TSTP Solution File: TOP050-1 by SNARK---20120808r022
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- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : TOP050-1 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n020.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 21:34:28 EDT 2022
% Result : Unsatisfiable 1.97s 2.13s
% Output : Refutation 1.97s
% 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,
product(a1,a31) = a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot) ).
cnf(knot_03,axiom,
product(a2,a25) = a3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_03) ).
cnf(knot_04,axiom,
product(a3,a29) = a4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_04) ).
cnf(knot_05,axiom,
product(a4,a11) = a5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_05) ).
cnf(knot_06,axiom,
product(a5,a15) = a6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_06) ).
cnf(knot_07,axiom,
product(a7,a19) = a8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_07) ).
cnf(knot_08,axiom,
product(a8,a5) = a9,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_08) ).
cnf(knot_09,axiom,
product(a9,a17) = a10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_09) ).
cnf(knot_10,axiom,
product(a10,a7) = a11,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_10) ).
cnf(knot_11,axiom,
product(a11,a5) = a12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_11) ).
cnf(knot_12,axiom,
product(a12,a19) = a13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_12) ).
cnf(knot_13,axiom,
product(a13,a7) = a14,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_13) ).
cnf(knot_14,axiom,
product(a14,a17) = a15,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_14) ).
cnf(knot_15,axiom,
product(a15,a5) = a16,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_15) ).
cnf(knot_16,axiom,
product(a16,a19) = a17,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_16) ).
cnf(knot_17,axiom,
product(a17,a9) = a18,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_17) ).
cnf(knot_18,axiom,
product(a18,a15) = a19,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_18) ).
cnf(knot_19,axiom,
product(a19,a11) = a20,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_19) ).
cnf(knot_20,axiom,
product(a20,a29) = a21,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_20) ).
cnf(knot_21,axiom,
product(a21,a25) = a22,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_21) ).
cnf(knot_22,axiom,
product(a22,a31) = a23,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_22) ).
cnf(knot_23,axiom,
product(a23,a21) = a24,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_23) ).
cnf(knot_24,axiom,
product(a24,a3) = a25,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_24) ).
cnf(knot_25,axiom,
product(a25,a23) = a26,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_25) ).
cnf(knot_26,axiom,
product(a26,a1) = a27,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_26) ).
cnf(knot_27,axiom,
product(a27,a21) = a28,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_27) ).
cnf(knot_28,axiom,
product(a28,a3) = a29,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_28) ).
cnf(knot_29,axiom,
product(a29,a1) = a30,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_29) ).
cnf(knot_30,axiom,
product(a30,a23) = a31,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_30) ).
cnf(knot_31,axiom,
product(a31,a3) = a32,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_31) ).
cnf(knot_32,axiom,
product(a32,a21) = a1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_32) ).
cnf(goal,negated_conjecture,
tuple(a1,a30,a31,a2,a24,a25,a3,a28,a29,a4,a10,a11,a5,a14,a15,a6,a7,a18,a19,a8,a9,a16,a17,a12,a13,a20,a21,a22,a23,a26,a27) != tuple(a2,a31,a32,a3,a25,a26,a4,a29,a30,a5,a11,a12,a6,a15,a16,a7,a8,a19,a20,a9,a10,a17,a18,a13,a14,a21,a22,a23,a24,a27,a28),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
cnf(36,plain,
product(a26,a23) = a25,
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_25,theory(equality)]) ).
cnf(37,plain,
product(a31,a23) = a30,
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_30,theory(equality)]) ).
cnf(40,plain,
product(a1,a21) = a32,
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_32,theory(equality)]) ).
cnf(41,plain,
product(a10,a17) = a9,
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_09,theory(equality)]) ).
cnf(42,plain,
product(a15,a17) = a14,
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_14,theory(equality)]) ).
cnf(44,plain,
product(a8,a19) = a7,
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_07,theory(equality)]) ).
cnf(45,plain,
product(a13,a19) = a12,
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_12,theory(equality)]) ).
cnf(46,plain,
product(a17,a19) = a16,
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_16,theory(equality)]) ).
cnf(47,plain,
product(a11,a7) = a10,
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_10,theory(equality)]) ).
cnf(48,plain,
product(a14,a7) = a13,
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_13,theory(equality)]) ).
cnf(50,plain,
product(a19,a15) = a18,
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_18,theory(equality)]) ).
cnf(51,plain,
product(a9,a5) = a8,
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_08,theory(equality)]) ).
cnf(52,plain,
product(a12,a5) = a11,
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_11,theory(equality)]) ).
cnf(54,plain,
product(a5,a11) = a4,
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_05,theory(equality)]) ).
cnf(55,plain,
product(a20,a11) = a19,
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_19,theory(equality)]) ).
cnf(57,plain,
product(a21,a29) = a20,
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_20,theory(equality)]) ).
cnf(58,plain,
product(a25,a3) = a24,
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_24,theory(equality)]) ).
cnf(59,plain,
product(a29,a3) = a28,
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_28,theory(equality)]) ).
cnf(60,plain,
product(a32,a3) = a31,
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_31,theory(equality)]) ).
cnf(61,plain,
product(a3,a25) = a2,
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_03,theory(equality)]) ).
cnf(62,plain,
product(a22,a25) = a21,
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_21,theory(equality)]) ).
cnf(63,plain,
product(a2,a31) = a1,
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot,theory(equality)]) ).
cnf(64,plain,
product(a23,a31) = a22,
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_22,theory(equality)]) ).
cnf(65,plain,
product(a27,a1) = a26,
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_26,theory(equality)]) ).
cnf(66,plain,
product(a30,a1) = a29,
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_29,theory(equality)]) ).
cnf(67,plain,
product(a26,X) = product(product(a25,X),product(a23,X)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_25,theory(equality)]) ).
cnf(68,plain,
product(a31,X) = product(product(a30,X),product(a23,X)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_30,theory(equality)]) ).
cnf(72,plain,
product(a10,X) = product(product(a9,X),product(a17,X)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_09,theory(equality)]) ).
cnf(75,plain,
product(a8,X) = product(product(a7,X),product(a19,X)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_07,theory(equality)]) ).
cnf(76,plain,
product(a13,X) = product(product(a12,X),product(a19,X)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_12,theory(equality)]) ).
cnf(77,plain,
product(a17,X) = product(product(a16,X),product(a19,X)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_16,theory(equality)]) ).
cnf(78,plain,
product(a11,X) = product(product(a10,X),product(a7,X)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_10,theory(equality)]) ).
cnf(79,plain,
product(a14,X) = product(product(a13,X),product(a7,X)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_13,theory(equality)]) ).
cnf(81,plain,
product(a19,X) = product(product(a18,X),product(a15,X)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_18,theory(equality)]) ).
cnf(82,plain,
product(a9,X) = product(product(a8,X),product(a5,X)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_08,theory(equality)]) ).
cnf(83,plain,
product(a12,X) = product(product(a11,X),product(a5,X)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_11,theory(equality)]) ).
cnf(84,plain,
product(a16,X) = product(product(a15,X),product(a5,X)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_15,theory(equality)]) ).
cnf(85,plain,
product(a5,X) = product(product(a4,X),product(a11,X)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_05,theory(equality)]) ).
cnf(87,plain,
product(a4,X) = product(product(a3,X),product(a29,X)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_04,theory(equality)]) ).
cnf(89,plain,
product(a25,X) = product(product(a24,X),product(a3,X)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_24,theory(equality)]) ).
cnf(90,plain,
product(a29,X) = product(product(a28,X),product(a3,X)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_28,theory(equality)]) ).
cnf(92,plain,
product(a3,X) = product(product(a2,X),product(a25,X)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_03,theory(equality)]) ).
cnf(93,plain,
product(a22,X) = product(product(a21,X),product(a25,X)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_21,theory(equality)]) ).
cnf(94,plain,
product(a2,X) = product(product(a1,X),product(a31,X)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot,theory(equality)]) ).
cnf(95,plain,
product(a23,X) = product(product(a22,X),product(a31,X)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_22,theory(equality)]) ).
cnf(96,plain,
product(a27,X) = product(product(a26,X),product(a1,X)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_26,theory(equality)]) ).
cnf(99,plain,
product(product(a30,X),a23) = product(a31,product(X,a23)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_30,theory(equality)]) ).
cnf(100,plain,
product(product(a23,X),a21) = product(a24,product(X,a21)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_23,theory(equality)]) ).
cnf(101,plain,
product(product(a27,X),a21) = product(a28,product(X,a21)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_27,theory(equality)]) ).
cnf(106,plain,
product(product(a7,X),a19) = product(a8,product(X,a19)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_07,theory(equality)]) ).
cnf(107,plain,
product(product(a12,X),a19) = product(a13,product(X,a19)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_12,theory(equality)]) ).
cnf(109,plain,
product(product(a10,X),a7) = product(a11,product(X,a7)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_10,theory(equality)]) ).
cnf(110,plain,
product(product(a13,X),a7) = product(a14,product(X,a7)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_13,theory(equality)]) ).
cnf(112,plain,
product(product(a18,X),a15) = product(a19,product(X,a15)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_18,theory(equality)]) ).
cnf(114,plain,
product(product(a11,X),a5) = product(a12,product(X,a5)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_11,theory(equality)]) ).
cnf(115,plain,
product(product(a15,X),a5) = product(a16,product(X,a5)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_15,theory(equality)]) ).
cnf(116,plain,
product(product(a4,X),a11) = product(a5,product(X,a11)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_05,theory(equality)]) ).
cnf(117,plain,
product(product(a19,X),a11) = product(a20,product(X,a11)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_19,theory(equality)]) ).
cnf(120,plain,
product(product(a24,X),a3) = product(a25,product(X,a3)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_24,theory(equality)]) ).
cnf(121,plain,
product(product(a28,X),a3) = product(a29,product(X,a3)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_28,theory(equality)]) ).
cnf(123,plain,
product(product(a2,X),a25) = product(a3,product(X,a25)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_03,theory(equality)]) ).
cnf(124,plain,
product(product(a21,X),a25) = product(a22,product(X,a25)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_21,theory(equality)]) ).
cnf(126,plain,
product(product(a22,X),a31) = product(a23,product(X,a31)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_22,theory(equality)]) ).
cnf(127,plain,
product(product(a26,X),a1) = product(a27,product(X,a1)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_26,theory(equality)]) ).
cnf(129,plain,
product(product(X,Y),X) = product(X,product(Y,X)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,involutory_quandle,theory(equality)]) ).
cnf(131,plain,
product(product(X,a30),a23) = product(product(X,a23),a31),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_30,theory(equality)]) ).
cnf(132,plain,
product(product(X,a23),a21) = product(product(X,a21),a24),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_23,theory(equality)]) ).
cnf(134,plain,
product(product(X,a32),a21) = product(product(X,a21),a1),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_32,theory(equality)]) ).
cnf(136,plain,
product(product(X,a14),a17) = product(product(X,a17),a15),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_14,theory(equality)]) ).
cnf(138,plain,
product(product(X,a7),a19) = product(product(X,a19),a8),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_07,theory(equality)]) ).
cnf(139,plain,
product(product(X,a12),a19) = product(product(X,a19),a13),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_12,theory(equality)]) ).
cnf(141,plain,
product(product(X,a10),a7) = product(product(X,a7),a11),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_10,theory(equality)]) ).
cnf(142,plain,
product(product(X,a13),a7) = product(product(X,a7),a14),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_13,theory(equality)]) ).
cnf(144,plain,
product(product(X,a18),a15) = product(product(X,a15),a19),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_18,theory(equality)]) ).
cnf(148,plain,
product(product(X,a4),a11) = product(product(X,a11),a5),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_05,theory(equality)]) ).
cnf(150,plain,
product(product(X,a3),a29) = product(product(X,a29),a4),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_04,theory(equality)]) ).
cnf(152,plain,
product(product(X,a24),a3) = product(product(X,a3),a25),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_24,theory(equality)]) ).
cnf(153,plain,
product(product(X,a28),a3) = product(product(X,a29),a4),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_28,theory(equality)]),150,theory(equality)]) ).
cnf(156,plain,
product(product(X,a2),a25) = product(product(X,a25),a3),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_03,theory(equality)]) ).
cnf(159,plain,
product(product(X,a22),a31) = product(product(X,a31),a23),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_22,theory(equality)]) ).
cnf(160,plain,
product(product(X,a26),a1) = product(product(X,a1),a27),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_26,theory(equality)]) ).
cnf(164,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(167,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(170,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(172,plain,
product(product(a26,X),a23) = product(a25,product(X,a23)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,36,theory(equality)]) ).
cnf(173,plain,
product(product(X,a26),a23) = product(product(X,a23),a25),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,36,theory(equality)]) ).
cnf(175,plain,
product(product(a31,X),a23) = product(a30,product(X,a23)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,37,theory(equality)]) ).
cnf(176,plain,
product(product(X,a22),a31) = product(product(X,a23),a30),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,37,theory(equality)]),159,theory(equality)]) ).
cnf(197,plain,
product(product(a8,X),a19) = product(a7,product(X,a19)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,44,theory(equality)]) ).
cnf(198,plain,
product(product(X,a8),a19) = product(product(X,a19),a7),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,44,theory(equality)]) ).
cnf(214,plain,
product(a18,X) = product(product(a19,X),product(a15,X)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,50,theory(equality)]) ).
cnf(215,plain,
product(product(a19,X),a15) = product(a18,product(X,a15)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,50,theory(equality)]) ).
cnf(216,plain,
product(product(X,a19),a15) = product(product(X,a15),a18),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,50,theory(equality)]) ).
cnf(218,plain,
product(product(a9,X),a5) = product(a8,product(X,a5)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,51,theory(equality)]) ).
cnf(221,plain,
product(product(a12,X),a5) = product(a11,product(X,a5)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,52,theory(equality)]) ).
cnf(222,plain,
product(product(X,a12),a5) = product(product(X,a5),a11),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,52,theory(equality)]) ).
cnf(227,plain,
product(product(a5,X),a11) = product(a4,product(X,a11)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,54,theory(equality)]) ).
cnf(228,plain,
product(product(X,a12),a5) = product(product(X,a11),a4),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,54,theory(equality)]),222,theory(equality)]) ).
cnf(229,plain,
product(product(X,a11),a4) = product(product(X,a5),a11),
inference('REWRITE',[status(thm)],[222,228,theory(equality)]) ).
cnf(239,plain,
product(a24,X) = product(product(a25,X),product(a3,X)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,58,theory(equality)]) ).
cnf(240,plain,
product(product(a25,X),a3) = product(a24,product(X,a3)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,58,theory(equality)]) ).
cnf(241,plain,
product(product(X,a2),a25) = product(product(X,a3),a24),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,58,theory(equality)]),156,theory(equality)]) ).
cnf(248,plain,
product(a2,X) = product(product(a3,X),product(a25,X)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,61,theory(equality)]) ).
cnf(250,plain,
product(product(X,a24),a3) = product(product(X,a25),a2),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,61,theory(equality)]),152,theory(equality)]) ).
cnf(251,plain,
product(a21,X) = product(product(a22,X),product(a25,X)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,62,theory(equality)]) ).
cnf(253,plain,
product(product(X,a22),a25) = product(product(X,a25),a21),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,62,theory(equality)]) ).
cnf(256,plain,
product(product(X,a2),a31) = product(product(X,a31),a1),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,63,theory(equality)]) ).
cnf(261,plain,
product(product(a27,X),a1) = product(a26,product(X,a1)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,65,theory(equality)]) ).
cnf(267,plain,
product(a26,a21) = product(product(a25,a21),a24),
inference('PARAMODULATE',[status(thm)],[67,knot_23,theory(equality)]) ).
cnf(280,plain,
product(a31,a30) = product(a30,product(a23,a30)),
inference('PARAMODULATE',[status(thm)],[68,involutory_quandle,theory(equality)]) ).
cnf(331,plain,
product(a10,a9) = product(a9,a18),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[72,involutory_quandle,theory(equality)]),knot_17,theory(equality)]) ).
cnf(367,plain,
product(a8,a7) = product(a7,product(a19,a7)),
inference('PARAMODULATE',[status(thm)],[75,involutory_quandle,theory(equality)]) ).
cnf(368,plain,
product(a8,a11) = product(product(a7,a11),a20),
inference('PARAMODULATE',[status(thm)],[75,knot_19,theory(equality)]) ).
cnf(369,plain,
product(a8,a15) = product(product(a7,a15),a18),
inference('PARAMODULATE',[status(thm)],[75,50,theory(equality)]) ).
cnf(376,plain,
product(product(X,a19),a7) = product(product(X,product(a19,a7)),product(a8,a7)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,367,theory(equality)]),involutory_quandle_02,theory(equality)]) ).
cnf(381,plain,
product(product(a8,a15),a18) = product(a7,a15),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,369,theory(equality)]) ).
cnf(385,plain,
product(a13,a12) = product(a12,product(a19,a12)),
inference('PARAMODULATE',[status(thm)],[76,involutory_quandle,theory(equality)]) ).
cnf(387,plain,
product(a13,a15) = product(product(a12,a15),a18),
inference('PARAMODULATE',[status(thm)],[76,50,theory(equality)]) ).
cnf(402,plain,
product(a17,a15) = product(product(a16,a15),a18),
inference('PARAMODULATE',[status(thm)],[77,50,theory(equality)]) ).
cnf(426,plain,
product(a14,a19) = product(a12,a8),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[79,45,theory(equality)]),knot_07,theory(equality)]) ).
cnf(432,plain,
product(product(a14,a19),a8) = a12,
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,426,theory(equality)]) ).
cnf(452,plain,
product(a19,a18) = product(a18,product(a15,a18)),
inference('PARAMODULATE',[status(thm)],[81,involutory_quandle,theory(equality)]) ).
cnf(458,plain,
product(product(a19,a18),X) = product(product(a18,X),product(product(a15,a18),X)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,452,theory(equality)]) ).
cnf(466,plain,
product(a9,a15) = product(product(a8,a15),a6),
inference('PARAMODULATE',[status(thm)],[82,knot_06,theory(equality)]) ).
cnf(467,plain,
product(a9,a11) = product(product(a8,a11),a4),
inference('PARAMODULATE',[status(thm)],[82,54,theory(equality)]) ).
cnf(485,plain,
product(product(a9,a11),a4) = product(a8,a11),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,467,theory(equality)]) ).
cnf(489,plain,
product(a12,a11) = product(a11,a4),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[83,involutory_quandle,theory(equality)]),54,theory(equality)]) ).
cnf(490,plain,
product(a12,a15) = product(product(a11,a15),a6),
inference('PARAMODULATE',[status(thm)],[83,knot_06,theory(equality)]) ).
cnf(502,plain,
product(product(a12,a15),a6) = product(a11,a15),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,490,theory(equality)]) ).
cnf(506,plain,
product(a16,a15) = product(a15,a6),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[84,involutory_quandle,theory(equality)]),knot_06,theory(equality)]) ).
cnf(511,plain,
product(product(a16,a15),a6) = a15,
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,506,theory(equality)]) ).
cnf(526,plain,
product(a5,a4) = product(a4,product(a12,a11)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[85,involutory_quandle,theory(equality)]),489,theory(equality)]) ).
cnf(554,plain,
product(a4,a3) = product(a3,a28),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[87,involutory_quandle,theory(equality)]),59,theory(equality)]) ).
cnf(559,plain,
product(product(a3,a28),a3) = a4,
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,554,theory(equality)]) ).
cnf(563,plain,
product(product(X,a4),a3) = product(product(X,a3),product(a3,a28)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,554,theory(equality)]) ).
cnf(587,plain,
product(a25,a24) = product(a24,product(a3,a24)),
inference('PARAMODULATE',[status(thm)],[89,involutory_quandle,theory(equality)]) ).
cnf(599,plain,
product(a29,a28) = product(a28,product(a3,a28)),
inference('PARAMODULATE',[status(thm)],[90,involutory_quandle,theory(equality)]) ).
cnf(625,plain,
product(a3,a2) = product(a2,product(a25,a2)),
inference('PARAMODULATE',[status(thm)],[92,involutory_quandle,theory(equality)]) ).
cnf(629,plain,
product(product(X,product(a2,Y)),product(a25,Y)) = product(product(X,product(a25,Y)),product(a3,Y)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,92,theory(equality)]) ).
cnf(637,plain,
product(a22,a3) = product(product(a21,a2),a25),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[93,58,theory(equality)]),241,theory(equality)]) ).
cnf(648,plain,
product(product(a22,a24),a3) = product(a21,a2),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,637,theory(equality)]),152,theory(equality)]) ).
cnf(653,plain,
product(a2,a3) = product(product(a1,a3),a32),
inference('PARAMODULATE',[status(thm)],[94,knot_31,theory(equality)]) ).
cnf(668,plain,
product(a23,a22) = product(a22,product(a31,a22)),
inference('PARAMODULATE',[status(thm)],[95,involutory_quandle,theory(equality)]) ).
cnf(669,plain,
product(a23,a3) = product(product(a22,a3),a32),
inference('PARAMODULATE',[status(thm)],[95,knot_31,theory(equality)]) ).
cnf(675,plain,
product(product(a23,a3),a32) = product(a22,a3),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,669,theory(equality)]) ).
cnf(680,plain,
product(a27,a26) = product(a26,product(a1,a26)),
inference('PARAMODULATE',[status(thm)],[96,involutory_quandle,theory(equality)]) ).
cnf(714,plain,
product(a30,a31) = product(a31,a22),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[99,280,theory(equality)]),64,involutory_quandle,131,knot_30,175,theory(equality)]) ).
cnf(718,plain,
product(product(a31,a22),a31) = a30,
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,714,theory(equality)]) ).
cnf(741,plain,
product(a26,a21) = product(a28,a32),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[101,65,theory(equality)]),40,theory(equality)]) ).
cnf(788,plain,
product(a7,a8) = product(a8,product(a19,a8)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[106,367,theory(equality)]),involutory_quandle,138,knot_07,197,theory(equality)]) ).
cnf(793,plain,
product(product(a12,a13),a19) = product(a13,a12),
inference('PARAMODULATE',[status(thm)],[107,45,theory(equality)]) ).
cnf(805,plain,
product(product(a13,a12),a19) = product(a12,a13),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,793,theory(equality)]) ).
cnf(843,plain,
product(product(a10,a13),a7) = product(a11,a14),
inference('PARAMODULATE',[status(thm)],[109,knot_13,theory(equality)]) ).
cnf(853,plain,
product(product(a11,a14),a7) = product(a10,a13),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,843,theory(equality)]) ).
cnf(869,plain,
product(product(a13,a11),a7) = product(a14,a10),
inference('PARAMODULATE',[status(thm)],[110,47,theory(equality)]) ).
cnf(882,plain,
product(product(a14,a10),a7) = product(a13,a11),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,869,theory(equality)]) ).
cnf(903,plain,
product(a18,a19) = product(a19,product(a15,a19)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[112,452,theory(equality)]),involutory_quandle,144,knot_18,215,theory(equality)]) ).
cnf(936,plain,
product(product(a15,a11),a5) = product(a16,a12),
inference('PARAMODULATE',[status(thm)],[115,knot_11,theory(equality)]) ).
cnf(950,plain,
product(a4,a5) = product(a5,a12),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[116,526,theory(equality)]),involutory_quandle_01,knot_05,227,theory(equality)]) ).
cnf(955,plain,
product(product(a12,a11),a5) = product(a12,product(a5,a12)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[114,950,theory(equality)]),489,theory(equality)]) ).
cnf(1005,plain,
product(product(a24,a2),a25) = product(a25,a24),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[120,58,theory(equality)]),156,theory(equality)]) ).
cnf(1015,plain,
product(product(a25,a24),a25) = product(a24,a2),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1005,theory(equality)]) ).
cnf(1026,plain,
product(product(a26,a21),a3) = product(a29,a31),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[121,60,theory(equality)]),741,theory(equality)]) ).
cnf(1070,plain,
product(product(a2,a21),a25) = product(a3,a22),
inference('PARAMODULATE',[status(thm)],[123,knot_21,theory(equality)]) ).
cnf(1071,plain,
product(product(a2,a24),a3) = product(a3,a2),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[123,61,theory(equality)]),152,theory(equality)]) ).
cnf(1072,plain,
product(product(a2,a22),a25) = product(a3,a21),
inference('PARAMODULATE',[status(thm)],[123,62,theory(equality)]) ).
cnf(1086,plain,
product(product(a3,a2),a3) = product(a2,a24),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1071,theory(equality)]) ).
cnf(1090,plain,
product(product(product(a2,a24),X),a3) = product(product(a3,a2),product(X,a3)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1071,theory(equality)]) ).
cnf(1096,plain,
product(product(a21,a24),a3) = product(a22,a2),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[124,61,theory(equality)]),152,theory(equality)]) ).
cnf(1097,plain,
product(product(a21,a22),a25) = product(a22,a21),
inference('PARAMODULATE',[status(thm)],[124,62,theory(equality)]) ).
cnf(1112,plain,
product(product(a22,a21),X) = product(product(product(a21,a22),X),product(a25,X)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1097,theory(equality)]) ).
cnf(1135,plain,
product(product(a22,a23),a31) = product(a23,a22),
inference('PARAMODULATE',[status(thm)],[126,64,theory(equality)]) ).
cnf(1137,plain,
product(product(a23,a22),a31) = product(a23,a30),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[126,718,theory(equality)]),668,theory(equality)]) ).
cnf(1158,plain,
product(a23,a30) = product(a22,a23),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1135,theory(equality)]),1137,theory(equality)]) ).
cnf(1170,plain,
product(a26,a30) = product(product(a25,a30),product(a22,a23)),
inference('PARAMODULATE',[status(thm)],[67,1158,theory(equality)]) ).
cnf(1173,plain,
product(product(X,a22),a31) = product(product(X,a30),product(a22,a23)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1158,theory(equality)]),176,theory(equality)]) ).
cnf(1174,plain,
product(a26,a30) = product(product(a25,a22),a31),
inference('REWRITE',[status(thm)],[1170,1173,theory(equality)]) ).
cnf(1176,plain,
product(a26,a27) = product(a27,product(a1,a27)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[127,680,theory(equality)]),involutory_quandle,160,knot_26,261,theory(equality)]) ).
cnf(1198,plain,
product(a14,a15) = product(a15,product(a17,a15)),
inference('PARAMODULATE',[status(thm)],[129,42,theory(equality)]) ).
cnf(1203,plain,
product(a13,a14) = product(a14,product(a7,a14)),
inference('PARAMODULATE',[status(thm)],[129,48,theory(equality)]) ).
cnf(1205,plain,
product(a11,a12) = product(product(a12,a11),a5),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[129,52,theory(equality)]),955,theory(equality)]) ).
cnf(1211,plain,
product(a24,a25) = product(a25,a2),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[129,58,theory(equality)]),61,theory(equality)]) ).
cnf(1212,plain,
product(a2,a3) = product(a3,a24),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[129,61,theory(equality)]),58,theory(equality)]) ).
cnf(1213,plain,
product(a25,a24) = product(product(a25,a2),a3),
inference('REWRITE',[status(thm)],[587,240,1212,theory(equality)]) ).
cnf(1215,plain,
product(a21,a22) = product(a22,product(a25,a22)),
inference('PARAMODULATE',[status(thm)],[129,62,theory(equality)]) ).
cnf(1218,plain,
product(product(a17,a14),a17) = product(a17,a15),
inference('PARAMODULATE',[status(thm)],[129,knot_14,theory(equality)]) ).
cnf(1224,plain,
product(product(a7,a10),a7) = product(a7,a11),
inference('PARAMODULATE',[status(thm)],[129,knot_10,theory(equality)]) ).
cnf(1227,plain,
product(product(a7,a14),a7) = product(a7,a13),
inference('PARAMODULATE',[status(thm)],[129,48,theory(equality)]) ).
cnf(1231,plain,
product(product(a25,a21),a25) = product(a25,a22),
inference('PARAMODULATE',[status(thm)],[129,knot_21,theory(equality)]) ).
cnf(1292,plain,
product(product(product(a12,X),a12),a19) = product(product(a12,product(X,a12)),a19),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[129,107,theory(equality)]),107,139,theory(equality)]) ).
cnf(1306,plain,
product(product(product(X,Y),Z),X) = product(product(X,product(Y,X)),product(Z,X)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,129,theory(equality)]) ).
cnf(1384,plain,
product(product(a8,a11),product(a7,a11)) = product(product(a7,a11),product(a20,product(a7,a11))),
inference('PARAMODULATE',[status(thm)],[129,368,theory(equality)]) ).
cnf(1404,plain,
product(product(a14,a10),product(a13,a11)) = product(product(a13,a11),product(a7,product(a13,a11))),
inference('PARAMODULATE',[status(thm)],[129,869,theory(equality)]) ).
cnf(1433,plain,
product(a3,product(a3,a28)) = product(a4,a28),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[129,599,theory(equality)]),87,involutory_quandle_01,theory(equality)]) ).
cnf(1454,plain,
product(a19,product(a19,a12)) = product(product(a19,a12),product(a13,a12)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[129,385,theory(equality)]),involutory_quandle_01,theory(equality)]) ).
cnf(1460,plain,
product(a19,product(a19,a7)) = product(product(a19,a8),a7),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[129,367,theory(equality)]),involutory_quandle_02,involutory_quandle_01,theory(equality)]) ).
cnf(1472,plain,
product(a25,product(a25,a2)) = product(a24,a2),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[129,625,theory(equality)]),239,involutory_quandle_01,theory(equality)]) ).
cnf(1555,plain,
product(product(a2,a24),a25) = product(a3,product(a25,a2)),
inference('PARAMODULATE',[status(thm)],[123,1211,theory(equality)]) ).
cnf(1562,plain,
product(product(a2,a3),X) = product(product(a3,X),product(a24,X)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1212,theory(equality)]) ).
cnf(1564,plain,
product(product(X,a2),a25) = product(product(X,a24),product(a2,a3)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1212,theory(equality)]),241,theory(equality)]) ).
cnf(1576,plain,
product(product(X,a15),product(a17,a15)) = product(product(X,product(a14,a15)),product(product(a17,a14),a15)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1198,theory(equality)]),170,theory(equality)]) ).
cnf(1577,plain,
product(a17,product(a17,a15)) = product(product(a17,a14),a15),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[129,1198,theory(equality)]),involutory_quandle_02,involutory_quandle_01,theory(equality)]) ).
cnf(1606,plain,
product(product(X,a14),product(a7,a14)) = product(product(X,product(a13,a14)),product(product(a7,a13),a14)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1203,theory(equality)]),170,theory(equality)]) ).
cnf(1607,plain,
product(a7,product(a7,a14)) = product(product(a7,a13),a14),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[129,1203,theory(equality)]),involutory_quandle_02,involutory_quandle_01,theory(equality)]) ).
cnf(1639,plain,
product(product(a25,a24),a3) = product(a25,a2),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1213,theory(equality)]) ).
cnf(1642,plain,
product(product(a3,a2),a24) = product(a3,product(a25,a24)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[129,1213,theory(equality)]),58,1090,1555,theory(equality)]) ).
cnf(1643,plain,
product(product(a25,a24),X) = product(product(product(a25,a2),X),product(a3,X)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1213,theory(equality)]) ).
cnf(1644,plain,
product(product(product(a25,a2),X),a3) = product(product(a25,a24),product(X,a3)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1213,theory(equality)]) ).
cnf(1716,plain,
product(product(a7,a13),X) = product(product(product(a7,a14),X),product(a7,X)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1227,theory(equality)]) ).
cnf(1779,plain,
product(product(product(X,a23),Y),a21) = product(product(product(X,a21),a24),product(Y,a21)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,132,theory(equality)]) ).
cnf(1780,plain,
product(product(X,product(Y,a23)),a21) = product(product(X,a21),product(product(Y,a21),a24)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,132,theory(equality)]) ).
cnf(1787,plain,
product(product(a2,a3),a21) = product(product(a1,product(a3,a1)),product(a21,a1)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[134,653,theory(equality)]),1306,theory(equality)]) ).
cnf(1805,plain,
product(product(X,a14),a17) = product(product(X,a15),product(a17,a15)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,136,theory(equality)]) ).
cnf(1806,plain,
product(product(X,a14),a17) = product(product(X,product(a14,a15)),product(product(a17,a14),a15)),
inference('REWRITE',[status(thm)],[1576,1805,theory(equality)]) ).
cnf(1844,plain,
product(product(a19,a10),a7) = product(a20,product(a7,a11)),
inference('PARAMODULATE',[status(thm)],[117,141,theory(equality)]) ).
cnf(1845,plain,
product(product(a8,a11),product(a7,a11)) = product(product(a7,a11),product(product(a19,a10),a7)),
inference('REWRITE',[status(thm)],[1384,1844,theory(equality)]) ).
cnf(1846,plain,
product(product(X,a10),a7) = product(product(X,a11),product(a7,a11)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,141,theory(equality)]) ).
cnf(1847,plain,
product(product(a8,a10),a7) = product(product(a7,a11),product(product(a19,a10),a7)),
inference('REWRITE',[status(thm)],[1845,1846,theory(equality)]) ).
cnf(1852,plain,
product(product(X,a13),a7) = product(product(X,a14),product(a7,a14)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,142,theory(equality)]) ).
cnf(1853,plain,
product(product(X,a13),a7) = product(product(X,product(a13,a14)),product(product(a7,a13),a14)),
inference('REWRITE',[status(thm)],[1606,1852,theory(equality)]) ).
cnf(1951,plain,
product(product(a21,a28),a3) = product(a20,a4),
inference('PARAMODULATE',[status(thm)],[153,57,theory(equality)]) ).
cnf(1965,plain,
product(product(a20,a3),product(a3,a28)) = product(a21,a28),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,1951,theory(equality)]),563,theory(equality)]) ).
cnf(2180,plain,
product(product(a22,a21),product(a3,a21)) = product(product(a24,a1),product(product(a3,a1),product(a21,a1))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[134,675,theory(equality)]),167,100,involutory_quandle_02,theory(equality)]) ).
cnf(2218,plain,
product(product(X,a19),a8) = product(product(X,product(a19,a8)),product(a7,a8)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,788,theory(equality)]),involutory_quandle_02,theory(equality)]) ).
cnf(2219,plain,
product(a19,product(a19,a8)) = product(product(a19,a7),a8),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[129,788,theory(equality)]),involutory_quandle_02,involutory_quandle_01,theory(equality)]) ).
cnf(2321,plain,
product(product(a19,X),product(a15,a19)) = product(product(a18,a19),product(X,product(a15,a19))),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,903,theory(equality)]) ).
cnf(2323,plain,
product(a15,product(a15,a19)) = product(product(a15,a18),a19),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[129,903,theory(equality)]),involutory_quandle_02,involutory_quandle_01,theory(equality)]) ).
cnf(2374,plain,
product(a2,a24) = product(a3,product(a2,a3)),
inference('PARAMODULATE',[status(thm)],[129,1086,theory(equality)]) ).
cnf(2458,plain,
product(product(X,a3),product(a3,a28)) = product(product(X,product(a3,a28)),product(a4,a28)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,1433,theory(equality)]) ).
cnf(2469,plain,
product(product(a2,a24),a25) = product(product(a2,a3),a2),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[92,1472,theory(equality)]),1562,625,1555,theory(equality)]) ).
cnf(2498,plain,
product(product(a25,a2),product(a25,a24)) = product(product(a25,a24),product(a3,product(a25,a24))),
inference('PARAMODULATE',[status(thm)],[129,1639,theory(equality)]) ).
cnf(2549,plain,
product(product(a25,a21),product(product(X,a21),a24)) = product(product(product(a26,X),a21),a24),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[132,172,theory(equality)]),1780,theory(equality)]) ).
cnf(2555,plain,
product(product(product(X,a21),a24),product(a25,a21)) = product(product(product(X,a26),a21),a24),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[132,173,theory(equality)]),1779,theory(equality)]) ).
cnf(2773,plain,
product(product(X,product(Y,a8)),a19) = product(product(X,a19),product(product(Y,a19),a7)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,198,theory(equality)]) ).
cnf(2877,plain,
product(a18,product(a15,a19)) = product(product(a19,a18),a19),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[214,903,theory(equality)]),458,2323,theory(equality)]) ).
cnf(2896,plain,
product(product(a12,a13),a15) = product(product(product(a13,a12),a15),a18),
inference('PARAMODULATE',[status(thm)],[216,805,theory(equality)]) ).
cnf(2946,plain,
product(product(product(a12,X),a11),a4) = product(a11,product(product(X,a11),a4)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[129,221,theory(equality)]),229,theory(equality)]) ).
cnf(3016,plain,
product(a12,a4) = product(product(a11,a12),a11),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[229,1205,theory(equality)]),involutory_quandle_01,theory(equality)]) ).
cnf(3021,plain,
product(product(product(a9,X),a11),a4) = product(product(a8,a11),product(product(X,a11),a4)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[229,218,theory(equality)]),229,involutory_quandle_02,theory(equality)]) ).
cnf(3108,plain,
product(product(a24,X),product(a25,X)) = product(product(a25,X),product(a2,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[129,239,theory(equality)]),248,theory(equality)]) ).
cnf(3109,plain,
product(product(product(a25,X),Y),product(a3,X)) = product(product(a24,X),product(Y,product(a3,X))),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,239,theory(equality)]) ).
cnf(3110,plain,
product(product(X,product(a2,Y)),product(a25,Y)) = product(product(X,product(a3,Y)),product(a24,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,239,theory(equality)]),629,theory(equality)]) ).
cnf(3111,plain,
product(product(a2,X),product(a3,X)) = product(product(a3,X),product(a24,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[129,239,theory(equality)]),248,theory(equality)]) ).
cnf(3236,plain,
product(a29,a31) = product(product(a25,a2),product(a22,a2)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[250,1231,theory(equality)]),involutory_quandle_02,1026,267,theory(equality)]) ).
cnf(3280,plain,
product(product(X,a22),a25) = product(product(X,a21),product(a25,a21)),
inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,253,theory(equality)]) ).
cnf(3403,plain,
a29 = product(a27,a29),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[256,1174,theory(equality)]),66,127,involutory_quandle_01,3236,involutory_quandle_02,theory(equality)]) ).
cnf(3414,plain,
a29 = a27,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,3403,theory(equality)]),involutory_quandle,theory(equality)]) ).
cnf(3418,plain,
a26 = a30,
inference('REWRITE',[status(thm)],[knot_29,65,3414,theory(equality)]) ).
cnf(3419,plain,
a25 = a31,
inference('REWRITE',[status(thm)],[knot_30,36,3418,theory(equality)]) ).
cnf(3420,plain,
product(a1,a25) = a2,
inference('REWRITE',[status(thm)],[knot,3419,theory(equality)]) ).
cnf(3421,plain,
a21 = a23,
inference('REWRITE',[status(thm)],[knot_22,62,3419,theory(equality)]) ).
cnf(3422,plain,
a21 = a24,
inference('REWRITE',[status(thm)],[knot_23,involutory_quandle,3421,theory(equality)]) ).
cnf(3423,plain,
product(a21,a3) = a25,
inference('REWRITE',[status(thm)],[knot_24,3422,theory(equality)]) ).
cnf(3436,plain,
product(product(X,a2),a25) = product(product(X,a3),a21),
inference('REWRITE',[status(thm)],[241,3422,theory(equality)]) ).
cnf(3438,plain,
a3 = product(product(a1,product(a3,a1)),product(a21,a1)),
inference('REWRITE',[status(thm)],[1787,knot_03,involutory_quandle,3436,theory(equality)]) ).
cnf(3449,plain,
product(product(a22,a21),a3) = product(a21,a2),
inference('REWRITE',[status(thm)],[648,3422,theory(equality)]) ).
cnf(3450,plain,
product(a22,a3) = product(a25,a21),
inference('REWRITE',[status(thm)],[1005,637,3422,theory(equality)]) ).
cnf(3460,plain,
product(a25,a22) = product(a21,a2),
inference('REWRITE',[status(thm)],[1015,1231,3422,theory(equality)]) ).
cnf(3461,plain,
product(a21,a22) = product(a22,product(a21,a2)),
inference('REWRITE',[status(thm)],[1215,3460,theory(equality)]) ).
cnf(3462,plain,
product(product(a25,a21),a25) = product(a21,a2),
inference('REWRITE',[status(thm)],[1231,3460,theory(equality)]) ).
cnf(3473,plain,
product(product(a3,a2),a3) = product(a2,a21),
inference('REWRITE',[status(thm)],[1086,3422,theory(equality)]) ).
cnf(3477,plain,
a25 = product(a22,a2),
inference('REWRITE',[status(thm)],[1096,3423,involutory_quandle,3422,theory(equality)]) ).
cnf(3481,plain,
a22 = product(a25,a2),
inference('REWRITE',[status(thm)],[1211,knot_21,3422,theory(equality)]) ).
cnf(3482,plain,
product(a3,a2) = product(a2,a22),
inference('REWRITE',[status(thm)],[625,3481,theory(equality)]) ).
cnf(3484,plain,
product(product(a2,a22),a3) = product(a2,a21),
inference('REWRITE',[status(thm)],[3473,3482,theory(equality)]) ).
cnf(3489,plain,
product(a2,a3) = product(a3,a21),
inference('REWRITE',[status(thm)],[1212,3422,theory(equality)]) ).
cnf(3490,plain,
product(product(a2,a22),a25) = product(a2,a3),
inference('REWRITE',[status(thm)],[1072,3489,theory(equality)]) ).
cnf(3501,plain,
product(product(X,a2),a25) = product(product(X,a21),product(a2,a3)),
inference('REWRITE',[status(thm)],[1564,3422,theory(equality)]) ).
cnf(3502,plain,
product(product(a2,a22),a21) = product(a3,product(a25,a21)),
inference('REWRITE',[status(thm)],[1642,3482,3422,theory(equality)]) ).
cnf(3503,plain,
product(product(a25,a21),X) = product(product(a22,X),product(a3,X)),
inference('REWRITE',[status(thm)],[1643,3481,3422,theory(equality)]) ).
cnf(3504,plain,
product(product(a22,X),a3) = product(product(a25,a21),product(X,a3)),
inference('REWRITE',[status(thm)],[1644,3481,3422,theory(equality)]) ).
cnf(3518,plain,
a25 = product(product(a21,a1),product(product(a3,a1),product(a21,a1))),
inference('REWRITE',[status(thm)],[2180,involutory_quandle,3477,3501,3489,3422,theory(equality)]) ).
cnf(3520,plain,
product(a2,a21) = product(a3,product(a2,a3)),
inference('REWRITE',[status(thm)],[2374,3422,theory(equality)]) ).
cnf(3525,plain,
product(a3,a22) = product(product(a2,a3),a2),
inference('REWRITE',[status(thm)],[2469,1070,3422,theory(equality)]) ).
cnf(3537,plain,
product(a22,product(a25,a21)) = product(product(a25,a21),product(product(a2,a22),a21)),
inference('REWRITE',[status(thm)],[2498,3502,3481,3422,theory(equality)]) ).
cnf(3538,plain,
product(product(a25,a21),X) = product(a26,X),
inference('REWRITE',[status(thm)],[2549,involutory_quandle_01,3422,theory(equality)]) ).
cnf(3539,plain,
product(a22,product(a25,a21)) = product(a26,product(product(a2,a22),a21)),
inference('REWRITE',[status(thm)],[3537,3538,theory(equality)]) ).
cnf(3541,plain,
product(product(a22,X),a3) = product(a26,product(X,a3)),
inference('REWRITE',[status(thm)],[3504,3538,theory(equality)]) ).
cnf(3542,plain,
product(a26,a25) = product(a21,a2),
inference('REWRITE',[status(thm)],[3462,3538,theory(equality)]) ).
cnf(3549,plain,
product(a26,X) = product(product(a22,X),product(a3,X)),
inference('REWRITE',[status(thm)],[3503,3538,theory(equality)]) ).
cnf(3552,plain,
product(X,product(a25,a21)) = product(X,a26),
inference('REWRITE',[status(thm)],[2555,involutory_quandle_01,3422,theory(equality)]) ).
cnf(3554,plain,
product(a22,a26) = product(a26,product(product(a2,a22),a21)),
inference('REWRITE',[status(thm)],[3539,3552,theory(equality)]) ).
cnf(3558,plain,
product(product(a2,a22),a21) = product(a3,a26),
inference('REWRITE',[status(thm)],[3502,3552,theory(equality)]) ).
cnf(3559,plain,
product(a22,a26) = product(a26,product(a3,a26)),
inference('REWRITE',[status(thm)],[3554,3558,theory(equality)]) ).
cnf(3564,plain,
product(product(X,a22),a25) = product(product(X,a21),a26),
inference('REWRITE',[status(thm)],[3280,3552,theory(equality)]) ).
cnf(3565,plain,
product(product(a2,a21),a26) = product(a2,a3),
inference('REWRITE',[status(thm)],[3490,3564,theory(equality)]) ).
cnf(3567,plain,
product(a21,a26) = product(a22,a21),
inference('REWRITE',[status(thm)],[1097,involutory_quandle,3564,theory(equality)]) ).
cnf(3579,plain,
product(a22,X) = product(product(a25,X),product(a2,X)),
inference('REWRITE',[status(thm)],[3108,93,3422,theory(equality)]) ).
cnf(3581,plain,
product(product(product(a25,X),Y),product(a3,X)) = product(product(a21,X),product(Y,product(a3,X))),
inference('REWRITE',[status(thm)],[3109,3422,theory(equality)]) ).
cnf(3582,plain,
product(product(X,product(a2,Y)),product(a25,Y)) = product(product(X,product(a3,Y)),product(a21,Y)),
inference('REWRITE',[status(thm)],[3110,3422,theory(equality)]) ).
cnf(3583,plain,
a3 = product(product(a1,product(a2,a1)),product(a25,a1)),
inference('REWRITE',[status(thm)],[3438,3582,theory(equality)]) ).
cnf(3584,plain,
product(product(a2,X),product(a3,X)) = product(product(a3,X),product(a21,X)),
inference('REWRITE',[status(thm)],[3111,3422,theory(equality)]) ).
cnf(3586,plain,
a25 = a27,
inference('REWRITE',[status(thm)],[3518,knot_26,3549,3579,3581,3584,theory(equality)]) ).
cnf(3588,plain,
product(a25,a21) = a28,
inference('REWRITE',[status(thm)],[knot_27,3586,theory(equality)]) ).
cnf(3589,plain,
product(a22,a3) = a28,
inference('REWRITE',[status(thm)],[3450,3588,theory(equality)]) ).
cnf(3610,plain,
product(X,a28) = product(X,a26),
inference('REWRITE',[status(thm)],[3552,3588,theory(equality)]) ).
cnf(3622,plain,
product(product(a3,a26),a3) = a4,
inference('REWRITE',[status(thm)],[559,3610,theory(equality)]) ).
cnf(3630,plain,
product(a3,product(a3,a26)) = product(a4,a26),
inference('REWRITE',[status(thm)],[1433,3610,theory(equality)]) ).
cnf(3632,plain,
product(product(a20,a3),product(a3,a26)) = product(a22,a21),
inference('REWRITE',[status(thm)],[1965,3567,3610,theory(equality)]) ).
cnf(3635,plain,
product(product(X,a3),product(a3,a26)) = product(product(X,product(a3,a26)),product(a4,a26)),
inference('REWRITE',[status(thm)],[2458,3610,theory(equality)]) ).
cnf(3644,plain,
product(a25,a1) = a26,
inference('REWRITE',[status(thm)],[65,3586,theory(equality)]) ).
cnf(3645,plain,
a3 = product(product(a1,product(a2,a1)),a26),
inference('REWRITE',[status(thm)],[3583,3644,theory(equality)]) ).
cnf(3674,plain,
product(a21,a2) = a22,
inference('REWRITE',[status(thm)],[1176,3481,3420,3542,3586,theory(equality)]) ).
cnf(3675,plain,
product(product(a22,a21),a3) = a22,
inference('REWRITE',[status(thm)],[3449,3674,theory(equality)]) ).
cnf(3677,plain,
product(a21,a22) = a22,
inference('REWRITE',[status(thm)],[3461,involutory_quandle,3674,theory(equality)]) ).
cnf(3679,plain,
product(product(a22,a21),X) = product(a21,X),
inference('REWRITE',[status(thm)],[1112,251,3677,theory(equality)]) ).
cnf(3680,plain,
a25 = a22,
inference('REWRITE',[status(thm)],[3675,3423,3679,theory(equality)]) ).
cnf(3681,plain,
product(a2,a22) = a3,
inference('REWRITE',[status(thm)],[knot_03,3680,theory(equality)]) ).
cnf(3682,plain,
product(a3,a2) = a3,
inference('REWRITE',[status(thm)],[3482,3681,theory(equality)]) ).
cnf(3684,plain,
a3 = product(a2,a21),
inference('REWRITE',[status(thm)],[3484,involutory_quandle,3681,theory(equality)]) ).
cnf(3685,plain,
a3 = product(a3,product(a2,a3)),
inference('REWRITE',[status(thm)],[3520,3684,theory(equality)]) ).
cnf(3686,plain,
product(a3,a26) = product(a2,a3),
inference('REWRITE',[status(thm)],[3565,3684,theory(equality)]) ).
cnf(3687,plain,
product(a22,a26) = product(product(a22,a2),a3),
inference('REWRITE',[status(thm)],[3559,3541,3686,theory(equality)]) ).
cnf(3689,plain,
a2 = a4,
inference('REWRITE',[status(thm)],[3622,involutory_quandle_01,3686,theory(equality)]) ).
cnf(3690,plain,
product(a2,a11) = a5,
inference('REWRITE',[status(thm)],[knot_05,3689,theory(equality)]) ).
cnf(3694,plain,
product(product(X,a2),a11) = product(product(X,a11),a5),
inference('REWRITE',[status(thm)],[148,3689,theory(equality)]) ).
cnf(3704,plain,
product(product(a9,a11),a2) = product(a8,a11),
inference('REWRITE',[status(thm)],[485,3689,theory(equality)]) ).
cnf(3708,plain,
product(a12,a11) = product(a11,a2),
inference('REWRITE',[status(thm)],[489,3689,theory(equality)]) ).
cnf(3763,plain,
product(product(product(a12,X),a11),a2) = product(a11,product(product(X,a11),a2)),
inference('REWRITE',[status(thm)],[2946,3689,theory(equality)]) ).
cnf(3786,plain,
product(a12,a2) = product(product(a11,a12),a11),
inference('REWRITE',[status(thm)],[3016,3689,theory(equality)]) ).
cnf(3791,plain,
product(product(product(a9,X),a11),a2) = product(product(a8,a11),product(product(X,a11),a2)),
inference('REWRITE',[status(thm)],[3021,3689,theory(equality)]) ).
cnf(3813,plain,
a3 = product(a2,a26),
inference('REWRITE',[status(thm)],[3630,3689,3685,3686,theory(equality)]) ).
cnf(3815,plain,
product(product(a20,a2),a3) = product(a22,a21),
inference('REWRITE',[status(thm)],[3632,involutory_quandle_02,3686,theory(equality)]) ).
cnf(3818,plain,
product(product(X,a2),a3) = product(product(X,a3),a2),
inference('REWRITE',[status(thm)],[3635,164,3813,3689,involutory_quandle_02,3686,theory(equality)]) ).
cnf(3819,plain,
product(a3,a22) = product(a2,a3),
inference('REWRITE',[status(thm)],[3525,involutory_quandle,3818,theory(equality)]) ).
cnf(3820,plain,
product(a2,a3) = a2,
inference('REWRITE',[status(thm)],[61,3819,3680,theory(equality)]) ).
cnf(3830,plain,
a2 = product(a3,a21),
inference('REWRITE',[status(thm)],[3489,3820,theory(equality)]) ).
cnf(3837,plain,
a22 = a21,
inference('REWRITE',[status(thm)],[62,involutory_quandle,3680,theory(equality)]) ).
cnf(3844,plain,
product(a21,a26) = a21,
inference('REWRITE',[status(thm)],[3567,involutory_quandle,3837,theory(equality)]) ).
cnf(3846,plain,
product(a21,a3) = a28,
inference('REWRITE',[status(thm)],[3589,3837,theory(equality)]) ).
cnf(3848,plain,
product(a21,a2) = a21,
inference('REWRITE',[status(thm)],[3674,3837,theory(equality)]) ).
cnf(3849,plain,
a25 = a21,
inference('REWRITE',[status(thm)],[3680,3837,theory(equality)]) ).
cnf(3850,plain,
a21 = a28,
inference('REWRITE',[status(thm)],[3687,3846,3848,3844,3837,theory(equality)]) ).
cnf(3859,plain,
product(X,a21) = product(X,a26),
inference('REWRITE',[status(thm)],[3610,3850,theory(equality)]) ).
cnf(3862,plain,
a3 = product(product(a1,product(a2,a1)),a21),
inference('REWRITE',[status(thm)],[3645,3859,theory(equality)]) ).
cnf(3875,plain,
product(product(a20,a2),a3) = a21,
inference('REWRITE',[status(thm)],[3815,involutory_quandle,3837,theory(equality)]) ).
cnf(3912,plain,
a21 = a31,
inference('REWRITE',[status(thm)],[3419,3837,3680,theory(equality)]) ).
cnf(3913,plain,
a32 = a2,
inference('REWRITE',[status(thm)],[3420,40,3837,3680,theory(equality)]) ).
cnf(3914,plain,
a3 = a1,
inference('REWRITE',[status(thm)],[knot_32,3684,3913,theory(equality)]) ).
cnf(3915,plain,
product(a1,a2) = a1,
inference('REWRITE',[status(thm)],[3682,3914,theory(equality)]) ).
cnf(3918,plain,
product(a2,a1) = a2,
inference('REWRITE',[status(thm)],[3820,3914,theory(equality)]) ).
cnf(3920,plain,
a2 = product(a1,a21),
inference('REWRITE',[status(thm)],[3830,3914,theory(equality)]) ).
cnf(3926,plain,
a1 = a2,
inference('REWRITE',[status(thm)],[3862,3920,3915,3918,3914,theory(equality)]) ).
cnf(3927,plain,
a1 = a4,
inference('REWRITE',[status(thm)],[3689,3926,theory(equality)]) ).
cnf(3928,plain,
product(a1,a11) = a5,
inference('REWRITE',[status(thm)],[3690,3926,theory(equality)]) ).
cnf(3935,plain,
product(product(X,a1),a11) = product(product(X,a11),a5),
inference('REWRITE',[status(thm)],[3694,3926,theory(equality)]) ).
cnf(3940,plain,
product(product(a15,a1),a11) = product(a16,a12),
inference('REWRITE',[status(thm)],[936,3935,theory(equality)]) ).
cnf(3955,plain,
product(product(a9,a1),product(a11,a1)) = product(a8,a11),
inference('REWRITE',[status(thm)],[3704,involutory_quandle_02,3926,theory(equality)]) ).
cnf(3956,plain,
product(a12,a11) = product(a11,a1),
inference('REWRITE',[status(thm)],[3708,3926,theory(equality)]) ).
cnf(3995,plain,
product(product(product(a12,X),a1),product(a11,a1)) = product(a11,product(product(X,a11),a1)),
inference('REWRITE',[status(thm)],[3763,involutory_quandle_02,3926,theory(equality)]) ).
cnf(4016,plain,
product(a12,a1) = product(product(a11,a12),a11),
inference('REWRITE',[status(thm)],[3786,3926,theory(equality)]) ).
cnf(4021,plain,
product(product(product(a9,X),a1),product(a11,a1)) = product(product(a8,a11),product(product(X,a11),a1)),
inference('REWRITE',[status(thm)],[3791,involutory_quandle_02,3926,theory(equality)]) ).
cnf(4031,plain,
product(a21,a1) = a21,
inference('REWRITE',[status(thm)],[3848,3926,theory(equality)]) ).
cnf(4036,plain,
a32 = a1,
inference('REWRITE',[status(thm)],[3913,3926,theory(equality)]) ).
cnf(4040,plain,
a20 = a21,
inference('REWRITE',[status(thm)],[3875,involutory_quandle_01,3926,3914,theory(equality)]) ).
cnf(4043,plain,
a20 = a23,
inference('REWRITE',[status(thm)],[3421,4040,theory(equality)]) ).
cnf(4044,plain,
a20 = a24,
inference('REWRITE',[status(thm)],[3422,4040,theory(equality)]) ).
cnf(4045,plain,
a22 = a20,
inference('REWRITE',[status(thm)],[3837,4040,theory(equality)]) ).
cnf(4046,plain,
a25 = a20,
inference('REWRITE',[status(thm)],[3849,4040,theory(equality)]) ).
cnf(4047,plain,
a20 = a28,
inference('REWRITE',[status(thm)],[3850,4040,theory(equality)]) ).
cnf(4050,plain,
a20 = a31,
inference('REWRITE',[status(thm)],[3912,4040,theory(equality)]) ).
cnf(4053,plain,
product(a20,a1) = a20,
inference('REWRITE',[status(thm)],[4031,4040,theory(equality)]) ).
cnf(4075,plain,
a20 = a27,
inference('REWRITE',[status(thm)],[3586,4045,3680,theory(equality)]) ).
cnf(4076,plain,
a20 = a26,
inference('REWRITE',[status(thm)],[3644,4053,4045,3680,theory(equality)]) ).
cnf(4077,plain,
a20 = a30,
inference('REWRITE',[status(thm)],[3418,4076,theory(equality)]) ).
cnf(4083,plain,
a20 = a1,
inference('REWRITE',[status(thm)],[knot_31,4036,4053,3914,4046,3419,theory(equality)]) ).
cnf(4084,plain,
product(a19,a11) = a1,
inference('REWRITE',[status(thm)],[knot_19,4083,theory(equality)]) ).
cnf(4085,plain,
a5 = a19,
inference('REWRITE',[status(thm)],[55,3928,4083,theory(equality)]) ).
cnf(4086,plain,
a18 = a6,
inference('REWRITE',[status(thm)],[knot_06,50,4085,theory(equality)]) ).
cnf(4087,plain,
product(a9,a15) = product(a7,a15),
inference('REWRITE',[status(thm)],[466,381,4086,theory(equality)]) ).
cnf(4099,plain,
product(a13,a15) = product(a11,a15),
inference('REWRITE',[status(thm)],[502,387,4086,theory(equality)]) ).
cnf(4117,plain,
product(a17,a15) = a15,
inference('REWRITE',[status(thm)],[511,402,4086,theory(equality)]) ).
cnf(4124,plain,
product(a14,a15) = a15,
inference('REWRITE',[status(thm)],[1198,involutory_quandle,4117,theory(equality)]) ).
cnf(4129,plain,
product(product(X,a14),a17) = product(product(X,a15),product(product(a17,a14),a15)),
inference('REWRITE',[status(thm)],[1806,4124,theory(equality)]) ).
cnf(4130,plain,
product(product(a17,a14),a17) = a15,
inference('REWRITE',[status(thm)],[1218,4117,theory(equality)]) ).
cnf(4131,plain,
a15 = product(product(a17,a14),a15),
inference('REWRITE',[status(thm)],[1577,4117,theory(equality)]) ).
cnf(4132,plain,
product(product(X,a14),a17) = X,
inference('REWRITE',[status(thm)],[4129,involutory_quandle_01,4131,theory(equality)]) ).
cnf(4133,plain,
a17 = a15,
inference('REWRITE',[status(thm)],[4130,4132,theory(equality)]) ).
cnf(4134,plain,
product(a7,a15) = a10,
inference('REWRITE',[status(thm)],[knot_09,4087,4133,theory(equality)]) ).
cnf(4146,plain,
product(a15,a9) = a18,
inference('REWRITE',[status(thm)],[knot_17,4133,theory(equality)]) ).
cnf(4147,plain,
product(a10,a15) = a9,
inference('REWRITE',[status(thm)],[41,4133,theory(equality)]) ).
cnf(4149,plain,
a15 = a14,
inference('REWRITE',[status(thm)],[42,involutory_quandle,4133,theory(equality)]) ).
cnf(4150,plain,
product(a18,a14) = a19,
inference('REWRITE',[status(thm)],[knot_18,4149,theory(equality)]) ).
cnf(4151,plain,
product(a19,a14) = a18,
inference('REWRITE',[status(thm)],[50,4149,theory(equality)]) ).
cnf(4154,plain,
product(product(X,a18),a14) = product(product(X,a14),a19),
inference('REWRITE',[status(thm)],[144,4149,theory(equality)]) ).
cnf(4161,plain,
product(a18,a19) = product(a19,product(a14,a19)),
inference('REWRITE',[status(thm)],[903,4149,theory(equality)]) ).
cnf(4173,plain,
product(product(a19,X),product(a14,a19)) = product(product(a18,a19),product(X,product(a14,a19))),
inference('REWRITE',[status(thm)],[2321,4149,theory(equality)]) ).
cnf(4175,plain,
product(a18,product(a14,a19)) = product(product(a19,a18),a19),
inference('REWRITE',[status(thm)],[2877,4149,theory(equality)]) ).
cnf(4185,plain,
product(product(a12,a13),a14) = product(product(product(a13,a12),a14),a18),
inference('REWRITE',[status(thm)],[2896,4149,theory(equality)]) ).
cnf(4193,plain,
product(product(a14,a1),a11) = product(a16,a12),
inference('REWRITE',[status(thm)],[3940,4149,theory(equality)]) ).
cnf(4200,plain,
product(a13,a14) = product(a11,a14),
inference('REWRITE',[status(thm)],[4099,4149,theory(equality)]) ).
cnf(4211,plain,
product(product(X,a13),a7) = product(product(X,product(a11,a14)),product(product(a7,a13),a14)),
inference('REWRITE',[status(thm)],[1853,4200,theory(equality)]) ).
cnf(4231,plain,
a17 = a14,
inference('REWRITE',[status(thm)],[4133,4149,theory(equality)]) ).
cnf(4232,plain,
product(a7,a14) = a10,
inference('REWRITE',[status(thm)],[4134,4149,theory(equality)]) ).
cnf(4234,plain,
product(a7,a10) = product(product(a7,a13),a14),
inference('REWRITE',[status(thm)],[1607,4232,theory(equality)]) ).
cnf(4235,plain,
product(product(X,a13),a7) = product(product(X,product(a11,a14)),product(a7,a10)),
inference('REWRITE',[status(thm)],[4211,4234,theory(equality)]) ).
cnf(4239,plain,
product(product(a7,a13),X) = product(a11,X),
inference('REWRITE',[status(thm)],[1716,78,4232,theory(equality)]) ).
cnf(4240,plain,
product(a7,a10) = product(a11,a14),
inference('REWRITE',[status(thm)],[4234,4239,theory(equality)]) ).
cnf(4243,plain,
product(a10,a13) = product(a7,a11),
inference('REWRITE',[status(thm)],[1224,853,4240,theory(equality)]) ).
cnf(4246,plain,
product(product(X,a10),a7) = product(product(X,a11),product(a10,a13)),
inference('REWRITE',[status(thm)],[1846,4243,theory(equality)]) ).
cnf(4247,plain,
product(product(a8,a10),a7) = product(product(a10,a13),product(product(a19,a10),a7)),
inference('REWRITE',[status(thm)],[1847,4243,theory(equality)]) ).
cnf(4256,plain,
product(product(X,a13),a7) = X,
inference('REWRITE',[status(thm)],[4235,involutory_quandle_01,4240,theory(equality)]) ).
cnf(4263,plain,
a10 = product(a11,a14),
inference('REWRITE',[status(thm)],[843,4256,theory(equality)]) ).
cnf(4264,plain,
a11 = product(a10,a13),
inference('REWRITE',[status(thm)],[853,knot_10,4263,theory(equality)]) ).
cnf(4274,plain,
product(product(X,a10),a7) = X,
inference('REWRITE',[status(thm)],[4246,involutory_quandle_01,4264,theory(equality)]) ).
cnf(4277,plain,
a14 = product(a13,a11),
inference('REWRITE',[status(thm)],[882,4274,theory(equality)]) ).
cnf(4278,plain,
a13 = product(a14,a10),
inference('REWRITE',[status(thm)],[869,48,4277,theory(equality)]) ).
cnf(4279,plain,
product(a13,a14) = a13,
inference('REWRITE',[status(thm)],[1404,4232,4278,4277,theory(equality)]) ).
cnf(4290,plain,
a8 = product(a11,a19),
inference('REWRITE',[status(thm)],[4247,4274,4264,theory(equality)]) ).
cnf(4297,plain,
a13 = a10,
inference('REWRITE',[status(thm)],[4200,4279,4263,theory(equality)]) ).
cnf(4298,plain,
product(a12,a19) = a10,
inference('REWRITE',[status(thm)],[knot_12,4297,theory(equality)]) ).
cnf(4299,plain,
a11 = a14,
inference('REWRITE',[status(thm)],[knot_13,knot_10,4297,theory(equality)]) ).
cnf(4301,plain,
a8 = a12,
inference('REWRITE',[status(thm)],[432,involutory_quandle,4290,4299,theory(equality)]) ).
cnf(4302,plain,
product(a7,a19) = a12,
inference('REWRITE',[status(thm)],[knot_07,4301,theory(equality)]) ).
cnf(4303,plain,
a10 = a7,
inference('REWRITE',[status(thm)],[44,4298,4301,theory(equality)]) ).
cnf(4304,plain,
a10 = a11,
inference('REWRITE',[status(thm)],[knot_10,involutory_quandle,4303,theory(equality)]) ).
cnf(4306,plain,
product(a12,a10) = product(a10,a1),
inference('REWRITE',[status(thm)],[3956,4304,theory(equality)]) ).
cnf(4309,plain,
product(product(product(a12,X),a1),product(a10,a1)) = product(a10,product(product(X,a10),a1)),
inference('REWRITE',[status(thm)],[3995,4304,theory(equality)]) ).
cnf(4310,plain,
product(a12,a1) = product(product(a10,a12),a10),
inference('REWRITE',[status(thm)],[4016,4304,theory(equality)]) ).
cnf(4315,plain,
product(a19,a10) = a1,
inference('REWRITE',[status(thm)],[4084,4304,theory(equality)]) ).
cnf(4316,plain,
a10 = a14,
inference('REWRITE',[status(thm)],[4299,4304,theory(equality)]) ).
cnf(4317,plain,
product(a10,a19) = a12,
inference('REWRITE',[status(thm)],[4302,4303,theory(equality)]) ).
cnf(4319,plain,
product(product(a10,X),a19) = product(a12,product(X,a19)),
inference('REWRITE',[status(thm)],[106,4303,4301,theory(equality)]) ).
cnf(4320,plain,
product(product(X,a10),a19) = product(product(X,a19),a12),
inference('REWRITE',[status(thm)],[138,4303,4301,theory(equality)]) ).
cnf(4323,plain,
product(product(X,a12),a19) = product(product(X,a19),a10),
inference('REWRITE',[status(thm)],[198,4303,4301,theory(equality)]) ).
cnf(4328,plain,
product(product(X,a12),a19) = product(product(X,a1),product(a10,a1)),
inference('REWRITE',[status(thm)],[376,4306,4315,4323,4303,4301,theory(equality)]) ).
cnf(4329,plain,
product(a10,product(product(X,a10),a1)) = product(product(a12,product(X,a12)),a19),
inference('REWRITE',[status(thm)],[1292,4309,4328,theory(equality)]) ).
cnf(4331,plain,
product(product(X,a1),product(a10,a1)) = product(product(X,a19),a10),
inference('REWRITE',[status(thm)],[4323,4328,theory(equality)]) ).
cnf(4333,plain,
product(a10,a12) = product(a12,product(a19,a12)),
inference('REWRITE',[status(thm)],[788,4303,4301,theory(equality)]) ).
cnf(4334,plain,
product(a19,a1) = product(a1,product(a10,a1)),
inference('REWRITE',[status(thm)],[1460,4306,involutory_quandle_02,4315,4303,4301,theory(equality)]) ).
cnf(4338,plain,
product(product(X,a10),a19) = product(product(X,product(a1,a12)),product(product(a10,a1),a12)),
inference('REWRITE',[status(thm)],[2218,4315,170,4303,4320,4301,theory(equality)]) ).
cnf(4339,plain,
product(a19,product(a19,a12)) = product(a1,a12),
inference('REWRITE',[status(thm)],[2219,4315,4303,4301,theory(equality)]) ).
cnf(4347,plain,
product(product(X,product(Y,a12)),a19) = product(product(X,a19),product(product(Y,a1),product(a10,a1))),
inference('REWRITE',[status(thm)],[2773,4331,4303,4301,theory(equality)]) ).
cnf(4348,plain,
product(a10,product(product(X,a10),a1)) = product(a10,product(product(X,a1),product(a10,a1))),
inference('REWRITE',[status(thm)],[4329,4298,4347,theory(equality)]) ).
cnf(4351,plain,
product(product(a9,a1),product(a10,a1)) = product(a10,a1),
inference('REWRITE',[status(thm)],[3955,4306,4304,4301,theory(equality)]) ).
cnf(4354,plain,
product(product(product(a9,X),a1),product(a10,a1)) = product(product(a10,a1),product(product(X,a10),a1)),
inference('REWRITE',[status(thm)],[4021,4306,4304,4301,theory(equality)]) ).
cnf(4357,plain,
a15 = a10,
inference('REWRITE',[status(thm)],[4149,4304,4299,theory(equality)]) ).
cnf(4358,plain,
product(a18,a10) = a19,
inference('REWRITE',[status(thm)],[4150,4304,4299,theory(equality)]) ).
cnf(4359,plain,
a1 = a18,
inference('REWRITE',[status(thm)],[4151,4315,4304,4299,theory(equality)]) ).
cnf(4360,plain,
product(a10,a9) = product(a9,a1),
inference('REWRITE',[status(thm)],[331,4359,theory(equality)]) ).
cnf(4363,plain,
a1 = a6,
inference('REWRITE',[status(thm)],[4086,4359,theory(equality)]) ).
cnf(4365,plain,
product(a1,a10) = a19,
inference('REWRITE',[status(thm)],[4358,4359,theory(equality)]) ).
cnf(4368,plain,
product(product(X,a1),a10) = product(product(X,a10),a19),
inference('REWRITE',[status(thm)],[4154,4304,4359,4299,theory(equality)]) ).
cnf(4371,plain,
product(product(X,a1),a10) = product(product(X,product(a1,a12)),product(product(a10,a1),a12)),
inference('REWRITE',[status(thm)],[4338,4368,theory(equality)]) ).
cnf(4381,plain,
product(a1,a19) = product(a19,a12),
inference('REWRITE',[status(thm)],[4161,4317,4304,4359,4299,theory(equality)]) ).
cnf(4382,plain,
product(a10,a12) = product(product(a10,a1),a19),
inference('REWRITE',[status(thm)],[4333,4319,4381,theory(equality)]) ).
cnf(4384,plain,
product(a19,product(a1,a19)) = product(a1,a12),
inference('REWRITE',[status(thm)],[4339,4381,theory(equality)]) ).
cnf(4388,plain,
product(product(a19,X),a12) = product(product(a1,a19),product(X,a12)),
inference('REWRITE',[status(thm)],[4173,4359,4317,4304,4299,theory(equality)]) ).
cnf(4390,plain,
product(a1,a12) = product(product(a19,a1),a19),
inference('REWRITE',[status(thm)],[4175,4317,4304,4359,4299,theory(equality)]) ).
cnf(4407,plain,
product(product(a10,a1),a10) = product(a16,a12),
inference('REWRITE',[status(thm)],[4193,4304,4299,theory(equality)]) ).
cnf(4412,plain,
a17 = a10,
inference('REWRITE',[status(thm)],[4231,4304,4299,theory(equality)]) ).
cnf(4422,plain,
product(a1,a12) = product(product(a1,a19),product(a10,a12)),
inference('REWRITE',[status(thm)],[1454,4384,4381,4297,theory(equality)]) ).
cnf(4436,plain,
product(a16,a12) = a12,
inference('REWRITE',[status(thm)],[4185,involutory_quandle_01,4359,4310,4407,4316,4306,4297,theory(equality)]) ).
cnf(4437,plain,
product(product(a10,a1),a10) = a12,
inference('REWRITE',[status(thm)],[4407,4436,theory(equality)]) ).
cnf(4444,plain,
product(a9,a1) = a1,
inference('REWRITE',[status(thm)],[4146,4359,4360,4316,4149,theory(equality)]) ).
cnf(4445,plain,
product(a19,a1) = product(a10,a1),
inference('REWRITE',[status(thm)],[4351,4334,4444,theory(equality)]) ).
cnf(4447,plain,
product(a1,a12) = product(a10,a12),
inference('REWRITE',[status(thm)],[4390,4382,4445,theory(equality)]) ).
cnf(4462,plain,
product(a1,a12) = product(product(a10,a1),a12),
inference('REWRITE',[status(thm)],[4422,4445,4388,4447,theory(equality)]) ).
cnf(4463,plain,
product(product(X,a1),a10) = X,
inference('REWRITE',[status(thm)],[4371,involutory_quandle_01,4462,theory(equality)]) ).
cnf(4480,plain,
a10 = a12,
inference('REWRITE',[status(thm)],[4437,4463,theory(equality)]) ).
cnf(4482,plain,
a8 = a10,
inference('REWRITE',[status(thm)],[4301,4480,theory(equality)]) ).
cnf(4483,plain,
a10 = product(a10,a1),
inference('REWRITE',[status(thm)],[4306,involutory_quandle,4480,theory(equality)]) ).
cnf(4485,plain,
product(a10,product(product(X,a10),a1)) = product(a10,X),
inference('REWRITE',[status(thm)],[4348,4463,4483,theory(equality)]) ).
cnf(4486,plain,
product(a9,X) = product(a10,X),
inference('REWRITE',[status(thm)],[4354,4485,4463,4483,theory(equality)]) ).
cnf(4487,plain,
a10 = a1,
inference('REWRITE',[status(thm)],[4444,4483,4486,theory(equality)]) ).
cnf(4488,plain,
a13 = a1,
inference('REWRITE',[status(thm)],[4297,4487,theory(equality)]) ).
cnf(4489,plain,
a1 = a7,
inference('REWRITE',[status(thm)],[4303,4487,theory(equality)]) ).
cnf(4490,plain,
a1 = a11,
inference('REWRITE',[status(thm)],[4304,4487,theory(equality)]) ).
cnf(4492,plain,
a1 = a14,
inference('REWRITE',[status(thm)],[4316,4487,theory(equality)]) ).
cnf(4493,plain,
a15 = a1,
inference('REWRITE',[status(thm)],[4357,4487,theory(equality)]) ).
cnf(4494,plain,
a1 = a19,
inference('REWRITE',[status(thm)],[4365,involutory_quandle,4487,theory(equality)]) ).
cnf(4497,plain,
a5 = a1,
inference('REWRITE',[status(thm)],[4085,4494,theory(equality)]) ).
cnf(4498,plain,
a17 = a1,
inference('REWRITE',[status(thm)],[4412,4487,theory(equality)]) ).
cnf(4501,plain,
a1 = a12,
inference('REWRITE',[status(thm)],[4480,4487,theory(equality)]) ).
cnf(4502,plain,
a8 = a1,
inference('REWRITE',[status(thm)],[4482,4487,theory(equality)]) ).
cnf(4507,plain,
a1 = a9,
inference('REWRITE',[status(thm)],[4147,involutory_quandle,4492,4487,4149,theory(equality)]) ).
cnf(4508,plain,
a1 = a16,
inference('REWRITE',[status(thm)],[46,involutory_quandle,4494,4493,4133,theory(equality)]) ).
cnf(4509,plain,
a1 = a21,
inference('REWRITE',[status(thm)],[4040,4083,theory(equality)]) ).
cnf(4510,plain,
a1 = a23,
inference('REWRITE',[status(thm)],[4043,4083,theory(equality)]) ).
cnf(4511,plain,
a1 = a24,
inference('REWRITE',[status(thm)],[4044,4083,theory(equality)]) ).
cnf(4512,plain,
a22 = a1,
inference('REWRITE',[status(thm)],[4045,4083,theory(equality)]) ).
cnf(4513,plain,
a25 = a1,
inference('REWRITE',[status(thm)],[4046,4083,theory(equality)]) ).
cnf(4514,plain,
a1 = a28,
inference('REWRITE',[status(thm)],[4047,4083,theory(equality)]) ).
cnf(4515,plain,
a1 = a31,
inference('REWRITE',[status(thm)],[4050,4083,theory(equality)]) ).
cnf(4518,plain,
a1 = a27,
inference('REWRITE',[status(thm)],[4075,4083,theory(equality)]) ).
cnf(4519,plain,
a1 = a26,
inference('REWRITE',[status(thm)],[4076,4083,theory(equality)]) ).
cnf(4520,plain,
a1 = a30,
inference('REWRITE',[status(thm)],[4077,4083,theory(equality)]) ).
cnf(4522,plain,
$false,
inference('REWRITE',[status(thm)],[goal,4036,4519,4510,4512,4509,4083,4488,4501,4498,4508,4507,4502,4494,4359,4489,4363,4493,4492,4497,4490,4487,3927,4518,4514,3914,4513,4511,3926,4515,4520,3414,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : TOP050-1 : TPTP v8.1.0. Released v8.1.0.
% 0.07/0.13 % Command : run-snark %s %d
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun May 29 03:45:54 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.46 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.47 *
% 0.20/0.47 *
% 0.20/0.48 #<PACKAGE "SNARK-USER">
% 0.20/0.48 *
% 0.20/0.48 SNARK-TPTP-OPTIONS
% 0.20/0.48 *
% 0.20/0.48 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.48 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.48 (USE-FACTORING :POS)
% 0.20/0.48 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.48 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.48 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.48 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.48 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.48 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.48 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.48 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.48 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.48 (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.48 *
% 0.20/0.48 "."
% 0.20/0.48 *
% 0.20/0.48 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-05-29T03:45:54
% 0.20/0.48 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n020.cluster.edu at 2022-05-29T03:45:54
% 1.97/2.13
% 1.97/2.13
% 1.97/2.13 #||
% 1.97/2.13 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.97/2.13 % SZS output start Refutation
% See solution above
% 1.97/2.17 ||#
% 1.97/2.17
% 1.97/2.17 ; Summary of computation:
% 1.97/2.17 ; 11876 formulas have been input or derived (from 505 formulas).
% 1.97/2.17 ; 4522 (38%) were retained. Of these,
% 1.97/2.17 ; 4461 (99%) were simplified or subsumed later,
% 1.97/2.17 ; 61 ( 1%) are still being kept.
% 1.97/2.17 ;
% 1.97/2.17 ; Run time in seconds excluding printing time:
% 1.97/2.17 ; 0.004 0% Read assertion file (1 call)
% 1.97/2.17 ; 0.001 0% Assert (35 calls)
% 1.97/2.17 ; 0.383 23% Process new row (11,497 calls)
% 1.97/2.17 ; 0.015 1% Resolution (1,008 calls)
% 1.97/2.17 ; 0.105 6% Paramodulation (504 calls)
% 1.97/2.17 ; 0.526 32% Forward simplification (11,486 calls)
% 1.97/2.17 ; 0.312 19% Backward simplification (4,522 calls)
% 1.97/2.17 ; 0.240 14% Ordering (49,027 calls)
% 1.97/2.17 ; 0.000 0% Sortal reasoning (32 calls)
% 1.97/2.17 ; 0.000 0% Purity testing (1 call)
% 1.97/2.17 ; 0.070 4% Other
% 1.97/2.17 ; 1.656 Total
% 1.97/2.17 ; 1.697 Real time
% 1.97/2.17 ;
% 1.97/2.17 ; Term-hash-array has 12,957 terms in all.
% 1.97/2.17 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 1.97/2.17 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 1.97/2.17 ; Path-index has 182 entries (8,602 at peak, 14,224 added, 14,042 deleted).
% 1.97/2.17 ; Path-index has 216 nodes (1,203 at peak, 1,583 added, 1,367 deleted).
% 1.97/2.17 ; Trie-index has 182 entries (8,602 at peak, 14,224 added, 14,042 deleted).
% 1.97/2.17 ; Trie-index has 408 nodes (36,591 at peak, 59,981 added, 59,573 deleted).
% 1.97/2.17 ; Retrieved 149,303 generalization terms in 78,978 calls.
% 1.97/2.17 ; Retrieved 9,044 instance terms in 4,711 calls.
% 1.97/2.17 ; Retrieved 29,932 unifiable terms in 3,700 calls.
% 1.97/2.17 ;
% 1.97/2.17 ; The agenda of backward simplifiable rows to process has 358 entries:
% 1.97/2.17 ; 358 with value 0
% 1.97/2.17 ; The agenda of rows to process has 15 entries:
% 1.97/2.17 ; 12 with value 18 3 with value 20
% 1.97/2.17 ; The agenda of input rows to give has 12 entries:
% 1.97/2.17 ; 12 with value 4
% 1.97/2.17 ; The agenda of rows to give has 44 entries:
% 1.97/2.17 ; 8 with value (4 5) 1 with value (4 10) 4 with value (4 24)
% 1.97/2.17 ; 2 with value (4 6) 3 with value (4 18) 3 with value (4 25)
% 1.97/2.17 ; 6 with value (4 7) 4 with value (4 21) 2 with value (4 26)
% 1.97/2.17 ; 2 with value (4 8) 6 with value (4 23) 3 with value (4 27)
% 1.97/2.17 Evaluation took:
% 1.97/2.17 1.698 seconds of real time
% 1.97/2.17 1.561345 seconds of user run time
% 1.97/2.17 0.136035 seconds of system run time
% 1.97/2.17 [Run times include 0.178 seconds GC run time.]
% 1.97/2.17 0 calls to %EVAL
% 1.97/2.17 0 page faults and
% 1.97/2.17 162,045,320 bytes consed.
% 1.97/2.17 :PROOF-FOUND
% 1.97/2.17 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-05-29T03:45:56
% 1.97/2.17 :PROOF-FOUND
% 1.97/2.17 *
%------------------------------------------------------------------------------