574,plain,
    product(a115,product(a115,a123)) = product(a124,a123),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,5834,theory(equality)]),1595,involutory_quandle_01,theory(equality)]) ).

cnf(7579,plain,
    product(a84,product(a84,a107)) = product(product(a84,a106),a107),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,5835,theory(equality)]),involutory_quandle_02,involutory_quandle_01,theory(equality)]) ).

cnf(7584,plain,
    product(a119,product(a119,a111)) = product(product(a119,a110),a111),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,5836,theory(equality)]),involutory_quandle_02,involutory_quandle_01,theory(equality)]) ).

cnf(7589,plain,
    product(a79,product(a79,a112)) = product(product(a79,a111),a112),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,5837,theory(equality)]),involutory_quandle_02,involutory_quandle_01,theory(equality)]) ).

cnf(7591,plain,
    product(a100,product(a75,a124)) = product(product(product(a100,a123),a75),product(a123,a124)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[289,5838,theory(equality)]),581,727,theory(equality)]) ).

cnf(7596,plain,
    product(a75,product(a75,a124)) = product(product(a75,a123),a124),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,5838,theory(equality)]),involutory_quandle_02,involutory_quandle_01,theory(equality)]) ).

cnf(7601,plain,
    product(a74,product(a74,a117)) = product(product(a74,a116),a117),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,5839,theory(equality)]),involutory_quandle_02,involutory_quandle_01,theory(equality)]) ).

cnf(7622,plain,
    product(a118,product(a118,a109)) = product(product(a118,a108),a109),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,5843,theory(equality)]),involutory_quandle_02,involutory_quandle_01,theory(equality)]) ).

cnf(7627,plain,
    product(a70,product(a70,a110)) = product(product(a70,a109),a110),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,5844,theory(equality)]),involutory_quandle_02,involutory_quandle_01,theory(equality)]) ).

cnf(7648,plain,
    product(a68,product(a68,a115)) = product(product(a68,a114),a115),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,5848,theory(equality)]),involutory_quandle_02,involutory_quandle_01,theory(equality)]) ).

cnf(7653,plain,
    product(a68,product(a68,a122)) = product(product(a68,a121),a122),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,5849,theory(equality)]),involutory_quandle_02,involutory_quandle_01,theory(equality)]) ).

cnf(7664,plain,
    product(product(X,product(a127,a63)),a41) = product(product(X,a41),product(a125,a126)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,5851,theory(equality)]) ).

cnf(7700,plain,
    product(product(X,a129),product(a62,a129)) = product(product(X,product(a128,a129)),product(product(a62,a128),a129)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,5857,theory(equality)]),719,theory(equality)]) ).

cnf(7701,plain,
    product(a62,product(a62,a129)) = product(product(a62,a128),a129),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,5857,theory(equality)]),involutory_quandle_02,involutory_quandle_01,theory(equality)]) ).

cnf(7762,plain,
    product(a35,product(a35,a21)) = product(product(a35,a20),a21),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,5868,theory(equality)]),involutory_quandle_02,involutory_quandle_01,theory(equality)]) ).

cnf(7904,plain,
    product(a7,product(a7,a39)) = product(product(a7,a38),a39),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,5891,theory(equality)]),involutory_quandle_02,involutory_quandle_01,theory(equality)]) ).

cnf(7976,plain,
    product(a115,a124) = product(a122,product(product(a75,a115),a122)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,5925,theory(equality)]),6070,theory(equality)]) ).

cnf(7979,plain,
    product(product(product(a75,a115),a122),product(a75,a115)) = product(product(a75,a115),product(a115,a123)),
    inference('PARAMODULATE',[status(thm)],[569,5925,theory(equality)]) ).

cnf(8002,plain,
    product(product(product(a119,a111),X),a119) = product(product(a119,a110),product(X,a119)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,5932,theory(equality)]) ).

cnf(8009,plain,
    product(product(a79,a112),product(a79,a111)) = product(product(a79,a111),product(a79,product(a79,a111))),
    inference('PARAMODULATE',[status(thm)],[569,5933,theory(equality)]) ).

cnf(8023,plain,
    product(product(X,product(a75,a124)),a75) = product(product(X,a75),product(a75,a123)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,5936,theory(equality)]) ).

cnf(8053,plain,
    product(product(product(a118,a108),X),a118) = product(product(a118,a109),product(X,a118)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,5942,theory(equality)]) ).

cnf(8060,plain,
    product(product(a118,a108),product(a118,a109)) = product(product(a118,a109),product(product(a118,a108),a109)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,5943,theory(equality)]),7622,theory(equality)]) ).

cnf(8066,plain,
    product(product(a70,a110),product(a70,a109)) = product(product(a70,a109),product(a70,product(a70,a109))),
    inference('PARAMODULATE',[status(thm)],[569,5944,theory(equality)]) ).

cnf(8072,plain,
    product(product(a70,a109),product(a70,a110)) = product(product(a70,a110),product(product(a70,a109),a110)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,5945,theory(equality)]),7627,theory(equality)]) ).

cnf(8123,plain,
    product(product(product(a63,a125),a65),product(product(a41,a125),a65)) = product(a65,product(a63,a41)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,5955,theory(equality)]),involutory_quandle_02,6989,theory(equality)]) ).

cnf(8159,plain,
    product(product(a96,a62),X) = product(product(product(a96,a63),X),product(a96,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,5961,theory(equality)]) ).

cnf(8194,plain,
    product(product(a62,a129),product(a62,a128)) = product(product(a62,a128),product(a62,product(a62,a128))),
    inference('PARAMODULATE',[status(thm)],[569,5967,theory(equality)]) ).

cnf(8290,plain,
    product(product(a138,a131),X) = product(product(product(a138,a132),X),product(a138,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,5985,theory(equality)]) ).

cnf(8347,plain,
    product(product(a26,a19),X) = product(product(product(a26,a20),X),product(a26,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,5995,theory(equality)]) ).

cnf(8710,plain,
    product(product(X,a122),product(a75,a122)) = product(product(X,product(a75,a122)),a124),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,6061,theory(equality)]) ).

cnf(8711,plain,
    product(a75,product(a75,a122)) = product(product(a75,a115),a122),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,6061,theory(equality)]),1597,involutory_quandle_01,theory(equality)]) ).

cnf(8739,plain,
    product(product(a86,a103),a87) = product(a87,a86),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[432,575,theory(equality)]),150,theory(equality)]) ).

cnf(8762,plain,
    product(product(X,a110),a119) = product(product(X,a111),product(a119,a111)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,578,theory(equality)]) ).

cnf(8772,plain,
    product(product(a114,a121),a114) = product(a121,a77),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[580,3793,theory(equality)]),involutory_quandle_01,theory(equality)]) ).

cnf(8778,plain,
    product(product(a115,a123),a75) = product(a123,a122),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[581,1578,theory(equality)]),1590,theory(equality)]) ).

cnf(8779,plain,
    product(product(a91,a123),a75) = product(a92,product(a75,a124)),
    inference('PARAMODULATE',[status(thm)],[429,581,theory(equality)]) ).

cnf(8781,plain,
    product(product(a122,a123),a75) = product(a115,a124),
    inference('PARAMODULATE',[status(thm)],[581,1579,theory(equality)]) ).

cnf(8782,plain,
    product(product(X,a123),a75) = product(product(X,a124),product(a75,a124)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,581,theory(equality)]) ).

cnf(8797,plain,
    product(product(a119,a108),a118) = product(product(a118,a109),a72),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[584,1481,theory(equality)]),588,theory(equality)]) ).

cnf(8798,plain,
    product(product(a110,a108),a118) = product(product(a108,a109),a72),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[584,1462,theory(equality)]),588,theory(equality)]) ).

cnf(8808,plain,
    product(product(X,product(Y,a81)),a109) = product(product(X,a109),product(product(Y,a109),a82)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,585,theory(equality)]) ).

cnf(8813,plain,
    product(product(a118,a119),a118) = product(a119,a71),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[586,5845,theory(equality)]),involutory_quandle_01,theory(equality)]) ).

cnf(8828,plain,
    product(product(X,a108),a118) = product(product(X,a109),product(a118,a109)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,588,theory(equality)]) ).

cnf(8830,plain,
    product(product(a112,a118),a71) = product(a109,a81),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[588,3680,theory(equality)]),involutory_quandle,767,586,6126,682,theory(equality)]) ).

cnf(8831,plain,
    product(product(product(X,a111),a118),a71) = product(product(product(X,a108),a118),a72),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[588,586,theory(equality)]),588,584,586,1271,theory(equality)]) ).

cnf(8843,plain,
    product(product(a111,a109),a70) = product(a108,a110),
    inference('PARAMODULATE',[status(thm)],[590,1263,theory(equality)]) ).

cnf(8844,plain,
    product(product(a108,a109),a70) = product(a111,a110),
    inference('PARAMODULATE',[status(thm)],[590,1268,theory(equality)]) ).

cnf(8852,plain,
    product(product(a110,a118),a70) = product(a109,a119),
    inference('PARAMODULATE',[status(thm)],[591,166,theory(equality)]) ).

cnf(8853,plain,
    product(product(a79,a118),a70) = product(a80,product(a70,a119)),
    inference('PARAMODULATE',[status(thm)],[435,591,theory(equality)]) ).

cnf(8856,plain,
    product(product(a80,a110),product(a70,a119)) = product(a83,a119),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[591,1417,theory(equality)]),1400,1393,1493,theory(equality)]) ).

cnf(8861,plain,
    product(product(a109,a119),a118) = product(a110,a71),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[586,8852,theory(equality)]),involutory_quandle_01,theory(equality)]) ).

cnf(8877,plain,
    a121 = product(a114,a76),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[593,1578,theory(equality)]),170,171,theory(equality)]) ).

cnf(8878,plain,
    product(a77,a76) = product(a76,a121),
    inference('REWRITE',[status(thm)],[1300,8877,theory(equality)]) ).

cnf(8880,plain,
    product(product(a111,a112),a33) = product(a121,a13),
    inference('REWRITE',[status(thm)],[6125,8877,theory(equality)]) ).

cnf(8882,plain,
    a114 = product(a121,a76),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[593,1579,theory(equality)]),171,170,theory(equality)]) ).

cnf(8883,plain,
    product(product(a124,a123),a68) = product(product(product(a123,a124),a68),a76),
    inference('PARAMODULATE',[status(thm)],[593,3606,theory(equality)]) ).

cnf(8893,plain,
    product(a121,a114) = product(a114,a77),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,8877,theory(equality)]),knot_77,theory(equality)]) ).

cnf(8894,plain,
    product(a76,a77) = product(a77,product(a121,a114)),
    inference('REWRITE',[status(thm)],[3598,8893,theory(equality)]) ).

cnf(8895,plain,
    product(product(a111,a13),a32) = product(a121,a114),
    inference('REWRITE',[status(thm)],[4857,8893,theory(equality)]) ).

cnf(8896,plain,
    product(product(a121,a114),a32) = product(a111,a13),
    inference('REWRITE',[status(thm)],[4871,8893,theory(equality)]) ).

cnf(8904,plain,
    product(product(a114,X),a76) = product(a121,product(X,a76)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,8877,theory(equality)]) ).

cnf(8909,plain,
    product(product(a76,a121),a77) = product(a77,product(a76,a77)),
    inference('PARAMODULATE',[status(thm)],[569,8878,theory(equality)]) ).

cnf(8912,plain,
    product(product(X,a77),a76) = product(product(X,a76),product(a76,a121)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,8878,theory(equality)]) ).

cnf(8915,plain,
    a114 = product(product(a121,a114),a77),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[580,8882,theory(equality)]),involutory_quandle,theory(equality)]) ).

cnf(8917,plain,
    product(product(a121,X),a76) = product(a114,product(X,a76)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,8882,theory(equality)]) ).

cnf(8923,plain,
    product(product(a114,X),a77) = product(product(a121,a114),product(X,a77)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,8893,theory(equality)]) ).

cnf(8925,plain,
    product(product(a123,a114),a68) = product(product(a121,a114),a115),
    inference('PARAMODULATE',[status(thm)],[594,1144,theory(equality)]) ).

cnf(8954,plain,
    product(a65,product(a63,a41)) = product(product(a63,a41),product(a125,a126)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[598,5956,theory(equality)]),5703,8123,involutory_quandle_02,theory(equality)]) ).

cnf(8975,plain,
    product(product(X,a62),a96) = product(product(X,a63),product(a96,a63)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,602,theory(equality)]) ).

cnf(9026,plain,
    product(product(X,a128),a62) = product(product(X,a129),product(a62,a129)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,609,theory(equality)]) ).

cnf(9027,plain,
    product(product(X,a128),a62) = product(product(X,product(a128,a129)),product(product(a62,a128),a129)),
    inference('REWRITE',[status(thm)],[7700,9026,theory(equality)]) ).

cnf(9252,plain,
    product(product(a140,a37),a20) = product(product(product(a139,a36),a20),a48),
    inference('PARAMODULATE',[status(thm)],[635,4081,theory(equality)]) ).

cnf(9335,plain,
    product(product(a29,a13),a32) = product(a30,product(a32,a14)),
    inference('PARAMODULATE',[status(thm)],[546,644,theory(equality)]) ).

cnf(9341,plain,
    product(a113,a32) = product(product(a112,a13),a14),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[644,2054,theory(equality)]),232,theory(equality)]) ).

cnf(9342,plain,
    product(a112,a32) = product(a114,a14),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[644,2049,theory(equality)]),involutory_quandle_01,theory(equality)]) ).

cnf(9366,plain,
    product(a111,a13) = product(product(a123,a32),a69),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[645,1144,theory(equality)]),8896,theory(equality)]) ).

cnf(9367,plain,
    product(product(a73,a13),product(a115,a32)) = product(product(a77,a32),a69),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[645,1299,theory(equality)]),3097,theory(equality)]) ).

cnf(9370,plain,
    product(a123,a32) = product(product(a111,a13),a69),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[645,1149,theory(equality)]),8896,theory(equality)]) ).

cnf(9372,plain,
    product(product(a115,a121),a32) = product(product(product(a114,a122),a32),a69),
    inference('PARAMODULATE',[status(thm)],[645,3784,theory(equality)]) ).

cnf(9407,plain,
    product(product(X,product(Y,a32)),a118) = product(product(X,a118),product(product(Y,a117),a32)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,647,theory(equality)]) ).

cnf(9412,plain,
    product(product(product(a112,a119),a13),a32) = product(a114,a121),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[648,2049,theory(equality)]),657,theory(equality)]) ).

cnf(9418,plain,
    product(product(a110,a13),a32) = product(product(a121,a114),a121),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[648,8895,theory(equality)]),154,657,theory(equality)]) ).

cnf(9526,plain,
    product(a116,a32) = product(a112,a70),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[654,2055,theory(equality)]),involutory_quandle_01,3133,652,theory(equality)]) ).

cnf(9527,plain,
    product(product(a106,a107),a39) = product(a116,a32),
    inference('REWRITE',[status(thm)],[6126,9526,theory(equality)]) ).

cnf(9528,plain,
    product(a79,a112) = product(a73,a70),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[654,3086,theory(equality)]),involutory_quandle_01,4850,652,theory(equality)]) ).

cnf(9531,plain,
    product(product(a79,a111),a79) = product(a73,a70),
    inference('REWRITE',[status(thm)],[5933,9528,theory(equality)]) ).

cnf(9532,plain,
    product(product(a73,a70),a79) = product(a79,a111),
    inference('REWRITE',[status(thm)],[5934,9528,theory(equality)]) ).

cnf(9535,plain,
    product(a79,product(a73,a70)) = product(product(a79,a111),a112),
    inference('REWRITE',[status(thm)],[7589,9528,theory(equality)]) ).

cnf(9540,plain,
    product(product(a73,a70),product(a79,a111)) = product(product(a79,a111),product(a79,product(a79,a111))),
    inference('REWRITE',[status(thm)],[8009,9528,theory(equality)]) ).

cnf(9553,plain,
    product(product(a116,a32),a70) = a112,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,9526,theory(equality)]) ).

cnf(9555,plain,
    product(product(a116,a112),product(a32,a112)) = product(a112,product(a70,a112)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,9526,theory(equality)]),involutory_quandle_02,theory(equality)]) ).

cnf(9558,plain,
    product(product(a116,a117),a32) = product(a109,a81),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[586,9526,theory(equality)]),8830,647,theory(equality)]) ).

cnf(9562,plain,
    product(product(a70,a112),a70) = product(a70,product(a116,a32)),
    inference('PARAMODULATE',[status(thm)],[569,9526,theory(equality)]) ).

cnf(9565,plain,
    product(product(X,a112),a70) = product(product(X,a70),product(a116,a32)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,9526,theory(equality)]) ).

cnf(9566,plain,
    product(product(a73,a112),product(a70,a112)) = a79,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,9528,theory(equality)]),involutory_quandle_02,theory(equality)]) ).

cnf(9567,plain,
    product(product(a73,a118),a70) = product(a80,product(a112,a119)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[435,9528,theory(equality)]),591,theory(equality)]) ).

cnf(9568,plain,
    product(a80,a112) = product(product(a73,a70),product(a119,a112)),
    inference('PARAMODULATE',[status(thm)],[294,9528,theory(equality)]) ).

cnf(9569,plain,
    product(product(a73,a70),X) = product(product(a79,X),product(a112,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,9528,theory(equality)]) ).

cnf(9571,plain,
    product(a79,product(a79,a111)) = product(product(a73,a108),a70),
    inference('REWRITE',[status(thm)],[6999,1274,9569,theory(equality)]) ).

cnf(9572,plain,
    product(product(a73,a70),product(a79,a111)) = product(product(a79,a111),product(product(a73,a108),a70)),
    inference('REWRITE',[status(thm)],[9540,9571,theory(equality)]) ).

cnf(9573,plain,
    product(product(a79,X),a112) = product(product(a73,a70),product(X,a112)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,9528,theory(equality)]) ).

cnf(9574,plain,
    product(a79,product(a73,a70)) = product(product(a73,a70),product(a111,a112)),
    inference('REWRITE',[status(thm)],[9535,9573,theory(equality)]) ).

cnf(9577,plain,
    product(product(product(a108,a73),a70),a79) = product(a112,product(a79,a111)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[437,9532,theory(equality)]),1273,theory(equality)]) ).

cnf(9602,plain,
    product(product(product(X,a13),Y),a120) = product(product(product(X,a119),a13),product(Y,a120)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,657,theory(equality)]) ).

cnf(9640,plain,
    product(product(X,a134),a37) = product(product(X,a135),product(a37,a135)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,663,theory(equality)]) ).

cnf(9645,plain,
    product(product(a23,a11),a140) = product(product(a21,a11),a47),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[664,2160,theory(equality)]),1007,theory(equality)]) ).

cnf(9647,plain,
    product(product(a1,a11),a140) = product(product(a139,product(a21,a11)),a47),
    inference('REWRITE',[status(thm)],[6254,470,9645,theory(equality)]) ).

cnf(9730,plain,
    product(product(a83,a38),a7) = product(a84,product(a7,a39)),
    inference('PARAMODULATE',[status(thm)],[539,674,theory(equality)]) ).

cnf(9836,plain,
    product(product(a103,a30),a5) = product(product(a101,a32),a39),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[684,1890,theory(equality)]),1049,theory(equality)]) ).

cnf(9875,plain,
    product(product(a136,a17),a14) = product(product(product(a135,a16),a14),a30),
    inference('PARAMODULATE',[status(thm)],[688,2393,theory(equality)]) ).

cnf(9906,plain,
    product(product(a104,a14),a3) = product(product(a102,a14),a89),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[691,1208,theory(equality)]),1073,theory(equality)]) ).

cnf(9907,plain,
    product(product(a86,a14),a3) = product(product(a91,a41),a89),
    inference('REWRITE',[status(thm)],[5599,6273,9906,theory(equality)]) ).

cnf(9927,plain,
    product(product(a115,a123),a14) = product(product(a116,a117),a116),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[693,1618,theory(equality)]),5924,theory(equality)]) ).

cnf(9932,plain,
    product(a30,a4) = product(a32,a40),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[694,2966,theory(equality)]),involutory_quandle_01,theory(equality)]) ).

cnf(9933,plain,
    product(a31,a4) = product(product(a30,a39),a40),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[694,2972,theory(equality)]),255,theory(equality)]) ).

cnf(9936,plain,
    product(product(product(X,a39),a14),a3) = product(product(product(X,a14),a2),a42),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[689,694,theory(equality)]),1103,1073,theory(equality)]) ).

cnf(9942,plain,
    product(product(X,product(Y,a4)),a40) = product(product(X,a40),product(product(Y,a39),a4)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,694,theory(equality)]) ).

cnf(9954,plain,
    product(product(a101,a32),a40) = product(product(a103,a30),a4),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[468,9932,theory(equality)]),1099,theory(equality)]) ).

cnf(9995,plain,
    product(product(a67,a1),a42) = product(a64,a94),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[700,1633,theory(equality)]),274,1133,theory(equality)]) ).

cnf(10009,plain,
    product(product(product(a39,a126),a41),product(product(a14,a126),a41)) = product(a42,a127),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[701,3406,theory(equality)]),involutory_quandle_02,theory(equality)]) ).

cnf(10066,plain,
    product(a92,product(a126,a2)) = product(a98,a66),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[707,1713,theory(equality)]),5780,1139,theory(equality)]) ).

cnf(10067,plain,
    product(a100,a2) = product(product(product(a102,a14),a2),a42),
    inference('PARAMODULATE',[status(thm)],[707,1886,theory(equality)]) ).

cnf(10072,plain,
    product(product(a127,a63),a2) = product(product(product(a125,a126),a2),a42),
    inference('PARAMODULATE',[status(thm)],[707,5957,theory(equality)]) ).

cnf(10090,plain,
    product(a93,product(a98,a2)) = product(product(product(a90,a124),a2),a93),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[709,5954,theory(equality)]),567,theory(equality)]) ).

cnf(10106,plain,
    product(product(a90,a1),a42) = product(a87,a14),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1134,275,theory(equality)]),3178,theory(equality)]) ).

cnf(10109,plain,
    product(product(a100,a1),a42) = product(a103,a14),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1134,1876,theory(equality)]),3199,theory(equality)]) ).

cnf(10110,plain,
    product(product(a95,a1),a42) = product(product(a93,a126),a3),
    inference('PARAMODULATE',[status(thm)],[1134,1713,theory(equality)]) ).

cnf(10163,plain,
    product(product(a72,a70),X) = product(product(product(a70,a111),X),product(a119,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1404,theory(equality)]) ).

cnf(10176,plain,
    product(product(a109,a110),a13) = product(product(a110,a13),product(a69,product(a110,a13))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,1477,theory(equality)]),involutory_quandle_02,theory(equality)]) ).

cnf(10194,plain,
    product(product(product(a116,a117),X),a74) = product(product(a117,a116),product(X,a74)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1620,theory(equality)]) ).

cnf(10195,plain,
    product(product(X,product(a116,a117)),a74) = product(product(X,a74),product(a117,a116)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1620,theory(equality)]) ).

cnf(10265,plain,
    product(product(a80,a13),a32) = product(a77,a121),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,2035,theory(equality)]) ).

cnf(10287,plain,
    product(product(product(a113,a131),X),a34) = product(product(a112,a131),product(X,a34)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,2068,theory(equality)]) ).

cnf(10335,plain,
    product(product(product(a20,a138),X),a25) = product(product(a19,a138),product(X,a25)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,2242,theory(equality)]) ).

cnf(10337,plain,
    product(product(a19,a138),product(a20,a138)) = product(product(a20,a138),product(a25,product(a20,a138))),
    inference('PARAMODULATE',[status(thm)],[569,2242,theory(equality)]) ).

cnf(10400,plain,
    product(product(a71,a13),a32) = product(a68,a122),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,2563,theory(equality)]),644,theory(equality)]) ).

cnf(10531,plain,
    product(a106,a4) = product(product(a105,a39),a40),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[694,3024,theory(equality)]),involutory_quandle_01,theory(equality)]) ).

cnf(10628,plain,
    product(product(X,a1),product(a14,a2)) = product(product(X,product(a14,a2)),product(a4,a2)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,3219,theory(equality)]) ).

cnf(10681,plain,
    product(a75,product(a75,a115)) = product(product(a75,a115),a123),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,3482,theory(equality)]),involutory_quandle_01,theory(equality)]) ).

cnf(10702,plain,
    product(product(X,product(a107,a106)),a84) = product(product(X,a84),product(a106,a107)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,3560,theory(equality)]) ).

cnf(10708,plain,
    product(a119,product(a119,a80)) = product(product(a119,a79),a80),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,3567,theory(equality)]),involutory_quandle_02,involutory_quandle_01,theory(equality)]) ).

cnf(10712,plain,
    product(product(product(a111,a110),X),a119) = product(product(a110,a111),product(X,a119)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,3581,theory(equality)]) ).

cnf(10713,plain,
    product(product(X,product(a111,a110)),a119) = product(product(X,a119),product(a110,a111)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,3581,theory(equality)]) ).

cnf(10739,plain,
    product(a109,product(a109,a82)) = product(product(a109,a81),a82),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,3648,theory(equality)]),involutory_quandle_02,involutory_quandle_01,theory(equality)]) ).

cnf(10741,plain,
    product(product(product(a80,a108),a118),product(product(a108,a109),a72)) = product(product(a83,a109),a72),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[588,3669,theory(equality)]),584,8798,588,knot_109,716,involutory_quandle_02,theory(equality)]) ).

cnf(10752,plain,
    product(a118,product(a118,a83)) = product(product(a118,a82),a83),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,3670,theory(equality)]),involutory_quandle_02,involutory_quandle_01,theory(equality)]) ).

cnf(10764,plain,
    product(product(a80,a108),a118) = product(product(a82,a72),product(product(a118,a109),a72)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[584,3719,theory(equality)]),involutory_quandle_02,3714,782,588,theory(equality)]) ).

cnf(10770,plain,
    product(product(a110,a108),a70) = product(a109,a111),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,3721,theory(equality)]) ).

cnf(10780,plain,
    product(product(a109,a72),a70) = product(product(a108,a111),a119),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[590,3723,theory(equality)]),746,5941,588,theory(equality)]) ).

cnf(10825,plain,
    product(product(a67,a68),a92) = product(product(product(a68,a67),a92),a99),
    inference('PARAMODULATE',[status(thm)],[597,3766,theory(equality)]) ).

cnf(10836,plain,
    product(a68,product(a68,a76)) = product(product(a68,a75),a76),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,3773,theory(equality)]),involutory_quandle_02,involutory_quandle_01,theory(equality)]) ).

cnf(10893,plain,
    product(product(X,a127),a64) = product(product(X,product(a125,a41)),product(a63,a64)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,3877,theory(equality)]),1692,theory(equality)]) ).

cnf(10905,plain,
    product(product(a64,a63),a96) = product(a62,a129),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,3912,theory(equality)]) ).

cnf(10932,plain,
    product(product(a129,a128),a96) = product(a125,a41),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,3931,theory(equality)]) ).

cnf(10939,plain,
    product(product(X,product(a125,a41)),a96) = product(product(X,a96),product(a129,a128)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,3931,theory(equality)]) ).

cnf(10957,plain,
    product(product(X,product(a128,a127)),a96) = product(product(X,a96),product(a127,a128)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,3945,theory(equality)]) ).

cnf(11054,plain,
    product(product(a139,a37),a20) = product(product(product(a140,a36),a20),a48),
    inference('PARAMODULATE',[status(thm)],[635,4096,theory(equality)]) ).

cnf(11113,plain,
    product(a85,product(a85,a105)) = product(product(a85,a105),product(a103,a30)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,4200,theory(equality)]),involutory_quandle_01,theory(equality)]) ).

cnf(11366,plain,
    product(product(a135,a17),a14) = product(product(product(a136,a16),a14),a30),
    inference('PARAMODULATE',[status(thm)],[688,4561,theory(equality)]) ).

cnf(12070,plain,
    product(product(a1,a14),a39) = product(product(a2,a14),a5),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[536,5466,theory(equality)]),6116,5893,theory(equality)]) ).

cnf(12071,plain,
    product(product(a1,a14),a39) = product(a5,product(a4,a5)),
    inference('REWRITE',[status(thm)],[6116,12070,theory(equality)]) ).

cnf(12090,plain,
    product(a42,product(a14,a41)) = product(a39,a41),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[424,5484,theory(equality)]),1092,knot_04,1102,theory(equality)]) ).

cnf(12220,plain,
    product(a93,a126) = product(product(a98,a2),a65),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[702,5780,theory(equality)]),1137,involutory_quandle_01,10110,3252,involutory_quandle_02,theory(equality)]) ).

cnf(12252,plain,
    product(a70,product(a70,a119)) = product(a71,a119),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,5846,theory(equality)]),303,involutory_quandle_01,theory(equality)]) ).

cnf(12302,plain,
    product(product(a103,a30),a5) = product(a107,a106),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,6076,theory(equality)]) ).

cnf(12303,plain,
    product(a107,a106) = product(product(a101,a32),a39),
    inference('REWRITE',[status(thm)],[9836,12302,theory(equality)]) ).

cnf(12342,plain,
    product(product(a103,a86),a87) = product(product(a103,a104),a103),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[292,7005,theory(equality)]),3551,1209,3533,theory(equality)]) ).

cnf(12343,plain,
    product(product(a103,a104),a103) = product(a104,product(a87,a103)),
    inference('REWRITE',[status(thm)],[3533,12342,theory(equality)]) ).

cnf(12396,plain,
    product(a124,product(a115,a123)) = product(product(a115,a124),a123),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,7574,theory(equality)]),involutory_quandle_02,1589,involutory_quandle,722,theory(equality)]) ).

cnf(12438,plain,
    product(a121,a77) = product(a114,product(a121,a114)),
    inference('PARAMODULATE',[status(thm)],[569,8772,theory(equality)]) ).

cnf(12442,plain,
    product(product(X,product(a114,a121)),a114) = product(product(X,a114),product(a121,a77)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,8772,theory(equality)]) ).

cnf(12444,plain,
    product(product(a123,a122),a68) = product(product(product(a115,a123),a68),a76),
    inference('PARAMODULATE',[status(thm)],[593,8778,theory(equality)]) ).

cnf(12447,plain,
    product(product(product(a115,a123),X),a75) = product(product(a123,a122),product(X,a75)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,8778,theory(equality)]) ).

cnf(12448,plain,
    product(product(X,product(a115,a123)),a75) = product(product(X,a75),product(a123,a122)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,8778,theory(equality)]) ).

cnf(12450,plain,
    product(product(a118,a109),product(product(a118,a109),a72)) = product(product(a119,a109),a72),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[588,8813,theory(equality)]),584,8797,8053,involutory_quandle_02,theory(equality)]) ).

cnf(12457,plain,
    product(a109,a82) = product(product(product(a112,a108),a118),a72),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[584,8830,theory(equality)]),588,involutory_quandle,585,theory(equality)]) ).

cnf(12462,plain,
    product(product(a109,a81),product(a112,a118)) = product(product(a112,a118),product(a71,product(a112,a118))),
    inference('PARAMODULATE',[status(thm)],[569,8830,theory(equality)]) ).

cnf(12463,plain,
    product(product(a108,a110),a70) = product(a111,a109),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,8843,theory(equality)]) ).

cnf(12465,plain,
    product(product(a108,a110),a118) = product(product(product(a111,a109),a118),a71),
    inference('PARAMODULATE',[status(thm)],[586,8843,theory(equality)]) ).

cnf(12480,plain,
    a119 = product(a111,a112),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,8880,theory(equality)]),2493,theory(equality)]) ).

cnf(12481,plain,
    product(a119,a79) = product(a112,a111),
    inference('REWRITE',[status(thm)],[3586,12480,theory(equality)]) ).

cnf(12482,plain,
    product(a80,a79) = product(a79,product(a112,a111)),
    inference('REWRITE',[status(thm)],[1244,12481,theory(equality)]) ).

cnf(12486,plain,
    product(a119,product(a112,a111)) = product(product(a119,a80),a79),
    inference('REWRITE',[status(thm)],[7036,12481,theory(equality)]) ).

cnf(12487,plain,
    product(a119,product(a119,a80)) = product(product(a112,a111),a80),
    inference('REWRITE',[status(thm)],[10708,12481,theory(equality)]) ).

cnf(12490,plain,
    product(product(a119,X),a79) = product(product(a112,a111),product(X,a79)),
    inference('REWRITE',[status(thm)],[3595,12480,theory(equality)]) ).

cnf(12493,plain,
    product(product(a112,a111),a119) = product(a119,a80),
    inference('REWRITE',[status(thm)],[6778,knot_80,12480,theory(equality)]) ).

cnf(12494,plain,
    product(a119,a80) = product(a110,product(a80,a110)),
    inference('REWRITE',[status(thm)],[6078,12493,theory(equality)]) ).

cnf(12499,plain,
    product(a79,product(a73,a70)) = product(a80,product(a112,a119)),
    inference('REWRITE',[status(thm)],[9574,9567,591,12480,theory(equality)]) ).

cnf(12506,plain,
    product(a119,a112) = a111,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,12480,theory(equality)]) ).

cnf(12507,plain,
    product(a80,a112) = product(product(a73,a108),a70),
    inference('REWRITE',[status(thm)],[9568,1274,12506,theory(equality)]) ).

cnf(12508,plain,
    product(a79,product(a79,a111)) = product(a80,a112),
    inference('REWRITE',[status(thm)],[9571,12507,theory(equality)]) ).

cnf(12509,plain,
    product(product(a73,a70),product(a79,a111)) = product(product(a79,a111),product(a80,a112)),
    inference('REWRITE',[status(thm)],[9572,12507,theory(equality)]) ).

cnf(12512,plain,
    product(a119,a111) = product(a111,product(a112,a111)),
    inference('PARAMODULATE',[status(thm)],[569,12480,theory(equality)]) ).

cnf(12513,plain,
    product(product(a112,a111),a112) = product(a112,a119),
    inference('PARAMODULATE',[status(thm)],[569,12480,theory(equality)]) ).

cnf(12515,plain,
    product(product(a111,X),a112) = product(a119,product(X,a112)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,12480,theory(equality)]) ).

cnf(12516,plain,
    product(product(X,a111),a112) = product(product(X,a112),a119),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,12480,theory(equality)]) ).

cnf(12517,plain,
    product(product(a119,a111),a79) = product(a112,a119),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[579,12481,theory(equality)]),12513,theory(equality)]) ).

cnf(12518,plain,
    product(a110,a79) = product(a112,product(a112,a111)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[437,12481,theory(equality)]),154,theory(equality)]) ).

cnf(12521,plain,
    a110 = product(a119,product(a112,a119)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,12506,theory(equality)]),154,theory(equality)]) ).

cnf(12524,plain,
    product(product(a119,X),a112) = product(a111,product(X,a112)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,12506,theory(equality)]) ).

cnf(12525,plain,
    product(product(X,a119),a112) = product(product(X,a112),a111),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,12506,theory(equality)]) ).

cnf(12598,plain,
    product(a106,a39) = product(product(a116,a108),product(a32,a108)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[682,9527,theory(equality)]),involutory_quandle_02,involutory_quandle_01,theory(equality)]) ).

cnf(12666,plain,
    product(product(a100,a91),a66) = a92,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,10066,theory(equality)]),1658,1685,theory(equality)]) ).

cnf(12675,plain,
    product(a92,a66) = product(a100,a91),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,12666,theory(equality)]) ).

cnf(12700,plain,
    product(product(X,a67),a92) = product(product(X,a66),product(a100,a91)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,12675,theory(equality)]),800,theory(equality)]) ).

cnf(12705,plain,
    product(a100,a42) = product(product(a103,a14),a2),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[702,10109,theory(equality)]),involutory_quandle_01,theory(equality)]) ).

cnf(12748,plain,
    product(product(product(a112,a110),a119),product(a110,a111)) = product(product(a119,a111),product(a80,a111)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[578,12493,theory(equality)]),10713,involutory_quandle_02,theory(equality)]) ).

cnf(12755,plain,
    product(product(a119,a80),product(a80,a110)) = a110,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,12494,theory(equality)]) ).

cnf(12761,plain,
    product(a80,product(a80,a110)) = product(product(a80,a110),product(a119,a80)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,12494,theory(equality)]),involutory_quandle_01,theory(equality)]) ).

cnf(12762,plain,
    product(product(a80,a112),product(a79,a111)) = a79,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,12508,theory(equality)]) ).

cnf(12763,plain,
    product(a79,product(a112,a119)) = product(a80,product(a80,a110)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[435,12508,theory(equality)]),154,435,742,theory(equality)]) ).

cnf(12764,plain,
    product(a79,product(a112,a119)) = product(product(a80,a110),product(a119,a80)),
    inference('REWRITE',[status(thm)],[12761,12763,theory(equality)]) ).

cnf(12768,plain,
    product(product(a79,X),product(a79,a111)) = product(product(a80,a112),product(X,product(a79,a111))),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,12508,theory(equality)]) ).

cnf(12770,plain,
    product(product(a112,a119),a79) = product(a119,a111),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,12517,theory(equality)]) ).

cnf(12771,plain,
    a112 = product(product(a119,a110),a80),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[577,12517,theory(equality)]),5932,involutory_quandle_01,theory(equality)]) ).

cnf(12772,plain,
    product(product(a110,a111),a79) = product(a112,product(a112,a119)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[437,12517,theory(equality)]),5836,theory(equality)]) ).

cnf(12778,plain,
    product(a112,a80) = product(a119,a110),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,12771,theory(equality)]) ).

cnf(12779,plain,
    product(a116,a32) = product(product(a118,a109),a81),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[589,12771,theory(equality)]),3745,9526,theory(equality)]) ).

cnf(12780,plain,
    product(product(a83,a109),a81) = product(a81,product(a116,a32)),
    inference('REWRITE',[status(thm)],[6213,12779,theory(equality)]) ).

cnf(12788,plain,
    product(a111,product(a110,a112)) = product(a112,product(a80,a112)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,12778,theory(equality)]),12524,theory(equality)]) ).

cnf(12798,plain,
    product(product(a112,a119),product(a112,a111)) = product(product(a119,a110),a79),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,12518,theory(equality)]),12490,12513,theory(equality)]) ).

cnf(12800,plain,
    product(a122,product(a115,a123)) = product(product(a123,a122),a123),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[720,5834,theory(equality)]),1591,7574,theory(equality)]) ).

cnf(12818,plain,
    product(a91,a66) = product(product(a100,a91),product(a126,a2)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[723,1674,theory(equality)]),12675,theory(equality)]) ).

cnf(12847,plain,
    product(a99,a122) = product(product(a100,a115),a123),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[726,1594,theory(equality)]),570,theory(equality)]) ).

cnf(12853,plain,
    product(product(a100,a115),a122) = product(a99,product(a123,a122)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[727,1590,theory(equality)]),1597,theory(equality)]) ).

cnf(12862,plain,
    product(product(a122,a100),a124) = product(product(a123,a122),a99),
    inference('PARAMODULATE',[status(thm)],[728,1590,theory(equality)]) ).

cnf(12920,plain,
    product(product(a104,a103),a104) = product(a103,a86),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[736,3519,theory(equality)]),knot_104,3548,12343,theory(equality)]) ).

cnf(12931,plain,
    product(a87,product(a104,a103)) = product(a86,product(a87,a103)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[737,8739,theory(equality)]),7007,involutory_quandle_02,involutory_quandle,3549,432,theory(equality)]) ).

cnf(12932,plain,
    product(a87,product(a104,a103)) = product(product(a87,a103),product(a86,a103)),
    inference('REWRITE',[status(thm)],[7007,12931,theory(equality)]) ).

cnf(12953,plain,
    product(product(X,a107),a84) = product(product(X,a106),product(a84,a106)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,740,theory(equality)]) ).

cnf(12962,plain,
    product(product(a79,X),Y) = product(product(product(a80,X),Y),product(product(a119,X),Y)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,741,theory(equality)]) ).

cnf(12963,plain,
    product(product(a79,X),product(a80,X)) = product(product(a80,X),product(product(a119,X),product(a80,X))),
    inference('PARAMODULATE',[status(thm)],[569,741,theory(equality)]) ).

cnf(12969,plain,
    product(product(a79,product(X,a119)),Y) = product(product(product(a80,X),Y),product(a119,Y)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,742,theory(equality)]) ).

cnf(12980,plain,
    product(a110,a112) = product(a119,a111),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[744,12480,theory(equality)]),12506,theory(equality)]) ).

cnf(12981,plain,
    product(product(a118,a108),a70) = product(a110,a112),
    inference('REWRITE',[status(thm)],[3737,12980,theory(equality)]) ).

cnf(12982,plain,
    product(a110,a111) = product(a111,product(a110,a112)),
    inference('REWRITE',[status(thm)],[5836,12980,theory(equality)]) ).

cnf(12983,plain,
    product(a110,a111) = product(a112,product(a80,a112)),
    inference('REWRITE',[status(thm)],[12788,12982,theory(equality)]) ).

cnf(12984,plain,
    product(product(a119,a110),a119) = product(a110,a112),
    inference('REWRITE',[status(thm)],[5931,12980,theory(equality)]) ).

cnf(12985,plain,
    product(product(a110,a111),a112) = product(a119,a110),
    inference('REWRITE',[status(thm)],[5932,12516,12980,theory(equality)]) ).

cnf(12988,plain,
    product(product(a111,a110),a112) = product(product(a119,a110),a111),
    inference('REWRITE',[status(thm)],[7584,12515,12980,theory(equality)]) ).

cnf(12995,plain,
    product(product(product(a110,a112),X),a119) = product(product(a119,a110),product(X,a119)),
    inference('REWRITE',[status(thm)],[8002,12980,theory(equality)]) ).

cnf(12998,plain,
    product(product(X,a110),a119) = product(product(X,a111),product(a110,a112)),
    inference('REWRITE',[status(thm)],[8762,12980,theory(equality)]) ).

cnf(13001,plain,
    product(a110,a112) = product(a111,product(a112,a111)),
    inference('REWRITE',[status(thm)],[12512,12980,theory(equality)]) ).

cnf(13002,plain,
    product(product(a110,a112),a79) = product(a112,a119),
    inference('REWRITE',[status(thm)],[12517,12980,theory(equality)]) ).

cnf(13004,plain,
    product(product(product(a112,a110),a119),product(a110,a111)) = product(product(a110,a112),product(a80,a111)),
    inference('REWRITE',[status(thm)],[12748,12980,theory(equality)]) ).

cnf(13005,plain,
    product(product(a112,a119),a79) = product(a110,a112),
    inference('REWRITE',[status(thm)],[12770,12980,theory(equality)]) ).

cnf(13017,plain,
    product(product(a110,a112),X) = product(product(a119,X),product(a111,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,12980,theory(equality)]) ).

cnf(13019,plain,
    product(a119,product(a119,a110)) = product(product(a110,a112),a110),
    inference('REWRITE',[status(thm)],[7000,13017,theory(equality)]) ).

cnf(13021,plain,
    product(product(a119,X),a111) = product(product(a110,a112),product(X,a111)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,12980,theory(equality)]) ).

cnf(13022,plain,
    product(product(a111,a110),a112) = product(product(a110,a112),product(a110,a111)),
    inference('REWRITE',[status(thm)],[12988,13021,theory(equality)]) ).

cnf(13023,plain,
    product(a110,product(a110,a112)) = product(product(a110,a111),product(product(a111,a110),a112)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[744,12982,theory(equality)]),12515,theory(equality)]) ).

cnf(13030,plain,
    product(a119,a110) = product(a110,product(a119,a80)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[745,12493,theory(equality)]),12985,12516,13001,theory(equality)]) ).

cnf(13043,plain,
    product(product(a110,a111),product(a112,a119)) = product(product(a110,a112),a110),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[746,12984,theory(equality)]),10712,13022,13021,theory(equality)]) ).

cnf(13048,plain,
    product(product(X,product(Y,a119)),a110) = product(product(X,a110),product(product(Y,a111),a119)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,746,theory(equality)]) ).

cnf(13064,plain,
    product(product(X,a112),a79) = product(product(X,a111),product(a79,a111)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,749,theory(equality)]) ).

cnf(13067,plain,
    product(product(a80,a79),product(a110,a112)) = product(a80,a112),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[749,9531,theory(equality)]),12507,1274,13005,involutory_quandle_02,9567,591,12480,9573,theory(equality)]) ).

cnf(13068,plain,
    product(a110,a79) = product(product(a112,a110),a119),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[749,13002,theory(equality)]),578,involutory_quandle_01,theory(equality)]) ).

cnf(13069,plain,
    product(product(a110,a79),product(a110,a111)) = product(product(a110,a112),product(a80,a111)),
    inference('REWRITE',[status(thm)],[13004,13068,theory(equality)]) ).

cnf(13075,plain,
    product(a76,product(a68,a114)) = product(product(a75,a114),product(a115,a114)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[750,3597,theory(equality)]),1557,theory(equality)]) ).

cnf(13076,plain,
    product(a76,product(a121,a114)) = product(product(a76,a121),a77),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[750,8894,theory(equality)]),involutory_quandle_02,12438,theory(equality)]) ).

cnf(13077,plain,
    product(a76,product(a121,a114)) = product(a77,product(a76,a77)),
    inference('REWRITE',[status(thm)],[8909,13076,theory(equality)]) ).

cnf(13109,plain,
    product(product(a115,a124),a75) = product(a122,a123),
    inference('PARAMODULATE',[status(thm)],[755,1578,theory(equality)]) ).

cnf(13110,plain,
    product(product(X,a124),a75) = product(product(X,a123),product(a75,a123)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,755,theory(equality)]) ).

cnf(13117,plain,
    product(a122,product(a115,a123)) = product(a123,product(a122,a123)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[754,13109,theory(equality)]),12800,157,12447,7560,theory(equality)]) ).

cnf(13118,plain,
    product(product(a122,a123),a68) = product(product(product(a115,a124),a68),a76),
    inference('PARAMODULATE',[status(thm)],[593,13109,theory(equality)]) ).

cnf(13119,plain,
    product(a123,product(a123,a122)) = product(product(a122,a123),a124),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[581,13109,theory(equality)]),157,12448,12396,theory(equality)]) ).

cnf(13124,plain,
    product(product(X,product(a115,a124)),a75) = product(product(X,a75),product(a122,a123)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,13109,theory(equality)]) ).

cnf(13125,plain,
    product(product(a122,a123),product(a115,a124)) = product(product(a115,a124),product(a75,product(a115,a124))),
    inference('PARAMODULATE',[status(thm)],[569,13109,theory(equality)]) ).

cnf(13126,plain,
    product(a116,product(a74,a117)) = product(product(a117,a116),a117),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[756,5839,theory(equality)]),1349,7601,theory(equality)]) ).

cnf(13162,plain,
    product(product(X,a73),a82) = product(product(X,a72),product(a82,a72)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,761,theory(equality)]) ).

cnf(13168,plain,
    product(a71,product(a118,a109)) = product(product(a70,a108),a109),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[762,3636,theory(equality)]),involutory_quandle_02,5843,theory(equality)]) ).

cnf(13187,plain,
    product(a81,product(a70,a109)) = product(product(a80,a109),product(a110,a109)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[765,3646,theory(equality)]),1463,theory(equality)]) ).

cnf(13188,plain,
    product(a81,product(a109,a82)) = product(product(a82,a81),a82),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[765,3648,theory(equality)]),1396,10739,theory(equality)]) ).

cnf(13205,plain,
    product(a70,product(a119,a118)) = product(product(a70,a119),a71),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[768,5842,theory(equality)]),involutory_quandle_02,6738,theory(equality)]) ).

cnf(13206,plain,
    product(a70,product(a119,a118)) = product(a71,product(a70,a71)),
    inference('REWRITE',[status(thm)],[6083,13205,theory(equality)]) ).

cnf(13211,plain,
    product(product(a73,a109),a118) = product(a70,product(a79,a70)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[769,1350,theory(equality)]),3698,theory(equality)]) ).

cnf(13226,plain,
    product(a82,a108) = product(product(a79,a70),product(a118,a108)),
    inference('PARAMODULATE',[status(thm)],[771,3703,theory(equality)]) ).

cnf(13245,plain,
    product(a108,product(a118,a109)) = product(product(a109,a108),a109),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[774,5843,theory(equality)]),1437,7622,theory(equality)]) ).

cnf(13253,plain,
    product(product(product(a110,X),a118),a71) = product(a108,product(product(X,a118),a71)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[775,586,theory(equality)]),586,781,theory(equality)]) ).

cnf(13261,plain,
    product(product(X,a109),a118) = product(product(X,a108),product(a118,a108)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,776,theory(equality)]) ).

cnf(13263,plain,
    product(product(a73,a108),product(a118,a108)) = product(a70,product(a79,a70)),
    inference('REWRITE',[status(thm)],[13211,13261,theory(equality)]) ).

cnf(13267,plain,
    product(product(product(X,a110),a118),a71) = product(product(product(X,a109),a118),product(a71,a108)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[776,586,theory(equality)]),776,involutory_quandle_02,586,782,theory(equality)]) ).

cnf(13281,plain,
    product(product(a79,a110),product(a111,a110)) = product(a80,product(a119,a110)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[778,1411,theory(equality)]),3734,involutory_quandle_02,knot_110,1419,theory(equality)]) ).

cnf(13305,plain,
    product(product(a110,a111),a70) = product(a109,a108),
    inference('PARAMODULATE',[status(thm)],[781,1263,theory(equality)]) ).

cnf(13306,plain,
    product(product(a110,a112),a70) = product(a109,product(a116,a32)),
    inference('PARAMODULATE',[status(thm)],[781,9526,theory(equality)]) ).

cnf(13307,plain,
    product(product(a111,a110),a70) = product(a108,a109),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[781,3745,theory(equality)]),5843,1264,theory(equality)]) ).

cnf(13330,plain,
    product(product(a112,a110),a70) = product(product(a116,a109),product(a32,a109)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[782,9526,theory(equality)]),involutory_quandle_02,theory(equality)]) ).

cnf(13331,plain,
    product(product(X,a110),a70) = product(product(X,a109),product(a70,a109)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,782,theory(equality)]) ).

cnf(13333,plain,
    product(product(a79,a109),product(a70,a109)) = product(a82,product(a118,a109)),
    inference('REWRITE',[status(thm)],[3714,13331,theory(equality)]) ).

cnf(13336,plain,
    product(product(X,product(Y,a70)),a109) = product(product(X,a109),product(product(Y,a110),a70)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,782,theory(equality)]) ).

cnf(13339,plain,
    product(a118,a111) = product(product(a110,a112),product(a70,a111)),
    inference('PARAMODULATE',[status(thm)],[783,12980,theory(equality)]) ).

cnf(13344,plain,
    product(product(a110,a112),a70) = product(a118,a108),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[784,1263,theory(equality)]),12980,theory(equality)]) ).

cnf(13345,plain,
    product(a118,a108) = product(a109,product(a116,a32)),
    inference('REWRITE',[status(thm)],[13306,13344,theory(equality)]) ).

cnf(13346,plain,
    a108 = product(product(a117,a116),a32),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[784,9526,theory(equality)]),505,1263,12506,theory(equality)]) ).

cnf(13347,plain,
    a108 = product(product(a116,a32),product(a73,product(a116,a32))),
    inference('REWRITE',[status(thm)],[6427,13346,theory(equality)]) ).

cnf(13348,plain,
    product(product(product(a110,a109),product(a112,a109)),product(a70,a109)) = product(product(a118,a108),a109),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[784,3745,theory(equality)]),7622,involutory_quandle_02,13331,13019,theory(equality)]) ).

cnf(13359,plain,
    product(a108,a32) = product(a117,a116),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,13346,theory(equality)]) ).

cnf(13382,plain,
    product(a109,a32) = product(product(a117,a116),a117),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[305,13359,theory(equality)]),223,theory(equality)]) ).

cnf(13383,plain,
    product(a116,product(a74,a117)) = product(a109,a32),
    inference('REWRITE',[status(thm)],[13126,13382,theory(equality)]) ).

cnf(13395,plain,
    product(product(X,a108),a32) = product(product(X,a32),product(a117,a116)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,13359,theory(equality)]) ).

cnf(13409,plain,
    product(product(a109,a32),product(a74,a117)) = a116,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,13383,theory(equality)]) ).

cnf(13418,plain,
    product(a118,a81) = product(a109,a82),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[785,12493,theory(equality)]),12457,8831,167,589,theory(equality)]) ).

cnf(13419,plain,
    product(a81,a82) = product(a82,product(a118,a81)),
    inference('REWRITE',[status(thm)],[3648,13418,theory(equality)]) ).

cnf(13425,plain,
    product(a109,product(a109,a81)) = a118,
    inference('REWRITE',[status(thm)],[7031,involutory_quandle_01,13418,theory(equality)]) ).

cnf(13429,plain,
    product(a109,product(a118,a81)) = product(product(a109,a81),a82),
    inference('REWRITE',[status(thm)],[10739,13418,theory(equality)]) ).

cnf(13432,plain,
    product(product(a79,a70),a81) = product(product(a82,a81),a82),
    inference('REWRITE',[status(thm)],[13188,6080,13418,theory(equality)]) ).

cnf(13445,plain,
    product(product(a118,a81),a82) = a109,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,13418,theory(equality)]) ).

cnf(13447,plain,
    product(a71,a82) = product(a73,product(a118,a81)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[762,13418,theory(equality)]),knot_73,theory(equality)]) ).

cnf(13451,plain,
    product(product(a118,a109),a82) = product(a109,a81),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,13418,theory(equality)]),161,585,theory(equality)]) ).

cnf(13452,plain,
    product(product(a109,a73),a82) = product(product(a118,a81),a72),
    inference('PARAMODULATE',[status(thm)],[761,13418,theory(equality)]) ).

cnf(13454,plain,
    product(product(a112,a111),a70) = product(a106,a39),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[587,13418,theory(equality)]),1232,164,12481,784,involutory_quandle,3718,theory(equality)]) ).

cnf(13459,plain,
    product(a118,product(a109,a81)) = a109,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,13425,theory(equality)]) ).

cnf(13460,plain,
    product(a118,a109) = product(product(a109,a81),a82),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,13425,theory(equality)]),13429,13418,involutory_quandle,585,theory(equality)]) ).

cnf(13462,plain,
    product(a109,product(a118,a81)) = product(a118,a109),
    inference('REWRITE',[status(thm)],[13429,13460,theory(equality)]) ).

cnf(13464,plain,
    product(a82,a81) = product(a83,product(a116,a32)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[765,13425,theory(equality)]),9526,knot_112,1270,164,3718,445,1386,theory(equality)]) ).

cnf(13465,plain,
    product(a71,product(a109,a81)) = product(product(a70,a108),product(a116,a32)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[762,13425,theory(equality)]),9526,knot_112,1270,164,3718,1379,theory(equality)]) ).

cnf(13467,plain,
    product(a82,product(a109,a81)) = product(a83,product(a79,a70)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[302,13425,theory(equality)]),3698,445,1386,theory(equality)]) ).

cnf(13469,plain,
    product(product(a109,X),product(a109,a81)) = product(a118,product(X,product(a109,a81))),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,13425,theory(equality)]) ).

cnf(13470,plain,
    product(product(X,a109),product(a109,a81)) = product(product(X,product(a109,a81)),a118),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,13425,theory(equality)]) ).

cnf(13471,plain,
    product(a83,product(a79,a70)) = product(product(a83,a109),product(a118,a81)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[771,13459,theory(equality)]),13418,involutory_quandle,8808,13467,theory(equality)]) ).

cnf(13472,plain,
    product(a70,product(a109,a81)) = product(product(a71,product(a118,a109)),product(product(a112,a110),a70)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[768,13459,theory(equality)]),13330,13168,716,13465,theory(equality)]) ).

cnf(13474,plain,
    product(a83,product(a109,a81)) = product(product(a81,a82),product(a118,a109)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[304,13459,theory(equality)]),1426,13333,13331,13336,13467,theory(equality)]) ).

cnf(13478,plain,
    product(product(X,a118),product(a109,a81)) = product(product(X,a109),product(a118,a81)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,13459,theory(equality)]),13418,involutory_quandle,8808,theory(equality)]) ).

cnf(13480,plain,
    product(product(a79,a70),a81) = product(a83,product(a109,a81)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[765,13419,theory(equality)]),13474,13462,6080,theory(equality)]) ).

cnf(13508,plain,
    product(a75,product(a68,a76)) = product(product(a76,a75),a76),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[789,3773,theory(equality)]),1550,10836,theory(equality)]) ).

cnf(13532,plain,
    product(a114,product(a68,a115)) = product(product(a115,a114),a115),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[792,5848,theory(equality)]),1562,7648,theory(equality)]) ).

cnf(13539,plain,
    product(product(a115,a123),a68) = product(a121,a77),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[793,1144,theory(equality)]),12438,theory(equality)]) ).

cnf(13540,plain,
    product(product(a123,a122),a68) = product(a114,product(a76,a121)),
    inference('REWRITE',[status(thm)],[12444,8882,8912,13539,theory(equality)]) ).

cnf(13541,plain,
    product(product(a115,a124),a68) = product(a114,product(a114,a121)),
    inference('PARAMODULATE',[status(thm)],[793,3792,theory(equality)]) ).

cnf(13542,plain,
    product(product(a122,a123),a68) = product(product(a114,product(a114,a121)),a76),
    inference('REWRITE',[status(thm)],[13118,13541,theory(equality)]) ).

cnf(13553,plain,
    product(product(a124,a123),a68) = product(a114,product(a121,a77)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[793,13539,theory(equality)]),7574,theory(equality)]) ).

cnf(13563,plain,
    product(product(X,a115),a68) = product(product(X,a114),product(a68,a114)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,794,theory(equality)]) ).

cnf(13566,plain,
    product(product(product(X,a122),a68),a76) = product(product(product(X,a115),a68),a77),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[794,593,theory(equality)]),794,580,593,1585,theory(equality)]) ).

cnf(13571,plain,
    product(a121,product(a68,a122)) = product(product(a122,a121),a122),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[795,5849,theory(equality)]),1617,7653,theory(equality)]) ).

cnf(13578,plain,
    product(product(a122,a123),a68) = product(a121,product(a121,a114)),
    inference('PARAMODULATE',[status(thm)],[796,1144,theory(equality)]) ).

cnf(13579,plain,
    product(a121,product(a121,a114)) = product(product(a114,product(a114,a121)),a76),
    inference('REWRITE',[status(thm)],[13542,13578,theory(equality)]) ).

cnf(13580,plain,
    product(product(a123,a122),a68) = product(a121,product(a114,a121)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[796,3792,theory(equality)]),1590,theory(equality)]) ).

cnf(13581,plain,
    product(a121,product(a114,a121)) = product(a114,product(a76,a121)),
    inference('REWRITE',[status(thm)],[13540,13580,theory(equality)]) ).

cnf(13590,plain,
    product(product(X,a122),a68) = product(product(X,a121),product(a68,a121)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,797,theory(equality)]) ).

cnf(13658,plain,
    product(product(X,a126),a65) = product(product(X,a125),product(a65,a125)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,806,theory(equality)]) ).

cnf(13660,plain,
    product(a96,a41) = product(product(a91,a2),product(a65,a125)),
    inference('REWRITE',[status(thm)],[1727,5811,13658,theory(equality)]) ).

cnf(13704,plain,
    product(a95,product(a125,a41)) = product(product(a94,a63),a64),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[813,3897,theory(equality)]),involutory_quandle_02,3877,theory(equality)]) ).

cnf(13722,plain,
    product(product(a64,a63),a64) = product(product(product(a62,a129),a64),a95),
    inference('PARAMODULATE',[status(thm)],[815,3912,theory(equality)]) ).

cnf(13725,plain,
    product(product(a129,a128),a64) = product(a127,a95),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[815,3931,theory(equality)]),1676,theory(equality)]) ).

cnf(13727,plain,
    product(product(a127,a128),a64) = product(product(product(a128,a127),a64),a95),
    inference('PARAMODULATE',[status(thm)],[815,3945,theory(equality)]) ).

cnf(13793,plain,
    product(a129,a63) = product(a127,product(a96,a63)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[820,5959,theory(equality)]),knot_63,1873,1855,838,theory(equality)]) ).

cnf(13815,plain,
    product(product(a95,product(a125,a41)),product(a96,a63)) = product(product(a96,a129),a63),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,13793,theory(equality)]),involutory_quandle_02,13704,knot_64,1732,theory(equality)]) ).

cnf(13971,plain,
    product(product(X,a129),a62) = product(product(X,a128),product(a62,a128)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,839,theory(equality)]) ).

cnf(14185,plain,
    product(a114,a14) = product(product(a113,a32),product(a32,a14)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[867,2529,theory(equality)]),9342,theory(equality)]) ).

cnf(14316,plain,
    product(product(a19,a139),a20) = product(product(a19,a138),product(a20,a138)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[878,4356,theory(equality)]),2237,10335,involutory_quandle_02,920,theory(equality)]) ).

cnf(14317,plain,
    product(product(a19,a139),a20) = product(product(a20,a138),product(a25,product(a20,a138))),
    inference('REWRITE',[status(thm)],[10337,14316,theory(equality)]) ).

cnf(14413,plain,
    product(a24,a20) = product(product(a25,a20),product(a47,a139)),
    inference('PARAMODULATE',[status(thm)],[888,2108,theory(equality)]) ).

cnf(14587,plain,
    product(a20,a134) = product(product(product(a18,a132),a26),a57),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[911,4449,theory(equality)]),4341,theory(equality)]) ).

cnf(14663,plain,
    product(product(product(a140,X),a20),a48) = product(a138,product(product(X,a20),a48)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[919,635,theory(equality)]),635,847,theory(equality)]) ).

cnf(14684,plain,
    product(product(X,a139),a20) = product(product(X,a138),product(a20,a138)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,920,theory(equality)]) ).

cnf(14922,plain,
    product(a88,a32) = product(product(a89,a13),a33),
    inference('PARAMODULATE',[status(thm)],[944,267,theory(equality)]) ).

cnf(14923,plain,
    product(a100,a32) = product(product(a101,a13),a33),
    inference('PARAMODULATE',[status(thm)],[944,268,theory(equality)]) ).

cnf(14925,plain,
    product(product(a88,a32),product(a40,a32)) = product(product(a90,a13),a33),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[944,3287,theory(equality)]),involutory_quandle_02,theory(equality)]) ).

cnf(14926,plain,
    product(a109,a81) = product(product(a124,a13),a33),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[944,1618,theory(equality)]),9558,theory(equality)]) ).

cnf(15055,plain,
    product(product(a81,a13),a32) = product(product(a75,a115),a122),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[947,1441,theory(equality)]),knot_122,1305,10265,theory(equality)]) ).

cnf(15057,plain,
    product(product(a109,a13),a32) = product(a123,a122),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[947,1477,theory(equality)]),knot_122,1154,9418,theory(equality)]) ).

cnf(15087,plain,
    product(a109,a81) = product(a108,a73),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[950,1619,theory(equality)]),13346,9558,theory(equality)]) ).

cnf(15088,plain,
    product(a82,a81) = product(a81,product(a108,a73)),
    inference('REWRITE',[status(thm)],[1386,15087,theory(equality)]) ).

cnf(15091,plain,
    product(product(X,a109),a81) = product(product(X,product(a108,a73)),product(a82,a81)),
    inference('REWRITE',[status(thm)],[1398,15087,theory(equality)]) ).

cnf(15094,plain,
    product(product(a116,a117),a32) = product(a108,a73),
    inference('REWRITE',[status(thm)],[9558,15087,theory(equality)]) ).

cnf(15099,plain,
    product(product(a108,a73),product(a112,a118)) = product(product(a112,a118),product(a71,product(a112,a118))),
    inference('REWRITE',[status(thm)],[12462,15087,theory(equality)]) ).

cnf(15100,plain,
    product(a109,product(a108,a73)) = a118,
    inference('REWRITE',[status(thm)],[13425,15087,theory(equality)]) ).

cnf(15101,plain,
    product(product(a118,a109),a82) = product(a108,a73),
    inference('REWRITE',[status(thm)],[13451,15087,theory(equality)]) ).

cnf(15103,plain,
    product(a118,a109) = product(product(a108,a73),a82),
    inference('REWRITE',[status(thm)],[13460,15087,theory(equality)]) ).

cnf(15105,plain,
    product(a71,product(a108,a73)) = product(product(a70,a108),product(a116,a32)),
    inference('REWRITE',[status(thm)],[13465,15087,theory(equality)]) ).

cnf(15106,plain,
    product(a82,product(a108,a73)) = product(a83,product(a79,a70)),
    inference('REWRITE',[status(thm)],[13467,15087,theory(equality)]) ).

cnf(15107,plain,
    product(a82,product(a108,a73)) = product(product(a83,a109),product(a118,a81)),
    inference('REWRITE',[status(thm)],[13471,15106,theory(equality)]) ).

cnf(15109,plain,
    product(product(a109,X),product(a108,a73)) = product(a118,product(X,product(a108,a73))),
    inference('REWRITE',[status(thm)],[13469,15087,theory(equality)]) ).

cnf(15110,plain,
    product(product(X,a109),product(a108,a73)) = product(product(X,product(a108,a73)),a118),
    inference('REWRITE',[status(thm)],[13470,15087,theory(equality)]) ).

cnf(15111,plain,
    product(a70,product(a108,a73)) = product(product(a71,product(a118,a109)),product(product(a112,a110),a70)),
    inference('REWRITE',[status(thm)],[13472,15087,theory(equality)]) ).

cnf(15114,plain,
    product(product(X,a118),product(a108,a73)) = product(product(X,a109),product(a118,a81)),
    inference('REWRITE',[status(thm)],[13478,15087,theory(equality)]) ).

cnf(15116,plain,
    product(product(a79,a70),a81) = product(a83,product(a108,a73)),
    inference('REWRITE',[status(thm)],[13480,15087,theory(equality)]) ).

cnf(15117,plain,
    product(a83,product(a108,a73)) = product(a81,product(a118,a81)),
    inference('REWRITE',[status(thm)],[6080,15116,theory(equality)]) ).

cnf(15118,plain,
    product(a83,product(a108,a73)) = product(product(a82,a81),a82),
    inference('REWRITE',[status(thm)],[13432,15116,theory(equality)]) ).

cnf(15120,plain,
    product(a108,a73) = product(product(a124,a13),a33),
    inference('REWRITE',[status(thm)],[14926,15087,theory(equality)]) ).

cnf(15133,plain,
    product(product(a108,a73),a81) = a109,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,15087,theory(equality)]) ).

cnf(15139,plain,
    product(product(a108,a73),a109) = product(a118,a81),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,15087,theory(equality)]),13418,knot_82,theory(equality)]) ).

cnf(15140,plain,
    product(product(a108,a73),a70) = product(a112,a119),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[779,15087,theory(equality)]),1276,knot_110,theory(equality)]) ).

cnf(15141,plain,
    product(a110,a112) = product(a112,product(a79,a111)),
    inference('REWRITE',[status(thm)],[9577,13005,15140,theory(equality)]) ).

cnf(15161,plain,
    product(product(a80,product(a112,a119)),product(a79,a111)) = product(a80,a111),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,15141,theory(equality)]),knot_111,435,12998,9567,591,12480,9573,theory(equality)]) ).

cnf(15173,plain,
    product(product(a118,a108),a32) = product(a117,product(a117,a116)),
    inference('PARAMODULATE',[status(thm)],[952,13359,theory(equality)]) ).

cnf(15221,plain,
    product(product(a114,a121),a32) = product(product(a112,a119),a13),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[956,2054,theory(equality)]),657,theory(equality)]) ).

cnf(15230,plain,
    product(product(product(X,a122),a32),a69) = product(product(product(X,a121),a32),product(a69,a120)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[956,645,theory(equality)]),956,involutory_quandle_02,645,797,theory(equality)]) ).

cnf(15231,plain,
    product(product(a115,a121),a32) = product(product(product(a112,a119),a13),product(a69,a120)),
    inference('REWRITE',[status(thm)],[9372,15221,15230,theory(equality)]) ).

cnf(15412,plain,
    product(a108,a13) = product(a123,a32),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[974,1263,theory(equality)]),9370,theory(equality)]) ).

cnf(15414,plain,
    product(a111,a13) = product(product(a108,a13),a69),
    inference('REWRITE',[status(thm)],[9366,15412,theory(equality)]) ).

cnf(15415,plain,
    product(a108,a13) = product(product(a111,a13),a69),
    inference('REWRITE',[status(thm)],[9370,15412,theory(equality)]) ).

cnf(15438,plain,
    product(product(product(X,a118),a13),a69) = product(product(product(X,a119),a13),product(a69,a120)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[657,974,theory(equality)]),9602,974,591,theory(equality)]) ).

cnf(15439,plain,
    product(product(a115,a121),a32) = product(product(product(a112,a118),a13),a69),
    inference('REWRITE',[status(thm)],[15231,15438,theory(equality)]) ).

cnf(15795,plain,
    product(product(a141,a12),a21) = product(a140,product(a21,a11)),
    inference('PARAMODULATE',[status(thm)],[989,1006,theory(equality)]) ).

cnf(15807,plain,
    product(product(product(X,a11),a140),product(a22,a11)) = product(product(product(X,a12),a140),product(a21,a140)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1007,628,theory(equality)]),989,1007,involutory_quandle_02,theory(equality)]) ).

cnf(15860,plain,
    product(a17,a26) = product(product(a20,a134),a56),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1013,2307,theory(equality)]),215,634,theory(equality)]) ).

cnf(16044,plain,
    product(a38,product(a7,a39)) = product(product(a39,a38),a39),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1032,5891,theory(equality)]),2867,7904,theory(equality)]) ).

cnf(16132,plain,
    product(product(a1,a14),a39) = product(a4,product(a40,a39)),
    inference('PARAMODULATE',[status(thm)],[1045,5678,theory(equality)]) ).

cnf(16253,plain,
    product(product(a107,a106),a39) = product(product(a116,a32),a83),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1055,3554,theory(equality)]),9527,theory(equality)]) ).

cnf(16467,plain,
    product(product(a103,a14),a41) = product(a100,a2),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1073,5604,theory(equality)]),10067,9936,689,theory(equality)]) ).

cnf(16579,plain,
    product(product(a127,a63),a14) = product(product(product(a125,a126),a14),a40),
    inference('PARAMODULATE',[status(thm)],[1079,5957,theory(equality)]) ).

cnf(16613,plain,
    product(product(a123,a122),a14) = product(a109,a32),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1082,8778,theory(equality)]),13382,knot_117,10194,9927,theory(equality)]) ).

cnf(16614,plain,
    product(product(a122,a123),a14) = product(a117,product(a117,a116)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1082,13109,theory(equality)]),knot_117,10195,5534,theory(equality)]) ).

cnf(16658,plain,
    product(product(a101,a117),a14) = product(a100,a122),
    inference('PARAMODULATE',[status(thm)],[1087,1577,theory(equality)]) ).

cnf(16840,plain,
    product(product(product(X,a3),a1),a42) = product(product(product(X,a1),a2),product(a42,a3)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1134,1103,theory(equality)]),3225,involutory_quandle_02,theory(equality)]) ).

cnf(16990,plain,
    product(a64,a42) = product(a66,a1),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1118,3259,theory(equality)]),involutory_quandle_01,theory(equality)]) ).

cnf(16992,plain,
    product(product(X,a2),a42) = product(product(X,a1),product(a42,a1)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1118,theory(equality)]) ).

cnf(17003,plain,
    product(product(a127,a63),a2) = product(product(product(a125,a1),product(a126,a1)),product(a42,a1)),
    inference('REWRITE',[status(thm)],[10072,involutory_quandle_02,16992,theory(equality)]) ).

cnf(17028,plain,
    product(product(a64,a42),a66) = product(a66,product(a1,a66)),
    inference('PARAMODULATE',[status(thm)],[569,16990,theory(equality)]) ).

cnf(17067,plain,
    product(product(a68,a1),a42) = product(product(a64,a94),a96),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1121,1521,theory(equality)]),9995,theory(equality)]) ).

cnf(17127,plain,
    product(product(a132,a1),product(a13,a1)) = product(a129,product(product(a138,a1),product(a13,a1))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1129,2133,theory(equality)]),involutory_quandle_02,theory(equality)]) ).

cnf(17194,plain,
    product(product(product(a67,X),a2),a93) = product(a65,product(product(X,a2),a93)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1136,799,theory(equality)]),709,theory(equality)]) ).

cnf(17308,plain,
    product(a83,product(a70,a108)) = product(a79,a108),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,3647,theory(equality)]),1368,445,theory(equality)]) ).

cnf(17430,plain,
    product(a121,a77) = product(product(a121,product(a114,a121)),a76),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[593,5927,theory(equality)]),13580,13539,theory(equality)]) ).

cnf(17431,plain,
    product(a115,product(a123,a122)) = product(product(a115,a123),a124),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[581,5927,theory(equality)]),1579,12448,12800,theory(equality)]) ).

cnf(17479,plain,
    product(product(a71,a72),product(a118,a109)) = product(product(a70,a109),product(a111,a109)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[782,6067,theory(equality)]),involutory_quandle_02,3645,13168,13331,theory(equality)]) ).

cnf(17481,plain,
    product(product(a70,a119),product(a119,a110)) = product(product(a70,a110),product(a111,a110)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[590,6067,theory(equality)]),involutory_quandle_02,3734,1406,13168,theory(equality)]) ).

cnf(17555,plain,
    product(product(a39,a40),a39) = product(a40,a5),
    inference('PARAMODULATE',[status(thm)],[569,6757,theory(equality)]) ).

cnf(17564,plain,
    product(product(a107,a40),a39) = product(product(product(a108,a40),a39),product(a40,a5)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[399,6757,theory(equality)]),1057,540,theory(equality)]) ).

cnf(17567,plain,
    product(product(a31,a40),a39) = product(product(a31,a4),a5),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[396,6757,theory(equality)]),9933,involutory_quandle_02,678,9932,1048,537,theory(equality)]) ).

cnf(17600,plain,
    product(product(a92,a75),product(a75,a123)) = product(a91,a123),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,8779,theory(equality)]),8023,theory(equality)]) ).

cnf(17602,plain,
    product(product(a92,a75),product(a124,a123)) = product(product(a92,a123),product(a75,product(a75,a123))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[755,8779,theory(equality)]),6990,716,3619,429,theory(equality)]) ).

cnf(17625,plain,
    product(product(product(a122,a123),X),a75) = product(product(a115,a124),product(X,a75)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,8781,theory(equality)]) ).

cnf(17630,plain,
    product(a108,product(a70,a109)) = product(product(a111,a109),product(a110,a109)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[782,8844,theory(equality)]),involutory_quandle_02,involutory_quandle_01,13331,theory(equality)]) ).

cnf(17636,plain,
    product(product(a111,a110),X) = product(product(product(a108,a109),X),product(a70,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,8844,theory(equality)]) ).

cnf(17643,plain,
    product(product(a80,a118),product(a70,a71)) = product(a79,a71),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[586,8853,theory(equality)]),involutory_quandle_01,5842,3662,theory(equality)]) ).

cnf(17828,plain,
    product(product(product(a32,a14),a30),product(a32,a14)) = product(product(a32,a14),product(product(a29,a13),a32)),
    inference('PARAMODULATE',[status(thm)],[569,9335,theory(equality)]) ).

cnf(17979,plain,
    product(a79,product(a70,a112)) = product(a73,a112),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,9566,theory(equality)]) ).

cnf(18069,plain,
    product(product(a84,a7),product(a39,a38)) = product(product(a84,a38),product(a7,product(a7,a38))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1034,9730,theory(equality)]),7088,716,5200,539,theory(equality)]) ).

cnf(18248,plain,
    product(product(a106,a4),X) = product(product(product(a105,a39),X),product(a40,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,10531,theory(equality)]) ).

cnf(18362,plain,
    product(a96,a41) = product(a98,a2),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,12220,theory(equality)]),13660,5811,13658,theory(equality)]) ).

cnf(18369,plain,
    product(a93,product(a96,a41)) = product(product(product(a90,a124),a2),a93),
    inference('REWRITE',[status(thm)],[10090,18362,theory(equality)]) ).

cnf(18395,plain,
    product(product(a71,a119),X) = product(product(a70,X),product(product(a70,a119),X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,12252,theory(equality)]) ).

cnf(18398,plain,
    product(a71,product(a70,a119)) = product(product(a70,a119),product(a71,a119)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,12252,theory(equality)]),involutory_quandle,knot_71,785,theory(equality)]) ).

cnf(18427,plain,
    product(product(a107,a106),a39) = product(a101,a32),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,12303,theory(equality)]) ).

cnf(18430,plain,
    product(a101,a32) = product(product(a116,a32),a83),
    inference('REWRITE',[status(thm)],[16253,18427,theory(equality)]) ).

cnf(18480,plain,
    product(a121,product(a121,a114)) = product(product(a114,a121),a77),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,12438,theory(equality)]),8923,involutory_quandle_01,theory(equality)]) ).

cnf(18490,plain,
    product(product(a111,a109),product(a108,a110)) = product(product(a108,a110),product(a70,product(a108,a110))),
    inference('PARAMODULATE',[status(thm)],[569,12463,theory(equality)]) ).

cnf(18491,plain,
    product(a81,product(a116,a32)) = product(a73,a108),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,12507,theory(equality)]),9526,447,theory(equality)]) ).

cnf(18492,plain,
    product(product(a83,a109),a81) = product(a73,a108),
    inference('REWRITE',[status(thm)],[12780,18491,theory(equality)]) ).

cnf(18508,plain,
    product(product(a73,a108),a109) = product(a83,a82),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[585,18492,theory(equality)]),involutory_quandle_01,theory(equality)]) ).

cnf(18522,plain,
    product(product(X,a111),a112) = product(product(X,a110),product(a119,a80)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,12521,theory(equality)]),12493,13048,12516,involutory_quandle_02,theory(equality)]) ).

cnf(18523,plain,
    product(a79,product(a112,a119)) = product(product(a80,a111),a112),
    inference('REWRITE',[status(thm)],[12764,18522,theory(equality)]) ).

cnf(18524,plain,
    product(product(a110,a111),a79) = product(a119,a80),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,12521,theory(equality)]),12493,746,12772,involutory_quandle_01,theory(equality)]) ).

cnf(18525,plain,
    product(a119,a80) = product(a112,product(a112,a119)),
    inference('REWRITE',[status(thm)],[12772,18524,theory(equality)]) ).

cnf(18569,plain,
    product(a119,a110) = product(product(a119,a80),product(a79,product(a112,a119))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,12755,theory(equality)]),18523,18522,13030,theory(equality)]) ).

cnf(18571,plain,
    product(product(X,product(a119,a80)),product(a80,a110)) = product(product(X,a110),a80),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,12755,theory(equality)]),713,theory(equality)]) ).

cnf(18572,plain,
    product(product(a79,product(a112,a119)),product(a80,a110)) = a80,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,12755,theory(equality)]),involutory_quandle_01,18523,18522,theory(equality)]) ).

cnf(18574,plain,
    product(a79,product(a80,a112)) = product(a80,a111),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,12762,theory(equality)]),15161,12499,12768,12509,theory(equality)]) ).

cnf(18588,plain,
    product(product(a110,a112),a13) = product(product(product(a118,a108),a13),a69),
    inference('PARAMODULATE',[status(thm)],[974,12981,theory(equality)]) ).

cnf(18593,plain,
    product(product(a110,a112),a118) = product(product(a118,a109),a71),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[586,12981,theory(equality)]),5942,theory(equality)]) ).

cnf(18603,plain,
    product(a119,product(a112,a111)) = product(a110,a111),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[748,13005,theory(equality)]),12982,12486,18525,theory(equality)]) ).

cnf(18604,plain,
    product(a110,a111) = product(product(a119,a80),a79),
    inference('REWRITE',[status(thm)],[12486,18603,theory(equality)]) ).

cnf(18606,plain,
    product(product(a119,a110),a79) = product(a112,product(a110,a112)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[437,13005,theory(equality)]),12985,12516,436,theory(equality)]) ).

cnf(18607,plain,
    product(product(a112,a119),product(a112,a111)) = product(a112,product(a110,a112)),
    inference('REWRITE',[status(thm)],[12798,18606,theory(equality)]) ).

cnf(18611,plain,
    product(product(X,product(a112,a119)),a79) = product(product(X,a79),product(a110,a112)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,13005,theory(equality)]) ).

cnf(18612,plain,
    product(product(a110,a112),product(a112,a119)) = product(product(a112,a119),product(a79,product(a112,a119))),
    inference('PARAMODULATE',[status(thm)],[569,13005,theory(equality)]) ).

cnf(18616,plain,
    product(a111,a110) = product(product(a112,a111),a80),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[577,18604,theory(equality)]),12481,involutory_quandle,743,3575,theory(equality)]) ).

cnf(18617,plain,
    product(a119,product(a119,a80)) = product(a111,a110),
    inference('REWRITE',[status(thm)],[12487,18616,theory(equality)]) ).

cnf(18621,plain,
    product(product(product(a119,a80),X),a79) = product(product(a110,a111),product(X,a79)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,18604,theory(equality)]) ).

cnf(18622,plain,
    product(product(X,product(a119,a80)),a79) = product(product(X,a79),product(a110,a111)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,18604,theory(equality)]) ).

cnf(18625,plain,
    product(a111,product(a119,a80)) = product(product(a110,a112),a110),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[295,13030,theory(equality)]),13017,18617,theory(equality)]) ).

cnf(18629,plain,
    product(a111,a80) = product(a112,a110),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,13068,theory(equality)]),knot_111,577,theory(equality)]) ).

cnf(18630,plain,
    product(product(a110,a79),a70) = product(product(product(a112,a109),a118),product(a71,a108)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[785,13068,theory(equality)]),13267,theory(equality)]) ).

cnf(18643,plain,
    product(product(a112,a110),a70) = product(a108,a81),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[589,18629,theory(equality)]),1263,theory(equality)]) ).

cnf(18644,plain,
    product(a108,a81) = product(product(a116,a109),product(a32,a109)),
    inference('REWRITE',[status(thm)],[13330,18643,theory(equality)]) ).

cnf(18645,plain,
    product(a70,product(a108,a73)) = product(product(a71,product(a118,a109)),product(a108,a81)),
    inference('REWRITE',[status(thm)],[15111,18643,theory(equality)]) ).

cnf(18662,plain,
    product(product(a118,a108),a109) = product(a109,product(a108,a81)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,13345,theory(equality)]),18644,involutory_quandle_02,theory(equality)]) ).

cnf(18663,plain,
    product(a108,product(a116,a32)) = a118,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[774,13345,theory(equality)]),involutory_quandle_01,13346,505,theory(equality)]) ).

cnf(18667,plain,
    product(a82,product(a116,a32)) = product(product(a73,a108),product(a118,a108)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[302,13345,theory(equality)]),18491,theory(equality)]) ).

cnf(18668,plain,
    product(a82,product(a116,a32)) = product(a70,product(a79,a70)),
    inference('REWRITE',[status(thm)],[13263,18667,theory(equality)]) ).

cnf(18674,plain,
    product(a118,a108) = product(a101,a32),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,18663,theory(equality)]),18427,540,12598,involutory_quandle_02,theory(equality)]) ).

cnf(18675,plain,
    product(a118,a108) = product(product(a100,a13),a33),
    inference('REWRITE',[status(thm)],[3122,18674,theory(equality)]) ).

cnf(18676,plain,
    product(product(a118,a108),a33) = product(a100,a13),
    inference('REWRITE',[status(thm)],[3128,18674,theory(equality)]) ).

cnf(18682,plain,
    product(product(a118,a108),a40) = product(product(a103,a30),a4),
    inference('REWRITE',[status(thm)],[9954,18674,theory(equality)]) ).

cnf(18688,plain,
    product(a107,a106) = product(product(a118,a108),a39),
    inference('REWRITE',[status(thm)],[12303,18674,theory(equality)]) ).

cnf(18694,plain,
    product(a118,a108) = product(product(a116,a32),a83),
    inference('REWRITE',[status(thm)],[18430,18674,theory(equality)]) ).

cnf(18707,plain,
    product(product(X,a108),product(a116,a32)) = product(product(X,a118),product(a108,a73)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,18663,theory(equality)]),15094,9407,theory(equality)]) ).

cnf(18708,plain,
    product(product(X,a108),product(a116,a32)) = product(product(X,a109),product(a118,a81)),
    inference('REWRITE',[status(thm)],[15114,18707,theory(equality)]) ).

cnf(18709,plain,
    product(a82,product(a108,a73)) = a73,
    inference('REWRITE',[status(thm)],[15107,involutory_quandle_01,9528,9565,3703,18708,theory(equality)]) ).

cnf(18710,plain,
    a73 = product(a83,product(a79,a70)),
    inference('REWRITE',[status(thm)],[15106,18709,theory(equality)]) ).

cnf(18713,plain,
    product(product(a118,a108),a13) = product(a100,a32),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[968,18675,theory(equality)]),involutory_quandle_01,theory(equality)]) ).

cnf(18715,plain,
    product(product(a110,a112),a13) = product(product(a100,a32),a69),
    inference('REWRITE',[status(thm)],[18588,18713,theory(equality)]) ).

cnf(18716,plain,
    product(a73,product(a79,a70)) = a83,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,18710,theory(equality)]) ).

cnf(18717,plain,
    product(a73,a118) = product(a82,a81),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[772,18710,theory(equality)]),1245,586,theory(equality)]) ).

cnf(18718,plain,
    product(a73,a118) = product(a83,product(a116,a32)),
    inference('REWRITE',[status(thm)],[13464,18717,theory(equality)]) ).

cnf(18719,plain,
    product(a73,a118) = product(a81,product(a108,a73)),
    inference('REWRITE',[status(thm)],[15088,18717,theory(equality)]) ).

cnf(18722,plain,
    product(product(X,a109),a81) = product(product(X,product(a108,a73)),product(a73,a118)),
    inference('REWRITE',[status(thm)],[15091,18717,theory(equality)]) ).

cnf(18723,plain,
    product(a83,product(a108,a73)) = product(product(a73,a118),a82),
    inference('REWRITE',[status(thm)],[15118,18717,theory(equality)]) ).

cnf(18726,plain,
    product(a73,a39) = product(product(a84,a106),a107),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[539,18710,theory(equality)]),7579,5299,involutory_quandle_02,theory(equality)]) ).

cnf(18727,plain,
    product(a84,product(a84,a107)) = product(a73,a39),
    inference('REWRITE',[status(thm)],[7579,18726,theory(equality)]) ).

cnf(18731,plain,
    product(a82,product(a79,a70)) = product(a73,product(a106,a39)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[771,18710,theory(equality)]),13454,12481,784,theory(equality)]) ).

cnf(18740,plain,
    a81 = product(product(a73,a108),product(a116,a32)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[765,18717,theory(equality)]),18707,15087,involutory_quandle,theory(equality)]) ).

cnf(18749,plain,
    a118 = product(product(a108,a73),product(a73,a118)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,18719,theory(equality)]),15100,15133,theory(equality)]) ).

cnf(18750,plain,
    product(a117,product(a117,a116)) = a101,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,18674,theory(equality)]),15173,theory(equality)]) ).

cnf(18751,plain,
    product(product(a118,a108),a32) = a101,
    inference('REWRITE',[status(thm)],[15173,18750,theory(equality)]) ).

cnf(18752,plain,
    product(product(a122,a123),a14) = a101,
    inference('REWRITE',[status(thm)],[16614,18750,theory(equality)]) ).

cnf(18778,plain,
    a100 = product(a122,a123),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,18752,theory(equality)]),268,theory(equality)]) ).

cnf(18779,plain,
    a100 = product(a123,product(a115,a123)),
    inference('REWRITE',[status(thm)],[5834,18778,theory(equality)]) ).

cnf(18783,plain,
    product(a100,a75) = product(a115,a124),
    inference('REWRITE',[status(thm)],[8781,18778,theory(equality)]) ).

cnf(18786,plain,
    product(product(a115,a124),a75) = a100,
    inference('REWRITE',[status(thm)],[13109,18778,theory(equality)]) ).

cnf(18787,plain,
    product(a122,product(a115,a123)) = product(a123,a100),
    inference('REWRITE',[status(thm)],[13117,18778,theory(equality)]) ).

cnf(18788,plain,
    product(a123,a100) = product(product(a123,a122),a123),
    inference('REWRITE',[status(thm)],[12800,18787,theory(equality)]) ).

cnf(18789,plain,
    product(a123,product(a123,a122)) = a99,
    inference('REWRITE',[status(thm)],[13119,148,18778,theory(equality)]) ).

cnf(18792,plain,
    product(product(X,product(a115,a124)),a75) = product(product(X,a75),a100),
    inference('REWRITE',[status(thm)],[13124,18778,theory(equality)]) ).

cnf(18793,plain,
    product(a100,product(a115,a124)) = product(product(a115,a124),product(a75,product(a115,a124))),
    inference('REWRITE',[status(thm)],[13125,18778,theory(equality)]) ).

cnf(18794,plain,
    product(a100,a68) = product(a121,product(a121,a114)),
    inference('REWRITE',[status(thm)],[13578,18778,theory(equality)]) ).

cnf(18796,plain,
    product(a100,a68) = product(product(a114,product(a114,a121)),a76),
    inference('REWRITE',[status(thm)],[13579,18794,theory(equality)]) ).

cnf(18797,plain,
    product(a100,a68) = product(product(a114,a121),a77),
    inference('REWRITE',[status(thm)],[18480,18794,theory(equality)]) ).

cnf(18799,plain,
    product(product(a100,X),a75) = product(product(a115,a124),product(X,a75)),
    inference('REWRITE',[status(thm)],[17625,18778,theory(equality)]) ).

cnf(18802,plain,
    product(a100,a123) = a122,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,18778,theory(equality)]) ).

cnf(18803,plain,
    product(a100,product(a75,a124)) = product(a115,product(a123,a124)),
    inference('REWRITE',[status(thm)],[7591,1579,18802,theory(equality)]) ).

cnf(18812,plain,
    product(a100,a115) = product(a123,a122),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[428,18778,theory(equality)]),146,theory(equality)]) ).

cnf(18813,plain,
    product(a100,a115) = product(a122,a124),
    inference('REWRITE',[status(thm)],[1590,18812,theory(equality)]) ).

cnf(18815,plain,
    product(product(a122,X),a124) = product(product(a100,a115),product(X,a124)),
    inference('REWRITE',[status(thm)],[1592,18812,theory(equality)]) ).

cnf(18817,plain,
    product(product(a100,a115),a75) = product(a115,a123),
    inference('REWRITE',[status(thm)],[5927,18812,theory(equality)]) ).

cnf(18823,plain,
    product(product(a100,a115),a122) = product(a99,product(a100,a115)),
    inference('REWRITE',[status(thm)],[12853,18812,theory(equality)]) ).

cnf(18824,plain,
    product(product(a122,a100),a124) = product(product(a100,a115),a99),
    inference('REWRITE',[status(thm)],[12862,18812,theory(equality)]) ).

cnf(18826,plain,
    product(product(a100,a115),a68) = product(a121,product(a114,a121)),
    inference('REWRITE',[status(thm)],[13580,18812,theory(equality)]) ).

cnf(18827,plain,
    product(product(a100,a115),a68) = product(a114,product(a76,a121)),
    inference('REWRITE',[status(thm)],[13581,18826,theory(equality)]) ).

cnf(18828,plain,
    product(a121,a77) = product(product(product(a100,a115),a68),a76),
    inference('REWRITE',[status(thm)],[17430,18826,theory(equality)]) ).

cnf(18829,plain,
    product(product(a109,a13),a32) = product(a100,a115),
    inference('REWRITE',[status(thm)],[15057,18812,theory(equality)]) ).

cnf(18830,plain,
    product(a101,a116) = product(a109,a32),
    inference('REWRITE',[status(thm)],[16613,5504,18812,theory(equality)]) ).

cnf(18835,plain,
    product(product(a101,a116),product(a74,a117)) = a116,
    inference('REWRITE',[status(thm)],[13409,18830,theory(equality)]) ).

cnf(18844,plain,
    product(a115,product(a100,a115)) = product(product(a115,a123),a124),
    inference('REWRITE',[status(thm)],[17431,18812,theory(equality)]) ).

cnf(18845,plain,
    product(a115,product(a100,a115)) = product(a124,product(a115,a124)),
    inference('REWRITE',[status(thm)],[7560,18844,theory(equality)]) ).

cnf(18850,plain,
    product(a123,a100) = product(a99,a122),
    inference('REWRITE',[status(thm)],[18788,12847,18812,theory(equality)]) ).

cnf(18851,plain,
    product(a123,a100) = product(product(a100,a115),a123),
    inference('REWRITE',[status(thm)],[12847,18850,theory(equality)]) ).

cnf(18852,plain,
    product(a123,product(a100,a115)) = a99,
    inference('REWRITE',[status(thm)],[18789,18812,theory(equality)]) ).

cnf(18854,plain,
    product(a100,a122) = product(a122,product(a100,a115)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,18778,theory(equality)]),18812,theory(equality)]) ).

cnf(18858,plain,
    product(product(X,a122),a123) = product(product(X,a123),a100),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,18778,theory(equality)]) ).

cnf(18859,plain,
    product(product(a100,a115),a124) = a122,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,18813,theory(equality)]) ).

cnf(18860,plain,
    product(product(a100,a115),a122) = a123,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,18813,theory(equality)]),knot_123,1594,theory(equality)]) ).

cnf(18861,plain,
    a123 = product(a99,product(a100,a115)),
    inference('REWRITE',[status(thm)],[18823,18860,theory(equality)]) ).

cnf(18862,plain,
    product(a115,a124) = product(a124,product(a100,a115)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,18813,theory(equality)]),1594,theory(equality)]) ).

cnf(18863,plain,
    product(product(a123,a100),a122) = a99,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,18850,theory(equality)]) ).

cnf(18866,plain,
    product(product(a123,a100),a124) = product(a100,product(a100,a115)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[430,18850,theory(equality)]),18813,theory(equality)]) ).

cnf(18872,plain,
    product(a99,a75) = product(a124,product(a115,a123)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[726,18783,theory(equality)]),12396,157,theory(equality)]) ).

cnf(18873,plain,
    product(a99,a75) = product(product(a115,a124),a123),
    inference('REWRITE',[status(thm)],[12396,18872,theory(equality)]) ).

cnf(18876,plain,
    product(product(a124,a100),a75) = product(a123,product(a115,a124)),
    inference('PARAMODULATE',[status(thm)],[754,18783,theory(equality)]) ).

cnf(18887,plain,
    product(product(a100,X),a123) = product(a122,product(X,a123)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,18802,theory(equality)]) ).

cnf(18888,plain,
    product(product(X,a100),a123) = product(product(X,a123),a122),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,18802,theory(equality)]) ).

cnf(18889,plain,
    product(a115,a124) = product(product(a115,a100),a123),
    inference('REWRITE',[status(thm)],[6070,18888,theory(equality)]) ).

cnf(18915,plain,
    product(product(X,product(a100,a115)),a124) = product(product(X,a115),a123),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,18859,theory(equality)]),1606,theory(equality)]) ).

cnf(18916,plain,
    product(a100,a122) = product(a123,a124),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,18859,theory(equality)]),knot_123,18815,18862,18854,theory(equality)]) ).

cnf(18917,plain,
    product(product(a100,a122),a75) = product(a124,a123),
    inference('REWRITE',[status(thm)],[3606,18916,theory(equality)]) ).

cnf(18921,plain,
    product(product(X,product(a100,a122)),a75) = product(product(X,a75),product(a124,a123)),
    inference('REWRITE',[status(thm)],[3619,18916,theory(equality)]) ).

cnf(18922,plain,
    product(a100,a122) = product(a124,product(a75,a124)),
    inference('REWRITE',[status(thm)],[5838,18916,theory(equality)]) ).

cnf(18926,plain,
    product(product(a124,a123),a68) = product(product(product(a100,a115),a68),a77),
    inference('REWRITE',[status(thm)],[8883,13566,18916,theory(equality)]) ).

cnf(18933,plain,
    product(a100,product(a75,a124)) = product(a115,product(a100,a122)),
    inference('REWRITE',[status(thm)],[18803,18916,theory(equality)]) ).

cnf(18941,plain,
    product(product(X,product(a100,a115)),a122) = product(product(X,a122),a123),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,18860,theory(equality)]) ).

cnf(18942,plain,
    a99 = product(product(a100,a115),product(a100,a122)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,18860,theory(equality)]),18854,18852,theory(equality)]) ).

cnf(18946,plain,
    product(a100,product(a100,a115)) = product(product(a124,a100),a75),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[289,18861,theory(equality)]),18876,18862,theory(equality)]) ).

cnf(18947,plain,
    product(a100,product(a100,a115)) = product(a123,product(a115,a124)),
    inference('REWRITE',[status(thm)],[18876,18946,theory(equality)]) ).

cnf(18951,plain,
    product(product(product(a100,a115),a99),product(a100,a115)) = product(a123,a100),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,18861,theory(equality)]),18851,theory(equality)]) ).

cnf(18954,plain,
    product(product(a100,a122),a123) = product(a123,product(a124,a123)),
    inference('PARAMODULATE',[status(thm)],[569,18916,theory(equality)]) ).

cnf(18955,plain,
    product(a100,product(a100,a115)) = product(product(a100,a122),a99),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[728,18916,theory(equality)]),18866,theory(equality)]) ).

cnf(18956,plain,
    product(a100,a115) = product(a99,product(a100,a122)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[727,18916,theory(equality)]),18813,18802,theory(equality)]) ).

cnf(18957,plain,
    product(product(a124,a123),a124) = product(product(a115,a100),a122),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,18916,theory(equality)]),1596,theory(equality)]) ).

cnf(18962,plain,
    product(product(X,a123),a124) = product(product(X,a124),product(a100,a122)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,18916,theory(equality)]) ).

cnf(18963,plain,
    product(a99,a115) = product(a122,a100),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[721,18852,theory(equality)]),involutory_quandle_01,theory(equality)]) ).

cnf(18975,plain,
    product(a122,a100) = product(product(a100,a122),a123),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[570,18863,theory(equality)]),18854,721,18963,theory(equality)]) ).

cnf(18976,plain,
    product(a122,a100) = product(a123,product(a124,a123)),
    inference('REWRITE',[status(thm)],[18954,18975,theory(equality)]) ).

cnf(18982,plain,
    product(product(product(a115,a100),a122),a75) = product(a122,a100),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[754,18917,theory(equality)]),18976,1596,theory(equality)]) ).

cnf(18983,plain,
    product(product(a122,a100),a75) = product(product(a115,a100),a122),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[581,18917,theory(equality)]),18957,18975,theory(equality)]) ).

cnf(18988,plain,
    product(product(X,a123),a75) = product(product(X,product(a75,a124)),product(a100,a122)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,18922,theory(equality)]),8782,theory(equality)]) ).

cnf(18991,plain,
    product(product(a100,a115),a99) = product(a100,product(a115,a124)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[430,18963,theory(equality)]),18824,theory(equality)]) ).

cnf(18992,plain,
    product(product(a100,a115),a99) = product(product(a115,a124),product(a75,product(a115,a124))),
    inference('REWRITE',[status(thm)],[18793,18991,theory(equality)]) ).

cnf(18998,plain,
    product(a73,product(a108,a73)) = a82,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,18709,theory(equality)]) ).

cnf(18999,plain,
    product(a73,a109) = product(a83,product(a108,a73)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[766,18709,theory(equality)]),15117,15139,theory(equality)]) ).

cnf(19001,plain,
    product(a73,a109) = product(a81,product(a118,a81)),
    inference('REWRITE',[status(thm)],[15117,18999,theory(equality)]) ).

cnf(19003,plain,
    product(a73,a109) = product(product(a73,a118),a82),
    inference('REWRITE',[status(thm)],[18723,18999,theory(equality)]) ).

cnf(19005,plain,
    a72 = product(a82,product(a118,a109)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,18709,theory(equality)]),15103,159,theory(equality)]) ).

cnf(19009,plain,
    product(a72,product(a108,a73)) = product(a82,a73),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[759,18709,theory(equality)]),18998,theory(equality)]) ).

cnf(19012,plain,
    product(product(X,a82),product(a108,a73)) = product(product(X,a73),a108),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,18709,theory(equality)]),713,theory(equality)]) ).

cnf(19029,plain,
    product(a72,product(a79,a70)) = product(a83,product(a73,product(a106,a39))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[759,18716,theory(equality)]),18731,theory(equality)]) ).

cnf(19032,plain,
    product(product(a73,X),product(a79,a70)) = product(a83,product(X,product(a79,a70))),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,18716,theory(equality)]) ).

cnf(19036,plain,
    product(product(a73,a39),a5) = product(a85,product(a85,product(a107,a5))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[543,18727,theory(equality)]),543,theory(equality)]) ).

cnf(19037,plain,
    product(product(a73,a39),a84) = product(a84,product(a84,a106)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,18727,theory(equality)]),involutory_quandle,12953,theory(equality)]) ).

cnf(19038,plain,
    product(product(a73,a39),a84) = product(product(a84,a106),product(a107,a106)),
    inference('REWRITE',[status(thm)],[7003,19037,theory(equality)]) ).

cnf(19049,plain,
    product(product(X,a109),a81) = product(product(X,a118),a73),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,18749,theory(equality)]),713,18722,theory(equality)]) ).

cnf(19050,plain,
    a71 = product(a73,product(a116,a32)),
    inference('REWRITE',[status(thm)],[6177,1356,19049,theory(equality)]) ).

cnf(19051,plain,
    a108 = product(product(a116,a32),a71),
    inference('REWRITE',[status(thm)],[13347,19050,theory(equality)]) ).

cnf(19052,plain,
    product(product(X,a109),a81) = product(product(X,a73),product(a116,a32)),
    inference('REWRITE',[status(thm)],[1345,19049,theory(equality)]) ).

cnf(19054,plain,
    product(a110,a118) = product(a116,a32),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,19051,theory(equality)]),1462,theory(equality)]) ).

cnf(19055,plain,
    a118 = product(product(a110,a109),a81),
    inference('REWRITE',[status(thm)],[1330,19049,19054,theory(equality)]) ).

cnf(19056,plain,
    product(a118,a73) = product(a110,a118),
    inference('REWRITE',[status(thm)],[1339,19054,theory(equality)]) ).

cnf(19059,plain,
    product(product(X,product(a110,a118)),a73) = product(product(X,a73),a118),
    inference('REWRITE',[status(thm)],[1342,19054,theory(equality)]) ).

cnf(19069,plain,
    product(a110,a118) = product(a112,a70),
    inference('REWRITE',[status(thm)],[9526,19054,theory(equality)]) ).

cnf(19071,plain,
    product(a109,a119) = a112,
    inference('REWRITE',[status(thm)],[9553,8852,19054,theory(equality)]) ).

cnf(19073,plain,
    product(a112,a118) = product(a110,a71),
    inference('REWRITE',[status(thm)],[8861,19071,theory(equality)]) ).

cnf(19082,plain,
    product(product(a70,a112),a70) = product(a70,product(a110,a118)),
    inference('REWRITE',[status(thm)],[9562,19054,theory(equality)]) ).

cnf(19099,plain,
    product(a118,a108) = product(product(a108,a110),a118),
    inference('REWRITE',[status(thm)],[13345,446,19054,theory(equality)]) ).

cnf(19100,plain,
    product(a118,a108) = product(product(product(a111,a109),a118),a71),
    inference('REWRITE',[status(thm)],[12465,19099,theory(equality)]) ).

cnf(19102,plain,
    product(a71,product(a108,a73)) = product(product(a70,a108),product(a110,a118)),
    inference('REWRITE',[status(thm)],[15105,19054,theory(equality)]) ).

cnf(19104,plain,
    product(a81,product(a110,a118)) = product(a73,a108),
    inference('REWRITE',[status(thm)],[18491,19054,theory(equality)]) ).

cnf(19109,plain,
    product(product(a109,a110),a118) = a118,
    inference('REWRITE',[status(thm)],[18663,775,19054,theory(equality)]) ).

cnf(19113,plain,
    product(a82,product(a110,a118)) = product(a70,product(a79,a70)),
    inference('REWRITE',[status(thm)],[18668,19054,theory(equality)]) ).

cnf(19116,plain,
    product(a118,a108) = product(product(a110,a118),a83),
    inference('REWRITE',[status(thm)],[18694,19054,theory(equality)]) ).

cnf(19123,plain,
    product(product(X,a108),product(a110,a118)) = product(product(X,a109),product(a118,a81)),
    inference('REWRITE',[status(thm)],[18708,19054,theory(equality)]) ).

cnf(19126,plain,
    product(a73,a118) = product(a83,product(a110,a118)),
    inference('REWRITE',[status(thm)],[18718,19054,theory(equality)]) ).

cnf(19127,plain,
    a81 = product(product(a73,a108),product(a110,a118)),
    inference('REWRITE',[status(thm)],[18740,19054,theory(equality)]) ).

cnf(19131,plain,
    a71 = product(a73,product(a110,a118)),
    inference('REWRITE',[status(thm)],[19050,19054,theory(equality)]) ).

cnf(19132,plain,
    product(product(X,a109),a81) = product(product(X,a73),product(a110,a118)),
    inference('REWRITE',[status(thm)],[19052,19054,theory(equality)]) ).

cnf(19133,plain,
    product(a112,a119) = a109,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,19071,theory(equality)]) ).

cnf(19134,plain,
    a109 = product(a110,a80),
    inference('REWRITE',[status(thm)],[1276,19133,theory(equality)]) ).

cnf(19145,plain,
    product(a100,a115) = product(a114,a121),
    inference('REWRITE',[status(thm)],[9412,18829,19133,theory(equality)]) ).

cnf(19146,plain,
    product(product(a100,a115),a68) = a124,
    inference('REWRITE',[status(thm)],[3782,19145,theory(equality)]) ).

cnf(19147,plain,
    a124 = product(a114,product(a76,a121)),
    inference('REWRITE',[status(thm)],[18827,19146,theory(equality)]) ).

cnf(19148,plain,
    product(a121,a77) = product(a124,a76),
    inference('REWRITE',[status(thm)],[18828,19146,theory(equality)]) ).

cnf(19149,plain,
    product(a124,a76) = product(a114,product(a121,a114)),
    inference('REWRITE',[status(thm)],[12438,19148,theory(equality)]) ).

cnf(19151,plain,
    product(product(a124,a123),a68) = product(product(a121,a124),a76),
    inference('REWRITE',[status(thm)],[13553,8917,19148,theory(equality)]) ).

cnf(19161,plain,
    product(product(a121,a124),a76) = product(a124,a77),
    inference('REWRITE',[status(thm)],[18926,19151,19146,theory(equality)]) ).

cnf(19162,plain,
    product(product(a124,a123),a68) = product(a124,a77),
    inference('REWRITE',[status(thm)],[19151,19161,theory(equality)]) ).

cnf(19163,plain,
    product(a124,a68) = product(a100,a115),
    inference('REWRITE',[status(thm)],[3792,19145,theory(equality)]) ).

cnf(19172,plain,
    product(product(a114,a124),a68) = product(a115,product(a100,a115)),
    inference('REWRITE',[status(thm)],[3806,19145,theory(equality)]) ).

cnf(19176,plain,
    product(product(a121,a124),a68) = product(a100,a122),
    inference('REWRITE',[status(thm)],[3823,18854,19145,theory(equality)]) ).

cnf(19177,plain,
    a122 = product(a124,product(a68,a124)),
    inference('REWRITE',[status(thm)],[6155,18859,19145,theory(equality)]) ).

cnf(19178,plain,
    product(product(a68,a124),a68) = product(a68,product(a100,a115)),
    inference('REWRITE',[status(thm)],[6180,19145,theory(equality)]) ).

cnf(19181,plain,
    product(product(a100,a115),a114) = product(a124,a76),
    inference('REWRITE',[status(thm)],[8772,19148,19145,theory(equality)]) ).

cnf(19188,plain,
    product(product(X,product(a100,a115)),a114) = product(product(X,a114),product(a124,a76)),
    inference('REWRITE',[status(thm)],[12442,19148,19145,theory(equality)]) ).

cnf(19190,plain,
    product(product(a115,a124),a68) = product(a114,product(a100,a115)),
    inference('REWRITE',[status(thm)],[13541,19145,theory(equality)]) ).

cnf(19194,plain,
    product(a100,a68) = product(product(a114,product(a100,a115)),a76),
    inference('REWRITE',[status(thm)],[18796,19145,theory(equality)]) ).

cnf(19195,plain,
    product(a100,a68) = product(product(a100,a115),a77),
    inference('REWRITE',[status(thm)],[18797,19145,theory(equality)]) ).

cnf(19196,plain,
    a124 = product(a121,product(a100,a115)),
    inference('REWRITE',[status(thm)],[18826,19146,19145,theory(equality)]) ).

cnf(19204,plain,
    a110 = product(a119,a109),
    inference('REWRITE',[status(thm)],[12521,19133,theory(equality)]) ).

cnf(19207,plain,
    a109 = product(a118,a110),
    inference('REWRITE',[status(thm)],[3751,166,19204,theory(equality)]) ).

cnf(19209,plain,
    product(product(a118,a109),product(product(a118,a109),a72)) = product(a110,a72),
    inference('REWRITE',[status(thm)],[12450,19204,theory(equality)]) ).

cnf(19214,plain,
    product(a109,a79) = product(a110,a112),
    inference('REWRITE',[status(thm)],[13005,19133,theory(equality)]) ).

cnf(19219,plain,
    product(product(a110,a109),product(a111,a109)) = product(product(a110,a112),a110),
    inference('REWRITE',[status(thm)],[13043,involutory_quandle_02,19133,theory(equality)]) ).

cnf(19220,plain,
    product(a119,product(a119,a110)) = product(product(a110,a109),product(a111,a109)),
    inference('REWRITE',[status(thm)],[13019,19219,theory(equality)]) ).

cnf(19222,plain,
    product(a111,product(a119,a80)) = product(product(a110,a109),product(a111,a109)),
    inference('REWRITE',[status(thm)],[18625,19219,theory(equality)]) ).

cnf(19229,plain,
    product(product(a100,a115),a32) = product(a109,a13),
    inference('REWRITE',[status(thm)],[15221,19145,19133,theory(equality)]) ).

cnf(19234,plain,
    product(a79,a109) = product(product(a80,a111),a112),
    inference('REWRITE',[status(thm)],[18523,19133,theory(equality)]) ).

cnf(19235,plain,
    product(a119,a80) = product(a112,a109),
    inference('REWRITE',[status(thm)],[18525,19133,theory(equality)]) ).

cnf(19251,plain,
    product(product(X,a111),a112) = product(product(X,a110),product(a112,a109)),
    inference('REWRITE',[status(thm)],[18522,19235,theory(equality)]) ).

cnf(19252,plain,
    product(a79,a109) = product(product(a80,a110),product(a112,a109)),
    inference('REWRITE',[status(thm)],[19234,19251,theory(equality)]) ).

cnf(19257,plain,
    product(product(X,product(a112,a109)),product(a80,a110)) = product(product(X,a110),a80),
    inference('REWRITE',[status(thm)],[18571,19235,theory(equality)]) ).

cnf(19258,plain,
    product(a110,a111) = product(product(a112,a109),a79),
    inference('REWRITE',[status(thm)],[18604,19235,theory(equality)]) ).

cnf(19261,plain,
    product(a119,product(a112,a109)) = product(a111,a110),
    inference('REWRITE',[status(thm)],[18617,19235,theory(equality)]) ).

cnf(19263,plain,
    product(product(product(a112,a109),X),a79) = product(product(a110,a111),product(X,a79)),
    inference('REWRITE',[status(thm)],[18621,19235,theory(equality)]) ).

cnf(19264,plain,
    product(product(X,product(a112,a109)),a79) = product(product(X,a79),product(a110,a111)),
    inference('REWRITE',[status(thm)],[18622,19235,theory(equality)]) ).

cnf(19269,plain,
    product(a111,product(a112,a109)) = product(product(a110,a109),product(a111,a109)),
    inference('REWRITE',[status(thm)],[19222,19235,theory(equality)]) ).

cnf(19271,plain,
    product(a119,a110) = product(a111,a109),
    inference('REWRITE',[status(thm)],[18569,747,19235,19133,theory(equality)]) ).

cnf(19272,plain,
    product(a111,a110) = product(a110,product(a111,a109)),
    inference('REWRITE',[status(thm)],[1264,19271,theory(equality)]) ).

cnf(19275,plain,
    product(a108,a110) = product(a118,a109),
    inference('REWRITE',[status(thm)],[3745,8843,19271,theory(equality)]) ).

cnf(19276,plain,
    product(a83,a109) = product(a81,product(a108,a110)),
    inference('REWRITE',[status(thm)],[1411,19275,theory(equality)]) ).

cnf(19280,plain,
    product(a70,a109) = product(a72,product(a108,a110)),
    inference('REWRITE',[status(thm)],[3636,19275,theory(equality)]) ).

cnf(19283,plain,
    product(product(X,a72),product(a108,a110)) = product(product(X,product(a108,a110)),product(a70,a109)),
    inference('REWRITE',[status(thm)],[3645,19275,theory(equality)]) ).

cnf(19284,plain,
    product(a108,a109) = product(a109,product(a108,a110)),
    inference('REWRITE',[status(thm)],[5843,19275,theory(equality)]) ).

cnf(19285,plain,
    product(product(a118,a108),a118) = product(a108,a110),
    inference('REWRITE',[status(thm)],[5942,19275,theory(equality)]) ).

cnf(19286,plain,
    product(product(a70,a109),a72) = product(a72,product(product(a108,a110),a72)),
    inference('REWRITE',[status(thm)],[6214,19275,theory(equality)]) ).

cnf(19288,plain,
    product(a118,product(a108,a110)) = product(product(a118,a108),a109),
    inference('REWRITE',[status(thm)],[7622,19275,theory(equality)]) ).

cnf(19290,plain,
    product(product(product(a110,a109),product(a112,a109)),product(a70,a109)) = product(a118,product(a108,a110)),
    inference('REWRITE',[status(thm)],[13348,19288,theory(equality)]) ).

cnf(19291,plain,
    product(a118,product(a108,a110)) = product(a109,product(a108,a81)),
    inference('REWRITE',[status(thm)],[18662,19288,theory(equality)]) ).

cnf(19298,plain,
    product(product(a118,a108),product(a108,a110)) = product(product(a108,a110),product(a118,product(a108,a110))),
    inference('REWRITE',[status(thm)],[8060,19288,19275,theory(equality)]) ).

cnf(19300,plain,
    product(product(X,a108),a118) = product(product(X,a109),product(a108,a110)),
    inference('REWRITE',[status(thm)],[8828,19275,theory(equality)]) ).

cnf(19301,plain,
    product(a109,a72) = product(product(a108,a110),product(a70,product(a108,a110))),
    inference('REWRITE',[status(thm)],[18490,5941,19300,theory(equality)]) ).

cnf(19302,plain,
    product(product(a80,a108),a118) = product(product(a82,a72),product(product(a108,a110),a72)),
    inference('REWRITE',[status(thm)],[10764,19275,theory(equality)]) ).

cnf(19305,plain,
    product(a71,product(a108,a110)) = product(product(a70,a108),a109),
    inference('REWRITE',[status(thm)],[13168,19275,theory(equality)]) ).

cnf(19306,plain,
    product(a108,product(a108,a110)) = product(product(a109,a108),a109),
    inference('REWRITE',[status(thm)],[13245,19275,theory(equality)]) ).

cnf(19309,plain,
    product(a109,product(a118,a81)) = product(a108,a110),
    inference('REWRITE',[status(thm)],[13462,19275,theory(equality)]) ).

cnf(19310,plain,
    product(product(a108,a110),a82) = product(a108,a73),
    inference('REWRITE',[status(thm)],[15101,19275,theory(equality)]) ).

cnf(19311,plain,
    product(a108,a110) = product(product(a108,a73),a82),
    inference('REWRITE',[status(thm)],[15103,19275,theory(equality)]) ).

cnf(19313,plain,
    product(product(a71,a72),product(a108,a110)) = product(product(a70,a109),product(a111,a109)),
    inference('REWRITE',[status(thm)],[17479,19275,theory(equality)]) ).

cnf(19315,plain,
    product(product(a110,a112),a118) = product(product(a108,a110),a71),
    inference('REWRITE',[status(thm)],[18593,19275,theory(equality)]) ).

cnf(19317,plain,
    product(a70,product(a108,a73)) = product(product(a71,product(a108,a110)),product(a108,a81)),
    inference('REWRITE',[status(thm)],[18645,19275,theory(equality)]) ).

cnf(19321,plain,
    a72 = product(a82,product(a108,a110)),
    inference('REWRITE',[status(thm)],[19005,19275,theory(equality)]) ).

cnf(19327,plain,
    product(product(a108,a110),product(product(a108,a110),a72)) = product(a110,a72),
    inference('REWRITE',[status(thm)],[19209,19275,theory(equality)]) ).

cnf(19340,plain,
    product(product(a111,a109),a119) = product(a110,a112),
    inference('REWRITE',[status(thm)],[12984,19271,theory(equality)]) ).

cnf(19346,plain,
    product(product(product(a110,a112),X),a119) = product(product(a111,a109),product(X,a119)),
    inference('REWRITE',[status(thm)],[12995,19271,theory(equality)]) ).

cnf(19360,plain,
    product(product(a79,a110),product(a111,a110)) = product(a80,product(a111,a109)),
    inference('REWRITE',[status(thm)],[13281,19271,theory(equality)]) ).

cnf(19361,plain,
    product(product(a70,a119),product(a111,a109)) = product(product(a70,a110),product(a111,a110)),
    inference('REWRITE',[status(thm)],[17481,19271,theory(equality)]) ).

cnf(19362,plain,
    product(product(a111,a109),a79) = product(a112,product(a110,a112)),
    inference('REWRITE',[status(thm)],[18606,19271,theory(equality)]) ).

cnf(19365,plain,
    product(a119,product(a111,a109)) = product(product(a110,a109),product(a111,a109)),
    inference('REWRITE',[status(thm)],[19220,19271,theory(equality)]) ).

cnf(19367,plain,
    product(a119,product(a111,a109)) = product(product(a110,a112),a110),
    inference('REWRITE',[status(thm)],[19219,19365,theory(equality)]) ).

cnf(19368,plain,
    product(a111,product(a112,a109)) = product(a119,product(a111,a109)),
    inference('REWRITE',[status(thm)],[19269,19365,theory(equality)]) ).

cnf(19373,plain,
    product(product(a79,a109),product(a80,a110)) = a80,
    inference('REWRITE',[status(thm)],[18572,19133,theory(equality)]) ).

cnf(19375,plain,
    product(a109,product(a112,a111)) = product(product(a111,a109),a79),
    inference('REWRITE',[status(thm)],[18607,19362,19133,theory(equality)]) ).

cnf(19378,plain,
    product(product(X,a109),a79) = product(product(X,a79),product(a110,a112)),
    inference('REWRITE',[status(thm)],[18611,19133,theory(equality)]) ).

cnf(19379,plain,
    product(product(a80,a109),a79) = product(a80,a112),
    inference('REWRITE',[status(thm)],[13067,19378,theory(equality)]) ).

cnf(19380,plain,
    product(product(a110,a109),product(a112,a109)) = product(a109,product(a79,a109)),
    inference('REWRITE',[status(thm)],[18612,involutory_quandle_02,19133,theory(equality)]) ).

cnf(19388,plain,
    product(a112,a109) = product(a109,a110),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,19071,theory(equality)]),19204,theory(equality)]) ).

cnf(19391,plain,
    product(product(a110,a79),a70) = product(a118,product(a71,a108)),
    inference('REWRITE',[status(thm)],[18630,19109,19388,theory(equality)]) ).

cnf(19392,plain,
    product(a119,a80) = product(a109,a110),
    inference('REWRITE',[status(thm)],[19235,19388,theory(equality)]) ).

cnf(19406,plain,
    product(product(X,a111),a112) = product(product(X,a109),a110),
    inference('REWRITE',[status(thm)],[19251,involutory_quandle_02,19388,theory(equality)]) ).

cnf(19409,plain,
    product(product(X,a109),a110) = product(product(X,a112),a119),
    inference('REWRITE',[status(thm)],[12516,19406,theory(equality)]) ).

cnf(19411,plain,
    product(a79,a109) = product(product(a80,a109),a110),
    inference('REWRITE',[status(thm)],[19252,involutory_quandle_02,19388,theory(equality)]) ).

cnf(19415,plain,
    product(product(X,product(a109,a110)),product(a80,a110)) = product(product(X,a110),a80),
    inference('REWRITE',[status(thm)],[19257,19388,theory(equality)]) ).

cnf(19416,plain,
    product(a110,a111) = product(product(a109,a110),a79),
    inference('REWRITE',[status(thm)],[19258,19388,theory(equality)]) ).

cnf(19419,plain,
    product(a119,product(a109,a110)) = product(a111,a110),
    inference('REWRITE',[status(thm)],[19261,19388,theory(equality)]) ).

cnf(19421,plain,
    product(product(product(a109,a110),X),a79) = product(product(a110,a111),product(X,a79)),
    inference('REWRITE',[status(thm)],[19263,19388,theory(equality)]) ).

cnf(19422,plain,
    product(product(X,product(a109,a110)),a79) = product(product(X,a79),product(a110,a111)),
    inference('REWRITE',[status(thm)],[19264,19388,theory(equality)]) ).

cnf(19424,plain,
    product(product(product(a110,a109),product(a109,a110)),product(a70,a109)) = product(a118,product(a108,a110)),
    inference('REWRITE',[status(thm)],[19290,19388,theory(equality)]) ).

cnf(19426,plain,
    product(a111,product(a109,a110)) = product(a119,product(a111,a109)),
    inference('REWRITE',[status(thm)],[19368,19388,theory(equality)]) ).

cnf(19429,plain,
    product(a111,product(a109,a110)) = product(product(a110,a112),a110),
    inference('REWRITE',[status(thm)],[19367,19426,theory(equality)]) ).

cnf(19435,plain,
    product(product(a110,a109),product(a109,a110)) = product(a109,product(a79,a109)),
    inference('REWRITE',[status(thm)],[19380,19388,theory(equality)]) ).

cnf(19438,plain,
    product(product(a109,a110),a119) = product(a112,a111),
    inference('PARAMODULATE',[status(thm)],[578,19071,theory(equality)]) ).

cnf(19442,plain,
    product(product(X,a109),a119) = product(product(X,a112),a111),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,19071,theory(equality)]),12525,theory(equality)]) ).

cnf(19444,plain,
    product(a112,a110) = product(a109,product(a109,a110)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[295,19134,theory(equality)]),19392,18629,theory(equality)]) ).

cnf(19445,plain,
    a110 = product(a108,a73),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[589,19134,theory(equality)]),15087,166,knot_110,theory(equality)]) ).

cnf(19453,plain,
    product(a110,product(a112,a118)) = product(product(a112,a118),product(a71,product(a112,a118))),
    inference('REWRITE',[status(thm)],[15099,19445,theory(equality)]) ).

cnf(19454,plain,
    product(a109,a110) = a118,
    inference('REWRITE',[status(thm)],[15100,19445,theory(equality)]) ).

cnf(19455,plain,
    a119 = product(a110,a109),
    inference('REWRITE',[status(thm)],[3720,knot_119,19454,theory(equality)]) ).

cnf(19460,plain,
    product(a70,product(a70,a109)) = product(product(a70,a109),a119),
    inference('REWRITE',[status(thm)],[7048,19455,theory(equality)]) ).

cnf(19461,plain,
    product(product(a70,a110),product(a70,a109)) = product(product(a70,a109),product(product(a70,a109),a119)),
    inference('REWRITE',[status(thm)],[8066,19460,theory(equality)]) ).

cnf(19462,plain,
    product(a81,product(a70,a109)) = product(a73,a70),
    inference('REWRITE',[status(thm)],[13187,9528,19071,742,19455,theory(equality)]) ).

cnf(19463,plain,
    product(a108,product(a70,a109)) = product(a110,a112),
    inference('REWRITE',[status(thm)],[17630,19340,19455,theory(equality)]) ).

cnf(19464,plain,
    a118 = product(a119,a81),
    inference('REWRITE',[status(thm)],[19055,19455,theory(equality)]) ).

cnf(19470,plain,
    product(a118,a13) = product(product(a110,a13),product(a69,product(a110,a13))),
    inference('REWRITE',[status(thm)],[10176,19454,theory(equality)]) ).

cnf(19471,plain,
    product(a112,a109) = a118,
    inference('REWRITE',[status(thm)],[19388,19454,theory(equality)]) ).

cnf(19488,plain,
    product(product(X,a118),product(a80,a110)) = product(product(X,a110),a80),
    inference('REWRITE',[status(thm)],[19415,19454,theory(equality)]) ).

cnf(19489,plain,
    product(a110,a111) = product(a118,a79),
    inference('REWRITE',[status(thm)],[19416,19454,theory(equality)]) ).

cnf(19492,plain,
    product(a119,a118) = product(a111,a110),
    inference('REWRITE',[status(thm)],[19419,19454,theory(equality)]) ).

cnf(19493,plain,
    product(a111,a110) = product(a118,a71),
    inference('REWRITE',[status(thm)],[1481,19492,theory(equality)]) ).

cnf(19502,plain,
    product(a70,a71) = product(a71,product(a111,a110)),
    inference('REWRITE',[status(thm)],[5842,19492,theory(equality)]) ).

cnf(19503,plain,
    product(a118,a119) = product(a108,a109),
    inference('REWRITE',[status(thm)],[5845,13307,19492,theory(equality)]) ).

cnf(19507,plain,
    product(a109,a108) = product(a119,a71),
    inference('REWRITE',[status(thm)],[8813,3681,19503,theory(equality)]) ).

cnf(19522,plain,
    product(a70,product(a111,a110)) = product(a71,product(a70,a71)),
    inference('REWRITE',[status(thm)],[13206,19492,theory(equality)]) ).

cnf(19532,plain,
    product(product(a118,X),a79) = product(product(a110,a111),product(X,a79)),
    inference('REWRITE',[status(thm)],[19421,19454,theory(equality)]) ).

cnf(19533,plain,
    product(product(X,a118),a79) = product(product(X,a79),product(a110,a111)),
    inference('REWRITE',[status(thm)],[19422,19454,theory(equality)]) ).

cnf(19534,plain,
    product(product(a110,a118),a79) = product(product(a110,a112),product(a80,a111)),
    inference('REWRITE',[status(thm)],[13069,19533,theory(equality)]) ).

cnf(19536,plain,
    product(product(a111,a110),product(a70,a109)) = product(a118,product(a108,a110)),
    inference('REWRITE',[status(thm)],[19424,19492,19455,19454,theory(equality)]) ).

cnf(19538,plain,
    product(a111,a118) = product(a119,product(a111,a109)),
    inference('REWRITE',[status(thm)],[19426,19454,theory(equality)]) ).

cnf(19540,plain,
    product(a111,a118) = product(product(a110,a112),a110),
    inference('REWRITE',[status(thm)],[19429,19454,theory(equality)]) ).

cnf(19545,plain,
    product(a111,a110) = product(a109,product(a79,a109)),
    inference('REWRITE',[status(thm)],[19435,19492,19455,19454,theory(equality)]) ).

cnf(19546,plain,
    product(a108,a109) = product(a112,a111),
    inference('REWRITE',[status(thm)],[19438,19503,19454,theory(equality)]) ).

cnf(19551,plain,
    product(a80,a79) = product(a79,product(a108,a109)),
    inference('REWRITE',[status(thm)],[12482,19546,theory(equality)]) ).

cnf(19562,plain,
    product(a110,a79) = product(a112,product(a108,a109)),
    inference('REWRITE',[status(thm)],[12518,19546,theory(equality)]) ).

cnf(19568,plain,
    product(a111,a110) = product(a106,a39),
    inference('REWRITE',[status(thm)],[13454,8844,19546,theory(equality)]) ).

cnf(19570,plain,
    product(a108,a83) = product(a111,a110),
    inference('REWRITE',[status(thm)],[1232,19568,theory(equality)]) ).

cnf(19576,plain,
    product(a111,a110) = product(product(a105,a39),a4),
    inference('REWRITE',[status(thm)],[3013,19568,theory(equality)]) ).

cnf(19582,plain,
    product(product(a79,a70),a83) = product(a83,product(a111,a110)),
    inference('REWRITE',[status(thm)],[6072,19568,theory(equality)]) ).

cnf(19604,plain,
    product(a82,product(a79,a70)) = product(a73,product(a111,a110)),
    inference('REWRITE',[status(thm)],[18731,19568,theory(equality)]) ).

cnf(19606,plain,
    product(a72,product(a79,a70)) = product(a83,product(a73,product(a111,a110))),
    inference('REWRITE',[status(thm)],[19029,19568,theory(equality)]) ).

cnf(19616,plain,
    product(a109,product(a108,a109)) = product(product(a111,a109),a79),
    inference('REWRITE',[status(thm)],[19375,19546,theory(equality)]) ).

cnf(19617,plain,
    product(a109,product(a108,a109)) = product(a112,product(a110,a112)),
    inference('REWRITE',[status(thm)],[19362,19616,theory(equality)]) ).

cnf(19627,plain,
    product(a112,a110) = a108,
    inference('REWRITE',[status(thm)],[19444,164,19454,theory(equality)]) ).

cnf(19629,plain,
    product(a110,a79) = product(a108,a119),
    inference('REWRITE',[status(thm)],[13068,19627,theory(equality)]) ).

cnf(19632,plain,
    product(a111,a118) = product(a118,product(a71,a108)),
    inference('REWRITE',[status(thm)],[19391,1488,knot_109,785,19629,theory(equality)]) ).

cnf(19633,plain,
    product(a108,a119) = product(a112,product(a108,a109)),
    inference('REWRITE',[status(thm)],[19562,19629,theory(equality)]) ).

cnf(19640,plain,
    a111 = product(a108,a81),
    inference('REWRITE',[status(thm)],[18643,1268,19627,theory(equality)]) ).

cnf(19643,plain,
    product(a118,product(a108,a110)) = product(a109,a111),
    inference('REWRITE',[status(thm)],[19291,19640,theory(equality)]) ).

cnf(19646,plain,
    product(product(a118,a108),product(a108,a110)) = product(product(a108,a110),product(a109,a111)),
    inference('REWRITE',[status(thm)],[19298,19643,theory(equality)]) ).

cnf(19647,plain,
    product(product(a111,a110),product(a70,a109)) = product(a109,a111),
    inference('REWRITE',[status(thm)],[19536,19643,theory(equality)]) ).

cnf(19660,plain,
    product(product(a109,X),a110) = product(a118,product(X,a110)),
    inference('REWRITE',[status(thm)],[15109,19445,theory(equality)]) ).

cnf(19664,plain,
    product(product(X,a109),a110) = product(product(X,a110),a118),
    inference('REWRITE',[status(thm)],[15110,19445,theory(equality)]) ).

cnf(19668,plain,
    product(a118,a108) = product(product(a108,a109),a110),
    inference('REWRITE',[status(thm)],[19099,19664,theory(equality)]) ).

cnf(19669,plain,
    product(a79,a109) = product(a83,a71),
    inference('REWRITE',[status(thm)],[3669,19411,19664,theory(equality)]) ).

cnf(19675,plain,
    a110 = product(product(a124,a13),a33),
    inference('REWRITE',[status(thm)],[15120,19445,theory(equality)]) ).

cnf(19678,plain,
    a119 = product(a118,a81),
    inference('REWRITE',[status(thm)],[15139,19455,19445,theory(equality)]) ).

cnf(19687,plain,
    product(a119,a82) = a109,
    inference('REWRITE',[status(thm)],[13445,19678,theory(equality)]) ).

cnf(19688,plain,
    product(a71,a82) = product(a73,a119),
    inference('REWRITE',[status(thm)],[13447,19678,theory(equality)]) ).

cnf(19689,plain,
    product(product(a109,a73),a82) = product(a119,a72),
    inference('REWRITE',[status(thm)],[13452,19678,theory(equality)]) ).

cnf(19701,plain,
    product(a73,a109) = product(a81,a119),
    inference('REWRITE',[status(thm)],[19001,19678,theory(equality)]) ).

cnf(19702,plain,
    product(a73,a109) = product(a79,product(a70,a119)),
    inference('REWRITE',[status(thm)],[1438,19701,theory(equality)]) ).

cnf(19710,plain,
    product(product(X,a108),product(a110,a118)) = product(product(X,a109),a119),
    inference('REWRITE',[status(thm)],[19123,19678,theory(equality)]) ).

cnf(19711,plain,
    product(a70,product(a70,a109)) = product(product(a70,a108),product(a110,a118)),
    inference('REWRITE',[status(thm)],[19460,19710,theory(equality)]) ).

cnf(19712,plain,
    product(product(a70,a110),product(a70,a109)) = product(product(a70,a109),product(product(a70,a108),product(a110,a118))),
    inference('REWRITE',[status(thm)],[19461,19710,theory(equality)]) ).

cnf(19713,plain,
    a112 = product(a108,a110),
    inference('REWRITE',[status(thm)],[19309,19071,19678,theory(equality)]) ).

cnf(19716,plain,
    product(a110,a118) = product(a111,a109),
    inference('REWRITE',[status(thm)],[12463,19069,19713,theory(equality)]) ).

cnf(19717,plain,
    product(a111,a109) = product(a108,a71),
    inference('REWRITE',[status(thm)],[1462,19716,theory(equality)]) ).

cnf(19721,plain,
    product(product(X,a108),a71) = product(product(X,a71),product(a111,a109)),
    inference('REWRITE',[status(thm)],[1472,19716,theory(equality)]) ).

cnf(19723,plain,
    product(product(product(a111,a109),X),a71) = product(a108,product(X,a71)),
    inference('REWRITE',[status(thm)],[1474,19716,theory(equality)]) ).

cnf(19724,plain,
    product(a118,a108) = product(a108,product(a111,a110)),
    inference('REWRITE',[status(thm)],[19100,19493,19723,theory(equality)]) ).

cnf(19726,plain,
    product(product(a71,a108),a71) = product(a71,product(a111,a109)),
    inference('REWRITE',[status(thm)],[6133,19716,theory(equality)]) ).

cnf(19729,plain,
    product(a118,a73) = product(a111,a109),
    inference('REWRITE',[status(thm)],[19056,19716,theory(equality)]) ).

cnf(19732,plain,
    product(product(X,product(a111,a109)),a73) = product(product(X,a73),a118),
    inference('REWRITE',[status(thm)],[19059,19716,theory(equality)]) ).

cnf(19742,plain,
    product(a111,a109) = product(a112,a70),
    inference('REWRITE',[status(thm)],[19069,19716,theory(equality)]) ).

cnf(19751,plain,
    product(product(a70,a112),a70) = product(a70,product(a111,a109)),
    inference('REWRITE',[status(thm)],[19082,19716,theory(equality)]) ).

cnf(19767,plain,
    product(a81,product(a111,a109)) = product(a73,a108),
    inference('REWRITE',[status(thm)],[19104,19716,theory(equality)]) ).

cnf(19774,plain,
    product(a82,product(a111,a109)) = product(a70,product(a79,a70)),
    inference('REWRITE',[status(thm)],[19113,19716,theory(equality)]) ).

cnf(19777,plain,
    product(a118,a108) = product(product(a111,a109),a83),
    inference('REWRITE',[status(thm)],[19116,19716,theory(equality)]) ).

cnf(19783,plain,
    product(a73,a118) = product(a83,product(a111,a109)),
    inference('REWRITE',[status(thm)],[19126,19716,theory(equality)]) ).

cnf(19784,plain,
    a81 = product(product(a73,a108),product(a111,a109)),
    inference('REWRITE',[status(thm)],[19127,19716,theory(equality)]) ).

cnf(19788,plain,
    a71 = product(a73,product(a111,a109)),
    inference('REWRITE',[status(thm)],[19131,19716,theory(equality)]) ).

cnf(19789,plain,
    product(product(X,a109),a81) = product(product(X,a73),product(a111,a109)),
    inference('REWRITE',[status(thm)],[19132,19716,theory(equality)]) ).

cnf(19790,plain,
    product(a109,product(a108,a109)) = product(product(a110,a112),product(a80,a111)),
    inference('REWRITE',[status(thm)],[19534,19616,19716,theory(equality)]) ).

cnf(19794,plain,
    product(a70,product(a70,a109)) = product(product(a70,a108),product(a111,a109)),
    inference('REWRITE',[status(thm)],[19711,19716,theory(equality)]) ).

cnf(19795,plain,
    product(product(a70,a110),product(a70,a109)) = product(product(a70,a109),product(product(a70,a108),product(a111,a109))),
    inference('REWRITE',[status(thm)],[19712,19716,theory(equality)]) ).

cnf(19797,plain,
    a112 = product(a118,a109),
    inference('REWRITE',[status(thm)],[19275,19713,theory(equality)]) ).

cnf(19798,plain,
    product(a83,a109) = product(a81,a112),
    inference('REWRITE',[status(thm)],[19276,19713,theory(equality)]) ).

cnf(19799,plain,
    product(product(product(a80,a108),a118),product(product(a108,a109),a72)) = product(product(a81,a112),a72),
    inference('REWRITE',[status(thm)],[10741,19798,theory(equality)]) ).

cnf(19806,plain,
    product(a70,a109) = product(a72,a112),
    inference('REWRITE',[status(thm)],[19280,19713,theory(equality)]) ).

cnf(19809,plain,
    product(product(X,a72),a112) = product(product(X,a112),product(a70,a109)),
    inference('REWRITE',[status(thm)],[19283,19713,theory(equality)]) ).

cnf(19810,plain,
    product(a108,a109) = product(a109,a112),
    inference('REWRITE',[status(thm)],[19284,19713,theory(equality)]) ).

cnf(19812,plain,
    product(product(a118,a108),a118) = a112,
    inference('REWRITE',[status(thm)],[19285,19713,theory(equality)]) ).

cnf(19813,plain,
    product(product(a70,a109),a72) = product(a72,product(a112,a72)),
    inference('REWRITE',[status(thm)],[19286,19713,theory(equality)]) ).

cnf(19823,plain,
    product(a109,a72) = product(product(a116,a112),product(a32,a112)),
    inference('REWRITE',[status(thm)],[19301,9555,19713,theory(equality)]) ).

cnf(19824,plain,
    product(a109,a72) = product(a112,product(a70,a112)),
    inference('REWRITE',[status(thm)],[9555,19823,theory(equality)]) ).

cnf(19827,plain,
    product(product(a80,a108),a118) = product(product(a82,a112),a72),
    inference('REWRITE',[status(thm)],[19302,involutory_quandle_02,19713,theory(equality)]) ).

cnf(19829,plain,
    product(a71,a112) = product(product(a70,a108),a109),
    inference('REWRITE',[status(thm)],[19305,19713,theory(equality)]) ).

cnf(19830,plain,
    product(a108,a112) = product(product(a109,a108),a109),
    inference('REWRITE',[status(thm)],[19306,19713,theory(equality)]) ).

cnf(19832,plain,
    product(product(a71,a112),product(a70,a109)) = product(product(a70,a109),product(a111,a109)),
    inference('REWRITE',[status(thm)],[19313,19809,19713,theory(equality)]) ).

cnf(19834,plain,
    product(product(a110,a112),a118) = product(a112,a71),
    inference('REWRITE',[status(thm)],[19315,19713,theory(equality)]) ).

cnf(19838,plain,
    a72 = product(a82,a112),
    inference('REWRITE',[status(thm)],[19321,19713,theory(equality)]) ).

cnf(19839,plain,
    product(product(a80,a108),a118) = a72,
    inference('REWRITE',[status(thm)],[19827,involutory_quandle,19838,theory(equality)]) ).

cnf(19840,plain,
    product(a72,product(product(a108,a109),a72)) = product(product(a81,a112),a72),
    inference('REWRITE',[status(thm)],[19799,19839,theory(equality)]) ).

cnf(19845,plain,
    product(a112,product(a112,a72)) = product(a110,a72),
    inference('REWRITE',[status(thm)],[19327,19713,theory(equality)]) ).

cnf(19847,plain,
    product(product(a118,a108),a112) = product(a112,product(a109,a111)),
    inference('REWRITE',[status(thm)],[19646,19713,theory(equality)]) ).

cnf(19865,plain,
    product(a82,a110) = a73,
    inference('REWRITE',[status(thm)],[18709,19445,theory(equality)]) ).

cnf(19871,plain,
    product(a73,a110) = a82,
    inference('REWRITE',[status(thm)],[18998,19445,theory(equality)]) ).

cnf(19874,plain,
    product(a72,a110) = product(a82,a73),
    inference('REWRITE',[status(thm)],[19009,19445,theory(equality)]) ).

cnf(19892,plain,
    product(product(X,a82),a110) = product(product(X,a73),a108),
    inference('REWRITE',[status(thm)],[19012,19445,theory(equality)]) ).

cnf(19895,plain,
    product(a71,a110) = product(product(a70,a108),product(a111,a109)),
    inference('REWRITE',[status(thm)],[19102,19716,19445,theory(equality)]) ).

cnf(19896,plain,
    product(a70,product(a70,a109)) = product(a71,a110),
    inference('REWRITE',[status(thm)],[19794,19895,theory(equality)]) ).

cnf(19897,plain,
    product(product(a70,a110),product(a70,a109)) = product(product(a70,a109),product(a71,a110)),
    inference('REWRITE',[status(thm)],[19795,19895,theory(equality)]) ).

cnf(19901,plain,
    product(a112,a82) = a110,
    inference('REWRITE',[status(thm)],[19310,19713,19445,theory(equality)]) ).

cnf(19902,plain,
    a112 = product(a110,a82),
    inference('REWRITE',[status(thm)],[19311,19713,19445,theory(equality)]) ).

cnf(19903,plain,
    product(a70,a110) = product(a72,a119),
    inference('REWRITE',[status(thm)],[19317,knot_72,19442,19640,19713,19445,theory(equality)]) ).

cnf(19911,plain,
    product(product(X,a110),a109) = product(product(X,a109),a119),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,19455,theory(equality)]) ).

cnf(19920,plain,
    a71 = product(a79,a70),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,19464,theory(equality)]),3698,1356,19701,theory(equality)]) ).

cnf(19921,plain,
    a71 = product(a81,a118),
    inference('REWRITE',[status(thm)],[3698,19920,theory(equality)]) ).

cnf(19926,plain,
    a71 = product(a83,a108),
    inference('REWRITE',[status(thm)],[3703,19920,theory(equality)]) ).

cnf(19934,plain,
    a71 = product(a80,a118),
    inference('REWRITE',[status(thm)],[3719,involutory_quandle,19920,theory(equality)]) ).

cnf(19936,plain,
    product(a70,product(a111,a110)) = product(a79,a71),
    inference('REWRITE',[status(thm)],[17643,19522,19934,theory(equality)]) ).

cnf(19939,plain,
    product(a79,a71) = product(a71,product(a70,a71)),
    inference('REWRITE',[status(thm)],[19522,19936,theory(equality)]) ).

cnf(19954,plain,
    product(a82,a108) = product(a71,product(a118,a108)),
    inference('REWRITE',[status(thm)],[13226,19920,theory(equality)]) ).

cnf(19956,plain,
    a73 = product(a79,a109),
    inference('REWRITE',[status(thm)],[18710,19669,19920,theory(equality)]) ).

cnf(19960,plain,
    product(a73,product(a80,a110)) = a80,
    inference('REWRITE',[status(thm)],[19373,19956,theory(equality)]) ).

cnf(19963,plain,
    product(a111,a110) = product(a109,a73),
    inference('REWRITE',[status(thm)],[19545,19956,theory(equality)]) ).

cnf(19964,plain,
    product(product(a111,a110),a82) = product(a119,a72),
    inference('REWRITE',[status(thm)],[19689,19963,theory(equality)]) ).

cnf(19965,plain,
    a73 = product(a83,a71),
    inference('REWRITE',[status(thm)],[19669,19956,theory(equality)]) ).

cnf(19975,plain,
    product(product(a73,X),a71) = product(a83,product(X,a71)),
    inference('REWRITE',[status(thm)],[19032,19920,theory(equality)]) ).

cnf(19976,plain,
    product(a83,product(a111,a118)) = product(a71,product(a79,a118)),
    inference('REWRITE',[status(thm)],[6077,1488,19975,theory(equality)]) ).

cnf(19977,plain,
    product(a81,product(a79,a118)) = product(product(a79,a118),product(a83,product(a111,a118))),
    inference('REWRITE',[status(thm)],[6428,1488,19975,theory(equality)]) ).

cnf(19980,plain,
    product(a71,a83) = product(a83,product(a111,a110)),
    inference('REWRITE',[status(thm)],[19582,19920,theory(equality)]) ).

cnf(19982,plain,
    product(a82,a71) = product(a73,product(a111,a110)),
    inference('REWRITE',[status(thm)],[19604,19920,theory(equality)]) ).

cnf(19983,plain,
    product(a72,a71) = product(a83,product(a82,a71)),
    inference('REWRITE',[status(thm)],[19606,19982,19920,theory(equality)]) ).

cnf(19984,plain,
    product(a82,product(a111,a109)) = product(a70,a71),
    inference('REWRITE',[status(thm)],[19774,19920,theory(equality)]) ).

cnf(20001,plain,
    a70 = a81,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,19921,theory(equality)]),162,theory(equality)]) ).

cnf(20003,plain,
    a82 = product(a70,a109),
    inference('REWRITE',[status(thm)],[knot_82,20001,theory(equality)]) ).

cnf(20004,plain,
    product(a80,a109) = a82,
    inference('REWRITE',[status(thm)],[3646,involutory_quandle,20003,theory(equality)]) ).

cnf(20012,plain,
    product(a82,a79) = product(a80,a112),
    inference('REWRITE',[status(thm)],[19379,20004,theory(equality)]) ).

cnf(20013,plain,
    product(a80,a110) = product(a70,a110),
    inference('REWRITE',[status(thm)],[5944,1385,20003,theory(equality)]) ).

cnf(20014,plain,
    product(a82,a70) = product(a70,a110),
    inference('REWRITE',[status(thm)],[1385,20013,theory(equality)]) ).

cnf(20015,plain,
    product(a73,a70) = product(product(a72,a70),product(a70,a110)),
    inference('REWRITE',[status(thm)],[1391,20013,theory(equality)]) ).

cnf(20020,plain,
    product(product(a70,a110),product(a70,a119)) = product(a83,a119),
    inference('REWRITE',[status(thm)],[8856,20013,theory(equality)]) ).

cnf(20027,plain,
    product(product(X,a118),product(a70,a110)) = product(product(X,a110),a80),
    inference('REWRITE',[status(thm)],[19488,20013,theory(equality)]) ).

cnf(20030,plain,
    product(a73,product(a70,a110)) = a80,
    inference('REWRITE',[status(thm)],[19960,20013,theory(equality)]) ).

cnf(20037,plain,
    product(a82,product(a70,a110)) = product(product(a70,a110),a73),
    inference('REWRITE',[status(thm)],[8072,19865,20003,theory(equality)]) ).

cnf(20038,plain,
    product(product(X,a110),a70) = product(product(X,a109),a82),
    inference('REWRITE',[status(thm)],[13331,20003,theory(equality)]) ).

cnf(20040,plain,
    product(product(a111,a109),a82) = product(a108,a109),
    inference('REWRITE',[status(thm)],[13307,20038,theory(equality)]) ).

cnf(20041,plain,
    product(product(X,a109),a82) = product(product(X,a70),a109),
    inference('REWRITE',[status(thm)],[782,20038,theory(equality)]) ).

cnf(20045,plain,
    product(a108,a82) = product(a110,a112),
    inference('REWRITE',[status(thm)],[19463,20003,theory(equality)]) ).

cnf(20048,plain,
    product(a119,a72) = product(a109,a111),
    inference('REWRITE',[status(thm)],[19647,19964,20003,theory(equality)]) ).

cnf(20051,plain,
    a82 = product(a72,a112),
    inference('REWRITE',[status(thm)],[19806,20003,theory(equality)]) ).

cnf(20054,plain,
    product(product(X,a72),a112) = product(product(X,a112),a82),
    inference('REWRITE',[status(thm)],[19809,20003,theory(equality)]) ).

cnf(20055,plain,
    product(a82,a72) = product(a72,product(a112,a72)),
    inference('REWRITE',[status(thm)],[19813,20003,theory(equality)]) ).

cnf(20056,plain,
    product(product(a71,a112),a82) = product(a70,a71),
    inference('REWRITE',[status(thm)],[19832,19984,20003,theory(equality)]) ).

cnf(20057,plain,
    product(a70,a82) = product(a71,a110),
    inference('REWRITE',[status(thm)],[19896,20003,theory(equality)]) ).

cnf(20058,plain,
    product(product(a70,a110),a82) = product(a82,product(a71,a110)),
    inference('REWRITE',[status(thm)],[19897,20003,theory(equality)]) ).

cnf(20060,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,a70,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,a70,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('REWRITE',[status(thm)],[goal,20001,theory(equality)]) ).

cnf(20061,plain,
    product(a82,a109) = a70,
    inference('REWRITE',[status(thm)],[161,20001,theory(equality)]) ).

cnf(20062,plain,
    a70 = a80,
    inference('REWRITE',[status(thm)],[165,involutory_quandle,20001,theory(equality)]) ).

cnf(20064,plain,
    product(a70,a119) = a79,
    inference('REWRITE',[status(thm)],[153,20062,theory(equality)]) ).

cnf(20067,plain,
    product(product(a71,X),a70) = product(a79,product(X,a70)),
    inference('REWRITE',[status(thm)],[1406,20064,theory(equality)]) ).

cnf(20073,plain,
    product(a70,a79) = product(a71,a119),
    inference('REWRITE',[status(thm)],[12252,20064,theory(equality)]) ).

cnf(20075,plain,
    product(product(a71,a119),X) = product(product(a70,X),product(a79,X)),
    inference('REWRITE',[status(thm)],[18395,20064,theory(equality)]) ).

cnf(20079,plain,
    product(a71,a79) = product(a79,product(a71,a119)),
    inference('REWRITE',[status(thm)],[18398,20064,theory(equality)]) ).

cnf(20081,plain,
    product(a79,product(a111,a109)) = product(product(a70,a110),product(a111,a110)),
    inference('REWRITE',[status(thm)],[19361,20064,theory(equality)]) ).

cnf(20083,plain,
    product(a73,a109) = a79,
    inference('REWRITE',[status(thm)],[19702,involutory_quandle,20064,theory(equality)]) ).

cnf(20084,plain,
    a79 = product(product(a73,a118),a82),
    inference('REWRITE',[status(thm)],[19003,20083,theory(equality)]) ).

cnf(20091,plain,
    product(product(a70,a110),a79) = product(a83,a119),
    inference('REWRITE',[status(thm)],[20020,20064,theory(equality)]) ).

cnf(20093,plain,
    product(product(a79,X),a119) = product(a70,product(X,a119)),
    inference('REWRITE',[status(thm)],[435,20062,theory(equality)]) ).

cnf(20096,plain,
    product(product(a70,X),a119) = product(a79,product(X,a119)),
    inference('REWRITE',[status(thm)],[742,20062,theory(equality)]) ).

cnf(20117,plain,
    a68 = product(a77,a121),
    inference('REWRITE',[status(thm)],[10265,221,230,20062,theory(equality)]) ).

cnf(20120,plain,
    product(a70,a112) = product(product(a73,a108),a70),
    inference('REWRITE',[status(thm)],[12507,20062,theory(equality)]) ).

cnf(20127,plain,
    product(product(a79,X),Y) = product(product(product(a70,X),Y),product(product(a119,X),Y)),
    inference('REWRITE',[status(thm)],[12962,20062,theory(equality)]) ).

cnf(20128,plain,
    product(a71,product(X,a70)) = product(product(a79,X),a70),
    inference('REWRITE',[status(thm)],[6506,20127,theory(equality)]) ).

cnf(20129,plain,
    product(a71,a108) = a83,
    inference('REWRITE',[status(thm)],[1417,1263,20128,theory(equality)]) ).

cnf(20132,plain,
    product(a111,a118) = product(a118,a83),
    inference('REWRITE',[status(thm)],[19632,20129,theory(equality)]) ).

cnf(20133,plain,
    product(a82,a83) = product(a83,product(a111,a118)),
    inference('REWRITE',[status(thm)],[3670,20132,theory(equality)]) ).

cnf(20134,plain,
    product(a82,a83) = product(a71,product(a79,a118)),
    inference('REWRITE',[status(thm)],[19976,20133,theory(equality)]) ).

cnf(20139,plain,
    product(a118,product(a111,a118)) = product(product(a118,a82),a83),
    inference('REWRITE',[status(thm)],[10752,20132,theory(equality)]) ).

cnf(20142,plain,
    a73 = product(a71,product(a111,a109)),
    inference('REWRITE',[status(thm)],[19726,19965,20129,theory(equality)]) ).

cnf(20145,plain,
    product(product(a79,X),product(a70,X)) = product(a71,X),
    inference('REWRITE',[status(thm)],[12963,303,783,20062,theory(equality)]) ).

cnf(20146,plain,
    product(a71,a39) = product(a84,a107),
    inference('REWRITE',[status(thm)],[5299,20145,theory(equality)]) ).

cnf(20157,plain,
    product(a84,product(a71,a39)) = product(a73,a39),
    inference('REWRITE',[status(thm)],[18727,20146,theory(equality)]) ).

cnf(20165,plain,
    product(product(a79,product(X,a119)),Y) = product(product(product(a70,X),Y),product(a119,Y)),
    inference('REWRITE',[status(thm)],[12969,20062,theory(equality)]) ).

cnf(20166,plain,
    product(product(a72,a70),X) = product(product(a79,a110),X),
    inference('REWRITE',[status(thm)],[10163,154,20165,theory(equality)]) ).

cnf(20171,plain,
    product(a110,a111) = product(a109,a72),
    inference('REWRITE',[status(thm)],[12983,19824,20062,theory(equality)]) ).

cnf(20184,plain,
    product(a109,a108) = product(product(a108,a111),a119),
    inference('REWRITE',[status(thm)],[10780,13305,20171,theory(equality)]) ).

cnf(20212,plain,
    product(a73,a112) = product(a70,a111),
    inference('REWRITE',[status(thm)],[18574,17979,20062,theory(equality)]) ).

cnf(20225,plain,
    product(product(a72,a70),product(a111,a110)) = product(a70,product(a111,a109)),
    inference('REWRITE',[status(thm)],[19360,20166,20062,theory(equality)]) ).

cnf(20226,plain,
    product(a71,a119) = product(a79,product(a108,a109)),
    inference('REWRITE',[status(thm)],[19551,20073,20062,theory(equality)]) ).

cnf(20232,plain,
    product(a109,product(a108,a109)) = product(a118,a111),
    inference('REWRITE',[status(thm)],[19790,13339,20062,theory(equality)]) ).

cnf(20234,plain,
    product(a118,a111) = product(a112,product(a110,a112)),
    inference('REWRITE',[status(thm)],[19617,20232,theory(equality)]) ).

cnf(20241,plain,
    product(a82,a79) = product(a70,a112),
    inference('REWRITE',[status(thm)],[20012,20062,theory(equality)]) ).

cnf(20243,plain,
    product(product(X,a118),product(a70,a110)) = product(product(X,a109),a82),
    inference('REWRITE',[status(thm)],[20027,20038,20062,theory(equality)]) ).

cnf(20244,plain,
    product(a73,product(a70,a110)) = a70,
    inference('REWRITE',[status(thm)],[20030,20062,theory(equality)]) ).

cnf(20245,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,a70,a82,a74,a75,a76,a77,a113,a114,a78,a79,a70,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,a70,a70,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('REWRITE',[status(thm)],[20060,20062,theory(equality)]) ).

cnf(20248,plain,
    product(product(a70,X),a109) = product(a82,product(X,a109)),
    inference('REWRITE',[status(thm)],[443,20001,theory(equality)]) ).

cnf(20249,plain,
    product(a71,a112) = product(a82,product(a108,a109)),
    inference('REWRITE',[status(thm)],[19829,20248,theory(equality)]) ).

cnf(20254,plain,
    product(a70,a71) = product(a79,a118),
    inference('REWRITE',[status(thm)],[1249,20001,theory(equality)]) ).

cnf(20256,plain,
    product(a82,a83) = product(a79,a71),
    inference('REWRITE',[status(thm)],[20134,19939,20254,theory(equality)]) ).

cnf(20257,plain,
    product(a79,a71) = product(a83,product(a111,a118)),
    inference('REWRITE',[status(thm)],[20133,20256,theory(equality)]) ).

cnf(20290,plain,
    a68 = product(product(a75,a115),a122),
    inference('REWRITE',[status(thm)],[15055,221,230,20001,theory(equality)]) ).

cnf(20291,plain,
    product(a115,a124) = a121,
    inference('REWRITE',[status(thm)],[7976,171,20290,theory(equality)]) ).

cnf(20292,plain,
    product(a100,a75) = a121,
    inference('REWRITE',[status(thm)],[18783,20291,theory(equality)]) ).

cnf(20294,plain,
    product(a121,a75) = a100,
    inference('REWRITE',[status(thm)],[18786,20291,theory(equality)]) ).

cnf(20297,plain,
    product(product(X,a121),a75) = product(product(X,a75),a100),
    inference('REWRITE',[status(thm)],[18792,20291,theory(equality)]) ).

cnf(20299,plain,
    product(product(a100,X),a75) = product(a121,product(X,a75)),
    inference('REWRITE',[status(thm)],[18799,20291,theory(equality)]) ).

cnf(20302,plain,
    product(a115,product(a100,a115)) = product(a124,a121),
    inference('REWRITE',[status(thm)],[18845,20291,theory(equality)]) ).

cnf(20303,plain,
    product(a124,a121) = product(product(a115,a123),a124),
    inference('REWRITE',[status(thm)],[18844,20302,theory(equality)]) ).

cnf(20305,plain,
    product(product(a114,a124),a68) = product(a124,a121),
    inference('REWRITE',[status(thm)],[19172,20302,theory(equality)]) ).

cnf(20306,plain,
    a121 = product(a124,product(a100,a115)),
    inference('REWRITE',[status(thm)],[18862,20291,theory(equality)]) ).

cnf(20307,plain,
    product(a99,a75) = product(a121,a123),
    inference('REWRITE',[status(thm)],[18873,20291,theory(equality)]) ).

cnf(20312,plain,
    a121 = product(product(a115,a100),a123),
    inference('REWRITE',[status(thm)],[18889,20291,theory(equality)]) ).

cnf(20313,plain,
    product(a100,product(a100,a115)) = product(a123,a121),
    inference('REWRITE',[status(thm)],[18947,20291,theory(equality)]) ).

cnf(20316,plain,
    product(a123,a121) = product(product(a100,a122),a99),
    inference('REWRITE',[status(thm)],[18955,20313,theory(equality)]) ).

cnf(20317,plain,
    product(product(a100,a115),a99) = product(a100,a121),
    inference('REWRITE',[status(thm)],[18991,20291,theory(equality)]) ).

cnf(20318,plain,
    product(product(a122,a100),a124) = product(a100,a121),
    inference('REWRITE',[status(thm)],[18824,20317,theory(equality)]) ).

cnf(20320,plain,
    product(product(a100,a121),product(a100,a115)) = product(a123,a100),
    inference('REWRITE',[status(thm)],[18951,20317,theory(equality)]) ).

cnf(20322,plain,
    product(a100,a121) = product(a121,product(a75,a121)),
    inference('REWRITE',[status(thm)],[18992,20317,20291,theory(equality)]) ).

cnf(20324,plain,
    a122 = product(a114,product(a100,a115)),
    inference('REWRITE',[status(thm)],[19190,knot_122,20291,theory(equality)]) ).

cnf(20327,plain,
    product(a100,a68) = product(a122,a76),
    inference('REWRITE',[status(thm)],[19194,20324,theory(equality)]) ).

cnf(20329,plain,
    product(a68,product(a75,a115)) = product(product(a75,a115),product(a115,a123)),
    inference('REWRITE',[status(thm)],[7979,20290,theory(equality)]) ).

cnf(20330,plain,
    product(a75,product(a75,a122)) = a68,
    inference('REWRITE',[status(thm)],[8711,20290,theory(equality)]) ).

cnf(20332,plain,
    product(a73,a118) = product(a70,a110),
    inference('REWRITE',[status(thm)],[18717,20014,20001,theory(equality)]) ).

cnf(20333,plain,
    product(a70,a110) = product(product(a70,a108),a83),
    inference('REWRITE',[status(thm)],[1369,20332,theory(equality)]) ).

cnf(20334,plain,
    product(product(a70,a110),a83) = product(a70,a108),
    inference('REWRITE',[status(thm)],[1370,20332,theory(equality)]) ).

cnf(20345,plain,
    product(a70,a110) = product(a83,product(a111,a109)),
    inference('REWRITE',[status(thm)],[19783,20332,theory(equality)]) ).

cnf(20346,plain,
    a79 = product(product(a70,a110),a82),
    inference('REWRITE',[status(thm)],[20084,20332,theory(equality)]) ).

cnf(20347,plain,
    a79 = product(a82,product(a71,a110)),
    inference('REWRITE',[status(thm)],[20058,20346,theory(equality)]) ).

cnf(20349,plain,
    product(a71,a110) = product(a73,a70),
    inference('REWRITE',[status(thm)],[19462,20057,20003,20001,theory(equality)]) ).

cnf(20375,plain,
    product(a71,a110) = product(product(a72,a70),product(a70,a110)),
    inference('REWRITE',[status(thm)],[20015,20349,theory(equality)]) ).

cnf(20395,plain,
    product(a70,product(a111,a109)) = product(a73,a108),
    inference('REWRITE',[status(thm)],[19767,20001,theory(equality)]) ).

cnf(20396,plain,
    product(product(a70,a112),a70) = product(a73,a108),
    inference('REWRITE',[status(thm)],[19751,20395,theory(equality)]) ).

cnf(20398,plain,
    product(product(a72,a70),product(a111,a110)) = product(a73,a108),
    inference('REWRITE',[status(thm)],[20225,20395,theory(equality)]) ).

cnf(20399,plain,
    a70 = product(product(a73,a108),product(a111,a109)),
    inference('REWRITE',[status(thm)],[19784,20001,theory(equality)]) ).

cnf(20400,plain,
    product(product(X,a109),a70) = product(product(X,a73),product(a111,a109)),
    inference('REWRITE',[status(thm)],[19789,20001,theory(equality)]) ).

cnf(20401,plain,
    product(a83,a109) = product(a70,a112),
    inference('REWRITE',[status(thm)],[19798,20001,theory(equality)]) ).

cnf(20406,plain,
    product(a72,product(product(a108,a109),a72)) = product(product(a70,a112),a72),
    inference('REWRITE',[status(thm)],[19840,20001,theory(equality)]) ).

cnf(20407,plain,
    product(a70,product(a70,a71)) = product(product(a71,a119),a71),
    inference('REWRITE',[status(thm)],[19977,20075,20257,20254,20001,theory(equality)]) ).

cnf(20409,plain,
    product(a82,a13) = product(a69,product(a109,a13)),
    inference('PARAMODULATE',[status(thm)],[973,20003,theory(equality)]) ).

cnf(20411,plain,
    product(a77,a32) = product(a69,a120),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[973,20064,theory(equality)]),knot_120,2028,theory(equality)]) ).

cnf(20412,plain,
    product(a79,a13) = product(a69,a120),
    inference('REWRITE',[status(thm)],[2028,20411,theory(equality)]) ).

cnf(20418,plain,
    product(product(a73,a13),product(a115,a32)) = product(a71,a13),
    inference('REWRITE',[status(thm)],[9367,6179,20411,theory(equality)]) ).

cnf(20423,plain,
    product(product(a111,a108),product(a110,a108)) = product(a111,a109),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,19926,theory(equality)]),19717,involutory_quandle_02,19570,theory(equality)]) ).

cnf(20424,plain,
    product(a70,a111) = product(a82,a72),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[300,20051,theory(equality)]),19838,20212,theory(equality)]) ).

cnf(20425,plain,
    product(a73,a72) = product(a72,product(a70,a111)),
    inference('REWRITE',[status(thm)],[1351,20424,theory(equality)]) ).

cnf(20428,plain,
    product(a82,product(a70,a111)) = product(product(a70,a111),product(a73,a72)),
    inference('REWRITE',[status(thm)],[7051,20424,theory(equality)]) ).

cnf(20429,plain,
    product(product(X,a73),a82) = product(product(X,a72),product(a70,a111)),
    inference('REWRITE',[status(thm)],[13162,20424,theory(equality)]) ).

cnf(20451,plain,
    product(a70,a111) = product(a72,product(a112,a72)),
    inference('REWRITE',[status(thm)],[20055,20424,theory(equality)]) ).

cnf(20452,plain,
    product(a79,a32) = product(a74,product(a101,a116)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[504,20083,theory(equality)]),18830,theory(equality)]) ).

cnf(20454,plain,
    product(a79,a73) = product(a82,a71),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,20083,theory(equality)]),19982,19963,theory(equality)]) ).

cnf(20455,plain,
    product(a79,a73) = product(product(a79,a111),a118),
    inference('REWRITE',[status(thm)],[1493,20454,theory(equality)]) ).

cnf(20461,plain,
    product(a72,a71) = product(a83,product(a79,a73)),
    inference('REWRITE',[status(thm)],[19983,20454,theory(equality)]) ).

cnf(20463,plain,
    product(product(a73,X),a109) = product(a79,product(X,a109)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,20083,theory(equality)]) ).

cnf(20464,plain,
    product(a71,a119) = product(a83,a82),
    inference('REWRITE',[status(thm)],[18508,20226,20463,theory(equality)]) ).

cnf(20465,plain,
    product(a71,a119) = product(a82,product(a118,a82)),
    inference('REWRITE',[status(thm)],[1412,20464,theory(equality)]) ).

cnf(20473,plain,
    product(a110,a73) = a108,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,19445,theory(equality)]) ).

cnf(20481,plain,
    product(product(X,a108),a73) = product(product(X,a73),a110),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,19445,theory(equality)]) ).

cnf(20482,plain,
    product(a72,a110) = product(a73,a108),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[301,19454,theory(equality)]),20395,19716,769,theory(equality)]) ).

cnf(20485,plain,
    product(a70,a112) = product(a73,a119),
    inference('REWRITE',[status(thm)],[20120,19688,160,20038,20482,theory(equality)]) ).

cnf(20486,plain,
    product(a71,a82) = product(a70,a112),
    inference('REWRITE',[status(thm)],[19688,20485,theory(equality)]) ).

cnf(20493,plain,
    product(product(a70,a112),a70) = product(a72,a110),
    inference('REWRITE',[status(thm)],[20396,20482,theory(equality)]) ).

cnf(20495,plain,
    product(product(a72,a70),product(a111,a110)) = product(a72,a110),
    inference('REWRITE',[status(thm)],[20398,20482,theory(equality)]) ).

cnf(20496,plain,
    a70 = product(product(a72,a110),product(a111,a109)),
    inference('REWRITE',[status(thm)],[20399,20482,theory(equality)]) ).

cnf(20505,plain,
    product(a108,a112) = product(a118,a111),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,19627,theory(equality)]),20234,theory(equality)]) ).

cnf(20506,plain,
    product(product(a108,a112),a70) = product(a119,a108),
    inference('REWRITE',[status(thm)],[3736,20505,theory(equality)]) ).

cnf(20522,plain,
    product(a108,a112) = product(a112,product(a110,a112)),
    inference('REWRITE',[status(thm)],[20234,20505,theory(equality)]) ).

cnf(20525,plain,
    product(a111,a118) = product(a110,a108),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,19627,theory(equality)]),19540,theory(equality)]) ).

cnf(20526,plain,
    product(a109,a71) = product(a110,a108),
    inference('REWRITE',[status(thm)],[1488,20525,theory(equality)]) ).

cnf(20539,plain,
    product(a109,a111) = product(a108,a119),
    inference('REWRITE',[status(thm)],[3723,10770,20525,theory(equality)]) ).

cnf(20548,plain,
    product(a109,a111) = product(a112,product(a108,a109)),
    inference('REWRITE',[status(thm)],[19633,20539,theory(equality)]) ).

cnf(20553,plain,
    product(a110,a108) = product(a119,product(a111,a109)),
    inference('REWRITE',[status(thm)],[19538,20525,theory(equality)]) ).

cnf(20557,plain,
    product(a110,a108) = product(a118,a83),
    inference('REWRITE',[status(thm)],[20132,20525,theory(equality)]) ).

cnf(20558,plain,
    product(a118,product(a110,a108)) = product(product(a118,a82),a83),
    inference('REWRITE',[status(thm)],[20139,20525,theory(equality)]) ).

cnf(20568,plain,
    product(product(X,a112),a110) = product(product(X,a110),a108),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,19627,theory(equality)]) ).

cnf(20570,plain,
    product(a112,a118) = product(a118,a108),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,19797,theory(equality)]),164,theory(equality)]) ).

cnf(20573,plain,
    product(product(a115,a121),a32) = product(product(a110,a112),a13),
    inference('REWRITE',[status(thm)],[15439,18715,18713,20570,theory(equality)]) ).

cnf(20575,plain,
    product(a118,a108) = product(a110,a71),
    inference('REWRITE',[status(thm)],[19073,20570,theory(equality)]) ).

cnf(20582,plain,
    product(a110,product(a118,a108)) = product(product(a118,a108),product(a82,a108)),
    inference('REWRITE',[status(thm)],[19453,19954,20570,theory(equality)]) ).

cnf(20590,plain,
    product(product(a118,X),a109) = product(a112,product(X,a109)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,19797,theory(equality)]) ).

cnf(20595,plain,
    a79 = product(product(a70,a112),a72),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[584,19965,theory(equality)]),20401,20083,theory(equality)]) ).

cnf(20596,plain,
    product(a72,product(product(a108,a109),a72)) = a79,
    inference('REWRITE',[status(thm)],[20406,20595,theory(equality)]) ).

cnf(20598,plain,
    product(a72,a108) = product(a83,product(a109,a108)),
    inference('PARAMODULATE',[status(thm)],[301,20129,theory(equality)]) ).

cnf(20602,plain,
    product(product(X,a71),a108) = product(product(X,a108),a83),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,20129,theory(equality)]) ).

cnf(20604,plain,
    product(a121,a124) = a115,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,20291,theory(equality)]) ).

cnf(20606,plain,
    product(a115,a76) = product(a124,a77),
    inference('REWRITE',[status(thm)],[19161,20604,theory(equality)]) ).

cnf(20607,plain,
    product(product(a124,a123),a68) = product(a115,a76),
    inference('REWRITE',[status(thm)],[19162,20606,theory(equality)]) ).

cnf(20608,plain,
    a114 = product(a100,a122),
    inference('REWRITE',[status(thm)],[19176,170,20604,theory(equality)]) ).

cnf(20609,plain,
    product(a114,a14) = product(a101,a117),
    inference('REWRITE',[status(thm)],[5508,20608,theory(equality)]) ).

cnf(20612,plain,
    product(a112,a32) = product(a101,a117),
    inference('REWRITE',[status(thm)],[9342,20609,theory(equality)]) ).

cnf(20622,plain,
    product(a101,a117) = product(product(a113,a32),product(a32,a14)),
    inference('REWRITE',[status(thm)],[14185,20609,theory(equality)]) ).

cnf(20627,plain,
    product(product(a101,a117),a14) = a114,
    inference('REWRITE',[status(thm)],[16658,20608,theory(equality)]) ).

cnf(20628,plain,
    a114 = product(a122,product(a100,a115)),
    inference('REWRITE',[status(thm)],[18854,20608,theory(equality)]) ).

cnf(20629,plain,
    a114 = product(a123,a124),
    inference('REWRITE',[status(thm)],[18916,20608,theory(equality)]) ).

cnf(20630,plain,
    product(a114,a75) = product(a124,a123),
    inference('REWRITE',[status(thm)],[18917,20608,theory(equality)]) ).

cnf(20634,plain,
    product(product(X,a114),a75) = product(product(X,a75),product(a124,a123)),
    inference('REWRITE',[status(thm)],[18921,20608,theory(equality)]) ).

cnf(20635,plain,
    product(product(a92,a114),a75) = product(product(a92,a123),product(a75,product(a75,a123))),
    inference('REWRITE',[status(thm)],[17602,20634,theory(equality)]) ).

cnf(20644,plain,
    product(a100,product(a75,a124)) = product(a115,a114),
    inference('REWRITE',[status(thm)],[18933,20608,theory(equality)]) ).

cnf(20650,plain,
    a99 = product(a124,a76),
    inference('REWRITE',[status(thm)],[18942,19181,20608,theory(equality)]) ).

cnf(20651,plain,
    product(a121,a77) = a99,
    inference('REWRITE',[status(thm)],[19148,20650,theory(equality)]) ).

cnf(20652,plain,
    a99 = product(a114,product(a121,a114)),
    inference('REWRITE',[status(thm)],[19149,20650,theory(equality)]) ).

cnf(20662,plain,
    product(product(a100,a115),a114) = a99,
    inference('REWRITE',[status(thm)],[19181,20650,theory(equality)]) ).

cnf(20665,plain,
    product(product(X,product(a100,a115)),a114) = product(product(X,a114),a99),
    inference('REWRITE',[status(thm)],[19188,20650,theory(equality)]) ).

cnf(20666,plain,
    product(a100,a115) = product(a99,a114),
    inference('REWRITE',[status(thm)],[18956,20608,theory(equality)]) ).

cnf(20670,plain,
    product(product(X,a123),a124) = product(product(X,a124),a114),
    inference('REWRITE',[status(thm)],[18962,20608,theory(equality)]) ).

cnf(20675,plain,
    product(product(X,a123),a75) = product(product(X,a114),product(product(a75,a114),product(a124,a114))),
    inference('REWRITE',[status(thm)],[18988,716,20608,theory(equality)]) ).

cnf(20676,plain,
    product(a123,a121) = product(a114,a99),
    inference('REWRITE',[status(thm)],[20316,20608,theory(equality)]) ).

cnf(20679,plain,
    a114 = product(product(a100,a115),a121),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[287,20291,theory(equality)]),18813,20629,theory(equality)]) ).

cnf(20680,plain,
    product(a121,a115) = product(a124,a123),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,20291,theory(equality)]),7574,5924,theory(equality)]) ).

cnf(20683,plain,
    product(a75,product(a75,a123)) = product(product(a75,a123),product(a121,a115)),
    inference('REWRITE',[status(thm)],[6990,20680,theory(equality)]) ).

cnf(20684,plain,
    product(a115,product(a115,a123)) = product(a121,a115),
    inference('REWRITE',[status(thm)],[7574,20680,theory(equality)]) ).

cnf(20689,plain,
    product(product(a121,a115),a124) = product(product(a115,a100),a122),
    inference('REWRITE',[status(thm)],[18957,20680,theory(equality)]) ).

cnf(20692,plain,
    product(a122,a114) = product(a115,a76),
    inference('REWRITE',[status(thm)],[20607,3820,20680,theory(equality)]) ).

cnf(20693,plain,
    product(a122,a114) = product(a124,a77),
    inference('REWRITE',[status(thm)],[20606,20692,theory(equality)]) ).

cnf(20694,plain,
    product(a114,a75) = product(a121,a115),
    inference('REWRITE',[status(thm)],[20630,20680,theory(equality)]) ).

cnf(20703,plain,
    product(product(a115,a100),a124) = product(a121,a99),
    inference('PARAMODULATE',[status(thm)],[728,20291,theory(equality)]) ).

cnf(20704,plain,
    a122 = product(a99,a121),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[727,20291,theory(equality)]),18859,theory(equality)]) ).

cnf(20712,plain,
    product(product(a123,a121),a75) = product(a124,a100),
    inference('PARAMODULATE',[status(thm)],[439,20294,theory(equality)]) ).

cnf(20713,plain,
    product(product(a75,a121),a75) = product(a75,a100),
    inference('PARAMODULATE',[status(thm)],[569,20294,theory(equality)]) ).

cnf(20715,plain,
    product(a110,a108) = product(product(a111,a109),product(a111,a110)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[305,19493,theory(equality)]),19717,20526,theory(equality)]) ).

cnf(20717,plain,
    product(a110,a112) = product(a112,a72),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[584,19493,theory(equality)]),19797,19340,19911,theory(equality)]) ).

cnf(20720,plain,
    product(a108,a112) = product(a110,a72),
    inference('REWRITE',[status(thm)],[19845,20522,20717,theory(equality)]) ).

cnf(20722,plain,
    product(a70,a111) = product(a72,product(a110,a112)),
    inference('REWRITE',[status(thm)],[20451,20717,theory(equality)]) ).

cnf(20737,plain,
    product(product(a110,a108),a110) = product(a110,a112),
    inference('PARAMODULATE',[status(thm)],[569,19713,theory(equality)]) ).

cnf(20739,plain,
    product(product(a108,X),a110) = product(a112,product(X,a110)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,19713,theory(equality)]) ).

cnf(20740,plain,
    product(product(X,a108),a110) = product(product(X,a110),a112),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,19713,theory(equality)]) ).

cnf(20742,plain,
    product(product(a111,a108),a110) = product(product(a110,a112),product(a110,a111)),
    inference('REWRITE',[status(thm)],[13022,20740,theory(equality)]) ).

cnf(20743,plain,
    product(a110,product(a110,a112)) = product(product(a110,a111),product(product(a111,a108),a110)),
    inference('REWRITE',[status(thm)],[13023,20740,theory(equality)]) ).

cnf(20744,plain,
    a111 = product(product(a108,a109),a72),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[584,19717,theory(equality)]),involutory_quandle_01,theory(equality)]) ).

cnf(20746,plain,
    product(a72,a111) = a79,
    inference('REWRITE',[status(thm)],[20596,20744,theory(equality)]) ).

cnf(20748,plain,
    product(a118,a112) = product(a109,a111),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,19810,theory(equality)]),20548,19471,theory(equality)]) ).

cnf(20757,plain,
    product(a111,a82) = a118,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[295,19902,theory(equality)]),19471,19687,theory(equality)]) ).

cnf(20760,plain,
    product(a112,X) = product(product(a110,X),product(a82,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,19902,theory(equality)]) ).

cnf(20765,plain,
    product(a73,a79) = product(a79,product(a110,a112)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,19956,theory(equality)]),19214,theory(equality)]) ).

cnf(20771,plain,
    product(a68,a121) = a77,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,20117,theory(equality)]) ).

cnf(20772,plain,
    product(a122,a121) = a99,
    inference('REWRITE',[status(thm)],[1568,20651,20771,theory(equality)]) ).

cnf(20774,plain,
    product(a99,a68) = product(a121,a122),
    inference('REWRITE',[status(thm)],[3835,20772,theory(equality)]) ).

cnf(20784,plain,
    product(a121,product(a68,a122)) = product(a123,a100),
    inference('REWRITE',[status(thm)],[13571,18850,20772,theory(equality)]) ).

cnf(20793,plain,
    product(a75,a115) = product(a68,a122),
    inference('REWRITE',[status(thm)],[5949,1299,20771,theory(equality)]) ).

cnf(20794,plain,
    product(a77,a68) = product(a68,a122),
    inference('REWRITE',[status(thm)],[1299,20793,theory(equality)]) ).

cnf(20804,plain,
    product(a115,a123) = product(a121,a122),
    inference('REWRITE',[status(thm)],[5925,5849,20793,theory(equality)]) ).

cnf(20805,plain,
    product(a124,a115) = product(a121,a122),
    inference('REWRITE',[status(thm)],[5924,20804,theory(equality)]) ).

cnf(20809,plain,
    product(product(X,a124),a115) = product(product(X,a115),product(a121,a122)),
    inference('REWRITE',[status(thm)],[7563,20804,theory(equality)]) ).

cnf(20811,plain,
    a100 = product(a123,product(a121,a122)),
    inference('REWRITE',[status(thm)],[18779,20804,theory(equality)]) ).

cnf(20814,plain,
    product(product(a100,a115),a75) = product(a121,a122),
    inference('REWRITE',[status(thm)],[18817,20804,theory(equality)]) ).

cnf(20829,plain,
    product(a124,a121) = product(product(a121,a115),a122),
    inference('REWRITE',[status(thm)],[20303,1597,20804,theory(equality)]) ).

cnf(20832,plain,
    product(a115,product(a121,a122)) = product(a121,a115),
    inference('REWRITE',[status(thm)],[20684,20804,theory(equality)]) ).

cnf(20836,plain,
    product(product(a68,a122),a75) = product(a75,a122),
    inference('REWRITE',[status(thm)],[6059,20793,theory(equality)]) ).

cnf(20843,plain,
    product(a75,product(a68,a122)) = product(product(a68,a122),a123),
    inference('REWRITE',[status(thm)],[10681,20793,theory(equality)]) ).

cnf(20852,plain,
    product(a68,product(a68,a122)) = product(a77,a122),
    inference('REWRITE',[status(thm)],[20329,20771,involutory_quandle_02,20804,20793,theory(equality)]) ).

cnf(20854,plain,
    product(a68,a77) = product(a77,a99),
    inference('REWRITE',[status(thm)],[6991,20772,20771,theory(equality)]) ).

cnf(20860,plain,
    product(product(X,a122),a68) = product(product(X,a121),a77),
    inference('REWRITE',[status(thm)],[13590,20771,theory(equality)]) ).

cnf(20862,plain,
    product(a100,a68) = product(a115,a121),
    inference('REWRITE',[status(thm)],[3784,19195,19145,20860,theory(equality)]) ).

cnf(20865,plain,
    product(a115,a121) = product(product(a100,a115),a77),
    inference('REWRITE',[status(thm)],[19195,20862,theory(equality)]) ).

cnf(20866,plain,
    product(a115,a121) = product(a122,a76),
    inference('REWRITE',[status(thm)],[20327,20862,theory(equality)]) ).

cnf(20869,plain,
    product(product(X,a121),a77) = product(product(X,a68),a121),
    inference('REWRITE',[status(thm)],[797,20860,theory(equality)]) ).

cnf(20875,plain,
    product(a68,a114) = product(a76,product(a121,a114)),
    inference('PARAMODULATE',[status(thm)],[751,20117,theory(equality)]) ).

cnf(20876,plain,
    product(a68,a114) = product(product(a76,a121),a77),
    inference('REWRITE',[status(thm)],[13076,20875,theory(equality)]) ).

cnf(20877,plain,
    product(a68,a114) = product(a77,product(a76,a77)),
    inference('REWRITE',[status(thm)],[13077,20875,theory(equality)]) ).

cnf(20880,plain,
    product(a76,a121) = product(a68,product(a100,a115)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[750,20117,theory(equality)]),19145,theory(equality)]) ).

cnf(20881,plain,
    product(product(a68,a124),a68) = product(a76,a121),
    inference('REWRITE',[status(thm)],[19178,20880,theory(equality)]) ).

cnf(20887,plain,
    a121 = product(a99,a77),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[795,20772,theory(equality)]),20771,involutory_quandle,theory(equality)]) ).

cnf(20888,plain,
    product(a123,a121) = product(a99,product(a115,a121)),
    inference('PARAMODULATE',[status(thm)],[287,20772,theory(equality)]) ).

cnf(20898,plain,
    a115 = product(a100,product(a77,a124)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[430,20887,theory(equality)]),20604,theory(equality)]) ).

cnf(20900,plain,
    product(a121,a99) = product(a99,product(a68,a77)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,20887,theory(equality)]),20854,theory(equality)]) ).

cnf(20919,plain,
    product(product(X,a110),a73) = product(product(X,a73),a108),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,20473,theory(equality)]) ).

cnf(20920,plain,
    product(product(X,a82),a110) = product(product(X,a110),a73),
    inference('REWRITE',[status(thm)],[19892,20919,theory(equality)]) ).

cnf(20930,plain,
    product(a114,a122) = a100,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,20608,theory(equality)]) ).

cnf(20931,plain,
    product(product(a115,a121),a68) = a100,
    inference('REWRITE',[status(thm)],[3815,20930,theory(equality)]) ).

cnf(20941,plain,
    product(a123,a100) = product(a114,a115),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[726,20608,theory(equality)]),1594,18850,theory(equality)]) ).

cnf(20962,plain,
    product(product(a100,a121),product(a100,a115)) = product(a114,a115),
    inference('REWRITE',[status(thm)],[20320,20941,theory(equality)]) ).

cnf(20965,plain,
    product(a121,product(a68,a122)) = product(a114,a115),
    inference('REWRITE',[status(thm)],[20784,20941,theory(equality)]) ).

cnf(20969,plain,
    product(a91,a122) = product(product(a90,a114),product(a122,a114)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[290,20608,theory(equality)]),involutory_quandle_02,theory(equality)]) ).

cnf(20974,plain,
    product(product(X,a100),a122) = product(product(X,a122),a114),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,20608,theory(equality)]) ).

cnf(20975,plain,
    product(a114,a124) = a123,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,20629,theory(equality)]) ).

cnf(20976,plain,
    product(a121,a114) = product(a124,a121),
    inference('REWRITE',[status(thm)],[20305,1144,20975,theory(equality)]) ).

cnf(20977,plain,
    product(a115,product(a100,a115)) = product(a121,a114),
    inference('REWRITE',[status(thm)],[20302,20976,theory(equality)]) ).

cnf(20978,plain,
    product(a121,a114) = product(product(a121,a115),a122),
    inference('REWRITE',[status(thm)],[20829,20976,theory(equality)]) ).

cnf(20982,plain,
    product(product(a115,a100),a122) = product(a124,a114),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,20629,theory(equality)]),20689,20680,theory(equality)]) ).

cnf(20984,plain,
    product(product(a124,a114),a75) = product(a122,a100),
    inference('REWRITE',[status(thm)],[18982,20982,theory(equality)]) ).

cnf(20985,plain,
    product(product(a122,a100),a75) = product(a124,a114),
    inference('REWRITE',[status(thm)],[18983,20982,theory(equality)]) ).

cnf(21009,plain,
    product(product(a124,X),a76) = product(a99,product(X,a76)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,20650,theory(equality)]) ).

cnf(21017,plain,
    product(product(a75,a114),a75) = product(a75,product(a121,a115)),
    inference('PARAMODULATE',[status(thm)],[569,20694,theory(equality)]) ).

cnf(21020,plain,
    product(a100,a121) = product(a122,product(a121,a114)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[289,20704,theory(equality)]),20976,theory(equality)]) ).

cnf(21021,plain,
    product(product(a121,a123),a68) = product(a100,a121),
    inference('REWRITE',[status(thm)],[3822,21020,theory(equality)]) ).

cnf(21027,plain,
    product(a79,a111) = a72,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,20746,theory(equality)]) ).

cnf(21028,plain,
    product(a83,a70) = a72,
    inference('REWRITE',[status(thm)],[1413,21027,theory(equality)]) ).

cnf(21031,plain,
    product(product(X,a83),a70) = product(product(X,a70),a72),
    inference('REWRITE',[status(thm)],[1420,21027,theory(equality)]) ).

cnf(21033,plain,
    product(product(a72,X),a70) = product(a83,product(X,a70)),
    inference('REWRITE',[status(thm)],[1422,21027,theory(equality)]) ).

cnf(21037,plain,
    product(a72,a83) = product(a83,product(a70,a83)),
    inference('REWRITE',[status(thm)],[6084,21027,theory(equality)]) ).

cnf(21039,plain,
    product(product(X,a112),a79) = product(product(X,a111),a72),
    inference('REWRITE',[status(thm)],[13064,21027,theory(equality)]) ).

cnf(21070,plain,
    product(a79,a73) = product(a70,a108),
    inference('REWRITE',[status(thm)],[20455,1368,21027,theory(equality)]) ).

cnf(21071,plain,
    product(a70,a108) = product(a82,a71),
    inference('REWRITE',[status(thm)],[20454,21070,theory(equality)]) ).

cnf(21073,plain,
    product(a72,a71) = product(a79,a108),
    inference('REWRITE',[status(thm)],[20461,17308,21070,theory(equality)]) ).

cnf(21074,plain,
    product(a83,product(a70,a108)) = product(a72,a71),
    inference('REWRITE',[status(thm)],[17308,21073,theory(equality)]) ).

cnf(21077,plain,
    product(a71,a111) = product(a79,product(a109,a111)),
    inference('PARAMODULATE',[status(thm)],[762,20746,theory(equality)]) ).

cnf(21079,plain,
    product(a73,a111) = product(a79,product(a82,a111)),
    inference('PARAMODULATE',[status(thm)],[300,20746,theory(equality)]) ).

cnf(21083,plain,
    product(a72,a70) = a83,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,21028,theory(equality)]) ).

cnf(21085,plain,
    product(a71,a110) = product(a83,product(a70,a110)),
    inference('REWRITE',[status(thm)],[20375,21083,theory(equality)]) ).

cnf(21088,plain,
    product(a71,a83) = product(a72,a110),
    inference('REWRITE',[status(thm)],[20495,19980,21083,theory(equality)]) ).

cnf(21089,plain,
    product(a72,a110) = product(a83,product(a111,a110)),
    inference('REWRITE',[status(thm)],[19980,21088,theory(equality)]) ).

cnf(21095,plain,
    product(a119,a108) = product(a109,a83),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[781,21083,theory(equality)]),20506,20720,theory(equality)]) ).

cnf(21097,plain,
    product(a70,a111) = product(a83,a119),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[591,21083,theory(equality)]),6067,1368,theory(equality)]) ).

cnf(21098,plain,
    product(product(a70,a110),a79) = product(a70,a111),
    inference('REWRITE',[status(thm)],[20091,21097,theory(equality)]) ).

cnf(21102,plain,
    product(a109,a108) = product(a110,a83),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[448,21083,theory(equality)]),13305,20171,theory(equality)]) ).

cnf(21108,plain,
    product(product(a68,a115),a123) = a75,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,20793,theory(equality)]),570,theory(equality)]) ).

cnf(21109,plain,
    product(a75,product(a68,a115)) = product(product(a68,a115),product(a121,a115)),
    inference('REWRITE',[status(thm)],[6996,21108,theory(equality)]) ).

cnf(21111,plain,
    product(a71,a32) = product(a74,a116),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1081,20793,theory(equality)]),knot_116,2563,theory(equality)]) ).

cnf(21112,plain,
    product(a117,a116) = product(a116,product(a71,a32)),
    inference('REWRITE',[status(thm)],[1329,21111,theory(equality)]) ).

cnf(21116,plain,
    product(a74,product(a71,a32)) = product(a83,a32),
    inference('REWRITE',[status(thm)],[6994,20129,13395,21111,theory(equality)]) ).

cnf(21135,plain,
    product(product(a68,a122),X) = product(product(a75,X),product(a115,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,20793,theory(equality)]) ).

cnf(21136,plain,
    product(a76,product(a68,a114)) = product(product(a68,a100),a122),
    inference('REWRITE',[status(thm)],[13075,20974,21135,theory(equality)]) ).

cnf(21139,plain,
    product(product(a121,a122),a123) = a115,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,20804,theory(equality)]) ).

cnf(21146,plain,
    product(product(X,a115),a123) = product(product(X,a123),product(a121,a122)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,20804,theory(equality)]) ).

cnf(21150,plain,
    product(product(a115,a100),a68) = product(a114,product(a115,a121)),
    inference('PARAMODULATE',[status(thm)],[793,20862,theory(equality)]) ).

cnf(21152,plain,
    product(product(a100,a114),a68) = product(product(a115,a121),a115),
    inference('PARAMODULATE',[status(thm)],[594,20862,theory(equality)]) ).

cnf(21155,plain,
    product(product(a68,a100),a68) = product(a68,product(a115,a121)),
    inference('PARAMODULATE',[status(thm)],[569,20862,theory(equality)]) ).

cnf(21164,plain,
    product(product(a121,a114),a121) = a124,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,19145,theory(equality)]),19196,theory(equality)]) ).

cnf(21165,plain,
    product(product(a110,a13),a32) = a124,
    inference('REWRITE',[status(thm)],[9418,21164,theory(equality)]) ).

cnf(21167,plain,
    product(product(a114,X),a121) = product(product(a100,a115),product(X,a121)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,19145,theory(equality)]) ).

cnf(21168,plain,
    product(product(X,a114),a121) = product(product(X,a121),product(a100,a115)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,19145,theory(equality)]) ).

cnf(21170,plain,
    product(product(a100,a114),a121) = product(a114,a115),
    inference('REWRITE',[status(thm)],[20962,21168,theory(equality)]) ).

cnf(21171,plain,
    product(a115,a121) = product(a124,a114),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[794,19146,theory(equality)]),20862,involutory_quandle_01,theory(equality)]) ).

cnf(21172,plain,
    product(product(X,a123),a75) = product(product(X,a114),product(product(a75,a114),product(a115,a121))),
    inference('REWRITE',[status(thm)],[20675,21171,theory(equality)]) ).

cnf(21175,plain,
    product(product(a115,a121),a75) = product(a122,a100),
    inference('REWRITE',[status(thm)],[20984,21171,theory(equality)]) ).

cnf(21176,plain,
    product(product(a122,a100),a75) = product(a115,a121),
    inference('REWRITE',[status(thm)],[20985,21171,theory(equality)]) ).

cnf(21180,plain,
    product(a75,a122) = product(a68,a124),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,19146,theory(equality)]),knot_122,790,20880,theory(equality)]) ).

cnf(21184,plain,
    product(product(X,a122),product(a68,a124)) = product(product(X,a124),a68),
    inference('REWRITE',[status(thm)],[8710,713,21180,theory(equality)]) ).

cnf(21188,plain,
    product(a75,product(a68,a124)) = a68,
    inference('REWRITE',[status(thm)],[20330,21180,theory(equality)]) ).

cnf(21189,plain,
    product(product(a68,a122),a75) = product(a68,a124),
    inference('REWRITE',[status(thm)],[20836,21180,theory(equality)]) ).

cnf(21196,plain,
    product(a115,a121) = product(product(a121,a122),product(a100,a115)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[289,19163,theory(equality)]),20774,20862,theory(equality)]) ).

cnf(21202,plain,
    product(a108,a79) = product(product(a111,a108),a110),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[774,19489,theory(equality)]),20742,19214,theory(equality)]) ).

cnf(21205,plain,
    product(a110,product(a110,a112)) = product(product(a118,a108),a79),
    inference('REWRITE',[status(thm)],[20743,19532,21202,theory(equality)]) ).

cnf(21209,plain,
    product(a110,product(a110,a112)) = product(a111,product(a110,a111)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[748,19489,theory(equality)]),21205,20570,theory(equality)]) ).

cnf(21210,plain,
    product(a111,product(a110,a111)) = product(product(a118,a108),a79),
    inference('REWRITE',[status(thm)],[21205,21209,theory(equality)]) ).

cnf(21226,plain,
    product(product(a71,a119),a71) = product(a71,product(a109,a108)),
    inference('PARAMODULATE',[status(thm)],[569,19507,theory(equality)]) ).

cnf(21227,plain,
    product(a70,product(a70,a71)) = product(a71,product(a109,a108)),
    inference('REWRITE',[status(thm)],[20407,21226,theory(equality)]) ).

cnf(21234,plain,
    product(a119,a108) = product(product(a111,a110),product(a110,a108)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[305,19570,theory(equality)]),20557,21095,theory(equality)]) ).

cnf(21236,plain,
    product(a118,a82) = product(a109,product(a71,a110)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[783,19687,theory(equality)]),20057,theory(equality)]) ).

cnf(21241,plain,
    product(a70,a73) = a83,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[768,19729,theory(equality)]),21083,knot_72,20400,theory(equality)]) ).

cnf(21242,plain,
    product(a119,a73) = product(a118,a108),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[308,19729,theory(equality)]),19777,21241,theory(equality)]) ).

cnf(21244,plain,
    product(a83,a73) = a70,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[304,19729,theory(equality)]),20496,19874,theory(equality)]) ).

cnf(21246,plain,
    product(a71,a73) = product(a70,a110),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[303,19729,theory(equality)]),20345,21241,theory(equality)]) ).

cnf(21247,plain,
    product(product(a70,a110),a73) = a71,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,19729,theory(equality)]),19788,20332,theory(equality)]) ).

cnf(21248,plain,
    product(a82,product(a70,a110)) = a71,
    inference('REWRITE',[status(thm)],[20037,21247,theory(equality)]) ).

cnf(21254,plain,
    a72 = product(a70,product(a71,a110)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,21241,theory(equality)]),20349,21028,theory(equality)]) ).

cnf(21255,plain,
    product(product(a71,a110),a73) = product(a73,a83),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,21241,theory(equality)]),20349,theory(equality)]) ).

cnf(21260,plain,
    product(product(a70,X),a73) = product(a83,product(X,a73)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,21241,theory(equality)]) ).

cnf(21264,plain,
    product(a70,a83) = product(a83,product(a73,a83)),
    inference('PARAMODULATE',[status(thm)],[569,21244,theory(equality)]) ).

cnf(21302,plain,
    product(product(X,a112),a82) = product(product(X,a110),a73),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,19901,theory(equality)]),20920,theory(equality)]) ).

cnf(21303,plain,
    product(a73,a83) = product(a70,a71),
    inference('REWRITE',[status(thm)],[20056,21255,21302,theory(equality)]) ).

cnf(21305,plain,
    product(product(a71,a110),a73) = product(a70,a71),
    inference('REWRITE',[status(thm)],[21255,21303,theory(equality)]) ).

cnf(21306,plain,
    product(a70,a83) = product(a83,product(a70,a71)),
    inference('REWRITE',[status(thm)],[21264,21303,theory(equality)]) ).

cnf(21307,plain,
    product(product(X,a72),a112) = product(product(X,a110),a73),
    inference('REWRITE',[status(thm)],[20054,21302,theory(equality)]) ).

cnf(21323,plain,
    product(product(a71,a39),X) = product(product(a84,X),product(a107,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,20146,theory(equality)]) ).

cnf(21324,plain,
    product(product(a73,a39),a84) = product(product(a71,a106),product(a39,a106)),
    inference('REWRITE',[status(thm)],[19038,involutory_quandle_02,21323,theory(equality)]) ).

cnf(21325,plain,
    product(product(a71,a106),product(a39,a106)) = product(a84,product(a84,a106)),
    inference('REWRITE',[status(thm)],[19037,21324,theory(equality)]) ).

cnf(21330,plain,
    product(product(a70,a111),a72) = a82,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,20241,theory(equality)]),21039,theory(equality)]) ).

cnf(21332,plain,
    product(a82,a108) = product(a70,a83),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[445,20241,theory(equality)]),21306,20254,19954,20570,444,theory(equality)]) ).

cnf(21333,plain,
    product(a72,a83) = product(a83,product(a82,a108)),
    inference('REWRITE',[status(thm)],[21037,21332,theory(equality)]) ).

cnf(21343,plain,
    product(a112,a71) = product(a108,product(a70,a71)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[775,20254,theory(equality)]),19834,19214,theory(equality)]) ).

cnf(21349,plain,
    product(a72,a83) = product(a71,product(a109,a108)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[759,20256,theory(equality)]),21226,20075,21303,theory(equality)]) ).

cnf(21351,plain,
    product(a70,product(a70,a71)) = product(a72,a83),
    inference('REWRITE',[status(thm)],[21227,21349,theory(equality)]) ).

cnf(21366,plain,
    a111 = product(a118,a82),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[781,20349,theory(equality)]),21236,1268,20473,theory(equality)]) ).

cnf(21368,plain,
    product(a71,a119) = product(a82,a111),
    inference('REWRITE',[status(thm)],[20465,21366,theory(equality)]) ).

cnf(21369,plain,
    product(a73,a111) = product(a71,a79),
    inference('REWRITE',[status(thm)],[21079,20079,21368,theory(equality)]) ).

cnf(21376,plain,
    product(a118,product(a110,a108)) = product(a111,a83),
    inference('REWRITE',[status(thm)],[20558,21366,theory(equality)]) ).

cnf(21389,plain,
    product(product(a70,a108),a82) = product(a73,a111),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[441,21366,theory(equality)]),1368,theory(equality)]) ).

cnf(21390,plain,
    product(a111,X) = product(product(a118,X),product(a82,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,21366,theory(equality)]) ).

cnf(21391,plain,
    product(a110,product(a118,a108)) = product(a111,a108),
    inference('REWRITE',[status(thm)],[20582,21390,theory(equality)]) ).

cnf(21397,plain,
    product(a108,a112) = product(product(a118,a108),a119),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,21368,theory(equality)]),20575,436,20505,20757,theory(equality)]) ).

cnf(21429,plain,
    product(product(a119,a108),a119) = product(a119,product(a109,a111)),
    inference('PARAMODULATE',[status(thm)],[569,20539,theory(equality)]) ).

cnf(21441,plain,
    product(a122,a77) = product(a121,a99),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[312,20651,theory(equality)]),20900,theory(equality)]) ).

cnf(21442,plain,
    product(product(a115,a100),a124) = product(a122,a77),
    inference('REWRITE',[status(thm)],[20703,21441,theory(equality)]) ).

cnf(21459,plain,
    product(product(a77,a124),a77) = product(a77,product(a122,a114)),
    inference('PARAMODULATE',[status(thm)],[569,20693,theory(equality)]) ).

cnf(21463,plain,
    product(product(X,a124),a77) = product(product(X,a77),product(a122,a114)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,20693,theory(equality)]) ).

cnf(21469,plain,
    product(a83,a112) = product(a72,product(a109,a111)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[304,20748,theory(equality)]),19838,theory(equality)]) ).

cnf(21475,plain,
    product(product(a118,X),a112) = product(product(a109,a111),product(X,a112)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,20748,theory(equality)]) ).

cnf(21476,plain,
    product(product(a109,a111),product(a108,a112)) = product(a112,product(a109,a111)),
    inference('REWRITE',[status(thm)],[19847,21475,theory(equality)]) ).

cnf(21493,plain,
    product(a75,a121) = product(a68,a114),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[789,20771,theory(equality)]),20876,theory(equality)]) ).

cnf(21495,plain,
    product(a100,a121) = product(a121,product(a68,a114)),
    inference('REWRITE',[status(thm)],[20322,21493,theory(equality)]) ).

cnf(21496,plain,
    product(product(a68,a114),a75) = product(a75,a100),
    inference('REWRITE',[status(thm)],[20713,21493,theory(equality)]) ).

cnf(21497,plain,
    product(a67,a121) = product(a77,product(a98,a121)),
    inference('PARAMODULATE',[status(thm)],[786,20771,theory(equality)]) ).

cnf(21499,plain,
    product(a76,a121) = product(product(a68,a114),a77),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[310,20771,theory(equality)]),21493,theory(equality)]) ).

cnf(21500,plain,
    product(product(a75,a114),a77) = product(a77,product(a76,a121)),
    inference('REWRITE',[status(thm)],[6212,21499,theory(equality)]) ).

cnf(21502,plain,
    product(a77,X) = product(product(a68,X),product(a121,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,20771,theory(equality)]) ).

cnf(21503,plain,
    product(a75,product(a68,a115)) = product(a77,a115),
    inference('REWRITE',[status(thm)],[21109,21502,theory(equality)]) ).

cnf(21505,plain,
    product(product(a68,X),a121) = product(a77,product(X,a121)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,20771,theory(equality)]) ).

cnf(21515,plain,
    product(product(X,a115),a123) = product(product(X,a100),product(product(a121,a100),product(a122,a100))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,20811,theory(equality)]),716,21146,theory(equality)]) ).

cnf(21516,plain,
    product(a121,a115) = product(product(a121,a100),product(a122,a100)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,20811,theory(equality)]),involutory_quandle_02,20832,21139,theory(equality)]) ).

cnf(21517,plain,
    product(product(X,a115),a123) = product(product(X,a100),product(a121,a115)),
    inference('REWRITE',[status(thm)],[21515,21516,theory(equality)]) ).

cnf(21519,plain,
    product(product(a68,a100),product(a121,a115)) = a75,
    inference('REWRITE',[status(thm)],[21108,21517,theory(equality)]) ).

cnf(21522,plain,
    product(a76,a99) = product(product(a68,a77),product(a123,a121)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[750,20854,theory(equality)]),20676,theory(equality)]) ).

cnf(21525,plain,
    product(product(a68,a124),product(a77,a124)) = product(product(a77,a100),product(a124,a100)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[572,20854,theory(equality)]),involutory_quandle_02,theory(equality)]) ).

cnf(21542,plain,
    product(a123,a114) = product(product(a115,a100),a68),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,20975,theory(equality)]),21150,21171,theory(equality)]) ).

cnf(21543,plain,
    product(a123,a114) = product(a114,product(a115,a121)),
    inference('REWRITE',[status(thm)],[21150,21542,theory(equality)]) ).

cnf(21546,plain,
    product(product(a115,a121),a124) = product(a121,a115),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,20975,theory(equality)]),20680,21171,theory(equality)]) ).

cnf(21549,plain,
    product(product(X,a114),a124) = product(product(X,a124),a123),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,20975,theory(equality)]) ).

cnf(21570,plain,
    product(a73,a111) = product(a82,product(a70,a112)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,21071,theory(equality)]),20486,21389,theory(equality)]) ).

cnf(21571,plain,
    product(product(a70,a112),a71) = product(a71,product(a70,a108)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,21071,theory(equality)]),20486,theory(equality)]) ).

cnf(21572,plain,
    product(a71,a112) = product(a70,a72),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[584,21071,theory(equality)]),20061,20249,20248,theory(equality)]) ).

cnf(21596,plain,
    product(a100,a114) = product(product(a114,a115),a121),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[289,21171,theory(equality)]),21167,20666,theory(equality)]) ).

cnf(21597,plain,
    product(a92,a114) = product(product(a91,a114),product(a115,a121)),
    inference('PARAMODULATE',[status(thm)],[288,21171,theory(equality)]) ).

cnf(21600,plain,
    product(product(X,a123),a124) = product(product(X,a114),product(a115,a121)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,21171,theory(equality)]),20670,theory(equality)]) ).

cnf(21601,plain,
    product(product(X,a114),product(a115,a121)) = product(product(X,a124),a114),
    inference('REWRITE',[status(thm)],[20670,21600,theory(equality)]) ).

cnf(21602,plain,
    product(a75,product(a75,a124)) = product(product(a75,a114),product(a115,a121)),
    inference('REWRITE',[status(thm)],[7596,21600,theory(equality)]) ).

cnf(21604,plain,
    product(product(a68,a124),a14) = product(a74,a117),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1081,21180,theory(equality)]),1598,theory(equality)]) ).

cnf(21608,plain,
    product(product(a68,a115),product(a121,a122)) = product(product(a68,a122),a123),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[570,21180,theory(equality)]),20793,20809,theory(equality)]) ).

cnf(21610,plain,
    product(a75,product(a68,a122)) = product(product(a68,a115),product(a121,a122)),
    inference('REWRITE',[status(thm)],[20843,21608,theory(equality)]) ).

cnf(21614,plain,
    product(product(X,a115),a75) = product(product(X,a122),product(a68,a124)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,21180,theory(equality)]),1582,theory(equality)]) ).

cnf(21615,plain,
    product(product(X,a115),a75) = product(product(X,a124),a68),
    inference('REWRITE',[status(thm)],[21184,21614,theory(equality)]) ).

cnf(21616,plain,
    product(product(a68,a115),a75) = product(a76,a121),
    inference('REWRITE',[status(thm)],[20881,21615,theory(equality)]) ).

cnf(21657,plain,
    product(product(X,a108),a73) = product(product(X,a110),a82),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,19871,theory(equality)]),20481,theory(equality)]) ).

cnf(21672,plain,
    product(product(a70,a110),a72) = product(a83,a112),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,20048,theory(equality)]),21469,19903,theory(equality)]) ).

cnf(21687,plain,
    product(product(X,a108),a71) = product(product(X,a73),a118),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,20142,theory(equality)]),19732,19721,theory(equality)]) ).

cnf(21695,plain,
    product(a92,product(a100,a115)) = product(product(a91,a114),product(a121,a114)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[288,20306,theory(equality)]),20679,involutory_quandle_02,theory(equality)]) ).

cnf(21721,plain,
    product(a83,product(a71,a110)) = product(a73,a79),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[304,20347,theory(equality)]),20765,20737,20526,19660,theory(equality)]) ).

cnf(21735,plain,
    product(product(a70,a71),a82) = product(a72,product(a71,a119)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[760,20464,theory(equality)]),21303,theory(equality)]) ).

cnf(21773,plain,
    product(a108,a111) = product(a112,product(a109,a111)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[774,20505,theory(equality)]),21476,theory(equality)]) ).

cnf(21781,plain,
    product(product(a108,a112),a118) = product(a111,a83),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,20505,theory(equality)]),21376,20525,theory(equality)]) ).

cnf(21803,plain,
    product(a122,a114) = product(a123,a121),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,20662,theory(equality)]),20676,20324,theory(equality)]) ).

cnf(21810,plain,
    product(product(a122,a114),a75) = product(a124,a100),
    inference('REWRITE',[status(thm)],[20712,21803,theory(equality)]) ).

cnf(21811,plain,
    product(a122,a114) = product(a99,product(a115,a121)),
    inference('REWRITE',[status(thm)],[20888,21803,theory(equality)]) ).

cnf(21813,plain,
    product(a76,a99) = product(product(a68,a124),a77),
    inference('REWRITE',[status(thm)],[21522,21463,21803,theory(equality)]) ).

cnf(21824,plain,
    product(product(X,a114),a124) = product(product(X,a123),product(a121,a115)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,20680,theory(equality)]),21549,theory(equality)]) ).

cnf(21825,plain,
    product(a75,product(a75,a123)) = product(product(a75,a114),a124),
    inference('REWRITE',[status(thm)],[20683,21824,theory(equality)]) ).

cnf(21827,plain,
    product(product(a92,a114),a75) = product(product(a92,a123),product(product(a75,a114),a124)),
    inference('REWRITE',[status(thm)],[20635,21825,theory(equality)]) ).

cnf(21833,plain,
    product(a123,a76) = product(product(a115,a121),product(a122,a114)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[287,20692,theory(equality)]),20866,theory(equality)]) ).

cnf(21835,plain,
    product(product(a76,a115),a76) = product(a76,product(a122,a114)),
    inference('PARAMODULATE',[status(thm)],[569,20692,theory(equality)]) ).

cnf(21839,plain,
    product(a112,a108) = product(a110,product(a72,a110)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,20720,theory(equality)]),19713,20568,theory(equality)]) ).

cnf(21843,plain,
    product(product(X,a110),a72) = product(product(X,a72),product(a108,a112)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,20720,theory(equality)]) ).

cnf(21863,plain,
    product(product(a100,a114),a68) = product(a123,product(a76,a115)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[428,20866,theory(equality)]),21152,theory(equality)]) ).

cnf(21870,plain,
    product(product(a121,a114),a115) = product(a115,a100),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[452,20931,theory(equality)]),8925,21543,theory(equality)]) ).

cnf(21871,plain,
    product(product(a123,a114),a68) = product(a115,a100),
    inference('REWRITE',[status(thm)],[8925,21870,theory(equality)]) ).

cnf(21875,plain,
    product(a125,a121) = product(product(a121,a114),product(a2,a121)),
    inference('PARAMODULATE',[status(thm)],[427,20976,theory(equality)]) ).

cnf(21892,plain,
    product(a112,a73) = product(product(a111,a73),product(a70,a108)),
    inference('PARAMODULATE',[status(thm)],[296,21070,theory(equality)]) ).

cnf(21930,plain,
    product(product(a109,a108),a83) = a110,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,21102,theory(equality)]) ).

cnf(21941,plain,
    product(a124,a13) = product(a110,a33),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[652,21165,theory(equality)]),involutory_quandle_01,theory(equality)]) ).

cnf(21965,plain,
    product(a111,a73) = product(a109,a108),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[295,21242,theory(equality)]),1433,20473,theory(equality)]) ).

cnf(21968,plain,
    product(a112,a73) = product(a110,a108),
    inference('REWRITE',[status(thm)],[21892,307,21965,theory(equality)]) ).

cnf(21972,plain,
    product(a72,a73) = product(a79,product(a111,a109)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[301,21246,theory(equality)]),20081,19963,theory(equality)]) ).

cnf(21978,plain,
    product(a72,product(a70,a110)) = product(a70,a71),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[759,21248,theory(equality)]),20244,theory(equality)]) ).

cnf(21988,plain,
    product(a119,a83) = product(a112,a108),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[308,21332,theory(equality)]),20760,20557,theory(equality)]) ).

cnf(21997,plain,
    product(a70,product(a118,a108)) = product(a71,product(a70,a108)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[444,21572,theory(equality)]),1368,20570,769,theory(equality)]) ).

cnf(21998,plain,
    product(product(a70,a112),a71) = product(a70,product(a118,a108)),
    inference('REWRITE',[status(thm)],[21571,21997,theory(equality)]) ).

cnf(22002,plain,
    product(a72,a73) = product(a82,a108),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,21572,theory(equality)]),21332,21083,21972,19742,20067,theory(equality)]) ).

cnf(22003,plain,
    product(a72,a73) = product(a71,product(a118,a108)),
    inference('REWRITE',[status(thm)],[19954,22002,theory(equality)]) ).

cnf(22005,plain,
    product(a72,a73) = product(a70,a83),
    inference('REWRITE',[status(thm)],[21332,22002,theory(equality)]) ).

cnf(22006,plain,
    product(a72,a83) = product(product(a71,a112),a73),
    inference('REWRITE',[status(thm)],[21333,21572,21260,22002,theory(equality)]) ).

cnf(22039,plain,
    product(a112,a108) = product(product(a110,a108),product(a72,a73)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[308,22005,theory(equality)]),20557,21988,theory(equality)]) ).

cnf(22042,plain,
    product(a73,a79) = product(a71,a112),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,22005,theory(equality)]),21572,21028,21721,20349,21033,theory(equality)]) ).

cnf(22049,plain,
    product(a115,a121) = product(a114,product(a76,a77)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,19147,theory(equality)]),8894,438,21171,theory(equality)]) ).

cnf(22051,plain,
    product(a76,product(a76,a121)) = product(product(product(a75,a114),a124),product(a77,a124)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[750,19147,theory(equality)]),involutory_quandle_02,21500,theory(equality)]) ).

cnf(22056,plain,
    product(product(X,a114),product(a76,a121)) = product(product(X,product(a76,a121)),a124),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,19147,theory(equality)]) ).

cnf(22064,plain,
    product(a68,product(a68,a124)) = a75,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,19177,theory(equality)]),21519,21517,1606,involutory_quandle_01,theory(equality)]) ).

cnf(22068,plain,
    product(product(X,a114),a121) = product(product(X,a115),a123),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,19196,theory(equality)]),18915,21168,theory(equality)]) ).

cnf(22071,plain,
    product(product(X,a122),a115) = product(product(X,a114),a121),
    inference('REWRITE',[status(thm)],[570,22068,theory(equality)]) ).

cnf(22080,plain,
    product(product(X,a114),a121) = product(product(X,a100),product(a121,a115)),
    inference('REWRITE',[status(thm)],[21517,22068,theory(equality)]) ).

cnf(22085,plain,
    product(a111,product(a111,a109)) = product(a119,a108),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[295,19272,theory(equality)]),21234,20553,theory(equality)]) ).

cnf(22090,plain,
    product(a119,product(a109,a111)) = product(a111,product(a110,a111)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[745,19340,theory(equality)]),21209,21429,22085,theory(equality)]) ).

cnf(22091,plain,
    product(a110,product(a110,a112)) = product(a119,product(a109,a111)),
    inference('REWRITE',[status(thm)],[21209,22090,theory(equality)]) ).

cnf(22092,plain,
    product(a119,product(a109,a111)) = product(product(a118,a108),a79),
    inference('REWRITE',[status(thm)],[21210,22090,theory(equality)]) ).

cnf(22213,plain,
    product(a118,a108) = product(a111,product(a70,a110)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[436,19903,theory(equality)]),19668,19409,20720,theory(equality)]) ).

cnf(22224,plain,
    product(product(a108,a72),a82) = product(product(a110,a112),a73),
    inference('PARAMODULATE',[status(thm)],[583,20045,theory(equality)]) ).

cnf(22226,plain,
    product(a73,a72) = product(a82,product(a110,a112)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,20045,theory(equality)]),20425,involutory_quandle,20429,22002,theory(equality)]) ).

cnf(22247,plain,
    product(product(a110,a108),a112) = product(a112,product(a70,a111)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,20212,theory(equality)]),21968,theory(equality)]) ).

cnf(22257,plain,
    product(product(X,a114),product(a100,a115)) = product(product(X,a122),a123),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,20324,theory(equality)]),18941,theory(equality)]) ).

cnf(22259,plain,
    product(product(a68,a115),product(a121,a122)) = product(product(a68,a114),product(a100,a115)),
    inference('REWRITE',[status(thm)],[21608,22257,theory(equality)]) ).

cnf(22261,plain,
    product(a75,product(a68,a122)) = product(product(a68,a114),product(a100,a115)),
    inference('REWRITE',[status(thm)],[21610,22259,theory(equality)]) ).

cnf(22263,plain,
    product(product(X,a114),product(a100,a115)) = product(product(X,a123),a100),
    inference('REWRITE',[status(thm)],[18858,22257,theory(equality)]) ).

cnf(22267,plain,
    product(product(a70,a110),X) = product(product(a73,X),product(a118,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,20332,theory(equality)]) ).

cnf(22269,plain,
    product(product(X,a108),a71) = product(product(X,a109),a82),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,20332,theory(equality)]),20243,21687,theory(equality)]) ).

cnf(22270,plain,
    product(product(a111,a108),a71) = product(a108,a109),
    inference('REWRITE',[status(thm)],[20040,22269,theory(equality)]) ).

cnf(22274,plain,
    product(product(X,a108),a71) = product(product(X,a70),a109),
    inference('REWRITE',[status(thm)],[20041,22269,theory(equality)]) ).

cnf(22308,plain,
    product(a99,product(a121,a114)) = a114,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,20652,theory(equality)]) ).

cnf(22360,plain,
    product(product(X,a100),product(a77,a124)) = product(product(X,a115),product(product(a77,a115),product(a121,a122))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,20898,theory(equality)]),20805,716,theory(equality)]) ).

cnf(22361,plain,
    product(product(product(a77,a100),product(a124,a100)),product(a77,a124)) = product(product(a77,a115),product(a121,a122)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,20898,theory(equality)]),20809,involutory_quandle_02,theory(equality)]) ).

cnf(22367,plain,
    product(product(X,a114),product(a100,a115)) = product(product(X,a100),product(a114,a115)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,20941,theory(equality)]),22263,theory(equality)]) ).

cnf(22368,plain,
    product(product(a68,a115),product(a121,a122)) = product(product(a68,a100),product(a114,a115)),
    inference('REWRITE',[status(thm)],[22259,22367,theory(equality)]) ).

cnf(22369,plain,
    product(a75,product(a68,a122)) = product(product(a68,a100),product(a114,a115)),
    inference('REWRITE',[status(thm)],[22261,22367,theory(equality)]) ).

cnf(22520,plain,
    product(product(a112,X),a73) = product(product(a110,a108),product(X,a73)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,21968,theory(equality)]) ).

cnf(22521,plain,
    product(a112,a108) = product(product(a110,a112),a73),
    inference('REWRITE',[status(thm)],[22039,20717,22520,theory(equality)]) ).

cnf(22522,plain,
    product(product(a108,a72),a82) = product(a112,a108),
    inference('REWRITE',[status(thm)],[22224,22521,theory(equality)]) ).

cnf(22547,plain,
    product(product(a71,a111),a72) = a73,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,22042,theory(equality)]),21039,theory(equality)]) ).

cnf(22574,plain,
    product(product(X,a100),a123) = product(product(X,a122),product(a100,a115)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,18812,theory(equality)]),18888,theory(equality)]) ).

cnf(22575,plain,
    product(a115,a121) = product(product(a121,a100),a123),
    inference('REWRITE',[status(thm)],[21196,22574,theory(equality)]) ).

cnf(22651,plain,
    product(a72,product(a71,a119)) = product(a71,a112),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,19984,theory(equality)]),20249,22270,22269,21735,theory(equality)]) ).

cnf(22652,plain,
    product(product(a70,a71),a82) = product(a71,a112),
    inference('REWRITE',[status(thm)],[21735,22651,theory(equality)]) ).

cnf(22657,plain,
    product(a71,a111) = product(a70,product(a70,a112)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[20093,21070,theory(equality)]),20485,21077,20539,20096,theory(equality)]) ).

cnf(22694,plain,
    product(a70,product(a118,a108)) = product(a72,a108),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[445,20249,theory(equality)]),20598,3681,20570,769,theory(equality)]) ).

cnf(22697,plain,
    product(product(a70,a112),a71) = product(a72,a108),
    inference('REWRITE',[status(thm)],[21998,22694,theory(equality)]) ).

cnf(22713,plain,
    product(a121,a123) = product(a115,a100),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,20312,theory(equality)]) ).

cnf(22717,plain,
    product(a99,a75) = product(a115,a100),
    inference('REWRITE',[status(thm)],[20307,22713,theory(equality)]) ).

cnf(22720,plain,
    product(a123,a114) = product(a100,a121),
    inference('REWRITE',[status(thm)],[21021,21542,22713,theory(equality)]) ).

cnf(22728,plain,
    product(product(a100,a121),a68) = product(a115,a100),
    inference('REWRITE',[status(thm)],[21871,22720,theory(equality)]) ).

cnf(22757,plain,
    product(product(X,a123),a114) = product(product(X,a114),product(a100,a121)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,22720,theory(equality)]) ).

cnf(22758,plain,
    product(a122,a77) = product(a115,a114),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[430,22717,theory(equality)]),20644,21442,theory(equality)]) ).

cnf(22759,plain,
    product(a115,a114) = product(a121,a99),
    inference('REWRITE',[status(thm)],[21441,22758,theory(equality)]) ).

cnf(22765,plain,
    product(product(a77,a122),a77) = product(a77,product(a115,a114)),
    inference('PARAMODULATE',[status(thm)],[569,22758,theory(equality)]) ).

cnf(22775,plain,
    product(product(a71,a110),a83) = product(a72,a71),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,20334,theory(equality)]),21074,21085,theory(equality)]) ).

cnf(22776,plain,
    product(product(a82,a13),a32) = product(a76,a121),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[946,20409,theory(equality)]),20880,18829,theory(equality)]) ).

cnf(22777,plain,
    product(product(a72,a13),a32) = product(a75,product(a76,a121)),
    inference('REWRITE',[status(thm)],[5490,22776,theory(equality)]) ).

cnf(22800,plain,
    a77 = product(a75,product(a100,a115)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[548,20452,theory(equality)]),5515,20771,knot_121,946,20412,644,theory(equality)]) ).

cnf(22808,plain,
    product(a77,product(a100,a115)) = a75,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,22800,theory(equality)]) ).

cnf(22819,plain,
    product(a68,a122) = product(a76,a124),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[451,22800,theory(equality)]),19146,20794,theory(equality)]) ).

cnf(22822,plain,
    product(a77,a75) = product(a75,product(a121,a122)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,22800,theory(equality)]),20814,theory(equality)]) ).

cnf(22825,plain,
    product(a76,product(a100,a115)) = product(product(a75,a114),a77),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[310,22800,theory(equality)]),21500,20880,theory(equality)]) ).

cnf(22826,plain,
    product(a76,product(a100,a115)) = product(a77,product(a76,a121)),
    inference('REWRITE',[status(thm)],[21500,22825,theory(equality)]) ).

cnf(22850,plain,
    product(product(a68,a115),a122) = a76,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,22819,theory(equality)]),1597,theory(equality)]) ).

cnf(22851,plain,
    product(a75,a124) = product(a76,a121),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[789,22819,theory(equality)]),21616,21614,theory(equality)]) ).

cnf(22852,plain,
    product(a77,a76) = product(a75,a124),
    inference('REWRITE',[status(thm)],[8878,22851,theory(equality)]) ).

cnf(22863,plain,
    product(a76,product(a75,a124)) = product(product(product(a75,a114),a124),product(a77,a124)),
    inference('REWRITE',[status(thm)],[22051,22851,theory(equality)]) ).

cnf(22866,plain,
    product(product(X,a114),product(a75,a124)) = product(product(X,a124),a75),
    inference('REWRITE',[status(thm)],[22056,713,22851,theory(equality)]) ).

cnf(22870,plain,
    product(product(a72,a13),a32) = product(product(a75,a114),product(a115,a121)),
    inference('REWRITE',[status(thm)],[22777,21602,22851,theory(equality)]) ).

cnf(22871,plain,
    product(product(X,a123),a75) = product(product(X,a114),product(product(a72,a13),a32)),
    inference('REWRITE',[status(thm)],[21172,22870,theory(equality)]) ).

cnf(22874,plain,
    product(a76,product(a100,a115)) = product(a77,product(a75,a124)),
    inference('REWRITE',[status(thm)],[22826,22851,theory(equality)]) ).

cnf(22875,plain,
    product(product(a68,a100),a122) = product(a77,product(a115,a121)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[438,22819,theory(equality)]),21171,20974,theory(equality)]) ).

cnf(22876,plain,
    product(a76,product(a68,a114)) = product(a77,product(a115,a121)),
    inference('REWRITE',[status(thm)],[21136,22875,theory(equality)]) ).

cnf(22877,plain,
    product(a77,a124) = product(product(a68,a100),product(a114,a115)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[297,22819,theory(equality)]),22367,22257,20975,theory(equality)]) ).

cnf(22878,plain,
    product(product(a68,a115),product(a121,a122)) = product(a77,a124),
    inference('REWRITE',[status(thm)],[22368,22877,theory(equality)]) ).

cnf(22879,plain,
    product(a75,product(a68,a122)) = product(a77,a124),
    inference('REWRITE',[status(thm)],[22369,22877,theory(equality)]) ).

cnf(22888,plain,
    product(product(a75,a124),a76) = a77,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,22852,theory(equality)]) ).

cnf(22889,plain,
    product(product(a72,a13),a32) = product(a76,a77),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[751,22852,theory(equality)]),knot_77,22870,21601,theory(equality)]) ).

cnf(22891,plain,
    product(product(X,a123),a75) = product(product(X,a114),product(a76,a77)),
    inference('REWRITE',[status(thm)],[22871,22889,theory(equality)]) ).

cnf(22897,plain,
    product(a76,product(a100,a115)) = product(a68,a124),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[791,22852,theory(equality)]),21189,20794,19163,451,theory(equality)]) ).

cnf(22905,plain,
    product(a68,a124) = product(a77,product(a75,a124)),
    inference('REWRITE',[status(thm)],[22874,22897,theory(equality)]) ).

cnf(22924,plain,
    product(a108,a72) = product(a119,product(a109,a111)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[591,20506,theory(equality)]),21429,1263,21031,21781,theory(equality)]) ).

cnf(22925,plain,
    product(product(a119,a108),a119) = product(a108,a72),
    inference('REWRITE',[status(thm)],[21429,22924,theory(equality)]) ).

cnf(22927,plain,
    product(a110,product(a110,a112)) = product(a108,a72),
    inference('REWRITE',[status(thm)],[22091,22924,theory(equality)]) ).

cnf(22928,plain,
    product(a108,a72) = product(product(a118,a108),a79),
    inference('REWRITE',[status(thm)],[22092,22924,theory(equality)]) ).

cnf(22986,plain,
    product(a73,product(a110,a112)) = product(a82,product(a70,a111)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[300,20722,theory(equality)]),20428,22226,theory(equality)]) ).

cnf(23044,plain,
    product(product(a68,a123),a75) = a77,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,20877,theory(equality)]),22891,theory(equality)]) ).

cnf(23045,plain,
    a68 = product(a76,product(a75,a124)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[751,20877,theory(equality)]),22852,156,438,involutory_quandle_01,theory(equality)]) ).

cnf(23046,plain,
    a68 = product(product(product(a75,a114),a124),product(a77,a124)),
    inference('REWRITE',[status(thm)],[22863,23045,theory(equality)]) ).

cnf(23047,plain,
    product(a76,product(a76,a77)) = product(product(a68,a114),product(a115,a121)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[750,20877,theory(equality)]),22049,theory(equality)]) ).

cnf(23053,plain,
    product(a77,a75) = product(a68,a123),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,23044,theory(equality)]) ).

cnf(23054,plain,
    product(a68,a123) = product(a75,product(a121,a122)),
    inference('REWRITE',[status(thm)],[22822,23053,theory(equality)]) ).

cnf(23058,plain,
    product(a68,a75) = product(a77,a124),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[581,23044,theory(equality)]),involutory_quandle_01,theory(equality)]) ).

cnf(23059,plain,
    product(product(a68,a75),a77) = product(a77,product(a122,a114)),
    inference('REWRITE',[status(thm)],[21459,23058,theory(equality)]) ).

cnf(23060,plain,
    product(product(a68,a124),product(a68,a75)) = product(product(a77,a100),product(a124,a100)),
    inference('REWRITE',[status(thm)],[21525,23058,theory(equality)]) ).

cnf(23064,plain,
    product(product(X,a100),product(a68,a75)) = product(product(X,a115),product(product(a77,a115),product(a121,a122))),
    inference('REWRITE',[status(thm)],[22360,23058,theory(equality)]) ).

cnf(23065,plain,
    product(a68,a124) = product(product(a77,a115),product(a121,a122)),
    inference('REWRITE',[status(thm)],[22361,involutory_quandle_01,23060,23058,theory(equality)]) ).

cnf(23066,plain,
    product(product(X,a100),product(a68,a75)) = product(product(X,a115),product(a68,a124)),
    inference('REWRITE',[status(thm)],[23064,23065,theory(equality)]) ).

cnf(23068,plain,
    product(product(a68,a115),product(a121,a122)) = product(a68,a75),
    inference('REWRITE',[status(thm)],[22878,23058,theory(equality)]) ).

cnf(23069,plain,
    product(a75,product(a68,a122)) = product(a68,a75),
    inference('REWRITE',[status(thm)],[22879,23058,theory(equality)]) ).

cnf(23073,plain,
    a68 = product(product(product(a75,a114),a124),product(a68,a75)),
    inference('REWRITE',[status(thm)],[23046,23058,theory(equality)]) ).

cnf(23081,plain,
    product(a68,a76) = product(a76,a77),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,23045,theory(equality)]),22888,theory(equality)]) ).

cnf(23088,plain,
    product(product(a72,a13),a32) = product(a68,a76),
    inference('REWRITE',[status(thm)],[22889,23081,theory(equality)]) ).

cnf(23090,plain,
    product(product(X,a123),a75) = product(product(X,a114),product(a68,a76)),
    inference('REWRITE',[status(thm)],[22891,23081,theory(equality)]) ).

cnf(23096,plain,
    product(a75,a76) = product(product(a68,a114),product(a115,a121)),
    inference('REWRITE',[status(thm)],[23047,3773,23081,theory(equality)]) ).

cnf(23110,plain,
    product(a124,a100) = product(product(a121,a114),a123),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[754,23053,theory(equality)]),6085,21810,20693,theory(equality)]) ).

cnf(23111,plain,
    product(a124,a100) = product(a123,product(a68,a123)),
    inference('REWRITE',[status(thm)],[6085,23110,theory(equality)]) ).

cnf(23138,plain,
    product(a100,a114) = product(a121,product(a68,a77)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,20965,theory(equality)]),20854,20772,21505,21596,theory(equality)]) ).

cnf(23149,plain,
    product(product(a115,a100),a115) = product(a121,a114),
    inference('PARAMODULATE',[status(thm)],[569,20977,theory(equality)]) ).

cnf(23205,plain,
    product(product(a83,a13),a32) = product(a68,a75),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[548,21116,theory(equality)]),23069,10400,644,theory(equality)]) ).

cnf(23240,plain,
    product(product(a100,a121),a75) = product(product(a115,a121),a123),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[755,21176,theory(equality)]),20318,theory(equality)]) ).

cnf(23277,plain,
    product(a71,product(a70,a112)) = product(a73,product(a110,a112)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[20248,21351,theory(equality)]),22986,20424,knot_72,20248,20401,763,theory(equality)]) ).

cnf(23299,plain,
    product(a119,a108) = product(a112,a71),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[785,21397,theory(equality)]),19812,20506,theory(equality)]) ).

cnf(23301,plain,
    product(a119,a108) = product(a108,product(a70,a71)),
    inference('REWRITE',[status(thm)],[21343,23299,theory(equality)]) ).

cnf(23340,plain,
    product(product(X,a112),a71) = product(product(X,a71),product(a119,a108)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,23299,theory(equality)]) ).

cnf(23360,plain,
    product(a68,a115) = product(a76,a122),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[451,21493,theory(equality)]),knot_122,5948,theory(equality)]) ).

cnf(23389,plain,
    product(a75,product(a121,a115)) = product(a68,a100),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,21519,theory(equality)]) ).

cnf(23391,plain,
    product(product(a75,a114),a75) = product(a68,a100),
    inference('REWRITE',[status(thm)],[21017,23389,theory(equality)]) ).

cnf(23432,plain,
    product(a110,a39) = product(product(product(a109,a108),a39),a84),
    inference('PARAMODULATE',[status(thm)],[681,21930,theory(equality)]) ).

cnf(23443,plain,
    product(a73,a111) = product(a83,a112),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[442,22003,theory(equality)]),21469,20548,20590,21369,20083,763,theory(equality)]) ).

cnf(23445,plain,
    product(product(a70,a110),a72) = product(a73,a111),
    inference('REWRITE',[status(thm)],[21672,23443,theory(equality)]) ).

cnf(23519,plain,
    product(a114,a92) = product(a98,product(product(a121,a114),a92)),
    inference('PARAMODULATE',[status(thm)],[802,22308,theory(equality)]) ).

cnf(23577,plain,
    product(a75,a114) = product(a76,a99),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[751,22808,theory(equality)]),20662,theory(equality)]) ).

cnf(23579,plain,
    product(a75,a114) = product(product(a68,a124),a77),
    inference('REWRITE',[status(thm)],[21813,23577,theory(equality)]) ).

cnf(23584,plain,
    product(a75,a77) = product(a77,product(a115,a121)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,22808,theory(equality)]),20865,theory(equality)]) ).

cnf(23586,plain,
    product(a76,product(a68,a114)) = product(a75,a77),
    inference('REWRITE',[status(thm)],[22876,23584,theory(equality)]) ).

cnf(23594,plain,
    product(a75,a76) = product(a68,a77),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[438,22897,theory(equality)]),20854,20662,23096,21601,theory(equality)]) ).

cnf(23596,plain,
    product(a75,a76) = product(a77,a99),
    inference('REWRITE',[status(thm)],[20854,23594,theory(equality)]) ).

cnf(23601,plain,
    product(a100,a114) = product(product(a121,a115),a76),
    inference('REWRITE',[status(thm)],[23138,20694,8904,23594,theory(equality)]) ).

cnf(23608,plain,
    product(a115,a114) = product(a123,a76),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,23596,theory(equality)]),157,21009,22759,20887,theory(equality)]) ).

cnf(23609,plain,
    product(a115,a114) = product(product(a115,a121),product(a122,a114)),
    inference('REWRITE',[status(thm)],[21833,23608,theory(equality)]) ).

cnf(23614,plain,
    product(a75,a77) = product(product(a68,a75),a76),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[789,23594,theory(equality)]),involutory_quandle_02,23081,theory(equality)]) ).

cnf(23615,plain,
    product(a68,product(a68,a76)) = product(a75,a77),
    inference('REWRITE',[status(thm)],[10836,23614,theory(equality)]) ).

cnf(23622,plain,
    product(a76,a75) = product(a77,a122),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,23594,theory(equality)]),20852,20794,169,451,theory(equality)]) ).

cnf(23628,plain,
    product(product(a76,a75),a77) = product(a77,product(a115,a114)),
    inference('REWRITE',[status(thm)],[22765,23622,theory(equality)]) ).

cnf(23638,plain,
    product(product(a68,X),a77) = product(product(a75,a76),product(X,a77)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,23594,theory(equality)]) ).

cnf(23641,plain,
    product(product(a115,a114),a115) = product(a122,product(a76,a115)),
    inference('PARAMODULATE',[status(thm)],[721,23608,theory(equality)]) ).

cnf(23644,plain,
    a115 = product(product(a100,a121),a77),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[580,23608,theory(equality)]),22720,involutory_quandle_01,theory(equality)]) ).

cnf(23653,plain,
    product(a77,product(a75,a114)) = product(a76,product(a122,a114)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[751,23622,theory(equality)]),438,theory(equality)]) ).

cnf(23654,plain,
    product(a68,a115) = product(a75,a123),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[750,23622,theory(equality)]),involutory_quandle,13110,22851,20297,20930,23360,theory(equality)]) ).

cnf(23661,plain,
    product(product(X,a124),a75) = product(product(X,a123),product(a68,a115)),
    inference('REWRITE',[status(thm)],[13110,23654,theory(equality)]) ).

cnf(23664,plain,
    product(product(a92,a75),product(a68,a115)) = product(a91,a123),
    inference('REWRITE',[status(thm)],[17600,23654,theory(equality)]) ).

cnf(23668,plain,
    product(a77,a115) = product(product(a75,a114),a124),
    inference('REWRITE',[status(thm)],[21825,21503,23654,theory(equality)]) ).

cnf(23669,plain,
    product(product(a92,a114),a75) = product(product(a92,a123),product(a77,a115)),
    inference('REWRITE',[status(thm)],[21827,23668,theory(equality)]) ).

cnf(23671,plain,
    a68 = product(product(a77,a115),product(a68,a75)),
    inference('REWRITE',[status(thm)],[23073,23668,theory(equality)]) ).

cnf(23723,plain,
    product(product(product(a109,a111),a13),a32) = product(a122,a114),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[506,23088,theory(equality)]),20692,knot_115,8904,20048,515,theory(equality)]) ).

cnf(23806,plain,
    product(a68,product(a115,a121)) = product(a76,product(a122,a114)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[593,23391,theory(equality)]),21835,knot_115,451,21155,theory(equality)]) ).

cnf(23809,plain,
    product(a77,product(a75,a114)) = product(a68,product(a115,a121)),
    inference('REWRITE',[status(thm)],[23653,23806,theory(equality)]) ).

cnf(23810,plain,
    product(a75,product(a68,a76)) = product(product(a68,a100),a124),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[581,23391,theory(equality)]),involutory_quandle_01,23090,theory(equality)]) ).

cnf(23811,plain,
    product(product(a68,a100),a124) = product(product(a76,a75),a76),
    inference('REWRITE',[status(thm)],[13508,23810,theory(equality)]) ).

cnf(23827,plain,
    product(a76,a115) = product(a68,a123),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[790,23577,theory(equality)]),23054,20774,knot_115,451,theory(equality)]) ).

cnf(23830,plain,
    product(product(a100,a114),a68) = product(a124,a100),
    inference('REWRITE',[status(thm)],[21863,23111,23827,theory(equality)]) ).

cnf(23831,plain,
    product(a124,a100) = product(product(a115,a121),a115),
    inference('REWRITE',[status(thm)],[21152,23830,theory(equality)]) ).

cnf(23833,plain,
    product(product(a115,a114),a115) = product(product(a100,a121),a75),
    inference('REWRITE',[status(thm)],[23641,23240,20862,18887,23827,theory(equality)]) ).

cnf(23836,plain,
    product(product(a115,a114),a115) = product(product(a115,a121),a123),
    inference('REWRITE',[status(thm)],[23240,23833,theory(equality)]) ).

cnf(23856,plain,
    product(product(a75,a77),product(a68,a114)) = a76,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,23586,theory(equality)]) ).

cnf(24124,plain,
    product(product(a109,a108),a39) = product(a107,product(a107,a106)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1057,18688,theory(equality)]),1433,theory(equality)]) ).

cnf(24126,plain,
    product(a110,a39) = product(a106,product(a106,a107)),
    inference('REWRITE',[status(thm)],[23432,152,10702,24124,theory(equality)]) ).

cnf(24218,plain,
    product(a110,a108) = product(product(a111,a110),product(a118,a108)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,19724,theory(equality)]),20715,20423,involutory_quandle_02,theory(equality)]) ).

cnf(24325,plain,
    product(product(a72,a110),a13) = product(a69,product(a115,a32)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[974,20493,theory(equality)]),involutory_quandle,2059,973,theory(equality)]) ).

cnf(24400,plain,
    product(product(X,a100),a123) = product(product(X,a114),a99),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,20628,theory(equality)]),20665,22574,theory(equality)]) ).

cnf(24518,plain,
    product(a108,a72) = product(product(a110,a108),a112),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[437,21098,theory(equality)]),22247,22928,22213,theory(equality)]) ).

cnf(24519,plain,
    product(a108,a72) = product(a112,product(a70,a111)),
    inference('REWRITE',[status(thm)],[22247,24518,theory(equality)]) ).

cnf(24559,plain,
    product(a73,product(a110,a112)) = product(a72,product(a108,a112)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[442,21349,theory(equality)]),19830,23277,20401,763,theory(equality)]) ).

cnf(24562,plain,
    product(a71,product(a70,a112)) = product(a72,product(a108,a112)),
    inference('REWRITE',[status(thm)],[23277,24559,theory(equality)]) ).

cnf(24666,plain,
    product(a75,product(a68,a114)) = product(product(a68,a114),product(a100,a121)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,21495,theory(equality)]),22808,19145,21505,theory(equality)]) ).

cnf(24707,plain,
    product(a72,product(a108,a112)) = product(product(a70,a112),product(a73,a111)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,21570,theory(equality)]),24562,21247,21302,theory(equality)]) ).

cnf(24785,plain,
    product(product(a124,a100),a68) = product(a100,a114),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[593,21810,theory(equality)]),23601,3829,theory(equality)]) ).

cnf(24839,plain,
    product(product(a73,a111),product(a70,a110)) = product(product(a70,a110),product(a70,a71)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,21978,theory(equality)]),23445,theory(equality)]) ).

cnf(24879,plain,
    product(product(a72,a108),a71) = product(a70,a112),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[22274,21083,theory(equality)]),20401,theory(equality)]) ).

cnf(24911,plain,
    product(product(a115,a114),a115) = product(a121,a100),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,22575,theory(equality)]),23836,theory(equality)]) ).

cnf(24912,plain,
    product(a114,product(a68,a115)) = product(a121,a100),
    inference('REWRITE',[status(thm)],[13532,24911,theory(equality)]) ).

cnf(24924,plain,
    product(product(a121,a100),product(a68,a115)) = a114,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,24912,theory(equality)]) ).

cnf(25014,plain,
    product(product(a72,a39),product(a71,a39)) = product(product(product(a71,a110),a39),a84),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[681,22775,theory(equality)]),involutory_quandle_02,theory(equality)]) ).

cnf(25025,plain,
    product(a76,X) = product(product(product(a68,a115),X),product(a122,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,22850,theory(equality)]) ).

cnf(25062,plain,
    product(product(a111,a109),product(a109,a108)) = product(product(a108,a72),a110),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[746,22925,theory(equality)]),20184,19346,13021,theory(equality)]) ).

cnf(25070,plain,
    product(product(a111,a109),product(a109,a108)) = product(a110,product(a110,a108)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,22927,theory(equality)]),involutory_quandle,20568,25062,theory(equality)]) ).

cnf(25071,plain,
    product(a110,product(a110,a108)) = product(product(a108,a72),a110),
    inference('REWRITE',[status(thm)],[25062,25070,theory(equality)]) ).

cnf(25100,plain,
    product(product(product(a112,a108),a13),a32) = product(a122,a100),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[506,23205,theory(equality)]),21175,20862,20299,21988,515,theory(equality)]) ).

cnf(25157,plain,
    product(product(a70,a110),product(a70,a71)) = product(a72,a108),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,23301,theory(equality)]),22697,23340,20333,20602,theory(equality)]) ).

cnf(25158,plain,
    product(product(a73,a111),product(a70,a110)) = product(a72,a108),
    inference('REWRITE',[status(thm)],[24839,25157,theory(equality)]) ).

cnf(25184,plain,
    product(a68,product(a68,a114)) = product(a77,product(a122,a114)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[438,23360,theory(equality)]),7038,involutory_quandle_02,theory(equality)]) ).

cnf(25185,plain,
    product(a77,product(a122,a114)) = product(product(a68,a114),product(a115,a114)),
    inference('REWRITE',[status(thm)],[7038,25184,theory(equality)]) ).

cnf(25189,plain,
    product(a76,a75) = product(product(a68,a100),product(a115,a100)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[297,23360,theory(equality)]),involutory_quandle_02,20930,23622,theory(equality)]) ).

cnf(25214,plain,
    product(product(a68,a100),X) = product(product(a75,X),product(product(a121,a115),X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,23389,theory(equality)]) ).

cnf(25286,plain,
    product(product(X,product(a68,a124)),a77) = product(product(X,a77),product(a75,a114)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,23579,theory(equality)]) ).

cnf(25308,plain,
    product(product(a68,a100),a124) = product(a77,product(a122,a114)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[789,23615,theory(equality)]),23059,23638,3773,23810,theory(equality)]) ).

cnf(25310,plain,
    product(a77,product(a122,a114)) = product(product(a76,a75),a76),
    inference('REWRITE',[status(thm)],[23811,25308,theory(equality)]) ).

cnf(25401,plain,
    product(a75,product(a68,a114)) = product(a77,product(a115,a114)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[438,23827,theory(equality)]),24666,22757,theory(equality)]) ).

cnf(25413,plain,
    a76 = product(product(a77,product(a115,a114)),product(a75,a114)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,23856,theory(equality)]),3597,25401,theory(equality)]) ).

cnf(25497,plain,
    product(a114,product(a121,a100)) = product(product(a121,a100),product(product(a68,a115),product(a121,a100))),
    inference('PARAMODULATE',[status(thm)],[569,24924,theory(equality)]) ).

cnf(25606,plain,
    a100 = product(product(a121,a122),product(a68,a115)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1580,20804,theory(equality)]),23654,18778,theory(equality)]) ).

cnf(25614,plain,
    product(a100,product(a68,a115)) = product(a121,a122),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,25606,theory(equality)]) ).

cnf(25619,plain,
    product(product(a68,a75),product(a68,a115)) = product(a76,a75),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,25606,theory(equality)]),25189,involutory_quandle_02,23068,theory(equality)]) ).

cnf(25663,plain,
    product(product(a8,a29),product(a37,a29)) = product(product(product(a11,a135),a29),a52),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1787,4943,theory(equality)]),involutory_quandle_02,theory(equality)]) ).

cnf(25888,plain,
    product(product(a125,a100),product(a121,a115)) = product(a115,product(product(a2,a100),product(a121,a115))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,3459,theory(equality)]),22080,22071,theory(equality)]) ).

cnf(25935,plain,
    product(product(a63,product(a62,a128)),X) = product(product(product(a62,a64),X),product(a96,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,3911,theory(equality)]) ).

cnf(26195,plain,
    product(a72,a110) = product(product(a88,a32),product(a40,a32)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[694,5592,theory(equality)]),involutory_quandle_02,2966,9942,21089,19576,712,3001,theory(equality)]) ).

cnf(26196,plain,
    product(a72,a110) = product(product(a90,a13),a33),
    inference('REWRITE',[status(thm)],[14925,26195,theory(equality)]) ).

cnf(26205,plain,
    product(product(a72,a110),a33) = product(a90,a13),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,26196,theory(equality)]) ).

cnf(26207,plain,
    product(a69,product(a115,a32)) = product(a90,a32),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[968,26196,theory(equality)]),involutory_quandle_01,24325,theory(equality)]) ).

cnf(26209,plain,
    product(product(a72,a110),a13) = product(a90,a32),
    inference('REWRITE',[status(thm)],[24325,26207,theory(equality)]) ).

cnf(26213,plain,
    product(product(product(a114,a90),a13),a33) = product(a110,product(a110,a108)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[868,26196,theory(equality)]),25071,20739,979,theory(equality)]) ).

cnf(26226,plain,
    product(product(a110,product(a110,a108)),a33) = product(product(a114,a90),a13),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[477,26205,theory(equality)]),979,25071,20739,theory(equality)]) ).

cnf(26233,plain,
    a90 = product(a68,a115),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[946,26207,theory(equality)]),involutory_quandle_01,theory(equality)]) ).

cnf(26237,plain,
    product(product(a68,a114),a68) = a90,
    inference('REWRITE',[status(thm)],[5948,26233,theory(equality)]) ).

cnf(26258,plain,
    product(a90,product(a121,a122)) = product(a68,a75),
    inference('REWRITE',[status(thm)],[23068,26233,theory(equality)]) ).

cnf(26299,plain,
    product(product(X,a124),a75) = product(product(X,a123),a90),
    inference('REWRITE',[status(thm)],[23661,26233,theory(equality)]) ).

cnf(26305,plain,
    product(product(X,a114),product(a75,a124)) = product(product(X,a123),a90),
    inference('REWRITE',[status(thm)],[22866,26299,theory(equality)]) ).

cnf(26308,plain,
    product(product(a92,a75),a90) = product(a91,a123),
    inference('REWRITE',[status(thm)],[23664,26233,theory(equality)]) ).

cnf(26329,plain,
    product(a114,a90) = product(a121,a100),
    inference('REWRITE',[status(thm)],[24912,26233,theory(equality)]) ).

cnf(26330,plain,
    product(product(product(a121,a100),a13),a33) = product(a110,product(a110,a108)),
    inference('REWRITE',[status(thm)],[26213,26329,theory(equality)]) ).

cnf(26331,plain,
    product(product(a110,product(a110,a108)),a33) = product(product(a121,a100),a13),
    inference('REWRITE',[status(thm)],[26226,26329,theory(equality)]) ).

cnf(26337,plain,
    product(a76,X) = product(product(a90,X),product(a122,X)),
    inference('REWRITE',[status(thm)],[25025,26233,theory(equality)]) ).

cnf(26338,plain,
    product(a91,a122) = a77,
    inference('REWRITE',[status(thm)],[20969,knot_77,26337,theory(equality)]) ).

cnf(26362,plain,
    product(a114,product(a121,a100)) = product(product(a121,a100),product(a90,product(a121,a100))),
    inference('REWRITE',[status(thm)],[25497,26233,theory(equality)]) ).

cnf(26368,plain,
    product(a100,a90) = product(a121,a122),
    inference('REWRITE',[status(thm)],[25614,26233,theory(equality)]) ).

cnf(26369,plain,
    product(a91,a90) = product(a68,a75),
    inference('REWRITE',[status(thm)],[1185,26258,26368,theory(equality)]) ).

cnf(26374,plain,
    product(a98,a99) = product(a121,a114),
    inference('REWRITE',[status(thm)],[3855,20978,1597,26368,theory(equality)]) ).

cnf(26383,plain,
    product(product(a68,a75),a90) = product(a76,a75),
    inference('REWRITE',[status(thm)],[25619,26233,theory(equality)]) ).

cnf(26385,plain,
    product(product(a90,a32),a69) = product(a69,product(a112,a13)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,26207,theory(equality)]),2056,theory(equality)]) ).

cnf(26408,plain,
    product(a76,a75) = a91,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,26369,theory(equality)]),26383,theory(equality)]) ).

cnf(26420,plain,
    product(a91,a77) = product(a77,product(a115,a114)),
    inference('REWRITE',[status(thm)],[23628,26408,theory(equality)]) ).

cnf(26430,plain,
    a76 = product(product(a91,a77),product(a75,a114)),
    inference('REWRITE',[status(thm)],[25413,26420,theory(equality)]) ).

cnf(26443,plain,
    product(a77,product(a122,a114)) = product(a91,a76),
    inference('REWRITE',[status(thm)],[25310,26408,theory(equality)]) ).

cnf(26445,plain,
    product(a68,product(a68,a114)) = product(a91,a76),
    inference('REWRITE',[status(thm)],[25184,26443,theory(equality)]) ).

cnf(26446,plain,
    product(a91,a76) = product(product(a68,a114),product(a115,a114)),
    inference('REWRITE',[status(thm)],[25185,26443,theory(equality)]) ).

cnf(26478,plain,
    product(product(a68,a41),product(a75,a41)) = product(product(a86,a14),a3),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1109,26369,theory(equality)]),9907,involutory_quandle_02,theory(equality)]) ).

cnf(26487,plain,
    product(a91,a75) = a76,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,26408,theory(equality)]) ).

cnf(26490,plain,
    product(a91,a114) = product(a68,product(a115,a121)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[438,26408,theory(equality)]),23809,theory(equality)]) ).

cnf(26552,plain,
    product(a68,a122) = product(a92,product(a75,a124)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[429,26487,theory(equality)]),22819,theory(equality)]) ).

cnf(26558,plain,
    product(a92,a75) = product(a76,a123),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[288,26487,theory(equality)]),157,theory(equality)]) ).

cnf(26560,plain,
    product(a68,a124) = product(a91,a123),
    inference('REWRITE',[status(thm)],[26308,22905,knot_77,26305,26558,theory(equality)]) ).

cnf(26572,plain,
    product(a67,a115) = product(a90,product(a98,a115)),
    inference('PARAMODULATE',[status(thm)],[786,26233,theory(equality)]) ).

cnf(26574,plain,
    product(a90,a68) = product(a68,a114),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[569,26233,theory(equality)]),170,theory(equality)]) ).

cnf(26575,plain,
    product(a90,X) = product(product(a68,X),product(a115,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,26233,theory(equality)]) ).

cnf(26576,plain,
    product(a91,a76) = product(a90,a114),
    inference('REWRITE',[status(thm)],[26446,26575,theory(equality)]) ).

cnf(26579,plain,
    product(a68,product(a68,a114)) = product(a90,a114),
    inference('REWRITE',[status(thm)],[26445,26576,theory(equality)]) ).

cnf(26604,plain,
    product(a68,a75) = product(a92,product(a100,a115)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[429,26338,theory(equality)]),18813,23058,theory(equality)]) ).

cnf(26605,plain,
    product(a68,a75) = product(product(a91,a114),product(a121,a114)),
    inference('REWRITE',[status(thm)],[21695,26604,theory(equality)]) ).

cnf(26606,plain,
    product(a92,a122) = product(a77,a115),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[288,26338,theory(equality)]),1594,theory(equality)]) ).

cnf(26614,plain,
    product(a115,a121) = a98,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,26374,theory(equality)]),22575,24400,theory(equality)]) ).

cnf(26615,plain,
    product(a98,a32) = product(product(a110,a112),a13),
    inference('REWRITE',[status(thm)],[20573,26614,theory(equality)]) ).

cnf(26619,plain,
    product(a98,a32) = product(product(a100,a32),a69),
    inference('REWRITE',[status(thm)],[18715,26615,theory(equality)]) ).

cnf(26620,plain,
    product(a100,a68) = a98,
    inference('REWRITE',[status(thm)],[20862,26614,theory(equality)]) ).

cnf(26624,plain,
    product(a98,a68) = a100,
    inference('REWRITE',[status(thm)],[20931,26614,theory(equality)]) ).

cnf(26625,plain,
    product(a67,a68) = product(a68,a100),
    inference('REWRITE',[status(thm)],[5847,26624,theory(equality)]) ).

cnf(26636,plain,
    product(product(a68,a100),a92) = product(product(product(a68,a67),a92),a99),
    inference('REWRITE',[status(thm)],[10825,26625,theory(equality)]) ).

cnf(26690,plain,
    product(product(a122,a100),a75) = a98,
    inference('REWRITE',[status(thm)],[21176,26614,theory(equality)]) ).

cnf(26698,plain,
    product(a100,a91) = product(a121,a115),
    inference('REWRITE',[status(thm)],[21546,1658,26614,theory(equality)]) ).

cnf(26706,plain,
    product(product(a121,a115),a66) = a92,
    inference('REWRITE',[status(thm)],[12666,26698,theory(equality)]) ).

cnf(26730,plain,
    product(product(X,a67),a92) = product(product(X,a66),product(a121,a115)),
    inference('REWRITE',[status(thm)],[12700,26698,theory(equality)]) ).

cnf(26733,plain,
    product(product(a68,a100),a92) = product(product(product(a68,a66),a99),product(product(a121,a115),a99)),
    inference('REWRITE',[status(thm)],[26636,involutory_quandle_02,26730,theory(equality)]) ).

cnf(26741,plain,
    product(a91,a66) = product(product(a121,a115),product(a126,a2)),
    inference('REWRITE',[status(thm)],[12818,26698,theory(equality)]) ).

cnf(26758,plain,
    product(a92,a114) = product(product(a91,a114),a98),
    inference('REWRITE',[status(thm)],[21597,26614,theory(equality)]) ).

cnf(26764,plain,
    product(a122,a114) = product(a99,a98),
    inference('REWRITE',[status(thm)],[21811,26614,theory(equality)]) ).

cnf(26818,plain,
    product(a115,a114) = product(a98,product(a122,a114)),
    inference('REWRITE',[status(thm)],[23609,26614,theory(equality)]) ).

cnf(26823,plain,
    product(a124,a100) = product(a98,a115),
    inference('REWRITE',[status(thm)],[23831,26614,theory(equality)]) ).

cnf(26825,plain,
    product(a67,a115) = product(a92,a100),
    inference('REWRITE',[status(thm)],[26572,1160,26823,theory(equality)]) ).

cnf(26866,plain,
    product(a91,a114) = a67,
    inference('REWRITE',[status(thm)],[26490,168,26614,theory(equality)]) ).

cnf(26874,plain,
    product(a68,a75) = product(a67,product(a121,a114)),
    inference('REWRITE',[status(thm)],[26605,26866,theory(equality)]) ).

cnf(26876,plain,
    product(a92,a114) = a68,
    inference('REWRITE',[status(thm)],[26758,knot_68,26866,theory(equality)]) ).

cnf(26880,plain,
    product(a68,a75) = product(product(a92,a123),product(a77,a115)),
    inference('REWRITE',[status(thm)],[23669,26876,theory(equality)]) ).

cnf(26895,plain,
    product(product(a121,a114),a92) = product(a122,a114),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[455,26374,theory(equality)]),26764,173,theory(equality)]) ).

cnf(26896,plain,
    product(a114,a92) = product(a115,a114),
    inference('REWRITE',[status(thm)],[23519,26818,26895,theory(equality)]) ).

cnf(26907,plain,
    a115 = product(a98,a121),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[20869,26620,theory(equality)]),23644,theory(equality)]) ).

cnf(26909,plain,
    product(a67,a121) = product(a77,a115),
    inference('REWRITE',[status(thm)],[21497,26907,theory(equality)]) ).

cnf(26913,plain,
    a68 = product(product(a67,a121),product(a68,a75)),
    inference('REWRITE',[status(thm)],[23671,26909,theory(equality)]) ).

cnf(26958,plain,
    product(a92,a122) = product(a67,a121),
    inference('REWRITE',[status(thm)],[26606,26909,theory(equality)]) ).

cnf(26963,plain,
    product(a68,a75) = product(product(a92,a123),product(a67,a121)),
    inference('REWRITE',[status(thm)],[26880,26909,theory(equality)]) ).

cnf(26965,plain,
    product(a100,a1) = product(a97,product(a68,a1)),
    inference('PARAMODULATE',[status(thm)],[1126,26624,theory(equality)]) ).

cnf(27023,plain,
    product(a67,a124) = product(a92,a123),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[429,26866,theory(equality)]),20975,theory(equality)]) ).

cnf(27024,plain,
    product(a68,a75) = product(product(a67,a124),product(a67,a121)),
    inference('REWRITE',[status(thm)],[26963,27023,theory(equality)]) ).

cnf(27030,plain,
    product(a68,a114) = a92,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,26876,theory(equality)]) ).

cnf(27036,plain,
    product(product(X,a115),a68) = product(product(X,a114),a92),
    inference('REWRITE',[status(thm)],[13563,27030,theory(equality)]) ).

cnf(27047,plain,
    product(a75,a121) = a92,
    inference('REWRITE',[status(thm)],[21493,27030,theory(equality)]) ).

cnf(27049,plain,
    product(a76,a123) = product(a75,a100),
    inference('REWRITE',[status(thm)],[21496,26558,27030,theory(equality)]) ).

cnf(27054,plain,
    product(a92,a75) = product(a75,a100),
    inference('REWRITE',[status(thm)],[26558,27049,theory(equality)]) ).

cnf(27117,plain,
    product(a92,a68) = a90,
    inference('REWRITE',[status(thm)],[26237,27030,theory(equality)]) ).

cnf(27133,plain,
    product(a90,a68) = a92,
    inference('REWRITE',[status(thm)],[26574,27030,theory(equality)]) ).

cnf(27134,plain,
    product(a68,a92) = product(a90,a114),
    inference('REWRITE',[status(thm)],[26579,27030,theory(equality)]) ).

cnf(27136,plain,
    product(a68,a124) = a66,
    inference('REWRITE',[status(thm)],[1526,26560,knot_91,24400,27134,theory(equality)]) ).

cnf(27140,plain,
    a122 = product(a126,a2),
    inference('REWRITE',[status(thm)],[19177,1674,27136,theory(equality)]) ).

cnf(27155,plain,
    product(product(X,a122),a42) = product(product(X,a42),product(a127,a2)),
    inference('REWRITE',[status(thm)],[3336,27140,theory(equality)]) ).

cnf(27156,plain,
    product(a95,a2) = product(product(a67,a121),a42),
    inference('REWRITE',[status(thm)],[3313,26958,27155,theory(equality)]) ).

cnf(27185,plain,
    product(a91,a66) = product(a121,a114),
    inference('REWRITE',[status(thm)],[26741,20978,27140,theory(equality)]) ).

cnf(27189,plain,
    product(a75,a66) = a68,
    inference('REWRITE',[status(thm)],[21188,27136,theory(equality)]) ).

cnf(27198,plain,
    product(a66,a14) = product(a74,a117),
    inference('REWRITE',[status(thm)],[21604,27136,theory(equality)]) ).

cnf(27202,plain,
    product(product(a101,a116),product(a66,a14)) = a116,
    inference('REWRITE',[status(thm)],[18835,27198,theory(equality)]) ).

cnf(27237,plain,
    product(a68,a66) = a75,
    inference('REWRITE',[status(thm)],[22064,27136,theory(equality)]) ).

cnf(27239,plain,
    product(product(a68,a100),a92) = product(product(a68,a100),a99),
    inference('REWRITE',[status(thm)],[26733,25214,27237,theory(equality)]) ).

cnf(27246,plain,
    product(product(X,a100),product(a68,a75)) = product(product(X,a115),a66),
    inference('REWRITE',[status(thm)],[23066,27136,theory(equality)]) ).

cnf(27283,plain,
    product(product(X,a66),a77) = product(product(X,a77),product(a75,a114)),
    inference('REWRITE',[status(thm)],[25286,27136,theory(equality)]) ).

cnf(27284,plain,
    a76 = a114,
    inference('REWRITE',[status(thm)],[26430,8915,27185,27283,theory(equality)]) ).

cnf(27286,plain,
    a77 = a114,
    inference('REWRITE',[status(thm)],[knot_77,involutory_quandle,27284,theory(equality)]) ).

cnf(27287,plain,
    a78 = a113,
    inference('REWRITE',[status(thm)],[knot_78,232,27286,theory(equality)]) ).

cnf(27288,plain,
    a79 = a112,
    inference('REWRITE',[status(thm)],[knot_79,195,27287,theory(equality)]) ).

cnf(27289,plain,
    a112 = a119,
    inference('REWRITE',[status(thm)],[knot_112,12480,27288,theory(equality)]) ).

cnf(27290,plain,
    a111 = product(a110,a112),
    inference('REWRITE',[status(thm)],[knot_111,27289,theory(equality)]) ).

cnf(27292,plain,
    product(a110,a111) = a111,
    inference('REWRITE',[status(thm)],[12982,involutory_quandle,27290,theory(equality)]) ).

cnf(27294,plain,
    a108 = product(a109,a108),
    inference('REWRITE',[status(thm)],[13305,1263,27292,theory(equality)]) ).

cnf(27298,plain,
    a109 = product(a108,a109),
    inference('REWRITE',[status(thm)],[3693,knot_109,27294,theory(equality)]) ).

cnf(27299,plain,
    product(product(a111,a110),X) = product(a110,X),
    inference('REWRITE',[status(thm)],[17636,307,27298,theory(equality)]) ).

cnf(27300,plain,
    product(a110,a108) = product(a111,a108),
    inference('REWRITE',[status(thm)],[24218,21391,27299,theory(equality)]) ).

cnf(27304,plain,
    product(a110,a108) = product(a111,a109),
    inference('REWRITE',[status(thm)],[20423,involutory_quandle,27300,theory(equality)]) ).

cnf(27305,plain,
    product(a111,a110) = product(a110,product(a110,a108)),
    inference('REWRITE',[status(thm)],[19272,27304,theory(equality)]) ).

cnf(27307,plain,
    product(product(product(a121,a100),a13),a33) = product(a111,a110),
    inference('REWRITE',[status(thm)],[26330,27305,theory(equality)]) ).

cnf(27308,plain,
    product(a124,a13) = product(product(a121,a100),a13),
    inference('REWRITE',[status(thm)],[26331,21941,27299,27305,theory(equality)]) ).

cnf(27309,plain,
    a110 = product(a111,a110),
    inference('REWRITE',[status(thm)],[27307,19675,27308,theory(equality)]) ).

cnf(27323,plain,
    product(a70,a71) = product(a71,a110),
    inference('REWRITE',[status(thm)],[19502,27309,theory(equality)]) ).

cnf(27327,plain,
    product(product(a71,a110),a73) = product(a71,a110),
    inference('REWRITE',[status(thm)],[21305,27323,theory(equality)]) ).

cnf(27328,plain,
    a72 = product(a72,a83),
    inference('REWRITE',[status(thm)],[21351,21254,27323,theory(equality)]) ).

cnf(27329,plain,
    a72 = product(product(a71,a112),a73),
    inference('REWRITE',[status(thm)],[22006,27328,theory(equality)]) ).

cnf(27383,plain,
    a70 = product(a71,a112),
    inference('REWRITE',[status(thm)],[22652,21244,20129,21657,27323,theory(equality)]) ).

cnf(27446,plain,
    a72 = a83,
    inference('REWRITE',[status(thm)],[27329,21241,27383,theory(equality)]) ).

cnf(27447,plain,
    a72 = product(a82,a118),
    inference('REWRITE',[status(thm)],[knot_83,27446,theory(equality)]) ).

cnf(27448,plain,
    a84 = product(a72,a39),
    inference('REWRITE',[status(thm)],[knot_84,27446,theory(equality)]) ).

cnf(27457,plain,
    product(a73,a39) = product(product(product(a71,a110),a39),a84),
    inference('REWRITE',[status(thm)],[25014,20157,27448,theory(equality)]) ).

cnf(27458,plain,
    product(a70,a108) = a82,
    inference('REWRITE',[status(thm)],[163,1368,27446,theory(equality)]) ).

cnf(27463,plain,
    product(a70,a110) = product(a70,a111),
    inference('REWRITE',[status(thm)],[6067,20014,27458,theory(equality)]) ).

cnf(27464,plain,
    product(a108,a111) = product(a118,a108),
    inference('REWRITE',[status(thm)],[6055,22213,27463,theory(equality)]) ).

cnf(27468,plain,
    product(a108,a111) = product(a101,a32),
    inference('REWRITE',[status(thm)],[18674,27464,theory(equality)]) ).

cnf(27470,plain,
    product(product(a108,a111),a33) = product(a100,a13),
    inference('REWRITE',[status(thm)],[18676,27464,theory(equality)]) ).

cnf(27476,plain,
    product(product(a108,a111),a40) = product(product(a103,a30),a4),
    inference('REWRITE',[status(thm)],[18682,27464,theory(equality)]) ).

cnf(27482,plain,
    product(a107,a106) = product(product(a108,a111),a39),
    inference('REWRITE',[status(thm)],[18688,27464,theory(equality)]) ).

cnf(27489,plain,
    product(product(a108,a111),a13) = product(a100,a32),
    inference('REWRITE',[status(thm)],[18713,27464,theory(equality)]) ).

cnf(27491,plain,
    product(product(a108,a111),a32) = a101,
    inference('REWRITE',[status(thm)],[18751,27464,theory(equality)]) ).

cnf(27564,plain,
    product(a73,a111) = a82,
    inference('REWRITE',[status(thm)],[21330,23445,27463,theory(equality)]) ).

cnf(27573,plain,
    product(a72,product(a108,a112)) = a71,
    inference('REWRITE',[status(thm)],[24707,21247,21302,27564,theory(equality)]) ).

cnf(27579,plain,
    a71 = product(a72,a108),
    inference('REWRITE',[status(thm)],[25158,21248,27564,theory(equality)]) ).

cnf(27606,plain,
    a71 = product(a70,a112),
    inference('REWRITE',[status(thm)],[24879,involutory_quandle,27579,theory(equality)]) ).

cnf(27611,plain,
    product(a71,a70) = product(a72,a110),
    inference('REWRITE',[status(thm)],[20493,27606,theory(equality)]) ).

cnf(27624,plain,
    product(a112,a108) = product(a109,a111),
    inference('REWRITE',[status(thm)],[21839,10770,20526,448,27611,theory(equality)]) ).

cnf(27639,plain,
    product(product(a108,a72),a82) = product(a109,a111),
    inference('REWRITE',[status(thm)],[22522,27624,theory(equality)]) ).

cnf(27658,plain,
    product(a122,a114) = product(a122,a100),
    inference('REWRITE',[status(thm)],[25100,23723,27624,theory(equality)]) ).

cnf(27677,plain,
    a98 = product(a124,a100),
    inference('REWRITE',[status(thm)],[21810,26690,27658,theory(equality)]) ).

cnf(27700,plain,
    a100 = product(a100,a114),
    inference('REWRITE',[status(thm)],[24785,26624,27677,theory(equality)]) ).

cnf(27701,plain,
    product(a100,a121) = product(a114,a115),
    inference('REWRITE',[status(thm)],[21170,27700,theory(equality)]) ).

cnf(27709,plain,
    product(a115,a114) = product(a115,a100),
    inference('REWRITE',[status(thm)],[22728,26896,involutory_quandle,27036,27701,theory(equality)]) ).

cnf(27740,plain,
    product(a121,a114) = product(a121,a100),
    inference('REWRITE',[status(thm)],[24911,23149,27709,theory(equality)]) ).

cnf(27753,plain,
    product(product(a121,a100),a32) = product(a111,a13),
    inference('REWRITE',[status(thm)],[8896,27740,theory(equality)]) ).

cnf(27783,plain,
    a99 = product(a114,product(a121,a100)),
    inference('REWRITE',[status(thm)],[20652,27740,theory(equality)]) ).

cnf(27784,plain,
    a99 = product(product(a121,a100),product(a90,product(a121,a100))),
    inference('REWRITE',[status(thm)],[26362,27783,theory(equality)]) ).

cnf(27796,plain,
    product(a125,a121) = product(product(a121,a100),product(a2,a121)),
    inference('REWRITE',[status(thm)],[21875,27740,theory(equality)]) ).

cnf(27857,plain,
    product(a68,a75) = product(a67,product(a121,a100)),
    inference('REWRITE',[status(thm)],[26874,27740,theory(equality)]) ).

cnf(28064,plain,
    product(a69,a120) = product(a90,a32),
    inference('REWRITE',[status(thm)],[26209,6178,974,27611,theory(equality)]) ).

cnf(28065,plain,
    product(a69,product(a115,a32)) = product(a69,a120),
    inference('REWRITE',[status(thm)],[26207,28064,theory(equality)]) ).

cnf(28067,plain,
    product(a71,a13) = product(a69,product(a112,a13)),
    inference('REWRITE',[status(thm)],[26385,6179,28064,theory(equality)]) ).

cnf(28105,plain,
    product(a71,a111) = product(a71,a110),
    inference('REWRITE',[status(thm)],[22657,27323,27606,theory(equality)]) ).

cnf(28106,plain,
    product(product(a71,a110),a72) = a73,
    inference('REWRITE',[status(thm)],[22547,28105,theory(equality)]) ).

cnf(28173,plain,
    product(a108,a72) = a110,
    inference('REWRITE',[status(thm)],[24519,27309,1268,20739,27463,theory(equality)]) ).

cnf(28177,plain,
    a112 = product(a109,a111),
    inference('REWRITE',[status(thm)],[27639,19902,28173,theory(equality)]) ).

cnf(28198,plain,
    product(a108,a111) = a112,
    inference('REWRITE',[status(thm)],[21773,involutory_quandle,28177,theory(equality)]) ).

cnf(28199,plain,
    a112 = product(a118,a108),
    inference('REWRITE',[status(thm)],[27464,28198,theory(equality)]) ).

cnf(28208,plain,
    a112 = product(a101,a32),
    inference('REWRITE',[status(thm)],[27468,28198,theory(equality)]) ).

cnf(28210,plain,
    a113 = product(a100,a13),
    inference('REWRITE',[status(thm)],[27470,knot_113,28198,theory(equality)]) ).

cnf(28211,plain,
    product(a112,a40) = product(product(a103,a30),a4),
    inference('REWRITE',[status(thm)],[27476,28198,theory(equality)]) ).

cnf(28212,plain,
    product(a107,a106) = product(a112,a39),
    inference('REWRITE',[status(thm)],[27482,28198,theory(equality)]) ).

cnf(28223,plain,
    product(a112,a13) = product(a100,a32),
    inference('REWRITE',[status(thm)],[27489,28198,theory(equality)]) ).

cnf(28224,plain,
    product(a112,a13) = product(product(a101,a13),a33),
    inference('REWRITE',[status(thm)],[14923,28223,theory(equality)]) ).

cnf(28241,plain,
    product(a98,a32) = product(a115,a32),
    inference('REWRITE',[status(thm)],[26619,2055,28223,theory(equality)]) ).

cnf(28242,plain,
    product(a67,a32) = product(a69,a120),
    inference('REWRITE',[status(thm)],[4624,28065,28241,theory(equality)]) ).

cnf(28277,plain,
    product(a101,a117) = a101,
    inference('REWRITE',[status(thm)],[27491,20612,28198,theory(equality)]) ).

cnf(28290,plain,
    a101 = product(product(a113,a32),product(a32,a14)),
    inference('REWRITE',[status(thm)],[20622,28277,theory(equality)]) ).

cnf(28295,plain,
    a100 = a114,
    inference('REWRITE',[status(thm)],[20627,268,28277,theory(equality)]) ).

cnf(28296,plain,
    a100 = product(a113,a13),
    inference('REWRITE',[status(thm)],[knot_114,28295,theory(equality)]) ).

cnf(28297,plain,
    a115 = a98,
    inference('REWRITE',[status(thm)],[knot_115,26620,28295,theory(equality)]) ).

cnf(28298,plain,
    a68 = product(a67,a115),
    inference('REWRITE',[status(thm)],[knot_68,28297,theory(equality)]) ).

cnf(28299,plain,
    a68 = product(a92,a100),
    inference('REWRITE',[status(thm)],[26825,28298,theory(equality)]) ).

cnf(28303,plain,
    a90 = a67,
    inference('REWRITE',[status(thm)],[168,26233,28297,theory(equality)]) ).

cnf(28313,plain,
    product(a67,a41) = a89,
    inference('REWRITE',[status(thm)],[275,28303,theory(equality)]) ).

cnf(28335,plain,
    product(a67,a14) = product(a88,a40),
    inference('REWRITE',[status(thm)],[3287,28303,theory(equality)]) ).

cnf(28355,plain,
    product(a67,a124) = product(a92,a99),
    inference('REWRITE',[status(thm)],[3487,28303,theory(equality)]) ).

cnf(28390,plain,
    product(a64,a94) = product(a87,a14),
    inference('REWRITE',[status(thm)],[10106,9995,28303,theory(equality)]) ).

cnf(28391,plain,
    product(product(a67,a1),a42) = product(a87,a14),
    inference('REWRITE',[status(thm)],[9995,28390,theory(equality)]) ).

cnf(28396,plain,
    product(product(a68,a1),a42) = product(product(a87,a14),a96),
    inference('REWRITE',[status(thm)],[17067,28390,theory(equality)]) ).

cnf(28471,plain,
    product(a93,product(a96,a41)) = product(a65,product(a125,a93)),
    inference('REWRITE',[status(thm)],[18369,knot_125,17194,28303,theory(equality)]) ).

cnf(28556,plain,
    product(a92,a68) = a67,
    inference('REWRITE',[status(thm)],[27117,28303,theory(equality)]) ).

cnf(28567,plain,
    product(a68,a100) = a92,
    inference('REWRITE',[status(thm)],[27133,26625,28303,theory(equality)]) ).

cnf(28583,plain,
    a92 = product(a67,a124),
    inference('REWRITE',[status(thm)],[27239,28355,involutory_quandle,28567,theory(equality)]) ).

cnf(28600,plain,
    product(a68,a75) = product(a92,product(a67,a121)),
    inference('REWRITE',[status(thm)],[27024,28583,theory(equality)]) ).

cnf(28615,plain,
    a99 = a92,
    inference('REWRITE',[status(thm)],[27784,26706,27246,27857,28303,theory(equality)]) ).

cnf(28616,plain,
    a100 = a91,
    inference('REWRITE',[status(thm)],[knot_100,147,28615,theory(equality)]) ).

cnf(28620,plain,
    product(product(a100,X),a124) = product(a92,product(X,a124)),
    inference('REWRITE',[status(thm)],[429,28616,theory(equality)]) ).

cnf(28622,plain,
    product(a68,a122) = a115,
    inference('REWRITE',[status(thm)],[26552,20604,20292,28620,theory(equality)]) ).

cnf(28623,plain,
    product(a71,a32) = a116,
    inference('REWRITE',[status(thm)],[2563,knot_116,28622,theory(equality)]) ).

cnf(28624,plain,
    a116 = product(a74,a116),
    inference('REWRITE',[status(thm)],[21111,28623,theory(equality)]) ).

cnf(28625,plain,
    product(a117,a116) = a116,
    inference('REWRITE',[status(thm)],[21112,involutory_quandle,28623,theory(equality)]) ).

cnf(28627,plain,
    product(a116,a117) = a117,
    inference('REWRITE',[status(thm)],[1619,knot_117,28625,theory(equality)]) ).

cnf(28629,plain,
    a122 = a124,
    inference('REWRITE',[status(thm)],[1624,1577,28627,theory(equality)]) ).

cnf(28632,plain,
    a115 = a123,
    inference('REWRITE',[status(thm)],[157,1579,28629,theory(equality)]) ).

cnf(28634,plain,
    a115 = a122,
    inference('REWRITE',[status(thm)],[146,involutory_quandle,28632,theory(equality)]) ).

cnf(28642,plain,
    product(a115,a32) = product(a118,a13),
    inference('REWRITE',[status(thm)],[1567,28634,theory(equality)]) ).

cnf(28644,plain,
    a120 = product(a112,a13),
    inference('REWRITE',[status(thm)],[2056,1482,28642,theory(equality)]) ).

cnf(28648,plain,
    product(a113,a32) = product(a120,a14),
    inference('REWRITE',[status(thm)],[9341,28644,theory(equality)]) ).

cnf(28650,plain,
    a101 = product(a121,a14),
    inference('REWRITE',[status(thm)],[28290,365,28648,theory(equality)]) ).

cnf(28651,plain,
    product(a120,a33) = product(a101,a13),
    inference('REWRITE',[status(thm)],[2601,28650,theory(equality)]) ).

cnf(28658,plain,
    product(a71,a13) = product(a67,a32),
    inference('REWRITE',[status(thm)],[28067,28242,28644,theory(equality)]) ).

cnf(28670,plain,
    a120 = product(a100,a32),
    inference('REWRITE',[status(thm)],[28223,28644,theory(equality)]) ).

cnf(28671,plain,
    a120 = product(product(a101,a13),a33),
    inference('REWRITE',[status(thm)],[28224,28644,theory(equality)]) ).

cnf(28705,plain,
    product(a69,product(a110,a13)) = product(a67,a32),
    inference('REWRITE',[status(thm)],[20418,28658,973,22267,28642,theory(equality)]) ).

cnf(28706,plain,
    product(a118,a13) = product(product(a110,a13),product(a67,a32)),
    inference('REWRITE',[status(thm)],[19470,28705,theory(equality)]) ).

cnf(28737,plain,
    a116 = a117,
    inference('REWRITE',[status(thm)],[1598,knot_116,28634,theory(equality)]) ).

cnf(28925,plain,
    product(a66,a14) = a116,
    inference('REWRITE',[status(thm)],[27198,28624,28737,theory(equality)]) ).

cnf(28928,plain,
    a101 = a116,
    inference('REWRITE',[status(thm)],[27202,involutory_quandle_01,28925,theory(equality)]) ).

cnf(28930,plain,
    a100 = a115,
    inference('REWRITE',[status(thm)],[269,268,28928,theory(equality)]) ).

cnf(28931,plain,
    product(product(a109,a13),a32) = a100,
    inference('REWRITE',[status(thm)],[18829,involutory_quandle,28930,theory(equality)]) ).

cnf(28932,plain,
    a120 = product(a109,a13),
    inference('REWRITE',[status(thm)],[19229,28670,involutory_quandle,28930,theory(equality)]) ).

cnf(28933,plain,
    product(a110,a13) = product(a118,a13),
    inference('REWRITE',[status(thm)],[1464,1499,28932,theory(equality)]) ).

cnf(28935,plain,
    product(a120,a69) = product(a110,a13),
    inference('REWRITE',[status(thm)],[1499,28933,theory(equality)]) ).

cnf(28945,plain,
    product(a110,a13) = product(product(a110,a13),product(a67,a32)),
    inference('REWRITE',[status(thm)],[28706,28933,theory(equality)]) ).

cnf(28954,plain,
    a121 = a100,
    inference('REWRITE',[status(thm)],[28931,knot_121,28932,theory(equality)]) ).

cnf(29062,plain,
    a68 = product(product(a67,a100),product(a68,a75)),
    inference('REWRITE',[status(thm)],[26913,28954,theory(equality)]) ).

cnf(29068,plain,
    product(a75,a100) = a92,
    inference('REWRITE',[status(thm)],[27047,28954,theory(equality)]) ).

cnf(29069,plain,
    product(a92,a75) = a92,
    inference('REWRITE',[status(thm)],[27054,29068,theory(equality)]) ).

cnf(29078,plain,
    product(a95,a2) = product(product(a67,a100),a42),
    inference('REWRITE',[status(thm)],[27156,28954,theory(equality)]) ).

cnf(29085,plain,
    a120 = product(a111,a13),
    inference('REWRITE',[status(thm)],[27753,28670,involutory_quandle,28954,theory(equality)]) ).

cnf(29087,plain,
    a120 = product(product(a108,a13),a69),
    inference('REWRITE',[status(thm)],[15414,29085,theory(equality)]) ).

cnf(29088,plain,
    product(a108,a13) = product(a110,a13),
    inference('REWRITE',[status(thm)],[15415,28935,29085,theory(equality)]) ).

cnf(29090,plain,
    product(a108,a13) = product(a118,a13),
    inference('REWRITE',[status(thm)],[28933,29088,theory(equality)]) ).

cnf(29100,plain,
    product(a108,a13) = product(product(a108,a13),product(a67,a32)),
    inference('REWRITE',[status(thm)],[28945,29088,theory(equality)]) ).

cnf(29110,plain,
    product(a125,a100) = product(a100,product(a2,a100)),
    inference('REWRITE',[status(thm)],[27796,involutory_quandle,28954,theory(equality)]) ).

cnf(29111,plain,
    product(a68,a75) = product(a67,a100),
    inference('REWRITE',[status(thm)],[27857,involutory_quandle,28954,theory(equality)]) ).

cnf(29114,plain,
    a68 = product(a67,a100),
    inference('REWRITE',[status(thm)],[29062,involutory_quandle,29111,theory(equality)]) ).

cnf(29116,plain,
    product(a95,a2) = product(a68,a42),
    inference('REWRITE',[status(thm)],[29078,29114,theory(equality)]) ).

cnf(29123,plain,
    product(a68,a75) = a68,
    inference('REWRITE',[status(thm)],[29111,29114,theory(equality)]) ).

cnf(29141,plain,
    a68 = a67,
    inference('REWRITE',[status(thm)],[28600,28556,29114,29123,28954,theory(equality)]) ).

cnf(29142,plain,
    a69 = product(a67,a32),
    inference('REWRITE',[status(thm)],[knot_69,29141,theory(equality)]) ).

cnf(29168,plain,
    product(a108,a13) = a120,
    inference('REWRITE',[status(thm)],[29100,29087,29142,theory(equality)]) ).

cnf(29171,plain,
    a120 = product(a118,a13),
    inference('REWRITE',[status(thm)],[29090,29168,theory(equality)]) ).

cnf(29189,plain,
    a70 = product(product(a67,a13),a33),
    inference('REWRITE',[status(thm)],[2439,29141,theory(equality)]) ).

cnf(29276,plain,
    product(a89,product(a75,a41)) = product(product(a86,a14),a3),
    inference('REWRITE',[status(thm)],[26478,28313,29141,theory(equality)]) ).

cnf(29278,plain,
    product(a100,a1) = product(a97,product(a67,a1)),
    inference('REWRITE',[status(thm)],[26965,29141,theory(equality)]) ).

cnf(29281,plain,
    product(a75,a66) = a67,
    inference('REWRITE',[status(thm)],[27189,29141,theory(equality)]) ).

cnf(29282,plain,
    product(a67,a66) = a75,
    inference('REWRITE',[status(thm)],[27237,29141,theory(equality)]) ).

cnf(29284,plain,
    product(a75,X) = product(product(product(a66,a67),X),product(a92,X)),
    inference('REWRITE',[status(thm)],[3849,29282,theory(equality)]) ).

cnf(29299,plain,
    a67 = product(a92,a100),
    inference('REWRITE',[status(thm)],[28299,29141,theory(equality)]) ).

cnf(29300,plain,
    product(a87,a14) = product(product(a87,a14),a96),
    inference('REWRITE',[status(thm)],[28396,28391,29141,theory(equality)]) ).

cnf(29301,plain,
    product(a92,a67) = a67,
    inference('REWRITE',[status(thm)],[28556,29141,theory(equality)]) ).

cnf(29302,plain,
    product(a66,a67) = a67,
    inference('REWRITE',[status(thm)],[5850,involutory_quandle,29301,theory(equality)]) ).

cnf(29304,plain,
    product(a75,X) = product(a66,X),
    inference('REWRITE',[status(thm)],[29284,798,29302,theory(equality)]) ).

cnf(29306,plain,
    a66 = a67,
    inference('REWRITE',[status(thm)],[29281,involutory_quandle,29304,theory(equality)]) ).

cnf(29316,plain,
    product(product(a65,X),a93) = product(a65,product(X,a93)),
    inference('REWRITE',[status(thm)],[1641,284,29306,theory(equality)]) ).

cnf(29317,plain,
    product(a93,product(a96,a41)) = product(product(a65,a125),a93),
    inference('REWRITE',[status(thm)],[28471,29316,theory(equality)]) ).

cnf(29333,plain,
    a90 = a66,
    inference('REWRITE',[status(thm)],[28303,29306,theory(equality)]) ).

cnf(29335,plain,
    product(a64,a3) = a89,
    inference('REWRITE',[status(thm)],[28313,3421,29306,theory(equality)]) ).

cnf(29336,plain,
    product(a66,a41) = a89,
    inference('REWRITE',[status(thm)],[3421,29335,theory(equality)]) ).

cnf(29361,plain,
    product(a66,a14) = product(a88,a40),
    inference('REWRITE',[status(thm)],[28335,29306,theory(equality)]) ).

cnf(29393,plain,
    a64 = product(a87,a14),
    inference('REWRITE',[status(thm)],[28391,involutory_quandle_01,16990,29306,theory(equality)]) ).

cnf(29394,plain,
    product(a89,a3) = a64,
    inference('REWRITE',[status(thm)],[3178,29393,theory(equality)]) ).

cnf(29410,plain,
    a64 = product(a62,a128),
    inference('REWRITE',[status(thm)],[29300,1697,29393,theory(equality)]) ).

cnf(29411,plain,
    product(a64,a96) = a64,
    inference('REWRITE',[status(thm)],[1702,29410,theory(equality)]) ).

cnf(29424,plain,
    product(a129,a128) = product(a128,a64),
    inference('REWRITE',[status(thm)],[1856,29410,theory(equality)]) ).

cnf(29443,plain,
    product(a64,a62) = product(a62,a129),
    inference('REWRITE',[status(thm)],[5967,29410,theory(equality)]) ).

cnf(29448,plain,
    product(a62,product(a62,a129)) = product(a64,a129),
    inference('REWRITE',[status(thm)],[7701,29410,theory(equality)]) ).

cnf(29453,plain,
    product(product(a62,a129),a64) = product(a64,product(a62,a64)),
    inference('REWRITE',[status(thm)],[8194,29410,theory(equality)]) ).

cnf(29458,plain,
    product(product(X,a128),a62) = product(product(X,product(a128,a129)),product(a64,a129)),
    inference('REWRITE',[status(thm)],[9027,29410,theory(equality)]) ).

cnf(29465,plain,
    product(product(X,a129),a62) = product(product(X,a128),a64),
    inference('REWRITE',[status(thm)],[13971,29410,theory(equality)]) ).

cnf(29467,plain,
    product(product(a42,a128),a64) = a44,
    inference('REWRITE',[status(thm)],[1831,29465,theory(equality)]) ).

cnf(29476,plain,
    product(product(a63,a64),X) = product(product(product(a62,a64),X),product(a96,X)),
    inference('REWRITE',[status(thm)],[25935,29410,theory(equality)]) ).

cnf(29531,plain,
    a68 = a66,
    inference('REWRITE',[status(thm)],[29141,29306,theory(equality)]) ).

cnf(29544,plain,
    a70 = product(product(a66,a13),a33),
    inference('REWRITE',[status(thm)],[29189,29306,theory(equality)]) ).

cnf(29626,plain,
    product(a100,a1) = product(a95,a42),
    inference('REWRITE',[status(thm)],[29278,5754,16990,29306,theory(equality)]) ).

cnf(29635,plain,
    a66 = a75,
    inference('REWRITE',[status(thm)],[29282,involutory_quandle,29306,theory(equality)]) ).

cnf(29653,plain,
    product(a92,a66) = a92,
    inference('REWRITE',[status(thm)],[29069,29635,theory(equality)]) ).

cnf(29656,plain,
    a66 = product(a92,a100),
    inference('REWRITE',[status(thm)],[29299,29306,theory(equality)]) ).

cnf(29657,plain,
    a92 = a66,
    inference('REWRITE',[status(thm)],[29301,29653,29306,theory(equality)]) ).

cnf(29658,plain,
    a93 = a65,
    inference('REWRITE',[status(thm)],[knot_93,284,29657,theory(equality)]) ).

cnf(29659,plain,
    a94 = a64,
    inference('REWRITE',[status(thm)],[knot_94,274,29658,theory(equality)]) ).

cnf(29660,plain,
    a95 = a63,
    inference('REWRITE',[status(thm)],[knot_95,175,29659,theory(equality)]) ).

cnf(29661,plain,
    a96 = product(a63,a64),
    inference('REWRITE',[status(thm)],[knot_96,29660,theory(equality)]) ).

cnf(29665,plain,
    product(product(X,a127),a64) = product(product(X,a96),product(a129,a128)),
    inference('REWRITE',[status(thm)],[10893,10939,29661,theory(equality)]) ).

cnf(29666,plain,
    product(product(X,product(a125,a41)),a96) = product(product(X,a127),a64),
    inference('REWRITE',[status(thm)],[10939,29665,theory(equality)]) ).

cnf(29668,plain,
    product(a96,X) = product(product(product(a62,a64),X),product(a96,X)),
    inference('REWRITE',[status(thm)],[29476,29661,theory(equality)]) ).

cnf(29682,plain,
    product(a96,a63) = product(a62,a64),
    inference('REWRITE',[status(thm)],[1755,29661,29660,theory(equality)]) ).

cnf(29683,plain,
    product(a62,a63) = product(a63,product(a62,a64)),
    inference('REWRITE',[status(thm)],[5852,29682,theory(equality)]) ).

cnf(29684,plain,
    product(product(a96,a62),a96) = product(a62,a64),
    inference('REWRITE',[status(thm)],[5959,29682,theory(equality)]) ).

cnf(29692,plain,
    product(product(a96,a62),X) = product(a96,X),
    inference('REWRITE',[status(thm)],[8159,29668,29682,theory(equality)]) ).

cnf(29694,plain,
    a96 = product(a62,a64),
    inference('REWRITE',[status(thm)],[29684,involutory_quandle,29692,theory(equality)]) ).

cnf(29696,plain,
    product(product(a62,a129),a64) = a64,
    inference('REWRITE',[status(thm)],[29453,29411,29694,theory(equality)]) ).

cnf(29697,plain,
    product(a96,a63) = a96,
    inference('REWRITE',[status(thm)],[29682,29694,theory(equality)]) ).

cnf(29698,plain,
    product(a62,a63) = a62,
    inference('REWRITE',[status(thm)],[29683,178,29694,theory(equality)]) ).

cnf(29708,plain,
    product(product(X,a62),a96) = product(product(X,a63),a96),
    inference('REWRITE',[status(thm)],[8975,29694,29682,theory(equality)]) ).

cnf(29711,plain,
    product(a64,a63) = product(a62,a129),
    inference('REWRITE',[status(thm)],[10905,3912,29443,29708,theory(equality)]) ).

cnf(29722,plain,
    product(a127,a63) = product(a127,a62),
    inference('REWRITE',[status(thm)],[3939,1855,knot_129,29708,theory(equality)]) ).

cnf(29729,plain,
    product(a129,X) = product(product(a128,a63),X),
    inference('REWRITE',[status(thm)],[1872,3942,29722,theory(equality)]) ).

cnf(29735,plain,
    product(a129,X) = product(product(product(a127,a62),X),product(a96,X)),
    inference('REWRITE',[status(thm)],[3942,29729,theory(equality)]) ).

cnf(29739,plain,
    product(a125,a126) = product(product(a127,a62),a41),
    inference('REWRITE',[status(thm)],[5851,29722,theory(equality)]) ).

cnf(29740,plain,
    product(product(a125,a126),a41) = product(a127,a62),
    inference('REWRITE',[status(thm)],[5957,29722,theory(equality)]) ).

cnf(29746,plain,
    product(product(X,product(a127,a62)),a41) = product(product(X,a41),product(a125,a126)),
    inference('REWRITE',[status(thm)],[7664,29722,theory(equality)]) ).

cnf(29758,plain,
    product(product(a127,a62),a14) = product(product(product(a125,a126),a14),a40),
    inference('REWRITE',[status(thm)],[16579,29722,theory(equality)]) ).

cnf(29760,plain,
    product(product(a127,a62),a2) = product(product(product(a125,a1),product(a126,a1)),product(a42,a1)),
    inference('REWRITE',[status(thm)],[17003,29722,theory(equality)]) ).

cnf(29766,plain,
    product(a128,a63) = a129,
    inference('REWRITE',[status(thm)],[1861,3929,29708,theory(equality)]) ).

cnf(29767,plain,
    product(product(a127,a62),a96) = a129,
    inference('REWRITE',[status(thm)],[3929,29766,theory(equality)]) ).

cnf(29777,plain,
    product(a129,a63) = a128,
    inference('REWRITE',[status(thm)],[13793,knot_128,29694,29682,theory(equality)]) ).

cnf(29789,plain,
    product(product(a96,X),a63) = product(a96,product(X,a63)),
    inference('REWRITE',[status(thm)],[1757,29661,29694,29660,theory(equality)]) ).

cnf(29812,plain,
    a64 = product(a62,a129),
    inference('REWRITE',[status(thm)],[13722,29696,29711,29660,theory(equality)]) ).

cnf(29814,plain,
    product(a128,a129) = product(a129,a64),
    inference('REWRITE',[status(thm)],[5857,29812,theory(equality)]) ).

cnf(29838,plain,
    a96 = product(a64,a129),
    inference('REWRITE',[status(thm)],[29448,29694,29812,theory(equality)]) ).

cnf(29839,plain,
    product(product(X,a128),a62) = product(product(X,product(a128,a129)),a96),
    inference('REWRITE',[status(thm)],[29458,29838,theory(equality)]) ).

cnf(29843,plain,
    product(a64,a63) = a64,
    inference('REWRITE',[status(thm)],[29711,29812,theory(equality)]) ).

cnf(29854,plain,
    product(product(a129,a128),a64) = product(a127,a62),
    inference('REWRITE',[status(thm)],[13725,29722,29660,theory(equality)]) ).

cnf(29855,plain,
    product(product(a127,a128),a64) = product(product(product(a128,a127),a63),a64),
    inference('REWRITE',[status(thm)],[13727,29843,involutory_quandle_02,29660,theory(equality)]) ).

cnf(29861,plain,
    a64 = product(a96,a128),
    inference('REWRITE',[status(thm)],[13815,29777,29789,involutory_quandle,knot_64,29666,29697,29660,theory(equality)]) ).

cnf(29862,plain,
    product(a127,a128) = product(a129,a128),
    inference('REWRITE',[status(thm)],[5853,29424,29861,theory(equality)]) ).

cnf(29870,plain,
    product(a128,a127) = product(a125,a41),
    inference('REWRITE',[status(thm)],[10932,3930,29862,theory(equality)]) ).

cnf(29873,plain,
    product(a127,a64) = product(a128,a127),
    inference('REWRITE',[status(thm)],[1686,29870,theory(equality)]) ).

cnf(29875,plain,
    product(product(product(a128,a127),X),a64) = product(a127,product(X,a64)),
    inference('REWRITE',[status(thm)],[1688,29870,theory(equality)]) ).

cnf(29876,plain,
    product(product(a127,a128),a64) = a128,
    inference('REWRITE',[status(thm)],[29855,knot_128,29661,29875,theory(equality)]) ).

cnf(29889,plain,
    product(product(X,a96),product(a127,a128)) = product(product(X,a127),a64),
    inference('REWRITE',[status(thm)],[29666,10957,29870,theory(equality)]) ).

cnf(29891,plain,
    product(product(X,product(a128,a127)),a96) = product(product(X,a127),a64),
    inference('REWRITE',[status(thm)],[10957,29889,theory(equality)]) ).

cnf(29910,plain,
    a128 = product(a127,a62),
    inference('REWRITE',[status(thm)],[29854,29876,29862,theory(equality)]) ).

cnf(29925,plain,
    product(a129,X) = product(a127,X),
    inference('REWRITE',[status(thm)],[29735,819,29910,theory(equality)]) ).

cnf(29927,plain,
    product(a128,a129) = product(a128,a127),
    inference('REWRITE',[status(thm)],[29814,29873,29925,theory(equality)]) ).

cnf(29934,plain,
    product(product(X,a128),a62) = product(product(X,a127),a64),
    inference('REWRITE',[status(thm)],[29839,29891,29927,theory(equality)]) ).

cnf(29939,plain,
    product(product(a42,a127),a64) = product(a43,a129),
    inference('REWRITE',[status(thm)],[3998,29934,theory(equality)]) ).

cnf(29956,plain,
    product(product(a132,a1),product(a13,a1)) = product(a127,product(product(a138,a1),product(a13,a1))),
    inference('REWRITE',[status(thm)],[17127,29925,theory(equality)]) ).

cnf(30016,plain,
    product(a131,a1) = product(a127,product(a13,a1)),
    inference('REWRITE',[status(thm)],[2607,29925,theory(equality)]) ).

cnf(30063,plain,
    a130 = product(a127,a1),
    inference('REWRITE',[status(thm)],[knot_130,29925,theory(equality)]) ).

cnf(30084,plain,
    product(a125,a126) = product(a128,a41),
    inference('REWRITE',[status(thm)],[29739,29910,theory(equality)]) ).

cnf(30085,plain,
    product(product(a125,a126),a41) = a128,
    inference('REWRITE',[status(thm)],[29740,29910,theory(equality)]) ).

cnf(30089,plain,
    product(product(X,a128),a41) = product(product(X,a41),product(a125,a126)),
    inference('REWRITE',[status(thm)],[29746,29910,theory(equality)]) ).

cnf(30090,plain,
    product(a65,product(a63,a41)) = product(product(a63,a128),a41),
    inference('REWRITE',[status(thm)],[8954,30089,theory(equality)]) ).

cnf(30099,plain,
    product(a128,a14) = product(product(product(a125,a126),a14),a40),
    inference('REWRITE',[status(thm)],[29758,29910,theory(equality)]) ).

cnf(30100,plain,
    product(a128,a2) = product(product(product(a125,a1),product(a126,a1)),product(a42,a1)),
    inference('REWRITE',[status(thm)],[29760,29910,theory(equality)]) ).

cnf(30101,plain,
    a127 = a129,
    inference('REWRITE',[status(thm)],[29767,179,29910,theory(equality)]) ).

cnf(30103,plain,
    product(a130,a1) = a127,
    inference('REWRITE',[status(thm)],[282,30101,theory(equality)]) ).

cnf(30156,plain,
    product(product(X,a127),a62) = product(product(X,a128),a64),
    inference('REWRITE',[status(thm)],[29465,30101,theory(equality)]) ).

cnf(30159,plain,
    product(product(a42,a127),a62) = a44,
    inference('REWRITE',[status(thm)],[29467,30156,theory(equality)]) ).

cnf(30169,plain,
    a64 = product(a62,a127),
    inference('REWRITE',[status(thm)],[29812,30101,theory(equality)]) ).

cnf(30170,plain,
    a64 = product(a63,a128),
    inference('REWRITE',[status(thm)],[3909,29411,30169,theory(equality)]) ).

cnf(30171,plain,
    product(a65,product(a63,a41)) = a65,
    inference('REWRITE',[status(thm)],[30090,knot_65,30170,theory(equality)]) ).

cnf(30188,plain,
    a96 = a63,
    inference('REWRITE',[status(thm)],[29838,175,30101,theory(equality)]) ).

cnf(30189,plain,
    a63 = a62,
    inference('REWRITE',[status(thm)],[knot_63,29698,30188,theory(equality)]) ).

cnf(30214,plain,
    product(a62,a41) = product(a65,a126),
    inference('REWRITE',[status(thm)],[5692,30189,theory(equality)]) ).

cnf(30218,plain,
    product(product(X,a125),a65) = product(product(X,a126),product(a62,a41)),
    inference('REWRITE',[status(thm)],[5704,30189,theory(equality)]) ).

cnf(30220,plain,
    product(product(a62,a41),a65) = product(a65,a125),
    inference('REWRITE',[status(thm)],[5956,30189,theory(equality)]) ).

cnf(30271,plain,
    a95 = a62,
    inference('REWRITE',[status(thm)],[29660,30189,theory(equality)]) ).

cnf(30281,plain,
    product(a65,product(a62,a41)) = a65,
    inference('REWRITE',[status(thm)],[30171,30189,theory(equality)]) ).

cnf(30289,plain,
    a96 = a62,
    inference('REWRITE',[status(thm)],[30188,30189,theory(equality)]) ).

cnf(30290,plain,
    a97 = product(a62,a42),
    inference('REWRITE',[status(thm)],[knot_97,30189,30188,theory(equality)]) ).

cnf(30317,plain,
    product(a97,a42) = a62,
    inference('REWRITE',[status(thm)],[279,30189,30188,theory(equality)]) ).

cnf(30330,plain,
    product(a97,a14) = product(product(a62,a14),product(a39,a40)),
    inference('REWRITE',[status(thm)],[5575,30189,30188,theory(equality)]) ).

cnf(30380,plain,
    product(product(a42,a127),a64) = product(a43,a127),
    inference('REWRITE',[status(thm)],[29939,30101,theory(equality)]) ).

cnf(30408,plain,
    product(a100,a1) = a97,
    inference('REWRITE',[status(thm)],[29626,30290,30189,29660,theory(equality)]) ).

cnf(30409,plain,
    product(product(a97,a14),a40) = product(a102,a5),
    inference('REWRITE',[status(thm)],[5679,30408,theory(equality)]) ).

cnf(30410,plain,
    a62 = product(a103,a14),
    inference('REWRITE',[status(thm)],[10109,30317,30408,theory(equality)]) ).

cnf(30411,plain,
    a62 = product(product(a102,a14),a3),
    inference('REWRITE',[status(thm)],[3199,30410,theory(equality)]) ).

cnf(30412,plain,
    product(a62,a3) = product(a102,a14),
    inference('REWRITE',[status(thm)],[3208,30410,theory(equality)]) ).

cnf(30420,plain,
    product(a100,a42) = product(a62,a2),
    inference('REWRITE',[status(thm)],[12705,30410,theory(equality)]) ).

cnf(30428,plain,
    product(a62,a41) = product(a100,a2),
    inference('REWRITE',[status(thm)],[16467,30410,theory(equality)]) ).

cnf(30431,plain,
    product(a100,a2) = product(a65,a126),
    inference('REWRITE',[status(thm)],[30214,30428,theory(equality)]) ).

cnf(30435,plain,
    product(product(X,a125),a65) = product(product(X,a126),product(a100,a2)),
    inference('REWRITE',[status(thm)],[30218,30428,theory(equality)]) ).

cnf(30437,plain,
    product(product(a100,a2),a65) = product(a65,a125),
    inference('REWRITE',[status(thm)],[30220,30428,theory(equality)]) ).

cnf(30450,plain,
    product(a65,product(a100,a2)) = a65,
    inference('REWRITE',[status(thm)],[30281,30428,theory(equality)]) ).

cnf(30495,plain,
    product(a65,a125) = product(a100,a2),
    inference('REWRITE',[status(thm)],[1738,30431,30437,30428,30289,29658,theory(equality)]) ).

cnf(30504,plain,
    product(product(a100,a2),a65) = product(a100,a2),
    inference('REWRITE',[status(thm)],[30437,30495,theory(equality)]) ).

cnf(30518,plain,
    a65 = product(a100,a2),
    inference('REWRITE',[status(thm)],[29317,30504,30495,30450,30428,30289,29658,theory(equality)]) ).

cnf(30519,plain,
    product(a103,a40) = product(a65,a14),
    inference('REWRITE',[status(thm)],[3239,30518,theory(equality)]) ).

cnf(30521,plain,
    a103 = product(a64,a14),
    inference('REWRITE',[status(thm)],[3283,involutory_quandle_01,30519,theory(equality)]) ).

cnf(30544,plain,
    product(product(X,a125),a65) = product(product(X,a126),a65),
    inference('REWRITE',[status(thm)],[30435,30518,theory(equality)]) ).

cnf(30546,plain,
    a126 = product(a126,a125),
    inference('REWRITE',[status(thm)],[3865,knot_126,involutory_quandle,30544,theory(equality)]) ).

cnf(30547,plain,
    a125 = product(a125,a126),
    inference('REWRITE',[status(thm)],[3871,174,30546,theory(equality)]) ).

cnf(30550,plain,
    a125 = product(a128,a41),
    inference('REWRITE',[status(thm)],[30084,30547,theory(equality)]) ).

cnf(30551,plain,
    product(a128,a127) = a128,
    inference('REWRITE',[status(thm)],[30085,29870,30547,theory(equality)]) ).

cnf(30556,plain,
    a128 = product(a125,a41),
    inference('REWRITE',[status(thm)],[29870,30551,theory(equality)]) ).

cnf(30580,plain,
    product(a128,a14) = product(product(a125,a14),a40),
    inference('REWRITE',[status(thm)],[30099,30547,theory(equality)]) ).

cnf(30627,plain,
    a99 = a66,
    inference('REWRITE',[status(thm)],[28615,29657,theory(equality)]) ).

cnf(30629,plain,
    a66 = product(a66,a100),
    inference('REWRITE',[status(thm)],[29656,29657,theory(equality)]) ).

cnf(30633,plain,
    a89 = product(product(a86,a14),a3),
    inference('REWRITE',[status(thm)],[29276,involutory_quandle,29336,29304,theory(equality)]) ).

cnf(30673,plain,
    product(a66,a14) = a74,
    inference('REWRITE',[status(thm)],[266,29304,theory(equality)]) ).

cnf(30674,plain,
    a74 = product(a88,a40),
    inference('REWRITE',[status(thm)],[29361,30673,theory(equality)]) ).

cnf(30686,plain,
    product(a100,a42) = product(a64,a2),
    inference('REWRITE',[status(thm)],[29116,3265,29306,30420,30271,29141,theory(equality)]) ).

cnf(30688,plain,
    product(a66,X) = product(a100,X),
    inference('REWRITE',[status(thm)],[3266,711,30686,theory(equality)]) ).

cnf(30706,plain,
    a66 = a100,
    inference('REWRITE',[status(thm)],[30629,involutory_quandle,30688,theory(equality)]) ).

cnf(30707,plain,
    a100 = product(a65,a2),
    inference('REWRITE',[status(thm)],[knot_66,30706,theory(equality)]) ).

cnf(30708,plain,
    product(product(X,a65),a2) = product(product(X,a2),a100),
    inference('REWRITE',[status(thm)],[708,30706,theory(equality)]) ).

cnf(30722,plain,
    a100 = a67,
    inference('REWRITE',[status(thm)],[29306,30706,theory(equality)]) ).

cnf(30723,plain,
    a90 = a100,
    inference('REWRITE',[status(thm)],[29333,30706,theory(equality)]) ).

cnf(30737,plain,
    a68 = a100,
    inference('REWRITE',[status(thm)],[29531,30706,theory(equality)]) ).

cnf(30750,plain,
    a100 = a75,
    inference('REWRITE',[status(thm)],[29635,30706,theory(equality)]) ).

cnf(30761,plain,
    a92 = a100,
    inference('REWRITE',[status(thm)],[29657,30706,theory(equality)]) ).

cnf(30764,plain,
    a99 = a100,
    inference('REWRITE',[status(thm)],[30627,30706,theory(equality)]) ).

cnf(30794,plain,
    a70 = a112,
    inference('REWRITE',[status(thm)],[29544,195,28210,30688,theory(equality)]) ).

cnf(30798,plain,
    product(a71,a118) = a112,
    inference('REWRITE',[status(thm)],[162,30794,theory(equality)]) ).

cnf(30799,plain,
    a111 = a109,
    inference('REWRITE',[status(thm)],[166,27290,30794,theory(equality)]) ).

cnf(30804,plain,
    product(a108,a112) = a112,
    inference('REWRITE',[status(thm)],[20505,19797,30799,theory(equality)]) ).

cnf(30809,plain,
    product(product(X,a110),a72) = product(product(X,a110),a73),
    inference('REWRITE',[status(thm)],[21843,21307,30804,theory(equality)]) ).

cnf(30810,plain,
    a73 = product(a71,a110),
    inference('REWRITE',[status(thm)],[27327,28106,30809,theory(equality)]) ).

cnf(30814,plain,
    product(a73,a39) = product(product(a71,a106),product(a39,a106)),
    inference('REWRITE',[status(thm)],[27457,21324,30810,theory(equality)]) ).

cnf(30816,plain,
    product(a73,a39) = product(a84,product(a84,a106)),
    inference('REWRITE',[status(thm)],[21325,30814,theory(equality)]) ).

cnf(30829,plain,
    a82 = a71,
    inference('REWRITE',[status(thm)],[27573,20051,30804,theory(equality)]) ).

cnf(30905,plain,
    a72 = a112,
    inference('REWRITE',[status(thm)],[27447,30798,30829,theory(equality)]) ).

cnf(30907,plain,
    a118 = a71,
    inference('REWRITE',[status(thm)],[160,19471,30905,theory(equality)]) ).

cnf(30912,plain,
    a69 = a120,
    inference('REWRITE',[status(thm)],[6217,29171,involutory_quandle_01,30907,theory(equality)]) ).

cnf(30931,plain,
    product(a110,X) = product(a108,X),
    inference('REWRITE',[status(thm)],[13253,involutory_quandle_01,30907,theory(equality)]) ).

cnf(30933,plain,
    a107 = product(a106,product(a106,a107)),
    inference('REWRITE',[status(thm)],[24126,258,30931,theory(equality)]) ).

cnf(30937,plain,
    a110 = a108,
    inference('REWRITE',[status(thm)],[20473,19445,30931,theory(equality)]) ).

cnf(30938,plain,
    a109 = a112,
    inference('REWRITE',[status(thm)],[19207,28199,30937,theory(equality)]) ).

cnf(30939,plain,
    a113 = product(a109,a33),
    inference('REWRITE',[status(thm)],[knot_113,30938,theory(equality)]) ).

cnf(30940,plain,
    product(a113,a33) = a109,
    inference('REWRITE',[status(thm)],[195,30938,theory(equality)]) ).

cnf(30998,plain,
    product(product(product(a113,a131),X),a34) = product(product(a109,a131),product(X,a34)),
    inference('REWRITE',[status(thm)],[10287,30938,theory(equality)]) ).

cnf(31043,plain,
    a109 = a118,
    inference('REWRITE',[status(thm)],[19471,involutory_quandle,30938,theory(equality)]) ).

cnf(31044,plain,
    a109 = a108,
    inference('REWRITE',[status(thm)],[164,involutory_quandle,31043,theory(equality)]) ).

cnf(31045,plain,
    a111 = a108,
    inference('REWRITE',[status(thm)],[30799,31044,theory(equality)]) ).

cnf(31047,plain,
    a108 = a112,
    inference('REWRITE',[status(thm)],[30938,31044,theory(equality)]) ).

cnf(31048,plain,
    a113 = product(a108,a33),
    inference('REWRITE',[status(thm)],[30939,31044,theory(equality)]) ).

cnf(31049,plain,
    product(a113,a33) = a108,
    inference('REWRITE',[status(thm)],[30940,31044,theory(equality)]) ).

cnf(31107,plain,
    product(product(product(a113,a131),X),a34) = product(product(a108,a131),product(X,a34)),
    inference('REWRITE',[status(thm)],[30998,31044,theory(equality)]) ).

cnf(31152,plain,
    a108 = a118,
    inference('REWRITE',[status(thm)],[31043,31044,theory(equality)]) ).

cnf(31161,plain,
    a108 = a71,
    inference('REWRITE',[status(thm)],[30907,31044,31043,theory(equality)]) ).

cnf(31175,plain,
    a79 = a108,
    inference('REWRITE',[status(thm)],[27288,31044,30938,theory(equality)]) ).

cnf(31176,plain,
    a108 = a119,
    inference('REWRITE',[status(thm)],[27289,31044,30938,theory(equality)]) ).

cnf(31177,plain,
    a108 = product(a101,a32),
    inference('REWRITE',[status(thm)],[28208,31044,30938,theory(equality)]) ).

cnf(31178,plain,
    product(a108,a40) = product(product(a103,a30),a4),
    inference('REWRITE',[status(thm)],[28211,31044,30938,theory(equality)]) ).

cnf(31179,plain,
    product(a107,a106) = a107,
    inference('REWRITE',[status(thm)],[28212,258,31044,30938,theory(equality)]) ).

cnf(31183,plain,
    a106 = product(a106,a107),
    inference('REWRITE',[status(thm)],[3560,152,31179,theory(equality)]) ).

cnf(31187,plain,
    a107 = a106,
    inference('REWRITE',[status(thm)],[30933,involutory_quandle,31183,theory(equality)]) ).

cnf(31190,plain,
    product(a108,a39) = a106,
    inference('REWRITE',[status(thm)],[258,31187,theory(equality)]) ).

cnf(31222,plain,
    a104 = product(a103,a104),
    inference('REWRITE',[status(thm)],[4206,5443,31187,theory(equality)]) ).

cnf(31223,plain,
    a87 = product(a87,a86),
    inference('REWRITE',[status(thm)],[3520,knot_87,31222,theory(equality)]) ).

cnf(31224,plain,
    a87 = product(a86,a103),
    inference('REWRITE',[status(thm)],[7006,involutory_quandle,31223,theory(equality)]) ).

cnf(31230,plain,
    product(a87,product(a104,a103)) = a86,
    inference('REWRITE',[status(thm)],[12932,3519,31224,theory(equality)]) ).

cnf(31235,plain,
    a103 = product(a104,a103),
    inference('REWRITE',[status(thm)],[3532,151,31222,theory(equality)]) ).

cnf(31236,plain,
    a103 = product(a103,product(a87,a103)),
    inference('REWRITE',[status(thm)],[1209,31235,theory(equality)]) ).

cnf(31239,plain,
    a104 = product(a103,a86),
    inference('REWRITE',[status(thm)],[12920,31222,31235,theory(equality)]) ).

cnf(31240,plain,
    product(a87,a103) = a86,
    inference('REWRITE',[status(thm)],[31230,31235,theory(equality)]) ).

cnf(31267,plain,
    a103 = a104,
    inference('REWRITE',[status(thm)],[31236,31239,31240,theory(equality)]) ).

cnf(31269,plain,
    a105 = product(a103,a30),
    inference('REWRITE',[status(thm)],[knot_105,31267,theory(equality)]) ).

cnf(31274,plain,
    product(a85,product(a85,a105)) = a85,
    inference('REWRITE',[status(thm)],[11113,involutory_quandle_01,31269,theory(equality)]) ).

cnf(31275,plain,
    product(a108,a40) = product(a105,a4),
    inference('REWRITE',[status(thm)],[31178,31269,theory(equality)]) ).

cnf(31276,plain,
    product(a105,a30) = a103,
    inference('REWRITE',[status(thm)],[197,31267,theory(equality)]) ).

cnf(31344,plain,
    product(a101,a39) = product(a106,a31),
    inference('REWRITE',[status(thm)],[5432,1890,31267,theory(equality)]) ).

cnf(31346,plain,
    product(a103,a5) = product(a106,a31),
    inference('REWRITE',[status(thm)],[1890,31344,theory(equality)]) ).

cnf(31675,plain,
    product(product(a106,a40),a39) = product(product(a106,a4),a5),
    inference('REWRITE',[status(thm)],[17564,18248,678,31275,31187,theory(equality)]) ).

cnf(31680,plain,
    product(product(a73,a39),a5) = a85,
    inference('REWRITE',[status(thm)],[19036,31274,262,31187,theory(equality)]) ).

cnf(31707,plain,
    a70 = a108,
    inference('REWRITE',[status(thm)],[30794,31044,30938,theory(equality)]) ).

cnf(31708,plain,
    a72 = a108,
    inference('REWRITE',[status(thm)],[30905,31044,30938,theory(equality)]) ).

cnf(31714,plain,
    a106 = product(a84,a106),
    inference('REWRITE',[status(thm)],[20146,31187,31190,31152,30907,theory(equality)]) ).

cnf(31722,plain,
    product(a73,a39) = a106,
    inference('REWRITE',[status(thm)],[30816,31714,theory(equality)]) ).

cnf(31730,plain,
    a105 = a85,
    inference('REWRITE',[status(thm)],[31680,262,31722,theory(equality)]) ).

cnf(31732,plain,
    a86 = a103,
    inference('REWRITE',[status(thm)],[knot_86,31276,31730,theory(equality)]) ).

cnf(31740,plain,
    a89 = product(a102,a14),
    inference('REWRITE',[status(thm)],[30633,30412,30410,31732,theory(equality)]) ).

cnf(31741,plain,
    a89 = product(a100,a41),
    inference('REWRITE',[status(thm)],[1876,31740,theory(equality)]) ).

cnf(31758,plain,
    a62 = a64,
    inference('REWRITE',[status(thm)],[30411,29394,31740,theory(equality)]) ).

cnf(31759,plain,
    product(a65,a41) = a62,
    inference('REWRITE',[status(thm)],[274,31758,theory(equality)]) ).

cnf(31820,plain,
    a94 = a62,
    inference('REWRITE',[status(thm)],[29659,31758,theory(equality)]) ).

cnf(31847,plain,
    a44 = product(a43,a127),
    inference('REWRITE',[status(thm)],[30380,30159,31758,theory(equality)]) ).

cnf(31869,plain,
    a103 = product(a62,a14),
    inference('REWRITE',[status(thm)],[30521,31758,theory(equality)]) ).

cnf(31871,plain,
    product(a97,a14) = product(a103,product(a39,a40)),
    inference('REWRITE',[status(thm)],[30330,31869,theory(equality)]) ).

cnf(31904,plain,
    a87 = a103,
    inference('REWRITE',[status(thm)],[31224,involutory_quandle,31732,theory(equality)]) ).

cnf(31905,plain,
    a88 = a102,
    inference('REWRITE',[status(thm)],[knot_88,272,31904,theory(equality)]) ).

cnf(31939,plain,
    product(a102,a32) = product(product(a89,a13),a33),
    inference('REWRITE',[status(thm)],[14922,31905,theory(equality)]) ).

cnf(31970,plain,
    a74 = a101,
    inference('REWRITE',[status(thm)],[30674,186,31905,theory(equality)]) ).

cnf(31972,plain,
    a108 = a73,
    inference('REWRITE',[status(thm)],[222,31177,31970,theory(equality)]) ).

cnf(32026,plain,
    a106 = a84,
    inference('REWRITE',[status(thm)],[261,knot_106,31730,theory(equality)]) ).

cnf(32027,plain,
    product(product(a106,a7),product(a39,a38)) = product(product(a106,a38),product(a7,product(a7,a38))),
    inference('REWRITE',[status(thm)],[18069,32026,theory(equality)]) ).

cnf(32048,plain,
    a82 = a108,
    inference('REWRITE',[status(thm)],[30829,31152,30907,theory(equality)]) ).

cnf(32051,plain,
    a108 = a83,
    inference('REWRITE',[status(thm)],[27446,31047,30905,theory(equality)]) ).

cnf(32123,plain,
    product(a97,a100) = product(a100,product(a1,a100)),
    inference('REWRITE',[status(thm)],[17028,30706,30290,31758,30688,theory(equality)]) ).

cnf(32180,plain,
    a125 = a65,
    inference('REWRITE',[status(thm)],[25888,30518,involutory_quandle_01,involutory_quandle,28954,28930,theory(equality)]) ).

cnf(32181,plain,
    a126 = a125,
    inference('REWRITE',[status(thm)],[knot_126,involutory_quandle,32180,theory(equality)]) ).

cnf(32182,plain,
    a127 = a128,
    inference('REWRITE',[status(thm)],[knot_127,30556,32181,theory(equality)]) ).

cnf(32304,plain,
    a125 = product(a127,a41),
    inference('REWRITE',[status(thm)],[30550,32182,theory(equality)]) ).

cnf(32305,plain,
    a127 = product(a125,a41),
    inference('REWRITE',[status(thm)],[30556,32182,theory(equality)]) ).

cnf(32316,plain,
    product(a127,a14) = product(product(a125,a14),a40),
    inference('REWRITE',[status(thm)],[30580,32182,theory(equality)]) ).

cnf(32376,plain,
    product(product(product(a39,a125),a41),product(product(a14,a125),a41)) = product(a42,a127),
    inference('REWRITE',[status(thm)],[10009,32181,theory(equality)]) ).

cnf(32446,plain,
    product(a127,a2) = product(product(a125,a2),a42),
    inference('REWRITE',[status(thm)],[30100,16992,involutory_quandle,32182,32181,theory(equality)]) ).

cnf(32477,plain,
    a93 = a125,
    inference('REWRITE',[status(thm)],[29658,32180,theory(equality)]) ).

cnf(32484,plain,
    a125 = product(a100,a2),
    inference('REWRITE',[status(thm)],[30518,32180,theory(equality)]) ).

cnf(32485,plain,
    product(a103,a40) = product(a125,a14),
    inference('REWRITE',[status(thm)],[30519,32180,theory(equality)]) ).

cnf(32486,plain,
    product(product(a102,a39),a4) = product(a125,a14),
    inference('REWRITE',[status(thm)],[5604,32485,theory(equality)]) ).

cnf(32504,plain,
    a100 = product(a125,a2),
    inference('REWRITE',[status(thm)],[30707,32180,theory(equality)]) ).

cnf(32508,plain,
    product(a127,a2) = product(a100,a42),
    inference('REWRITE',[status(thm)],[32446,32504,theory(equality)]) ).

cnf(32523,plain,
    product(product(X,a125),a2) = product(product(X,a2),a100),
    inference('REWRITE',[status(thm)],[30708,32180,theory(equality)]) ).

cnf(32530,plain,
    a127 = a62,
    inference('REWRITE',[status(thm)],[31759,32305,32180,theory(equality)]) ).

cnf(32531,plain,
    a43 = product(a42,a127),
    inference('REWRITE',[status(thm)],[knot_43,32530,theory(equality)]) ).

cnf(32535,plain,
    product(product(product(a39,a125),a41),product(product(a14,a125),a41)) = a43,
    inference('REWRITE',[status(thm)],[32376,32531,theory(equality)]) ).

cnf(32537,plain,
    a44 = a42,
    inference('REWRITE',[status(thm)],[184,31847,32530,theory(equality)]) ).

cnf(32538,plain,
    a45 = product(a42,a23),
    inference('REWRITE',[status(thm)],[knot_45,32537,theory(equality)]) ).

cnf(32546,plain,
    product(a46,a23) = product(a42,a1),
    inference('REWRITE',[status(thm)],[2187,32537,theory(equality)]) ).

cnf(32582,plain,
    product(product(a139,a11),a23) = product(a2,a1),
    inference('REWRITE',[status(thm)],[4793,3341,32537,theory(equality)]) ).

cnf(32745,plain,
    a130 = a61,
    inference('REWRITE',[status(thm)],[280,30063,32530,theory(equality)]) ).

cnf(32747,plain,
    a131 = a60,
    inference('REWRITE',[status(thm)],[229,knot_131,32745,theory(equality)]) ).

cnf(32748,plain,
    a35 = a33,
    inference('REWRITE',[status(thm)],[knot_35,191,32747,theory(equality)]) ).

cnf(32749,plain,
    a21 = product(a20,a33),
    inference('REWRITE',[status(thm)],[knot_21,32748,theory(equality)]) ).

cnf(32750,plain,
    a24 = product(a23,a33),
    inference('REWRITE',[status(thm)],[knot_24,32748,theory(equality)]) ).

cnf(32751,plain,
    a36 = product(a33,a139),
    inference('REWRITE',[status(thm)],[knot_36,32748,theory(equality)]) ).

cnf(32752,plain,
    product(a36,a139) = a33,
    inference('REWRITE',[status(thm)],[189,32748,theory(equality)]) ).

cnf(32761,plain,
    product(product(X,a33),a139) = product(product(X,a139),a36),
    inference('REWRITE',[status(thm)],[613,32748,theory(equality)]) ).

cnf(32769,plain,
    product(product(X,a21),a33) = product(product(X,a33),a20),
    inference('REWRITE',[status(thm)],[902,32748,theory(equality)]) ).

cnf(32775,plain,
    product(a36,a33) = product(a33,product(a139,a33)),
    inference('REWRITE',[status(thm)],[1940,32748,theory(equality)]) ).

cnf(32894,plain,
    product(a33,product(a33,a21)) = product(product(a33,a20),a21),
    inference('REWRITE',[status(thm)],[7762,32748,theory(equality)]) ).

cnf(33069,plain,
    a131 = a59,
    inference('REWRITE',[status(thm)],[193,involutory_quandle,32747,theory(equality)]) ).

cnf(33070,plain,
    a51 = a49,
    inference('REWRITE',[status(thm)],[knot_51,192,33069,theory(equality)]) ).

cnf(33086,plain,
    product(a52,a39) = a49,
    inference('REWRITE',[status(thm)],[256,33070,theory(equality)]) ).

cnf(33160,plain,
    product(a137,a138) = product(a140,a20),
    inference('REWRITE',[status(thm)],[5855,1919,199,33070,theory(equality)]) ).

cnf(33163,plain,
    product(product(a138,X),a48) = product(product(a137,a138),product(X,a48)),
    inference('REWRITE',[status(thm)],[1927,33160,theory(equality)]) ).

cnf(33164,plain,
    product(a138,X) = product(product(product(a137,a138),X),product(a48,X)),
    inference('REWRITE',[status(thm)],[1936,33160,theory(equality)]) ).

cnf(33314,plain,
    a132 = a58,
    inference('REWRITE',[status(thm)],[200,knot_132,33069,theory(equality)]) ).

cnf(33315,plain,
    a19 = product(a18,a132),
    inference('REWRITE',[status(thm)],[knot_19,33314,theory(equality)]) ).

cnf(33316,plain,
    product(a20,a134) = product(a18,a26),
    inference('REWRITE',[status(thm)],[14587,2307,knot_20,33315,theory(equality)]) ).

cnf(33317,plain,
    a20 = product(product(a20,a134),a57),
    inference('REWRITE',[status(thm)],[2302,33316,theory(equality)]) ).

cnf(33330,plain,
    a133 = a132,
    inference('REWRITE',[status(thm)],[knot_133,involutory_quandle,33314,theory(equality)]) ).

cnf(33331,plain,
    a18 = product(a17,a132),
    inference('REWRITE',[status(thm)],[knot_18,33330,theory(equality)]) ).

cnf(33332,plain,
    a134 = product(a132,a26),
    inference('REWRITE',[status(thm)],[knot_134,33330,theory(equality)]) ).

cnf(33338,plain,
    product(product(X,a134),a57) = product(product(X,a134),a56),
    inference('REWRITE',[status(thm)],[2344,33332,theory(equality)]) ).

cnf(33339,plain,
    a20 = product(a17,a26),
    inference('REWRITE',[status(thm)],[33317,15860,33338,theory(equality)]) ).

cnf(33387,plain,
    product(a134,a26) = a132,
    inference('REWRITE',[status(thm)],[210,33330,theory(equality)]) ).

cnf(33388,plain,
    a19 = a17,
    inference('REWRITE',[status(thm)],[215,33315,33330,theory(equality)]) ).

cnf(33393,plain,
    product(a17,X) = product(product(a20,X),product(a26,X)),
    inference('REWRITE',[status(thm)],[906,33388,theory(equality)]) ).

cnf(33396,plain,
    product(a20,a17) = product(a17,product(a26,a17)),
    inference('REWRITE',[status(thm)],[2236,33388,theory(equality)]) ).

cnf(33417,plain,
    product(product(a26,a17),a26) = product(a26,a20),
    inference('REWRITE',[status(thm)],[5993,33388,theory(equality)]) ).

cnf(33421,plain,
    product(product(a20,a138),product(a17,a138)) = product(product(a17,a138),product(a25,product(a17,a138))),
    inference('REWRITE',[status(thm)],[6856,33388,theory(equality)]) ).

cnf(33424,plain,
    product(product(a20,X),product(a17,X)) = product(product(a17,X),product(product(a26,X),product(a17,X))),
    inference('REWRITE',[status(thm)],[7333,33388,theory(equality)]) ).

cnf(33434,plain,
    product(product(a26,a17),X) = product(product(product(a26,a20),X),product(a26,X)),
    inference('REWRITE',[status(thm)],[8347,33388,theory(equality)]) ).

cnf(33453,plain,
    product(product(a17,a139),a20) = product(product(a20,a138),product(a25,product(a20,a138))),
    inference('REWRITE',[status(thm)],[14317,33388,theory(equality)]) ).

cnf(33745,plain,
    a134 = a57,
    inference('REWRITE',[status(thm)],[209,33332,33314,theory(equality)]) ).

cnf(33747,plain,
    a134 = a56,
    inference('REWRITE',[status(thm)],[243,involutory_quandle,33745,theory(equality)]) ).

cnf(33748,plain,
    a9 = product(a8,a134),
    inference('REWRITE',[status(thm)],[knot_09,33747,theory(equality)]) ).

cnf(33750,plain,
    a135 = a55,
    inference('REWRITE',[status(thm)],[238,knot_135,33747,theory(equality)]) ).

cnf(33752,plain,
    a135 = a54,
    inference('REWRITE',[status(thm)],[180,involutory_quandle,33750,theory(equality)]) ).

cnf(33754,plain,
    a136 = a53,
    inference('REWRITE',[status(thm)],[217,knot_136,33752,theory(equality)]) ).

cnf(33755,plain,
    a15 = product(a14,a136),
    inference('REWRITE',[status(thm)],[knot_15,33754,theory(equality)]) ).

cnf(33776,plain,
    a16 = a14,
    inference('REWRITE',[status(thm)],[219,knot_16,33754,theory(equality)]) ).

cnf(33777,plain,
    a14 = product(a15,a136),
    inference('REWRITE',[status(thm)],[knot_16,33776,theory(equality)]) ).

cnf(33778,plain,
    a17 = product(a14,a29),
    inference('REWRITE',[status(thm)],[knot_17,33776,theory(equality)]) ).

cnf(33779,plain,
    product(a30,a29) = a28,
    inference('REWRITE',[status(thm)],[3042,246,33778,theory(equality)]) ).

cnf(33782,plain,
    product(a14,a17) = product(product(a14,a30),a29),
    inference('REWRITE',[status(thm)],[7130,33778,theory(equality)]) ).

cnf(33784,plain,
    product(a17,a29) = a14,
    inference('REWRITE',[status(thm)],[216,33776,theory(equality)]) ).

cnf(33792,plain,
    product(a14,X) = product(product(a17,X),product(a29,X)),
    inference('REWRITE',[status(thm)],[930,33776,theory(equality)]) ).

cnf(33806,plain,
    product(product(X,a14),a136) = product(product(X,a136),a15),
    inference('REWRITE',[status(thm)],[1040,33776,theory(equality)]) ).

cnf(33807,plain,
    product(product(a1,a136),a15) = product(a6,product(a40,a136)),
    inference('REWRITE',[status(thm)],[5683,33806,theory(equality)]) ).

cnf(33808,plain,
    product(a17,a14) = product(a14,a30),
    inference('REWRITE',[status(thm)],[2363,knot_30,33776,theory(equality)]) ).

cnf(33809,plain,
    product(a29,a30) = product(a28,a14),
    inference('REWRITE',[status(thm)],[5474,5472,33808,theory(equality)]) ).

cnf(33812,plain,
    product(a14,a17) = product(product(a17,a14),a29),
    inference('REWRITE',[status(thm)],[33782,33808,theory(equality)]) ).

cnf(33860,plain,
    product(a14,a17) = product(a17,a28),
    inference('REWRITE',[status(thm)],[5141,33776,theory(equality)]) ).

cnf(33899,plain,
    product(product(a136,a17),a14) = product(a135,a30),
    inference('REWRITE',[status(thm)],[9875,involutory_quandle_01,33776,theory(equality)]) ).

cnf(33919,plain,
    product(product(a135,a17),a14) = product(a136,a30),
    inference('REWRITE',[status(thm)],[11366,involutory_quandle_01,33776,theory(equality)]) ).

cnf(34039,plain,
    a136 = a52,
    inference('REWRITE',[status(thm)],[253,involutory_quandle,33754,theory(equality)]) ).

cnf(34040,plain,
    a7 = a5,
    inference('REWRITE',[status(thm)],[knot_07,251,34039,theory(equality)]) ).

cnf(34041,plain,
    a8 = product(a5,a17),
    inference('REWRITE',[status(thm)],[knot_08,34040,theory(equality)]) ).

cnf(34042,plain,
    a39 = product(a38,a5),
    inference('REWRITE',[status(thm)],[knot_39,34040,theory(equality)]) ).

cnf(34044,plain,
    product(a40,a39) = a38,
    inference('REWRITE',[status(thm)],[250,3143,34040,theory(equality)]) ).

cnf(34045,plain,
    a38 = product(a39,a5),
    inference('REWRITE',[status(thm)],[3143,34044,theory(equality)]) ).

cnf(34046,plain,
    product(a32,a5) = product(a30,a38),
    inference('REWRITE',[status(thm)],[3154,34044,theory(equality)]) ).

cnf(34055,plain,
    product(product(X,a38),a5) = product(product(X,a39),a4),
    inference('REWRITE',[status(thm)],[3169,34044,theory(equality)]) ).

cnf(34056,plain,
    product(product(a102,a38),a5) = product(a125,a14),
    inference('REWRITE',[status(thm)],[32486,34055,theory(equality)]) ).

cnf(34070,plain,
    product(product(X,a38),a5) = product(product(X,a4),a40),
    inference('REWRITE',[status(thm)],[694,34055,theory(equality)]) ).

cnf(34083,plain,
    product(a4,a5) = product(a5,a38),
    inference('REWRITE',[status(thm)],[5894,34044,theory(equality)]) ).

cnf(34090,plain,
    product(product(a1,a14),a39) = product(a5,product(a5,a38)),
    inference('REWRITE',[status(thm)],[12071,34083,theory(equality)]) ).

cnf(34096,plain,
    product(a39,a38) = product(a40,a5),
    inference('REWRITE',[status(thm)],[6757,34044,theory(equality)]) ).

cnf(34098,plain,
    product(product(a39,a40),a39) = product(a39,a38),
    inference('REWRITE',[status(thm)],[17555,34096,theory(equality)]) ).

cnf(34105,plain,
    product(product(a1,a14),a39) = product(a4,a38),
    inference('REWRITE',[status(thm)],[16132,34044,theory(equality)]) ).

cnf(34107,plain,
    product(a4,a38) = product(a5,product(a5,a38)),
    inference('REWRITE',[status(thm)],[34090,34105,theory(equality)]) ).

cnf(34227,plain,
    product(a38,a4) = product(product(a39,a38),a39),
    inference('REWRITE',[status(thm)],[16044,254,34040,theory(equality)]) ).

cnf(34256,plain,
    product(a105,product(a39,a38)) = product(product(a106,a4),a38),
    inference('REWRITE',[status(thm)],[32027,involutory_quandle_02,34107,262,34040,theory(equality)]) ).

cnf(34299,plain,
    product(product(a39,a136),a6) = product(a38,a136),
    inference('REWRITE',[status(thm)],[2868,34039,theory(equality)]) ).

cnf(34300,plain,
    product(product(a4,a136),a6) = product(a6,product(a38,a136)),
    inference('REWRITE',[status(thm)],[6266,34299,theory(equality)]) ).

cnf(34324,plain,
    product(product(a8,a29),product(a37,a29)) = product(a11,a29),
    inference('REWRITE',[status(thm)],[25663,involutory_quandle_01,642,34039,theory(equality)]) ).

cnf(34326,plain,
    a137 = a49,
    inference('REWRITE',[status(thm)],[33086,knot_137,34039,theory(equality)]) ).

cnf(34327,plain,
    a25 = product(a24,a137),
    inference('REWRITE',[status(thm)],[knot_25,34326,theory(equality)]) ).

cnf(34329,plain,
    a137 = product(a48,a138),
    inference('REWRITE',[status(thm)],[knot_49,34326,theory(equality)]) ).

cnf(34330,plain,
    a50 = product(a137,a131),
    inference('REWRITE',[status(thm)],[knot_50,34326,theory(equality)]) ).

cnf(34333,plain,
    product(a50,a131) = a137,
    inference('REWRITE',[status(thm)],[192,34326,theory(equality)]) ).

cnf(34334,plain,
    product(a137,a138) = a48,
    inference('REWRITE',[status(thm)],[199,34326,theory(equality)]) ).

cnf(34338,plain,
    product(product(a138,X),a48) = product(a48,product(X,a48)),
    inference('REWRITE',[status(thm)],[33163,34334,theory(equality)]) ).

cnf(34342,plain,
    product(a138,X) = product(a48,X),
    inference('REWRITE',[status(thm)],[33164,involutory_quandle,34334,theory(equality)]) ).

cnf(34343,plain,
    product(product(a138,X),a48) = product(a138,product(X,a48)),
    inference('REWRITE',[status(thm)],[34338,34342,theory(equality)]) ).

cnf(34344,plain,
    product(product(product(a140,X),a20),a48) = product(product(product(a139,X),a20),a48),
    inference('REWRITE',[status(thm)],[14663,919,34343,theory(equality)]) ).

cnf(34345,plain,
    product(product(a139,a37),a20) = product(product(a140,a37),a20),
    inference('REWRITE',[status(thm)],[11054,9252,34344,theory(equality)]) ).

cnf(34346,plain,
    product(product(a139,a37),a20) = product(product(product(a139,a36),a20),a48),
    inference('REWRITE',[status(thm)],[9252,34345,theory(equality)]) ).

cnf(34349,plain,
    a137 = a138,
    inference('REWRITE',[status(thm)],[34329,involutory_quandle,34342,theory(equality)]) ).

cnf(34350,plain,
    a26 = product(a25,a137),
    inference('REWRITE',[status(thm)],[knot_26,34349,theory(equality)]) ).

cnf(34351,plain,
    a132 = product(a131,a137),
    inference('REWRITE',[status(thm)],[knot_132,34349,theory(equality)]) ).

cnf(34354,plain,
    product(a132,a137) = a131,
    inference('REWRITE',[status(thm)],[201,34349,theory(equality)]) ).

cnf(34355,plain,
    product(a139,a20) = a137,
    inference('REWRITE',[status(thm)],[212,34349,theory(equality)]) ).

cnf(34358,plain,
    product(a139,X) = product(product(a137,X),product(a20,X)),
    inference('REWRITE',[status(thm)],[353,34349,theory(equality)]) ).

cnf(34364,plain,
    product(product(X,a137),a20) = product(product(X,a20),a139),
    inference('REWRITE',[status(thm)],[636,34349,theory(equality)]) ).

cnf(34395,plain,
    product(a139,a137) = product(a137,product(a20,a137)),
    inference('REWRITE',[status(thm)],[2292,34349,theory(equality)]) ).

cnf(34459,plain,
    product(a50,X) = product(product(product(a137,a132),X),product(a137,X)),
    inference('REWRITE',[status(thm)],[8290,34330,34349,theory(equality)]) ).

cnf(34549,plain,
    product(product(X,a139),a20) = product(product(X,a137),product(a20,a137)),
    inference('REWRITE',[status(thm)],[14684,34349,theory(equality)]) ).

cnf(34560,plain,
    product(product(a132,a1),product(a13,a1)) = product(a127,product(product(a137,a1),product(a13,a1))),
    inference('REWRITE',[status(thm)],[29956,34349,theory(equality)]) ).

cnf(34579,plain,
    product(product(a20,a137),product(a17,a137)) = product(product(a17,a137),product(a25,product(a17,a137))),
    inference('REWRITE',[status(thm)],[33421,34349,theory(equality)]) ).

cnf(34586,plain,
    product(product(a17,a139),a20) = product(product(a20,a137),product(a25,product(a20,a137))),
    inference('REWRITE',[status(thm)],[33453,34349,theory(equality)]) ).

cnf(34609,plain,
    a137 = a48,
    inference('REWRITE',[status(thm)],[34334,involutory_quandle,34349,theory(equality)]) ).

cnf(34628,plain,
    product(product(a139,a37),a20) = product(product(product(a139,a137),product(a36,a137)),product(a20,a137)),
    inference('REWRITE',[status(thm)],[34346,715,34609,theory(equality)]) ).

cnf(34663,plain,
    product(a47,X) = product(a139,X),
    inference('REWRITE',[status(thm)],[915,34358,34349,34342,theory(equality)]) ).

cnf(34761,plain,
    product(a139,a140) = product(a45,a11),
    inference('REWRITE',[status(thm)],[2196,34663,theory(equality)]) ).

cnf(34762,plain,
    a47 = a139,
    inference('REWRITE',[status(thm)],[2189,involutory_quandle_01,34761,theory(equality)]) ).

cnf(34763,plain,
    a37 = a33,
    inference('REWRITE',[status(thm)],[knot_37,32752,34762,theory(equality)]) ).

cnf(34764,plain,
    a11 = product(a10,a33),
    inference('REWRITE',[status(thm)],[knot_11,34763,theory(equality)]) ).

cnf(34765,plain,
    a28 = product(a27,a33),
    inference('REWRITE',[status(thm)],[knot_28,34763,theory(equality)]) ).

cnf(34766,plain,
    a38 = product(a33,a17),
    inference('REWRITE',[status(thm)],[knot_38,34763,theory(equality)]) ).

cnf(34767,plain,
    a135 = product(a134,a33),
    inference('REWRITE',[status(thm)],[knot_135,34763,theory(equality)]) ).

cnf(34768,plain,
    product(a11,a33) = a10,
    inference('REWRITE',[status(thm)],[236,34763,theory(equality)]) ).

cnf(34770,plain,
    product(a135,a33) = a134,
    inference('REWRITE',[status(thm)],[239,34763,theory(equality)]) ).

cnf(34771,plain,
    product(a38,a17) = a33,
    inference('REWRITE',[status(thm)],[247,34763,theory(equality)]) ).

cnf(34783,plain,
    product(product(X,a33),a17) = product(product(X,a17),a38),
    inference('REWRITE',[status(thm)],[671,34763,theory(equality)]) ).

cnf(34786,plain,
    product(product(X,a11),a33) = product(product(X,a33),a10),
    inference('REWRITE',[status(thm)],[992,34763,theory(equality)]) ).

cnf(34802,plain,
    product(a11,a10) = product(a10,product(a33,a10)),
    inference('REWRITE',[status(thm)],[2630,34763,theory(equality)]) ).

cnf(34818,plain,
    product(a38,a33) = product(a33,product(a17,a33)),
    inference('REWRITE',[status(thm)],[2791,34763,theory(equality)]) ).

cnf(34834,plain,
    product(a9,a33) = product(a11,a135),
    inference('REWRITE',[status(thm)],[4941,34763,theory(equality)]) ).

cnf(34837,plain,
    product(product(a10,a135),a33) = product(a11,a134),
    inference('REWRITE',[status(thm)],[4949,34763,theory(equality)]) ).

cnf(34842,plain,
    product(product(a11,a135),a33) = a9,
    inference('REWRITE',[status(thm)],[4957,34763,theory(equality)]) ).

cnf(34861,plain,
    product(product(a11,a134),a33) = product(a10,a135),
    inference('REWRITE',[status(thm)],[4981,34763,theory(equality)]) ).

cnf(34897,plain,
    product(product(a134,a28),a33) = product(a135,a27),
    inference('REWRITE',[status(thm)],[5037,34763,theory(equality)]) ).

cnf(34933,plain,
    product(product(a33,a134),a33) = product(a33,a135),
    inference('REWRITE',[status(thm)],[6023,34763,theory(equality)]) ).

cnf(35017,plain,
    product(product(X,a134),a33) = product(product(X,a135),product(a33,a135)),
    inference('REWRITE',[status(thm)],[9640,34763,theory(equality)]) ).

cnf(35229,plain,
    product(product(a8,a29),product(a33,a29)) = product(a11,a29),
    inference('REWRITE',[status(thm)],[34324,34763,theory(equality)]) ).

cnf(35231,plain,
    product(product(a139,a21),a33) = product(product(product(a139,a137),product(a36,a137)),product(a20,a137)),
    inference('REWRITE',[status(thm)],[34628,32769,34763,theory(equality)]) ).

cnf(35260,plain,
    a140 = a139,
    inference('REWRITE',[status(thm)],[knot_140,involutory_quandle,34762,theory(equality)]) ).

cnf(35261,plain,
    a141 = product(a139,a11),
    inference('REWRITE',[status(thm)],[knot_141,35260,theory(equality)]) ).

cnf(35286,plain,
    a1 = product(a2,a1),
    inference('REWRITE',[status(thm)],[32582,knot_142,35261,theory(equality)]) ).

cnf(35287,plain,
    a3 = a2,
    inference('REWRITE',[status(thm)],[3214,knot,35286,theory(equality)]) ).

cnf(35289,plain,
    a4 = product(a2,a14),
    inference('REWRITE',[status(thm)],[knot_04,35287,theory(equality)]) ).

cnf(35290,plain,
    product(a4,a40) = a4,
    inference('REWRITE',[status(thm)],[3226,35289,theory(equality)]) ).

cnf(35296,plain,
    product(a31,a4) = a30,
    inference('REWRITE',[status(thm)],[3232,involutory_quandle_01,35289,theory(equality)]) ).

cnf(35298,plain,
    product(product(a31,a40),a39) = a31,
    inference('REWRITE',[status(thm)],[17567,knot_31,35296,theory(equality)]) ).

cnf(35303,plain,
    product(a106,a4) = a105,
    inference('REWRITE',[status(thm)],[3234,involutory_quandle_01,35289,theory(equality)]) ).

cnf(35309,plain,
    product(product(a106,a40),a39) = a106,
    inference('REWRITE',[status(thm)],[31675,knot_106,35303,theory(equality)]) ).

cnf(35310,plain,
    product(a105,product(a39,a38)) = product(a105,a38),
    inference('REWRITE',[status(thm)],[34256,35303,theory(equality)]) ).

cnf(35315,plain,
    product(product(X,a38),a5) = product(product(X,a39),a5),
    inference('REWRITE',[status(thm)],[3237,34070,35289,theory(equality)]) ).

cnf(35350,plain,
    product(a103,a39) = product(a125,a14),
    inference('REWRITE',[status(thm)],[3198,34056,35315,theory(equality)]) ).

cnf(35398,plain,
    a4 = a5,
    inference('REWRITE',[status(thm)],[3238,involutory_quandle,35289,theory(equality)]) ).

cnf(35400,plain,
    a6 = product(a4,a136),
    inference('REWRITE',[status(thm)],[knot_06,35398,theory(equality)]) ).

cnf(35406,plain,
    a6 = product(a6,product(a38,a136)),
    inference('REWRITE',[status(thm)],[34300,involutory_quandle,35400,theory(equality)]) ).

cnf(35419,plain,
    product(a6,a136) = a4,
    inference('REWRITE',[status(thm)],[251,35398,theory(equality)]) ).

cnf(35505,plain,
    a4 = product(a1,a14),
    inference('REWRITE',[status(thm)],[5678,35290,35398,theory(equality)]) ).

cnf(35513,plain,
    product(a30,a31) = product(a31,product(a4,a31)),
    inference('REWRITE',[status(thm)],[5898,35398,theory(equality)]) ).

cnf(35672,plain,
    product(product(a97,a14),a40) = a103,
    inference('REWRITE',[status(thm)],[30409,knot_103,35398,theory(equality)]) ).

cnf(35677,plain,
    a102 = product(a106,a31),
    inference('REWRITE',[status(thm)],[31346,272,35398,theory(equality)]) ).

cnf(35731,plain,
    a7 = a4,
    inference('REWRITE',[status(thm)],[34040,35398,theory(equality)]) ).

cnf(35732,plain,
    a8 = product(a4,a17),
    inference('REWRITE',[status(thm)],[34041,35398,theory(equality)]) ).

cnf(35733,plain,
    a39 = product(a38,a4),
    inference('REWRITE',[status(thm)],[34042,35398,theory(equality)]) ).

cnf(35734,plain,
    a39 = product(product(a39,a38),a39),
    inference('REWRITE',[status(thm)],[34227,35733,theory(equality)]) ).

cnf(35736,plain,
    a38 = a40,
    inference('REWRITE',[status(thm)],[34045,knot_40,35398,theory(equality)]) ).

cnf(35738,plain,
    a41 = product(a38,a14),
    inference('REWRITE',[status(thm)],[knot_41,35736,theory(equality)]) ).

cnf(35739,plain,
    product(product(a27,a14),product(a17,a14)) = product(a30,a41),
    inference('REWRITE',[status(thm)],[5473,35738,theory(equality)]) ).

cnf(35750,plain,
    a102 = product(a101,a38),
    inference('REWRITE',[status(thm)],[knot_102,35736,theory(equality)]) ).

cnf(35751,plain,
    product(a102,a38) = a101,
    inference('REWRITE',[status(thm)],[186,35736,theory(equality)]) ).

cnf(35752,plain,
    product(a41,a14) = a38,
    inference('REWRITE',[status(thm)],[265,35736,theory(equality)]) ).

cnf(35819,plain,
    product(a38,a2) = product(a42,product(a14,a2)),
    inference('REWRITE',[status(thm)],[5796,35736,theory(equality)]) ).

cnf(35950,plain,
    product(a97,a14) = product(a103,product(a39,a38)),
    inference('REWRITE',[status(thm)],[31871,35736,theory(equality)]) ).

cnf(35956,plain,
    product(a127,a14) = product(product(a125,a14),a38),
    inference('REWRITE',[status(thm)],[32316,35736,theory(equality)]) ).

cnf(35976,plain,
    product(product(a1,a136),a15) = a6,
    inference('REWRITE',[status(thm)],[33807,35406,35736,theory(equality)]) ).

cnf(35978,plain,
    a39 = product(a39,a38),
    inference('REWRITE',[status(thm)],[34098,35734,35736,theory(equality)]) ).

cnf(35979,plain,
    product(a105,a39) = product(a105,a38),
    inference('REWRITE',[status(thm)],[35310,35978,theory(equality)]) ).

cnf(35989,plain,
    product(a97,a14) = product(a125,a14),
    inference('REWRITE',[status(thm)],[35950,35350,35978,theory(equality)]) ).

cnf(35995,plain,
    product(product(a31,a38),a39) = a31,
    inference('REWRITE',[status(thm)],[35298,35736,theory(equality)]) ).

cnf(36000,plain,
    product(product(a106,a38),a39) = a106,
    inference('REWRITE',[status(thm)],[35309,35736,theory(equality)]) ).

cnf(36033,plain,
    product(a127,a14) = a103,
    inference('REWRITE',[status(thm)],[35672,35956,35989,35736,theory(equality)]) ).

cnf(36056,plain,
    product(a30,a39) = product(a30,a38),
    inference('REWRITE',[status(thm)],[34046,2972,35398,theory(equality)]) ).

cnf(36246,plain,
    product(product(X,a14),a2) = product(product(X,a1),product(a14,a2)),
    inference('REWRITE',[status(thm)],[3036,10628,35287,theory(equality)]) ).

cnf(36248,plain,
    product(product(a39,a1),product(a14,a2)) = product(a42,a1),
    inference('REWRITE',[status(thm)],[5797,36246,theory(equality)]) ).

cnf(36253,plain,
    a41 = product(a42,a1),
    inference('REWRITE',[status(thm)],[3144,36248,36246,35287,theory(equality)]) ).

cnf(36282,plain,
    product(a46,a23) = a41,
    inference('REWRITE',[status(thm)],[32546,36253,theory(equality)]) ).

cnf(36364,plain,
    a42 = product(a39,a14),
    inference('REWRITE',[status(thm)],[3159,knot_42,35287,theory(equality)]) ).

cnf(36371,plain,
    a2 = a1,
    inference('REWRITE',[status(thm)],[3212,involutory_quandle,35287,theory(equality)]) ).

cnf(36420,plain,
    product(a125,a100) = product(a97,a100),
    inference('REWRITE',[status(thm)],[29110,32123,36371,theory(equality)]) ).

cnf(36421,plain,
    product(a125,a100) = product(a100,product(a1,a100)),
    inference('REWRITE',[status(thm)],[32123,36420,theory(equality)]) ).

cnf(36427,plain,
    a125 = a97,
    inference('REWRITE',[status(thm)],[32484,30408,36371,theory(equality)]) ).

cnf(36428,plain,
    product(a100,a1) = a125,
    inference('REWRITE',[status(thm)],[30408,36427,theory(equality)]) ).

cnf(36433,plain,
    a100 = product(a125,a1),
    inference('REWRITE',[status(thm)],[32504,36371,theory(equality)]) ).

cnf(36444,plain,
    a130 = product(a100,a42),
    inference('REWRITE',[status(thm)],[32508,30063,36371,theory(equality)]) ).

cnf(36445,plain,
    product(product(X,a125),a1) = product(product(X,a1),a100),
    inference('REWRITE',[status(thm)],[32523,36371,theory(equality)]) ).

cnf(36452,plain,
    a3 = a1,
    inference('REWRITE',[status(thm)],[35287,36371,theory(equality)]) ).

cnf(36462,plain,
    product(a38,a1) = product(a42,product(a14,a1)),
    inference('REWRITE',[status(thm)],[35819,36371,theory(equality)]) ).

cnf(36565,plain,
    product(X,a42) = product(X,a41),
    inference('REWRITE',[status(thm)],[16840,36253,involutory_quandle_01,36371,35287,theory(equality)]) ).

cnf(36566,plain,
    a130 = a89,
    inference('REWRITE',[status(thm)],[36444,31741,36565,theory(equality)]) ).

cnf(36610,plain,
    product(a102,a32) = product(a131,a33),
    inference('REWRITE',[status(thm)],[31939,knot_131,36566,theory(equality)]) ).

cnf(36824,plain,
    product(a141,a11) = a139,
    inference('REWRITE',[status(thm)],[241,35260,theory(equality)]) ).

cnf(36825,plain,
    product(a141,X) = product(product(a139,X),product(a11,X)),
    inference('REWRITE',[status(thm)],[382,35260,theory(equality)]) ).

cnf(36839,plain,
    product(a141,a139) = product(a139,product(a11,a139)),
    inference('REWRITE',[status(thm)],[2700,35260,theory(equality)]) ).

cnf(36845,plain,
    product(product(X,a11),a139) = product(product(X,product(a11,a139)),product(a141,a139)),
    inference('REWRITE',[status(thm)],[2707,35260,theory(equality)]) ).

cnf(36873,plain,
    product(product(a141,a12),a21) = product(a139,product(a21,a11)),
    inference('REWRITE',[status(thm)],[15795,35260,theory(equality)]) ).

cnf(36881,plain,
    product(product(product(X,a11),a139),product(a22,a11)) = product(product(product(X,a12),a139),product(a21,a139)),
    inference('REWRITE',[status(thm)],[15807,35260,theory(equality)]) ).

cnf(36916,plain,
    product(product(a1,a11),a139) = product(a139,product(a22,a11)),
    inference('REWRITE',[status(thm)],[9647,involutory_quandle,36824,36881,involutory_quandle_02,36873,35260,34762,theory(equality)]) ).

cnf(36935,plain,
    product(a24,a20) = product(a26,a20),
    inference('REWRITE',[status(thm)],[14413,34350,34364,involutory_quandle,34663,theory(equality)]) ).

cnf(36937,plain,
    product(product(a26,a17),a26) = product(a24,a20),
    inference('REWRITE',[status(thm)],[33417,36935,theory(equality)]) ).

cnf(36945,plain,
    product(product(a26,a17),X) = product(product(product(a24,a20),X),product(a26,X)),
    inference('REWRITE',[status(thm)],[33434,36935,theory(equality)]) ).

cnf(36965,plain,
    product(a46,X) = product(a141,X),
    inference('REWRITE',[status(thm)],[1002,36825,34663,theory(equality)]) ).

cnf(36970,plain,
    a1 = a41,
    inference('REWRITE',[status(thm)],[36282,knot_142,36965,theory(equality)]) ).

cnf(36974,plain,
    product(a38,a1) = product(a39,a1),
    inference('REWRITE',[status(thm)],[12090,36462,36970,theory(equality)]) ).

cnf(36980,plain,
    a125 = a130,
    inference('REWRITE',[status(thm)],[32304,30063,36970,theory(equality)]) ).

cnf(36981,plain,
    a131 = product(a125,a13),
    inference('REWRITE',[status(thm)],[knot_131,36980,theory(equality)]) ).

cnf(37090,plain,
    a100 = a127,
    inference('REWRITE',[status(thm)],[30103,36433,36980,theory(equality)]) ).

cnf(37092,plain,
    product(a131,a1) = product(a100,product(a13,a1)),
    inference('REWRITE',[status(thm)],[30016,37090,theory(equality)]) ).

cnf(37094,plain,
    a100 = a129,
    inference('REWRITE',[status(thm)],[30101,37090,theory(equality)]) ).

cnf(37096,plain,
    a100 = a128,
    inference('REWRITE',[status(thm)],[32182,37090,theory(equality)]) ).

cnf(37106,plain,
    a100 = a62,
    inference('REWRITE',[status(thm)],[32530,37090,theory(equality)]) ).

cnf(37128,plain,
    product(product(a132,a1),product(a13,a1)) = product(a100,product(product(a137,a1),product(a13,a1))),
    inference('REWRITE',[status(thm)],[34560,37090,theory(equality)]) ).

cnf(37132,plain,
    a101 = a103,
    inference('REWRITE',[status(thm)],[36033,knot_101,37090,theory(equality)]) ).

cnf(37215,plain,
    a101 = a104,
    inference('REWRITE',[status(thm)],[31267,37132,theory(equality)]) ).

cnf(37216,plain,
    a105 = product(a101,a30),
    inference('REWRITE',[status(thm)],[31269,37132,theory(equality)]) ).

cnf(37290,plain,
    a86 = a101,
    inference('REWRITE',[status(thm)],[31732,37132,theory(equality)]) ).

cnf(37291,plain,
    a87 = a101,
    inference('REWRITE',[status(thm)],[31904,37132,theory(equality)]) ).

cnf(37395,plain,
    a125 = a61,
    inference('REWRITE',[status(thm)],[32745,36980,theory(equality)]) ).

cnf(37402,plain,
    a125 = a89,
    inference('REWRITE',[status(thm)],[36566,36980,theory(equality)]) ).

cnf(37456,plain,
    product(product(product(a38,a1),a100),product(product(a14,a1),a100)) = a43,
    inference('REWRITE',[status(thm)],[32535,36974,36445,36970,theory(equality)]) ).

cnf(37457,plain,
    a1 = product(a38,a14),
    inference('REWRITE',[status(thm)],[35738,36970,theory(equality)]) ).

cnf(37458,plain,
    product(product(a27,a14),product(a17,a14)) = product(a30,a1),
    inference('REWRITE',[status(thm)],[35739,36970,theory(equality)]) ).

cnf(37476,plain,
    a4 = a38,
    inference('REWRITE',[status(thm)],[35752,35505,36970,theory(equality)]) ).

cnf(37485,plain,
    product(a31,a38) = a30,
    inference('REWRITE',[status(thm)],[35296,37476,theory(equality)]) ).

cnf(37486,plain,
    product(a30,a38) = a31,
    inference('REWRITE',[status(thm)],[35995,36056,37485,theory(equality)]) ).

cnf(37488,plain,
    product(a106,a38) = a105,
    inference('REWRITE',[status(thm)],[35303,37476,theory(equality)]) ).

cnf(37489,plain,
    product(a105,a38) = a106,
    inference('REWRITE',[status(thm)],[36000,35979,37488,theory(equality)]) ).

cnf(37492,plain,
    a38 = a5,
    inference('REWRITE',[status(thm)],[35398,37476,theory(equality)]) ).

cnf(37543,plain,
    product(a6,a136) = a38,
    inference('REWRITE',[status(thm)],[35419,37476,theory(equality)]) ).

cnf(37628,plain,
    product(a30,a31) = product(a31,product(a38,a31)),
    inference('REWRITE',[status(thm)],[35513,37476,theory(equality)]) ).

cnf(37773,plain,
    a7 = a38,
    inference('REWRITE',[status(thm)],[35731,37476,theory(equality)]) ).

cnf(37774,plain,
    a8 = a33,
    inference('REWRITE',[status(thm)],[35732,34771,37476,theory(equality)]) ).

cnf(37776,plain,
    a28 = a26,
    inference('REWRITE',[status(thm)],[248,34765,37774,theory(equality)]) ).

cnf(37777,plain,
    a29 = product(a26,a17),
    inference('REWRITE',[status(thm)],[knot_29,37776,theory(equality)]) ).

cnf(37778,plain,
    product(a20,a17) = a14,
    inference('REWRITE',[status(thm)],[33396,33784,37777,theory(equality)]) ).

cnf(37805,plain,
    product(a29,a26) = product(a24,a20),
    inference('REWRITE',[status(thm)],[36937,37777,theory(equality)]) ).

cnf(37812,plain,
    product(a29,X) = product(product(product(a24,a20),X),product(a26,X)),
    inference('REWRITE',[status(thm)],[36945,37777,theory(equality)]) ).

cnf(37816,plain,
    product(a29,a17) = a26,
    inference('REWRITE',[status(thm)],[246,37776,theory(equality)]) ).

cnf(37817,plain,
    product(a29,X) = product(product(a26,X),product(a17,X)),
    inference('REWRITE',[status(thm)],[387,37776,theory(equality)]) ).

cnf(37819,plain,
    product(product(a20,X),product(a17,X)) = product(a14,X),
    inference('REWRITE',[status(thm)],[33424,33792,37817,theory(equality)]) ).

cnf(37820,plain,
    product(a14,a137) = product(product(a17,a137),product(a25,product(a17,a137))),
    inference('REWRITE',[status(thm)],[34579,37819,theory(equality)]) ).

cnf(37832,plain,
    product(a26,a14) = product(a30,product(a17,a14)),
    inference('REWRITE',[status(thm)],[5472,37776,theory(equality)]) ).

cnf(37860,plain,
    product(a30,a29) = a26,
    inference('REWRITE',[status(thm)],[33779,37776,theory(equality)]) ).

cnf(37876,plain,
    product(a29,a30) = product(a26,a14),
    inference('REWRITE',[status(thm)],[33809,37776,theory(equality)]) ).

cnf(37887,plain,
    product(a14,a17) = a20,
    inference('REWRITE',[status(thm)],[33860,33339,37776,theory(equality)]) ).

cnf(37888,plain,
    a20 = product(product(a17,a14),a29),
    inference('REWRITE',[status(thm)],[33812,37887,theory(equality)]) ).

cnf(37992,plain,
    product(a132,a33) = product(a135,a27),
    inference('REWRITE',[status(thm)],[34897,33387,37776,theory(equality)]) ).

cnf(38101,plain,
    a9 = product(a33,a134),
    inference('REWRITE',[status(thm)],[33748,37774,theory(equality)]) ).

cnf(38116,plain,
    product(a11,a135) = product(a33,a135),
    inference('REWRITE',[status(thm)],[34933,34834,38101,theory(equality)]) ).

cnf(38120,plain,
    product(product(X,a134),a33) = product(product(X,a11),a135),
    inference('REWRITE',[status(thm)],[35017,involutory_quandle_02,38116,theory(equality)]) ).

cnf(38126,plain,
    product(a11,a135) = product(a10,a135),
    inference('REWRITE',[status(thm)],[34861,involutory_quandle,38120,theory(equality)]) ).

cnf(38131,plain,
    product(a11,a134) = a9,
    inference('REWRITE',[status(thm)],[34842,34837,38126,theory(equality)]) ).

cnf(38195,plain,
    product(a33,a29) = product(a11,a29),
    inference('REWRITE',[status(thm)],[35229,involutory_quandle,37774,theory(equality)]) ).

cnf(38197,plain,
    a39 = a38,
    inference('REWRITE',[status(thm)],[35733,involutory_quandle,37476,theory(equality)]) ).

cnf(38198,plain,
    a32 = a30,
    inference('REWRITE',[status(thm)],[knot_32,37485,38197,theory(equality)]) ).

cnf(38200,plain,
    a33 = product(a30,a13),
    inference('REWRITE',[status(thm)],[knot_33,38198,theory(equality)]) ).

cnf(38201,plain,
    product(a17,a14) = a13,
    inference('REWRITE',[status(thm)],[220,33808,38198,theory(equality)]) ).

cnf(38253,plain,
    product(product(a27,a13),product(a14,a13)) = product(a30,a1),
    inference('REWRITE',[status(thm)],[37458,involutory_quandle_02,38201,theory(equality)]) ).

cnf(38255,plain,
    product(a26,a14) = a33,
    inference('REWRITE',[status(thm)],[37832,38200,38201,theory(equality)]) ).

cnf(38256,plain,
    product(a29,a30) = a33,
    inference('REWRITE',[status(thm)],[37876,38255,theory(equality)]) ).

cnf(38277,plain,
    a20 = product(a13,a29),
    inference('REWRITE',[status(thm)],[37888,38201,theory(equality)]) ).

cnf(38395,plain,
    product(product(a29,a13),a30) = a26,
    inference('REWRITE',[status(thm)],[9335,37860,264,38198,theory(equality)]) ).

cnf(38448,plain,
    product(a11,a29) = product(a24,a20),
    inference('REWRITE',[status(thm)],[17828,37805,38395,38195,38256,264,38198,theory(equality)]) ).

cnf(38462,plain,
    a120 = product(a100,a30),
    inference('REWRITE',[status(thm)],[28670,38198,theory(equality)]) ).

cnf(38561,plain,
    a108 = a105,
    inference('REWRITE',[status(thm)],[31177,37216,38198,theory(equality)]) ).

cnf(38563,plain,
    a110 = a105,
    inference('REWRITE',[status(thm)],[30937,38561,theory(equality)]) ).

cnf(38564,plain,
    a109 = a105,
    inference('REWRITE',[status(thm)],[31044,38561,theory(equality)]) ).

cnf(38565,plain,
    a111 = a105,
    inference('REWRITE',[status(thm)],[31045,38561,theory(equality)]) ).

cnf(38567,plain,
    a105 = a112,
    inference('REWRITE',[status(thm)],[31047,38561,theory(equality)]) ).

cnf(38568,plain,
    a113 = product(a105,a33),
    inference('REWRITE',[status(thm)],[31048,38561,theory(equality)]) ).

cnf(38569,plain,
    product(a113,a33) = a105,
    inference('REWRITE',[status(thm)],[31049,38561,theory(equality)]) ).

cnf(38623,plain,
    product(product(product(a113,a131),X),a34) = product(product(a105,a131),product(X,a34)),
    inference('REWRITE',[status(thm)],[31107,38561,theory(equality)]) ).

cnf(38651,plain,
    a105 = a118,
    inference('REWRITE',[status(thm)],[31152,38561,theory(equality)]) ).

cnf(38652,plain,
    a105 = a71,
    inference('REWRITE',[status(thm)],[31161,38561,theory(equality)]) ).

cnf(38655,plain,
    a79 = a105,
    inference('REWRITE',[status(thm)],[31175,38561,theory(equality)]) ).

cnf(38656,plain,
    a105 = a119,
    inference('REWRITE',[status(thm)],[31176,38561,theory(equality)]) ).

cnf(38660,plain,
    a70 = a105,
    inference('REWRITE',[status(thm)],[31707,38561,theory(equality)]) ).

cnf(38661,plain,
    a72 = a105,
    inference('REWRITE',[status(thm)],[31708,38561,theory(equality)]) ).

cnf(38663,plain,
    a105 = a73,
    inference('REWRITE',[status(thm)],[31972,38561,theory(equality)]) ).

cnf(38664,plain,
    a82 = a105,
    inference('REWRITE',[status(thm)],[32048,38561,theory(equality)]) ).

cnf(38667,plain,
    a105 = a83,
    inference('REWRITE',[status(thm)],[32051,38561,theory(equality)]) ).

cnf(38725,plain,
    product(a102,a30) = product(a131,a33),
    inference('REWRITE',[status(thm)],[36610,38198,theory(equality)]) ).

cnf(38772,plain,
    a137 = product(a136,a38),
    inference('REWRITE',[status(thm)],[knot_137,38197,theory(equality)]) ).

cnf(38779,plain,
    product(a137,a38) = a136,
    inference('REWRITE',[status(thm)],[259,38197,theory(equality)]) ).

cnf(38785,plain,
    product(product(a137,X),a38) = product(a136,product(X,a38)),
    inference('REWRITE',[status(thm)],[1060,38197,theory(equality)]) ).

cnf(38897,plain,
    a42 = a1,
    inference('REWRITE',[status(thm)],[36364,37457,38197,theory(equality)]) ).

cnf(38898,plain,
    a44 = a1,
    inference('REWRITE',[status(thm)],[32537,38897,theory(equality)]) ).

cnf(38899,plain,
    a45 = a141,
    inference('REWRITE',[status(thm)],[32538,227,38897,theory(equality)]) ).

cnf(38900,plain,
    a23 = a21,
    inference('REWRITE',[status(thm)],[knot_23,204,38899,theory(equality)]) ).

cnf(38901,plain,
    a13 = a11,
    inference('REWRITE',[status(thm)],[knot_13,235,38900,theory(equality)]) ).

cnf(38902,plain,
    product(a14,a11) = a10,
    inference('REWRITE',[status(thm)],[2426,34768,38901,theory(equality)]) ).

cnf(38908,plain,
    a113 = product(a100,a11),
    inference('REWRITE',[status(thm)],[28210,38901,theory(equality)]) ).

cnf(38909,plain,
    a100 = product(a113,a11),
    inference('REWRITE',[status(thm)],[28296,38901,theory(equality)]) ).

cnf(38912,plain,
    product(a120,a33) = product(a101,a11),
    inference('REWRITE',[status(thm)],[28651,38901,theory(equality)]) ).

cnf(38913,plain,
    a120 = product(product(a101,a11),a33),
    inference('REWRITE',[status(thm)],[28671,38901,theory(equality)]) ).

cnf(38925,plain,
    a131 = product(a125,a11),
    inference('REWRITE',[status(thm)],[36981,38901,theory(equality)]) ).

cnf(38966,plain,
    product(a131,a1) = product(a100,product(a11,a1)),
    inference('REWRITE',[status(thm)],[37092,38901,theory(equality)]) ).

cnf(38969,plain,
    product(product(a132,a1),product(a11,a1)) = product(a100,product(product(a137,a1),product(a11,a1))),
    inference('REWRITE',[status(thm)],[37128,38901,theory(equality)]) ).

cnf(38977,plain,
    a33 = product(a30,a11),
    inference('REWRITE',[status(thm)],[38200,38901,theory(equality)]) ).

cnf(38978,plain,
    product(a17,a14) = a11,
    inference('REWRITE',[status(thm)],[38201,38901,theory(equality)]) ).

cnf(39021,plain,
    product(product(a27,a10),product(a11,a10)) = product(a30,a1),
    inference('REWRITE',[status(thm)],[38253,involutory_quandle_02,38902,38901,theory(equality)]) ).

cnf(39026,plain,
    a20 = product(a24,a20),
    inference('REWRITE',[status(thm)],[38277,38448,38901,theory(equality)]) ).

cnf(39035,plain,
    product(a29,X) = product(a17,X),
    inference('REWRITE',[status(thm)],[37812,33393,39026,theory(equality)]) ).

cnf(39049,plain,
    a17 = a26,
    inference('REWRITE',[status(thm)],[37816,involutory_quandle,39035,theory(equality)]) ).

cnf(39061,plain,
    a20 = a17,
    inference('REWRITE',[status(thm)],[33339,involutory_quandle,39049,theory(equality)]) ).

cnf(39062,plain,
    product(a21,a139) = product(product(a17,a139),a36),
    inference('REWRITE',[status(thm)],[2215,39061,theory(equality)]) ).

cnf(39072,plain,
    a21 = product(a17,a33),
    inference('REWRITE',[status(thm)],[32749,39061,theory(equality)]) ).

cnf(39073,plain,
    product(a38,a33) = product(a33,a21),
    inference('REWRITE',[status(thm)],[34818,39072,theory(equality)]) ).

cnf(39089,plain,
    product(product(X,a21),a33) = product(product(X,a17),a38),
    inference('REWRITE',[status(thm)],[32769,34783,39061,theory(equality)]) ).

cnf(39121,plain,
    product(a33,product(a33,a21)) = product(a38,a21),
    inference('REWRITE',[status(thm)],[32894,34766,39061,theory(equality)]) ).

cnf(39151,plain,
    product(a139,a17) = a137,
    inference('REWRITE',[status(thm)],[34355,39061,theory(equality)]) ).

cnf(39170,plain,
    product(a139,a137) = product(a137,product(a17,a137)),
    inference('REWRITE',[status(thm)],[34395,39061,theory(equality)]) ).

cnf(39227,plain,
    product(product(X,a139),a17) = product(product(X,a137),product(a17,a137)),
    inference('REWRITE',[status(thm)],[34549,39061,theory(equality)]) ).

cnf(39244,plain,
    product(a17,a137) = product(a14,a137),
    inference('REWRITE',[status(thm)],[34586,37820,involutory_quandle,39227,39061,theory(equality)]) ).

cnf(39246,plain,
    product(a139,a137) = product(a137,product(a14,a137)),
    inference('REWRITE',[status(thm)],[39170,39244,theory(equality)]) ).

cnf(39276,plain,
    a136 = product(product(product(a139,a137),product(a36,a137)),product(a14,a137)),
    inference('REWRITE',[status(thm)],[35231,39244,38779,39151,39089,39061,theory(equality)]) ).

cnf(39286,plain,
    a17 = a14,
    inference('REWRITE',[status(thm)],[37778,involutory_quandle,39061,theory(equality)]) ).

cnf(39330,plain,
    a18 = product(a14,a132),
    inference('REWRITE',[status(thm)],[33331,39286,theory(equality)]) ).

cnf(39331,plain,
    a19 = a14,
    inference('REWRITE',[status(thm)],[33388,39286,theory(equality)]) ).

cnf(39376,plain,
    a136 = product(a135,a30),
    inference('REWRITE',[status(thm)],[33899,involutory_quandle_01,39286,theory(equality)]) ).

cnf(39379,plain,
    a135 = product(a136,a30),
    inference('REWRITE',[status(thm)],[33919,involutory_quandle_01,39286,theory(equality)]) ).

cnf(39392,plain,
    a1 = a33,
    inference('REWRITE',[status(thm)],[34771,37457,39286,theory(equality)]) ).

cnf(39393,plain,
    a34 = product(a1,a131),
    inference('REWRITE',[status(thm)],[knot_34,39392,theory(equality)]) ).

cnf(39394,plain,
    product(a34,a131) = a1,
    inference('REWRITE',[status(thm)],[191,39392,theory(equality)]) ).

cnf(39399,plain,
    product(product(X,a1),a131) = product(product(X,a131),a34),
    inference('REWRITE',[status(thm)],[615,39392,theory(equality)]) ).

cnf(39435,plain,
    a35 = a1,
    inference('REWRITE',[status(thm)],[32748,39392,theory(equality)]) ).

cnf(39436,plain,
    a36 = product(a1,a139),
    inference('REWRITE',[status(thm)],[32751,39392,theory(equality)]) ).

cnf(39437,plain,
    product(a36,a139) = a1,
    inference('REWRITE',[status(thm)],[32752,39392,theory(equality)]) ).

cnf(39441,plain,
    product(product(X,a1),a139) = product(product(X,a139),a36),
    inference('REWRITE',[status(thm)],[32761,39392,theory(equality)]) ).

cnf(39445,plain,
    product(a36,a1) = product(a1,product(a139,a1)),
    inference('REWRITE',[status(thm)],[32775,39392,theory(equality)]) ).

cnf(39471,plain,
    a37 = a1,
    inference('REWRITE',[status(thm)],[34763,39392,theory(equality)]) ).

cnf(39472,plain,
    a11 = product(a10,a1),
    inference('REWRITE',[status(thm)],[34764,39392,theory(equality)]) ).

cnf(39473,plain,
    a135 = product(a134,a1),
    inference('REWRITE',[status(thm)],[34767,39392,theory(equality)]) ).

cnf(39474,plain,
    product(a11,a1) = a10,
    inference('REWRITE',[status(thm)],[34768,39392,theory(equality)]) ).

cnf(39476,plain,
    product(a131,a1) = product(a100,a10),
    inference('REWRITE',[status(thm)],[38966,39474,theory(equality)]) ).

cnf(39478,plain,
    product(product(a132,a1),a10) = product(a100,product(product(a137,a1),a10)),
    inference('REWRITE',[status(thm)],[38969,39474,theory(equality)]) ).

cnf(39479,plain,
    product(a135,a1) = a134,
    inference('REWRITE',[status(thm)],[34770,39392,theory(equality)]) ).

cnf(39487,plain,
    product(product(X,a11),a1) = product(product(X,a1),a10),
    inference('REWRITE',[status(thm)],[34786,39392,theory(equality)]) ).

cnf(39492,plain,
    product(a11,a10) = product(a10,product(a1,a10)),
    inference('REWRITE',[status(thm)],[34802,39392,theory(equality)]) ).

cnf(39568,plain,
    a8 = a1,
    inference('REWRITE',[status(thm)],[37774,39392,theory(equality)]) ).

cnf(39569,plain,
    product(a132,a1) = product(a135,a27),
    inference('REWRITE',[status(thm)],[37992,39392,theory(equality)]) ).

cnf(39574,plain,
    a9 = product(a1,a134),
    inference('REWRITE',[status(thm)],[38101,39392,theory(equality)]) ).

cnf(39634,plain,
    a113 = product(a105,a1),
    inference('REWRITE',[status(thm)],[38568,39392,theory(equality)]) ).

cnf(39636,plain,
    product(a113,a1) = a105,
    inference('REWRITE',[status(thm)],[38569,39392,theory(equality)]) ).

cnf(39672,plain,
    product(a102,a30) = product(a100,a10),
    inference('REWRITE',[status(thm)],[38725,39476,39392,theory(equality)]) ).

cnf(39693,plain,
    product(a120,a1) = product(a101,a11),
    inference('REWRITE',[status(thm)],[38912,39392,theory(equality)]) ).

cnf(39695,plain,
    a120 = product(product(a101,a1),a10),
    inference('REWRITE',[status(thm)],[38913,39487,39392,theory(equality)]) ).

cnf(39704,plain,
    a1 = product(a30,a11),
    inference('REWRITE',[status(thm)],[38977,39392,theory(equality)]) ).

cnf(39707,plain,
    product(a38,a1) = product(a1,a21),
    inference('REWRITE',[status(thm)],[39073,39392,theory(equality)]) ).

cnf(39708,plain,
    product(product(product(a1,a21),a100),product(product(a14,a1),a100)) = a43,
    inference('REWRITE',[status(thm)],[37456,39707,theory(equality)]) ).

cnf(39712,plain,
    product(a1,product(a1,a21)) = product(a38,a21),
    inference('REWRITE',[status(thm)],[39121,39392,theory(equality)]) ).

cnf(39754,plain,
    a14 = a11,
    inference('REWRITE',[status(thm)],[38978,involutory_quandle,39286,theory(equality)]) ).

cnf(39755,plain,
    a101 = a113,
    inference('REWRITE',[status(thm)],[knot_101,38908,39754,theory(equality)]) ).

cnf(39756,plain,
    a78 = a101,
    inference('REWRITE',[status(thm)],[27287,39755,theory(equality)]) ).

cnf(39761,plain,
    product(product(product(a101,a131),X),a34) = product(product(a105,a131),product(X,a34)),
    inference('REWRITE',[status(thm)],[38623,39755,theory(equality)]) ).

cnf(39765,plain,
    a100 = product(a101,a11),
    inference('REWRITE',[status(thm)],[38909,39755,theory(equality)]) ).

cnf(39766,plain,
    product(a120,a1) = a100,
    inference('REWRITE',[status(thm)],[39693,39765,theory(equality)]) ).

cnf(39774,plain,
    a101 = product(a105,a1),
    inference('REWRITE',[status(thm)],[39634,39755,theory(equality)]) ).

cnf(39775,plain,
    product(a101,a1) = a105,
    inference('REWRITE',[status(thm)],[39636,39755,theory(equality)]) ).

cnf(39776,plain,
    a120 = product(a105,a10),
    inference('REWRITE',[status(thm)],[39695,39775,theory(equality)]) ).

cnf(39811,plain,
    a1 = a29,
    inference('REWRITE',[status(thm)],[264,39704,39754,theory(equality)]) ).

cnf(39812,plain,
    a136 = a134,
    inference('REWRITE',[status(thm)],[knot_136,39479,39811,theory(equality)]) ).

cnf(39845,plain,
    a134 = a53,
    inference('REWRITE',[status(thm)],[33754,39812,theory(equality)]) ).

cnf(39846,plain,
    a134 = a52,
    inference('REWRITE',[status(thm)],[34039,39812,theory(equality)]) ).

cnf(39847,plain,
    product(a9,a15) = a6,
    inference('REWRITE',[status(thm)],[35976,39574,39812,theory(equality)]) ).

cnf(39854,plain,
    product(a6,a134) = a38,
    inference('REWRITE',[status(thm)],[37543,39812,theory(equality)]) ).

cnf(39886,plain,
    a137 = product(a134,a38),
    inference('REWRITE',[status(thm)],[38772,39812,theory(equality)]) ).

cnf(39895,plain,
    product(product(a137,X),a38) = product(a134,product(X,a38)),
    inference('REWRITE',[status(thm)],[38785,39812,theory(equality)]) ).

cnf(39974,plain,
    a134 = product(a135,a30),
    inference('REWRITE',[status(thm)],[39376,39812,theory(equality)]) ).

cnf(39975,plain,
    a135 = product(a134,a30),
    inference('REWRITE',[status(thm)],[39379,39812,theory(equality)]) ).

cnf(40056,plain,
    a15 = a9,
    inference('REWRITE',[status(thm)],[33755,38131,39812,39754,theory(equality)]) ).

cnf(40057,plain,
    a10 = product(a15,a134),
    inference('REWRITE',[status(thm)],[knot_10,40056,theory(equality)]) ).

cnf(40094,plain,
    a15 = product(a1,a134),
    inference('REWRITE',[status(thm)],[39574,40056,theory(equality)]) ).

cnf(40119,plain,
    a15 = a6,
    inference('REWRITE',[status(thm)],[39847,involutory_quandle,40056,theory(equality)]) ).

cnf(40152,plain,
    a10 = a38,
    inference('REWRITE',[status(thm)],[39854,40057,40119,theory(equality)]) ).

cnf(40153,plain,
    a10 = a40,
    inference('REWRITE',[status(thm)],[35736,40152,theory(equality)]) ).

cnf(40154,plain,
    a102 = product(a101,a10),
    inference('REWRITE',[status(thm)],[35750,40152,theory(equality)]) ).

cnf(40155,plain,
    product(a102,a10) = a101,
    inference('REWRITE',[status(thm)],[35751,40152,theory(equality)]) ).

cnf(40190,plain,
    a4 = a10,
    inference('REWRITE',[status(thm)],[37476,40152,theory(equality)]) ).

cnf(40191,plain,
    product(a31,a10) = a30,
    inference('REWRITE',[status(thm)],[37485,40152,theory(equality)]) ).

cnf(40192,plain,
    product(a30,a10) = a31,
    inference('REWRITE',[status(thm)],[37486,40152,theory(equality)]) ).

cnf(40193,plain,
    product(a106,a10) = a105,
    inference('REWRITE',[status(thm)],[37488,40152,theory(equality)]) ).

cnf(40194,plain,
    a120 = a106,
    inference('REWRITE',[status(thm)],[37489,39776,40152,theory(equality)]) ).

cnf(40195,plain,
    a69 = a106,
    inference('REWRITE',[status(thm)],[30912,40194,theory(equality)]) ).

cnf(40197,plain,
    a106 = product(a100,a30),
    inference('REWRITE',[status(thm)],[38462,40194,theory(equality)]) ).

cnf(40269,plain,
    product(a106,a1) = a100,
    inference('REWRITE',[status(thm)],[39766,40194,theory(equality)]) ).

cnf(40279,plain,
    a10 = a5,
    inference('REWRITE',[status(thm)],[37492,40152,theory(equality)]) ).

cnf(40305,plain,
    product(a30,a31) = product(a31,product(a10,a31)),
    inference('REWRITE',[status(thm)],[37628,40152,theory(equality)]) ).

cnf(40353,plain,
    a7 = a10,
    inference('REWRITE',[status(thm)],[37773,40152,theory(equality)]) ).

cnf(40354,plain,
    a39 = a10,
    inference('REWRITE',[status(thm)],[38197,40152,theory(equality)]) ).

cnf(40379,plain,
    a11 = product(a1,a21),
    inference('REWRITE',[status(thm)],[39707,39472,40152,theory(equality)]) ).

cnf(40383,plain,
    product(a1,a11) = product(a10,a21),
    inference('REWRITE',[status(thm)],[39712,40379,40152,theory(equality)]) ).

cnf(40385,plain,
    a137 = product(a134,a10),
    inference('REWRITE',[status(thm)],[39886,40152,theory(equality)]) ).

cnf(40408,plain,
    product(product(a137,X),a10) = product(a134,product(X,a10)),
    inference('REWRITE',[status(thm)],[39895,40152,theory(equality)]) ).

cnf(40409,plain,
    product(product(a132,a1),a10) = product(a100,product(a134,product(a1,a10))),
    inference('REWRITE',[status(thm)],[39478,40408,theory(equality)]) ).

cnf(40428,plain,
    a16 = a11,
    inference('REWRITE',[status(thm)],[33776,39754,theory(equality)]) ).

cnf(40429,plain,
    a11 = a10,
    inference('REWRITE',[status(thm)],[33777,40057,39812,39754,theory(equality)]) ).

cnf(40430,plain,
    a12 = product(a10,a21),
    inference('REWRITE',[status(thm)],[knot_12,40429,theory(equality)]) ).

cnf(40448,plain,
    product(product(a10,a12),a21) = product(a12,a10),
    inference('REWRITE',[status(thm)],[4929,40429,theory(equality)]) ).

cnf(40509,plain,
    a141 = product(a139,a10),
    inference('REWRITE',[status(thm)],[35261,40429,theory(equality)]) ).

cnf(40510,plain,
    product(a141,a10) = a139,
    inference('REWRITE',[status(thm)],[36824,40429,theory(equality)]) ).

cnf(40522,plain,
    product(a141,a139) = product(a139,product(a10,a139)),
    inference('REWRITE',[status(thm)],[36839,40429,theory(equality)]) ).

cnf(40528,plain,
    product(product(X,a10),a139) = product(product(X,product(a10,a139)),product(a141,a139)),
    inference('REWRITE',[status(thm)],[36845,40429,theory(equality)]) ).

cnf(40558,plain,
    product(product(product(X,a10),a139),product(a22,a10)) = product(product(product(X,a12),a139),product(a21,a139)),
    inference('REWRITE',[status(thm)],[36881,40429,theory(equality)]) ).

cnf(40569,plain,
    product(product(a1,a10),a139) = product(a139,product(a22,a10)),
    inference('REWRITE',[status(thm)],[36916,40429,theory(equality)]) ).

cnf(40581,plain,
    a13 = a10,
    inference('REWRITE',[status(thm)],[38901,40429,theory(equality)]) ).

cnf(40582,plain,
    a131 = product(a125,a10),
    inference('REWRITE',[status(thm)],[38925,40429,theory(equality)]) ).

cnf(40623,plain,
    a27 = product(a30,a1),
    inference('REWRITE',[status(thm)],[39021,involutory_quandle_01,involutory_quandle,40429,theory(equality)]) ).

cnf(40626,plain,
    product(a10,a1) = a10,
    inference('REWRITE',[status(thm)],[39474,40429,theory(equality)]) ).

cnf(40632,plain,
    a10 = product(a10,product(a1,a10)),
    inference('REWRITE',[status(thm)],[39492,involutory_quandle,40429,theory(equality)]) ).

cnf(40654,plain,
    a1 = a31,
    inference('REWRITE',[status(thm)],[39704,40192,40429,theory(equality)]) ).

cnf(40655,plain,
    a102 = a100,
    inference('REWRITE',[status(thm)],[35677,40269,40654,theory(equality)]) ).

cnf(40656,plain,
    a88 = a100,
    inference('REWRITE',[status(thm)],[31905,40655,theory(equality)]) ).

cnf(40657,plain,
    a106 = product(a100,a10),
    inference('REWRITE',[status(thm)],[39672,40197,40655,theory(equality)]) ).

cnf(40681,plain,
    a100 = product(a101,a10),
    inference('REWRITE',[status(thm)],[40154,40655,theory(equality)]) ).

cnf(40682,plain,
    a106 = a101,
    inference('REWRITE',[status(thm)],[40155,40657,40655,theory(equality)]) ).

cnf(40683,plain,
    a107 = a101,
    inference('REWRITE',[status(thm)],[31187,40682,theory(equality)]) ).

cnf(40684,plain,
    a101 = a84,
    inference('REWRITE',[status(thm)],[32026,40682,theory(equality)]) ).

cnf(40685,plain,
    a100 = a105,
    inference('REWRITE',[status(thm)],[40193,40681,40682,theory(equality)]) ).

cnf(40686,plain,
    a100 = a85,
    inference('REWRITE',[status(thm)],[31730,40685,theory(equality)]) ).

cnf(40751,plain,
    a108 = a100,
    inference('REWRITE',[status(thm)],[38561,40685,theory(equality)]) ).

cnf(40752,plain,
    a110 = a100,
    inference('REWRITE',[status(thm)],[38563,40685,theory(equality)]) ).

cnf(40753,plain,
    a109 = a100,
    inference('REWRITE',[status(thm)],[38564,40685,theory(equality)]) ).

cnf(40754,plain,
    a111 = a100,
    inference('REWRITE',[status(thm)],[38565,40685,theory(equality)]) ).

cnf(40755,plain,
    a100 = a112,
    inference('REWRITE',[status(thm)],[38567,40685,theory(equality)]) ).

cnf(40756,plain,
    a100 = a118,
    inference('REWRITE',[status(thm)],[38651,40685,theory(equality)]) ).

cnf(40757,plain,
    a100 = a71,
    inference('REWRITE',[status(thm)],[38652,40685,theory(equality)]) ).

cnf(40758,plain,
    a79 = a100,
    inference('REWRITE',[status(thm)],[38655,40685,theory(equality)]) ).

cnf(40759,plain,
    a100 = a119,
    inference('REWRITE',[status(thm)],[38656,40685,theory(equality)]) ).

cnf(40760,plain,
    a70 = a100,
    inference('REWRITE',[status(thm)],[38660,40685,theory(equality)]) ).

cnf(40761,plain,
    a72 = a100,
    inference('REWRITE',[status(thm)],[38661,40685,theory(equality)]) ).

cnf(40762,plain,
    a100 = a73,
    inference('REWRITE',[status(thm)],[38663,40685,theory(equality)]) ).

cnf(40763,plain,
    a82 = a100,
    inference('REWRITE',[status(thm)],[38664,40685,theory(equality)]) ).

cnf(40766,plain,
    a100 = a83,
    inference('REWRITE',[status(thm)],[38667,40685,theory(equality)]) ).

cnf(40773,plain,
    product(product(product(a101,a131),X),a34) = product(product(a100,a131),product(X,a34)),
    inference('REWRITE',[status(thm)],[39761,40685,theory(equality)]) ).

cnf(40775,plain,
    a101 = a125,
    inference('REWRITE',[status(thm)],[39774,36428,40685,theory(equality)]) ).

cnf(40776,plain,
    a101 = a65,
    inference('REWRITE',[status(thm)],[32180,40775,theory(equality)]) ).

cnf(40777,plain,
    a126 = a101,
    inference('REWRITE',[status(thm)],[32181,40775,theory(equality)]) ).

cnf(40778,plain,
    a93 = a101,
    inference('REWRITE',[status(thm)],[32477,40775,theory(equality)]) ).

cnf(40779,plain,
    product(a101,a100) = product(a100,product(a1,a100)),
    inference('REWRITE',[status(thm)],[36421,40775,theory(equality)]) ).

cnf(40783,plain,
    a101 = a97,
    inference('REWRITE',[status(thm)],[36427,40775,theory(equality)]) ).

cnf(40784,plain,
    product(a100,a1) = a101,
    inference('REWRITE',[status(thm)],[36428,40775,theory(equality)]) ).

cnf(40788,plain,
    a100 = product(a101,a1),
    inference('REWRITE',[status(thm)],[36433,40775,theory(equality)]) ).

cnf(40793,plain,
    a101 = a130,
    inference('REWRITE',[status(thm)],[36980,40775,theory(equality)]) ).

cnf(40826,plain,
    a101 = a61,
    inference('REWRITE',[status(thm)],[37395,40775,theory(equality)]) ).

cnf(40827,plain,
    a101 = a89,
    inference('REWRITE',[status(thm)],[37402,40775,theory(equality)]) ).

cnf(40832,plain,
    a131 = a100,
    inference('REWRITE',[status(thm)],[40582,40681,40775,theory(equality)]) ).

cnf(40843,plain,
    a100 = a60,
    inference('REWRITE',[status(thm)],[32747,40832,theory(equality)]) ).

cnf(40844,plain,
    a100 = a59,
    inference('REWRITE',[status(thm)],[33069,40832,theory(equality)]) ).

cnf(40845,plain,
    a50 = product(a137,a100),
    inference('REWRITE',[status(thm)],[34330,40832,theory(equality)]) ).

cnf(40846,plain,
    product(a50,a100) = a137,
    inference('REWRITE',[status(thm)],[34333,40832,theory(equality)]) ).

cnf(40847,plain,
    a132 = product(a100,a137),
    inference('REWRITE',[status(thm)],[34351,40832,theory(equality)]) ).

cnf(40848,plain,
    product(a132,a137) = a100,
    inference('REWRITE',[status(thm)],[34354,40832,theory(equality)]) ).

cnf(40914,plain,
    a34 = product(a1,a100),
    inference('REWRITE',[status(thm)],[39393,40832,theory(equality)]) ).

cnf(40915,plain,
    product(a101,a100) = product(a100,a34),
    inference('REWRITE',[status(thm)],[40779,40914,theory(equality)]) ).

cnf(40925,plain,
    product(a34,a100) = a1,
    inference('REWRITE',[status(thm)],[39394,40832,theory(equality)]) ).

cnf(40928,plain,
    product(product(X,a1),a100) = product(product(X,a100),a34),
    inference('REWRITE',[status(thm)],[39399,40832,theory(equality)]) ).

cnf(40944,plain,
    product(product(product(a101,a100),X),a34) = product(a100,product(X,a34)),
    inference('REWRITE',[status(thm)],[40773,involutory_quandle,40832,theory(equality)]) ).

cnf(40988,plain,
    a120 = a101,
    inference('REWRITE',[status(thm)],[40194,40682,theory(equality)]) ).

cnf(40989,plain,
    a69 = a101,
    inference('REWRITE',[status(thm)],[40195,40682,theory(equality)]) ).

cnf(41020,plain,
    product(a1,a10) = a30,
    inference('REWRITE',[status(thm)],[40191,40654,theory(equality)]) ).

cnf(41022,plain,
    product(product(a132,a1),a10) = product(a100,a135),
    inference('REWRITE',[status(thm)],[40409,39975,41020,theory(equality)]) ).

cnf(41023,plain,
    product(a30,a139) = product(a139,product(a22,a10)),
    inference('REWRITE',[status(thm)],[40569,41020,theory(equality)]) ).

cnf(41030,plain,
    a10 = product(a10,a30),
    inference('REWRITE',[status(thm)],[40632,41020,theory(equality)]) ).

cnf(41047,plain,
    product(a30,a10) = a1,
    inference('REWRITE',[status(thm)],[40192,40654,theory(equality)]) ).

cnf(41061,plain,
    a27 = a30,
    inference('REWRITE',[status(thm)],[40305,41020,40626,40623,40654,theory(equality)]) ).

cnf(41063,plain,
    a32 = a27,
    inference('REWRITE',[status(thm)],[38198,41061,theory(equality)]) ).

cnf(41066,plain,
    a134 = product(a132,a1),
    inference('REWRITE',[status(thm)],[39974,39569,41061,theory(equality)]) ).

cnf(41068,plain,
    a137 = product(a100,a135),
    inference('REWRITE',[status(thm)],[41022,40385,41066,theory(equality)]) ).

cnf(41138,plain,
    product(a1,a10) = a27,
    inference('REWRITE',[status(thm)],[41020,41061,theory(equality)]) ).

cnf(41140,plain,
    product(a27,a139) = product(a139,product(a22,a10)),
    inference('REWRITE',[status(thm)],[41023,41061,theory(equality)]) ).

cnf(41145,plain,
    a10 = product(a10,a27),
    inference('REWRITE',[status(thm)],[41030,41061,theory(equality)]) ).

cnf(41163,plain,
    product(a27,a10) = a1,
    inference('REWRITE',[status(thm)],[41047,41061,theory(equality)]) ).

cnf(41182,plain,
    a14 = a10,
    inference('REWRITE',[status(thm)],[39754,40429,theory(equality)]) ).

cnf(41190,plain,
    a10 = product(a1,a21),
    inference('REWRITE',[status(thm)],[40379,40429,theory(equality)]) ).

cnf(41193,plain,
    a27 = a12,
    inference('REWRITE',[status(thm)],[40383,40430,41138,40429,theory(equality)]) ).

cnf(41199,plain,
    a12 = a30,
    inference('REWRITE',[status(thm)],[41061,41193,theory(equality)]) ).

cnf(41201,plain,
    a32 = a12,
    inference('REWRITE',[status(thm)],[41063,41193,theory(equality)]) ).

cnf(41277,plain,
    product(a12,a139) = product(a139,product(a22,a10)),
    inference('REWRITE',[status(thm)],[41140,41193,theory(equality)]) ).

cnf(41282,plain,
    a10 = product(a10,a12),
    inference('REWRITE',[status(thm)],[41145,41193,theory(equality)]) ).

cnf(41283,plain,
    a12 = product(a12,a10),
    inference('REWRITE',[status(thm)],[40448,40430,41282,theory(equality)]) ).

cnf(41313,plain,
    a12 = a1,
    inference('REWRITE',[status(thm)],[41163,41283,41193,theory(equality)]) ).

cnf(41369,plain,
    product(product(product(X,a10),a139),product(a22,a10)) = product(product(product(X,a1),a139),product(a21,a139)),
    inference('REWRITE',[status(thm)],[40558,41313,theory(equality)]) ).

cnf(41370,plain,
    a27 = a1,
    inference('REWRITE',[status(thm)],[41193,41313,theory(equality)]) ).

cnf(41374,plain,
    a1 = a30,
    inference('REWRITE',[status(thm)],[41199,41313,theory(equality)]) ).

cnf(41375,plain,
    a32 = a1,
    inference('REWRITE',[status(thm)],[41201,41313,theory(equality)]) ).

cnf(41381,plain,
    a36 = product(a139,product(a22,a10)),
    inference('REWRITE',[status(thm)],[41277,39436,41313,theory(equality)]) ).

cnf(41414,plain,
    a16 = a10,
    inference('REWRITE',[status(thm)],[40428,40429,theory(equality)]) ).

cnf(41423,plain,
    a1 = a10,
    inference('REWRITE',[status(thm)],[37457,involutory_quandle,40429,40152,39754,theory(equality)]) ).

cnf(41446,plain,
    a1 = a38,
    inference('REWRITE',[status(thm)],[40152,41423,theory(equality)]) ).

cnf(41447,plain,
    a1 = a40,
    inference('REWRITE',[status(thm)],[40153,41423,theory(equality)]) ).

cnf(41448,plain,
    a4 = a1,
    inference('REWRITE',[status(thm)],[40190,41423,theory(equality)]) ).

cnf(41449,plain,
    a1 = a5,
    inference('REWRITE',[status(thm)],[40279,41423,theory(equality)]) ).

cnf(41450,plain,
    a7 = a1,
    inference('REWRITE',[status(thm)],[40353,41423,theory(equality)]) ).

cnf(41451,plain,
    a39 = a1,
    inference('REWRITE',[status(thm)],[40354,41423,theory(equality)]) ).

cnf(41458,plain,
    a137 = a135,
    inference('REWRITE',[status(thm)],[40385,39473,41423,theory(equality)]) ).

cnf(41459,plain,
    a135 = a49,
    inference('REWRITE',[status(thm)],[34326,41458,theory(equality)]) ).

cnf(41460,plain,
    a25 = product(a24,a135),
    inference('REWRITE',[status(thm)],[34327,41458,theory(equality)]) ).

cnf(41461,plain,
    a135 = a138,
    inference('REWRITE',[status(thm)],[34349,41458,theory(equality)]) ).

cnf(41468,plain,
    product(a50,X) = product(product(product(a135,a132),X),product(a135,X)),
    inference('REWRITE',[status(thm)],[34459,41458,theory(equality)]) ).

cnf(41473,plain,
    a135 = a48,
    inference('REWRITE',[status(thm)],[34609,41458,theory(equality)]) ).

cnf(41477,plain,
    a50 = product(a135,a100),
    inference('REWRITE',[status(thm)],[40845,41458,theory(equality)]) ).

cnf(41478,plain,
    product(a50,a100) = a135,
    inference('REWRITE',[status(thm)],[40846,41458,theory(equality)]) ).

cnf(41479,plain,
    a132 = product(a100,a135),
    inference('REWRITE',[status(thm)],[40847,41458,theory(equality)]) ).

cnf(41480,plain,
    product(a132,a135) = a100,
    inference('REWRITE',[status(thm)],[40848,41458,theory(equality)]) ).

cnf(41543,plain,
    a135 = a132,
    inference('REWRITE',[status(thm)],[41068,41479,41458,theory(equality)]) ).

cnf(41544,plain,
    a132 = a55,
    inference('REWRITE',[status(thm)],[33750,41543,theory(equality)]) ).

cnf(41545,plain,
    a132 = a54,
    inference('REWRITE',[status(thm)],[33752,41543,theory(equality)]) ).

cnf(41577,plain,
    a137 = a132,
    inference('REWRITE',[status(thm)],[41458,41543,theory(equality)]) ).

cnf(41578,plain,
    a132 = a49,
    inference('REWRITE',[status(thm)],[41459,41543,theory(equality)]) ).

cnf(41579,plain,
    a25 = product(a24,a132),
    inference('REWRITE',[status(thm)],[41460,41543,theory(equality)]) ).

cnf(41580,plain,
    a132 = a138,
    inference('REWRITE',[status(thm)],[41461,41543,theory(equality)]) ).

cnf(41586,plain,
    product(a50,X) = product(a132,X),
    inference('REWRITE',[status(thm)],[41468,involutory_quandle,41543,theory(equality)]) ).

cnf(41595,plain,
    a132 = a48,
    inference('REWRITE',[status(thm)],[41473,41543,theory(equality)]) ).

cnf(41599,plain,
    a50 = product(a132,a100),
    inference('REWRITE',[status(thm)],[41477,41543,theory(equality)]) ).

cnf(41602,plain,
    a50 = a132,
    inference('REWRITE',[status(thm)],[41478,41599,41586,41543,theory(equality)]) ).

cnf(41612,plain,
    a132 = a100,
    inference('REWRITE',[status(thm)],[41480,involutory_quandle,41543,theory(equality)]) ).

cnf(41613,plain,
    a100 = a58,
    inference('REWRITE',[status(thm)],[33314,41612,theory(equality)]) ).

cnf(41614,plain,
    a133 = a100,
    inference('REWRITE',[status(thm)],[33330,41612,theory(equality)]) ).

cnf(41616,plain,
    a134 = a101,
    inference('REWRITE',[status(thm)],[41066,40784,41612,theory(equality)]) ).

cnf(41617,plain,
    a101 = a57,
    inference('REWRITE',[status(thm)],[33745,41616,theory(equality)]) ).

cnf(41618,plain,
    a101 = a56,
    inference('REWRITE',[status(thm)],[33747,41616,theory(equality)]) ).

cnf(41619,plain,
    a136 = a101,
    inference('REWRITE',[status(thm)],[39812,41616,theory(equality)]) ).

cnf(41620,plain,
    a101 = a53,
    inference('REWRITE',[status(thm)],[39845,41616,theory(equality)]) ).

cnf(41621,plain,
    a101 = a52,
    inference('REWRITE',[status(thm)],[39846,41616,theory(equality)]) ).

cnf(41622,plain,
    a15 = product(a1,a101),
    inference('REWRITE',[status(thm)],[40094,41616,theory(equality)]) ).

cnf(41675,plain,
    a135 = a100,
    inference('REWRITE',[status(thm)],[41543,41612,theory(equality)]) ).

cnf(41676,plain,
    a100 = a55,
    inference('REWRITE',[status(thm)],[41544,41612,theory(equality)]) ).

cnf(41677,plain,
    a100 = a54,
    inference('REWRITE',[status(thm)],[41545,41612,theory(equality)]) ).

cnf(41685,plain,
    a137 = a100,
    inference('REWRITE',[status(thm)],[41577,41612,theory(equality)]) ).

cnf(41686,plain,
    a100 = a49,
    inference('REWRITE',[status(thm)],[41578,41612,theory(equality)]) ).

cnf(41687,plain,
    a25 = product(a24,a100),
    inference('REWRITE',[status(thm)],[41579,41612,theory(equality)]) ).

cnf(41688,plain,
    a100 = a138,
    inference('REWRITE',[status(thm)],[41580,41612,theory(equality)]) ).

cnf(41690,plain,
    a100 = a48,
    inference('REWRITE',[status(thm)],[41595,41612,theory(equality)]) ).

cnf(41694,plain,
    a50 = a100,
    inference('REWRITE',[status(thm)],[41602,41612,theory(equality)]) ).

cnf(41716,plain,
    a11 = a1,
    inference('REWRITE',[status(thm)],[40429,41423,theory(equality)]) ).

cnf(41717,plain,
    a141 = product(a139,a1),
    inference('REWRITE',[status(thm)],[40509,41423,theory(equality)]) ).

cnf(41718,plain,
    product(a36,a1) = product(a1,a141),
    inference('REWRITE',[status(thm)],[39445,41717,theory(equality)]) ).

cnf(41726,plain,
    product(a141,a1) = a139,
    inference('REWRITE',[status(thm)],[40510,41423,theory(equality)]) ).

cnf(41746,plain,
    product(a141,a139) = product(a139,a36),
    inference('REWRITE',[status(thm)],[40522,39436,41423,theory(equality)]) ).

cnf(41759,plain,
    product(product(X,a1),a139) = product(product(X,a36),product(a141,a139)),
    inference('REWRITE',[status(thm)],[40528,39436,41423,theory(equality)]) ).

cnf(41802,plain,
    a13 = a1,
    inference('REWRITE',[status(thm)],[40581,41423,theory(equality)]) ).

cnf(41803,plain,
    a14 = a1,
    inference('REWRITE',[status(thm)],[41182,41423,theory(equality)]) ).

cnf(41808,plain,
    a1 = product(a1,a21),
    inference('REWRITE',[status(thm)],[41190,41423,theory(equality)]) ).

cnf(41838,plain,
    product(product(product(X,a1),a139),product(a22,a1)) = product(product(product(X,a1),a139),product(a21,a139)),
    inference('REWRITE',[status(thm)],[41369,41423,theory(equality)]) ).

cnf(41839,plain,
    a36 = product(a139,product(a22,a1)),
    inference('REWRITE',[status(thm)],[41381,41423,theory(equality)]) ).

cnf(41845,plain,
    a16 = a1,
    inference('REWRITE',[status(thm)],[41414,41423,theory(equality)]) ).

cnf(41847,plain,
    product(a139,a100) = product(a101,a100),
    inference('REWRITE',[status(thm)],[39246,40915,40914,41716,41685,39754,theory(equality)]) ).

cnf(41853,plain,
    a101 = product(a100,product(product(a1,a141),a100)),
    inference('REWRITE',[status(thm)],[39276,41718,40928,40944,40914,41716,41847,41685,41619,39754,theory(equality)]) ).

cnf(41855,plain,
    a17 = a1,
    inference('REWRITE',[status(thm)],[39286,41716,39754,theory(equality)]) ).

cnf(41857,plain,
    a18 = a34,
    inference('REWRITE',[status(thm)],[39330,40914,41612,41716,39754,theory(equality)]) ).

cnf(41858,plain,
    a18 = product(a1,a100),
    inference('REWRITE',[status(thm)],[40914,41857,theory(equality)]) ).

cnf(41859,plain,
    product(a101,a100) = product(a100,a18),
    inference('REWRITE',[status(thm)],[40915,41857,theory(equality)]) ).

cnf(41865,plain,
    product(a18,a100) = a1,
    inference('REWRITE',[status(thm)],[40925,41857,theory(equality)]) ).

cnf(41921,plain,
    a19 = a1,
    inference('REWRITE',[status(thm)],[39331,41716,39754,theory(equality)]) ).

cnf(41922,plain,
    a18 = a43,
    inference('REWRITE',[status(thm)],[39708,involutory_quandle,41716,41858,41808,39754,theory(equality)]) ).

cnf(41923,plain,
    a1 = a26,
    inference('REWRITE',[status(thm)],[39049,41803,39286,theory(equality)]) ).

cnf(41924,plain,
    a20 = a1,
    inference('REWRITE',[status(thm)],[39061,41803,39286,theory(equality)]) ).

cnf(41925,plain,
    product(a21,a139) = a36,
    inference('REWRITE',[status(thm)],[39062,involutory_quandle,39436,41803,39286,theory(equality)]) ).

cnf(41926,plain,
    product(product(product(X,a1),a139),product(a22,a1)) = product(X,a139),
    inference('REWRITE',[status(thm)],[41838,involutory_quandle_01,39441,41925,theory(equality)]) ).

cnf(41927,plain,
    a21 = a1,
    inference('REWRITE',[status(thm)],[39072,involutory_quandle,39392,41803,39286,theory(equality)]) ).

cnf(41928,plain,
    a22 = product(a1,a141),
    inference('REWRITE',[status(thm)],[knot_22,41927,theory(equality)]) ).

cnf(41952,plain,
    a101 = product(a100,product(a22,a100)),
    inference('REWRITE',[status(thm)],[41853,41928,theory(equality)]) ).

cnf(41961,plain,
    product(a22,a1) = a36,
    inference('REWRITE',[status(thm)],[2173,39436,41726,41927,theory(equality)]) ).

cnf(41962,plain,
    a36 = product(a141,a139),
    inference('REWRITE',[status(thm)],[41839,41746,41961,theory(equality)]) ).

cnf(41963,plain,
    a36 = product(a139,a36),
    inference('REWRITE',[status(thm)],[41746,41962,theory(equality)]) ).

cnf(41970,plain,
    product(product(X,a1),a139) = X,
    inference('REWRITE',[status(thm)],[41759,involutory_quandle_01,41962,theory(equality)]) ).

cnf(41989,plain,
    product(X,a36) = product(X,a139),
    inference('REWRITE',[status(thm)],[41926,41970,41961,theory(equality)]) ).

cnf(41992,plain,
    a36 = a139,
    inference('REWRITE',[status(thm)],[41963,involutory_quandle,41989,theory(equality)]) ).

cnf(41994,plain,
    a139 = a1,
    inference('REWRITE',[status(thm)],[39437,involutory_quandle,41992,theory(equality)]) ).

cnf(41995,plain,
    a47 = a1,
    inference('REWRITE',[status(thm)],[34762,41994,theory(equality)]) ).

cnf(41996,plain,
    a140 = a1,
    inference('REWRITE',[status(thm)],[35260,41994,theory(equality)]) ).

cnf(41997,plain,
    a141 = a1,
    inference('REWRITE',[status(thm)],[41717,involutory_quandle,41994,theory(equality)]) ).

cnf(42003,plain,
    a45 = a1,
    inference('REWRITE',[status(thm)],[38899,41997,theory(equality)]) ).

cnf(42005,plain,
    a22 = a1,
    inference('REWRITE',[status(thm)],[41928,involutory_quandle,41997,theory(equality)]) ).

cnf(42006,plain,
    a101 = product(a101,a100),
    inference('REWRITE',[status(thm)],[41952,41859,41858,42005,theory(equality)]) ).

cnf(42044,plain,
    a18 = a101,
    inference('REWRITE',[status(thm)],[41847,42006,41858,41994,theory(equality)]) ).

cnf(42045,plain,
    a101 = a34,
    inference('REWRITE',[status(thm)],[41857,42044,theory(equality)]) ).

cnf(42047,plain,
    a101 = a1,
    inference('REWRITE',[status(thm)],[41865,42006,42044,theory(equality)]) ).

cnf(42048,plain,
    a1 = a116,
    inference('REWRITE',[status(thm)],[28928,42047,theory(equality)]) ).

cnf(42049,plain,
    a74 = a1,
    inference('REWRITE',[status(thm)],[31970,42047,theory(equality)]) ).

cnf(42050,plain,
    a1 = a103,
    inference('REWRITE',[status(thm)],[37132,42047,theory(equality)]) ).

cnf(42051,plain,
    a1 = a104,
    inference('REWRITE',[status(thm)],[37215,42047,theory(equality)]) ).

cnf(42052,plain,
    a86 = a1,
    inference('REWRITE',[status(thm)],[37290,42047,theory(equality)]) ).

cnf(42053,plain,
    a87 = a1,
    inference('REWRITE',[status(thm)],[37291,42047,theory(equality)]) ).

cnf(42054,plain,
    a1 = a113,
    inference('REWRITE',[status(thm)],[39755,42047,theory(equality)]) ).

cnf(42055,plain,
    a78 = a1,
    inference('REWRITE',[status(thm)],[39756,42047,theory(equality)]) ).

cnf(42056,plain,
    a106 = a1,
    inference('REWRITE',[status(thm)],[40682,42047,theory(equality)]) ).

cnf(42057,plain,
    a107 = a1,
    inference('REWRITE',[status(thm)],[40683,42047,theory(equality)]) ).

cnf(42058,plain,
    a1 = a84,
    inference('REWRITE',[status(thm)],[40684,42047,theory(equality)]) ).

cnf(42059,plain,
    a1 = a125,
    inference('REWRITE',[status(thm)],[40775,42047,theory(equality)]) ).

cnf(42060,plain,
    a1 = a65,
    inference('REWRITE',[status(thm)],[40776,42047,theory(equality)]) ).

cnf(42061,plain,
    a126 = a1,
    inference('REWRITE',[status(thm)],[40777,42047,theory(equality)]) ).

cnf(42062,plain,
    a93 = a1,
    inference('REWRITE',[status(thm)],[40778,42047,theory(equality)]) ).

cnf(42063,plain,
    a1 = a97,
    inference('REWRITE',[status(thm)],[40783,42047,theory(equality)]) ).

cnf(42068,plain,
    a100 = a1,
    inference('REWRITE',[status(thm)],[40788,involutory_quandle,42047,theory(equality)]) ).

cnf(42069,plain,
    a1 = a114,
    inference('REWRITE',[status(thm)],[28295,42068,theory(equality)]) ).

cnf(42070,plain,
    a1 = a91,
    inference('REWRITE',[status(thm)],[28616,42068,theory(equality)]) ).

cnf(42071,plain,
    a1 = a115,
    inference('REWRITE',[status(thm)],[28930,42068,theory(equality)]) ).

cnf(42072,plain,
    a121 = a1,
    inference('REWRITE',[status(thm)],[28954,42068,theory(equality)]) ).

cnf(42073,plain,
    a66 = a1,
    inference('REWRITE',[status(thm)],[30706,42068,theory(equality)]) ).

cnf(42074,plain,
    a1 = a67,
    inference('REWRITE',[status(thm)],[30722,42068,theory(equality)]) ).

cnf(42075,plain,
    a90 = a1,
    inference('REWRITE',[status(thm)],[30723,42068,theory(equality)]) ).

cnf(42076,plain,
    a68 = a1,
    inference('REWRITE',[status(thm)],[30737,42068,theory(equality)]) ).

cnf(42077,plain,
    a1 = a75,
    inference('REWRITE',[status(thm)],[30750,42068,theory(equality)]) ).

cnf(42078,plain,
    a92 = a1,
    inference('REWRITE',[status(thm)],[30761,42068,theory(equality)]) ).

cnf(42079,plain,
    a99 = a1,
    inference('REWRITE',[status(thm)],[30764,42068,theory(equality)]) ).

cnf(42080,plain,
    a1 = a127,
    inference('REWRITE',[status(thm)],[37090,42068,theory(equality)]) ).

cnf(42081,plain,
    a1 = a129,
    inference('REWRITE',[status(thm)],[37094,42068,theory(equality)]) ).

cnf(42082,plain,
    a1 = a128,
    inference('REWRITE',[status(thm)],[37096,42068,theory(equality)]) ).

cnf(42083,plain,
    a1 = a62,
    inference('REWRITE',[status(thm)],[37106,42068,theory(equality)]) ).

cnf(42084,plain,
    a102 = a1,
    inference('REWRITE',[status(thm)],[40655,42068,theory(equality)]) ).

cnf(42085,plain,
    a88 = a1,
    inference('REWRITE',[status(thm)],[40656,42068,theory(equality)]) ).

cnf(42086,plain,
    a1 = a105,
    inference('REWRITE',[status(thm)],[40685,42068,theory(equality)]) ).

cnf(42087,plain,
    a1 = a85,
    inference('REWRITE',[status(thm)],[40686,42068,theory(equality)]) ).

cnf(42088,plain,
    a108 = a1,
    inference('REWRITE',[status(thm)],[40751,42068,theory(equality)]) ).

cnf(42089,plain,
    a110 = a1,
    inference('REWRITE',[status(thm)],[40752,42068,theory(equality)]) ).

cnf(42090,plain,
    a109 = a1,
    inference('REWRITE',[status(thm)],[40753,42068,theory(equality)]) ).

cnf(42091,plain,
    a111 = a1,
    inference('REWRITE',[status(thm)],[40754,42068,theory(equality)]) ).

cnf(42092,plain,
    a1 = a112,
    inference('REWRITE',[status(thm)],[40755,42068,theory(equality)]) ).

cnf(42093,plain,
    a1 = a118,
    inference('REWRITE',[status(thm)],[40756,42068,theory(equality)]) ).

cnf(42094,plain,
    a1 = a71,
    inference('REWRITE',[status(thm)],[40757,42068,theory(equality)]) ).

cnf(42095,plain,
    a79 = a1,
    inference('REWRITE',[status(thm)],[40758,42068,theory(equality)]) ).

cnf(42096,plain,
    a1 = a119,
    inference('REWRITE',[status(thm)],[40759,42068,theory(equality)]) ).

cnf(42097,plain,
    a70 = a1,
    inference('REWRITE',[status(thm)],[40760,42068,theory(equality)]) ).

cnf(42098,plain,
    a72 = a1,
    inference('REWRITE',[status(thm)],[40761,42068,theory(equality)]) ).

cnf(42099,plain,
    a1 = a73,
    inference('REWRITE',[status(thm)],[40762,42068,theory(equality)]) ).

cnf(42100,plain,
    a82 = a1,
    inference('REWRITE',[status(thm)],[40763,42068,theory(equality)]) ).

cnf(42101,plain,
    a1 = a83,
    inference('REWRITE',[status(thm)],[40766,42068,theory(equality)]) ).

cnf(42104,plain,
    a131 = a1,
    inference('REWRITE',[status(thm)],[40832,42068,theory(equality)]) ).

cnf(42105,plain,
    a1 = a60,
    inference('REWRITE',[status(thm)],[40843,42068,theory(equality)]) ).

cnf(42106,plain,
    a1 = a59,
    inference('REWRITE',[status(thm)],[40844,42068,theory(equality)]) ).

cnf(42107,plain,
    a132 = a1,
    inference('REWRITE',[status(thm)],[41612,42068,theory(equality)]) ).

cnf(42108,plain,
    a1 = a58,
    inference('REWRITE',[status(thm)],[41613,42068,theory(equality)]) ).

cnf(42109,plain,
    a133 = a1,
    inference('REWRITE',[status(thm)],[41614,42068,theory(equality)]) ).

cnf(42110,plain,
    a135 = a1,
    inference('REWRITE',[status(thm)],[41675,42068,theory(equality)]) ).

cnf(42111,plain,
    a1 = a55,
    inference('REWRITE',[status(thm)],[41676,42068,theory(equality)]) ).

cnf(42112,plain,
    a1 = a54,
    inference('REWRITE',[status(thm)],[41677,42068,theory(equality)]) ).

cnf(42113,plain,
    a137 = a1,
    inference('REWRITE',[status(thm)],[41685,42068,theory(equality)]) ).

cnf(42114,plain,
    a1 = a49,
    inference('REWRITE',[status(thm)],[41686,42068,theory(equality)]) ).

cnf(42115,plain,
    a25 = product(a24,a1),
    inference('REWRITE',[status(thm)],[41687,42068,theory(equality)]) ).

cnf(42116,plain,
    a1 = a138,
    inference('REWRITE',[status(thm)],[41688,42068,theory(equality)]) ).

cnf(42117,plain,
    a1 = a48,
    inference('REWRITE',[status(thm)],[41690,42068,theory(equality)]) ).

cnf(42118,plain,
    a50 = a1,
    inference('REWRITE',[status(thm)],[41694,42068,theory(equality)]) ).

cnf(42123,plain,
    a1 = a130,
    inference('REWRITE',[status(thm)],[40793,42047,theory(equality)]) ).

cnf(42124,plain,
    a1 = a61,
    inference('REWRITE',[status(thm)],[40826,42047,theory(equality)]) ).

cnf(42125,plain,
    a1 = a89,
    inference('REWRITE',[status(thm)],[40827,42047,theory(equality)]) ).

cnf(42126,plain,
    a120 = a1,
    inference('REWRITE',[status(thm)],[40988,42047,theory(equality)]) ).

cnf(42127,plain,
    a69 = a1,
    inference('REWRITE',[status(thm)],[40989,42047,theory(equality)]) ).

cnf(42128,plain,
    a134 = a1,
    inference('REWRITE',[status(thm)],[41616,42047,theory(equality)]) ).

cnf(42129,plain,
    a1 = a57,
    inference('REWRITE',[status(thm)],[41617,42047,theory(equality)]) ).

cnf(42130,plain,
    a1 = a56,
    inference('REWRITE',[status(thm)],[41618,42047,theory(equality)]) ).

cnf(42131,plain,
    a136 = a1,
    inference('REWRITE',[status(thm)],[41619,42047,theory(equality)]) ).

cnf(42132,plain,
    a1 = a53,
    inference('REWRITE',[status(thm)],[41620,42047,theory(equality)]) ).

cnf(42133,plain,
    a1 = a52,
    inference('REWRITE',[status(thm)],[41621,42047,theory(equality)]) ).

cnf(42134,plain,
    a15 = a1,
    inference('REWRITE',[status(thm)],[41622,involutory_quandle,42047,theory(equality)]) ).

cnf(42135,plain,
    a1 = a9,
    inference('REWRITE',[status(thm)],[40056,42134,theory(equality)]) ).

cnf(42136,plain,
    a1 = a6,
    inference('REWRITE',[status(thm)],[40119,42134,theory(equality)]) ).

cnf(42137,plain,
    a18 = a1,
    inference('REWRITE',[status(thm)],[42044,42047,theory(equality)]) ).

cnf(42138,plain,
    a1 = a34,
    inference('REWRITE',[status(thm)],[42045,42047,theory(equality)]) ).

cnf(42139,plain,
    a1 = a43,
    inference('REWRITE',[status(thm)],[41922,42047,42044,theory(equality)]) ).

cnf(42140,plain,
    a36 = a1,
    inference('REWRITE',[status(thm)],[41992,41994,theory(equality)]) ).

cnf(42141,plain,
    a23 = a1,
    inference('REWRITE',[status(thm)],[38900,41927,theory(equality)]) ).

cnf(42143,plain,
    a1 = a25,
    inference('REWRITE',[status(thm)],[39026,42115,41855,39061,theory(equality)]) ).

cnf(42145,plain,
    a28 = a1,
    inference('REWRITE',[status(thm)],[37776,41855,39049,theory(equality)]) ).

cnf(42146,plain,
    a24 = a1,
    inference('REWRITE',[status(thm)],[32750,involutory_quandle,39392,41927,38900,theory(equality)]) ).

cnf(42147,plain,
    a46 = a1,
    inference('REWRITE',[status(thm)],[knot_46,involutory_quandle,41997,38899,theory(equality)]) ).

cnf(42148,plain,
    a51 = a1,
    inference('REWRITE',[status(thm)],[33070,42113,34326,theory(equality)]) ).

cnf(42149,plain,
    a63 = a1,
    inference('REWRITE',[status(thm)],[30189,42080,32530,theory(equality)]) ).

cnf(42150,plain,
    a95 = a1,
    inference('REWRITE',[status(thm)],[30271,42080,32530,theory(equality)]) ).

cnf(42151,plain,
    a96 = a1,
    inference('REWRITE',[status(thm)],[30289,42080,32530,theory(equality)]) ).

cnf(42152,plain,
    a1 = a64,
    inference('REWRITE',[status(thm)],[31758,42080,32530,theory(equality)]) ).

cnf(42153,plain,
    a94 = a1,
    inference('REWRITE',[status(thm)],[31820,42080,32530,theory(equality)]) ).

cnf(42154,plain,
    a1 = a98,
    inference('REWRITE',[status(thm)],[28297,42068,28930,theory(equality)]) ).

cnf(42155,plain,
    a1 = a123,
    inference('REWRITE',[status(thm)],[28632,42068,28930,theory(equality)]) ).

cnf(42156,plain,
    a1 = a122,
    inference('REWRITE',[status(thm)],[28634,42068,28930,theory(equality)]) ).

cnf(42157,plain,
    a1 = a117,
    inference('REWRITE',[status(thm)],[28737,42047,28928,theory(equality)]) ).

cnf(42158,plain,
    a1 = a124,
    inference('REWRITE',[status(thm)],[28629,42071,28634,theory(equality)]) ).

cnf(42160,plain,
    a77 = a1,
    inference('REWRITE',[status(thm)],[27286,42068,28295,theory(equality)]) ).

cnf(42161,plain,
    $false,
    inference('REWRITE',[status(thm)],[20245,41997,42005,42081,42059,42156,42072,42126,42048,42071,42092,42091,42089,42057,42056,42086,42084,42047,42153,42062,42158,42155,42068,42079,42075,42125,42085,42051,42050,42053,42052,42087,42058,42101,42096,42095,42055,42054,42160,42069,42077,42049,42100,42099,42090,42088,42098,42157,42093,42094,42097,42127,42154,42063,42076,42078,42070,42074,42073,42060,42061,42152,42151,42150,42149,42112,42118,42082,42080,42083,42124,42139,41995,42147,41994,42105,42106,42104,42123,39392,41374,41370,42113,42116,42114,42117,42146,42003,38898,41996,39435,42138,41923,42143,42129,42108,41921,42107,42137,39811,42145,42132,42134,41375,40654,42141,41924,41927,41313,39471,42140,41716,42128,42109,41423,42130,42111,42135,41855,41845,39568,42148,42133,41450,42131,42110,42136,41451,41446,41449,41803,41802,41448,41447,36452,38897,36970,36371,27284,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : TOP052-1 : TPTP v8.1.0. Released v8.1.0.
% 0.11/0.12  % Command  : run-snark %s %d
% 0.13/0.33  % Computer : n018.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sun May 29 09:50:10 EDT 2022
% 0.19/0.33  % CPUTime  : 
% 0.19/0.44  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45  * 
% 0.19/0.45  * 
% 0.19/0.46  #<PACKAGE "SNARK-USER">
% 0.19/0.46  * 
% 0.19/0.46  SNARK-TPTP-OPTIONS
% 0.19/0.46  * 
% 0.19/0.46  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.46   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.46   (USE-FACTORING :POS)
% 0.19/0.46   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.46   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.46   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.46   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.46   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.46   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.46   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.46   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.46   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.46   (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.46  * 
% 0.19/0.46  "."
% 0.19/0.46  * 
% 0.19/0.46  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-05-29T09:50:10
% 0.19/0.46  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n018.cluster.edu at 2022-05-29T09:50:10
% 19.07/19.29  
% 19.07/19.29  
% 19.07/19.29  #||
% 19.07/19.29  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.13/19.29  % SZS output start Refutation
% See solution above
% 19.45/19.67  ||#
% 19.45/19.67  
% 19.45/19.67  ; Summary of computation:
% 19.45/19.67  ;     92337 formulas have been input or derived (from 3376 formulas).
% 19.45/19.67  ;     42161 (46%) were retained.  Of these,
% 19.45/19.67  ;        41991 (100%) were simplified or subsumed later,
% 19.45/19.67  ;          170 ( 0%) are still being kept.
% 19.45/19.67  ; 
% 19.45/19.67  ; Run time in seconds excluding printing time:
% 19.45/19.67  ;     0.016   0%   Read assertion file          (1 call)
% 19.45/19.67  ;     0.005   0%   Assert                       (145 calls)
% 19.45/19.67  ;     4.956  26%   Process new row              (91,847 calls)
% 19.45/19.67  ;     0.149   1%   Resolution                   (6,750 calls)
% 19.45/19.67  ;     1.653   9%   Paramodulation               (3,375 calls)
% 19.45/19.67  ;     4.384  23%   Forward simplification       (91,695 calls)
% 19.45/19.67  ;     4.645  25%   Backward simplification      (42,161 calls)
% 19.45/19.67  ;     2.549  14%   Ordering                     (374,633 calls)
% 19.45/19.67  ;     0.001   0%   Sortal reasoning             (32 calls)
% 19.45/19.67  ;     0.000   0%   Purity testing               (1 call)
% 19.45/19.67  ;     0.468   2%   Other
% 19.45/19.67  ;    18.826        Total
% 19.45/19.67  ;    19.212        Real time
% 19.45/19.68  ; 
% 19.45/19.68  ; Term-hash-array has 109,150 terms in all.
% 19.45/19.68  ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 19.45/19.68  ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 19.45/19.68  ; Path-index has 400 entries (53,435 at peak, 127,227 added, 126,827 deleted).
% 19.45/19.68  ; Path-index has 652 nodes (5,099 at peak, 7,668 added, 7,016 deleted).
% 19.45/19.68  ; Trie-index has 400 entries (53,435 at peak, 127,227 added, 126,827 deleted).
% 19.45/19.68  ; Trie-index has 691 nodes (222,985 at peak, 522,426 added, 521,735 deleted).
% 19.45/19.68  ; Retrieved 1,183,393 generalization terms in 623,903 calls.
% 19.45/19.68  ; Retrieved 65,711 instance terms in 43,320 calls.
% 19.45/19.68  ; Retrieved 282,618 unifiable terms in 24,967 calls.
% 19.45/19.68  ; 
% 19.45/19.68  ; The agenda of backward simplifiable rows to process has 418 entries:
% 19.45/19.68  ;   418 with value 0
% 19.45/19.68  ; The agenda of rows to process has 13 entries:
% 19.45/19.68  ;    10 with value 17              3 with value 19
% 19.45/19.68  ; The agenda of input rows to give has 45 entries:
% 19.45/19.68  ;    45 with value 4
% 19.45/19.68  ; The agenda of rows to give has 120 entries:
% 19.45/19.68  ;    39 with value (4 5)           5 with value (4 10)           5 with value (4 24)
% 19.45/19.68  ;    16 with value (4 6)           3 with value (4 18)           3 with value (4 25)
% 19.45/19.68  ;    16 with value (4 7)           3 with value (4 21)           2 with value (4 26)
% 19.45/19.68  ;     8 with value (4 8)           1 with value (4 22)           3 with value (4 27)
% 19.45/19.68  ;    11 with value (4 9)           5 with value (4 23)
% 19.45/19.68  Evaluation took:
% 19.45/19.68    19.215 seconds of real time
% 19.45/19.68    17.478365 seconds of user run time
% 19.45/19.68    1.736634 seconds of system run time
% 19.45/19.68    [Run times include 4.947 seconds GC run time.]
% 19.45/19.68    0 calls to %EVAL
% 19.45/19.68    0 page faults and
% 19.45/19.68    1,408,659,568 bytes consed.
% 19.45/19.68  :PROOF-FOUND
% 19.45/19.68  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-05-29T09:50:30
% 19.45/19.68  :PROOF-FOUND
% 19.45/19.68  * 
%------------------------------------------------------------------------------