TSTP Solution File: TOP049-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : TOP049-1 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 21:32:27 EDT 2022
% Result : Unsatisfiable 0.18s 0.41s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 98
% Number of leaves : 161
% Syntax : Number of clauses : 597 ( 272 unt; 0 nHn; 546 RR)
% Number of literals : 1070 (1069 equ; 475 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-9 aty)
% Number of variables : 118 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(involutory_quandle,axiom,
product(X,X) = X ).
cnf(involutory_quandle_01,axiom,
product(product(X,Y),Y) = X ).
cnf(involutory_quandle_02,axiom,
product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)) ).
cnf(knot,axiom,
a1 = product(a9,a7) ).
cnf(knot_03,axiom,
a3 = product(a1,a2) ).
cnf(knot_04,axiom,
a2 = product(a3,a4) ).
cnf(knot_06,axiom,
a6 = product(a5,a4) ).
cnf(knot_07,axiom,
a7 = product(a6,a1) ).
cnf(knot_08,axiom,
a8 = product(a7,a4) ).
cnf(knot_09,axiom,
a10 = product(a8,a9) ).
cnf(knot_10,axiom,
a4 = product(a10,a3) ).
cnf(knot_11,axiom,
a9 = product(a4,a8) ).
cnf(goal,negated_conjecture,
tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5) != tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6) ).
cnf(refute_0_0,plain,
product(product(a5,a4),a4) = a5,
inference(subst,[],[involutory_quandle_01:[bind(X,$fot(a5)),bind(Y,$fot(a4))]]) ).
cnf(refute_0_1,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_2,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_3,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( a6 != product(a5,a4)
| product(a5,a4) = a6 ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(a6)),bind(Y0,$fot(product(a5,a4)))]]) ).
cnf(refute_0_5,plain,
product(a5,a4) = a6,
inference(resolve,[$cnf( $equal(a6,product(a5,a4)) )],[knot_06,refute_0_4]) ).
cnf(refute_0_6,plain,
( product(a5,a4) != a6
| product(product(a5,a4),a4) != a5
| product(a6,a4) = a5 ),
introduced(tautology,[equality,[$cnf( $equal(product(product(a5,a4),a4),a5) ),[0,0],$fot(a6)]]) ).
cnf(refute_0_7,plain,
( product(product(a5,a4),a4) != a5
| product(a6,a4) = a5 ),
inference(resolve,[$cnf( $equal(product(a5,a4),a6) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
product(a6,a4) = a5,
inference(resolve,[$cnf( $equal(product(product(a5,a4),a4),a5) )],[refute_0_0,refute_0_7]) ).
cnf(refute_0_9,plain,
( a7 != product(a6,a1)
| product(a6,a1) = a7 ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(a7)),bind(Y0,$fot(product(a6,a1)))]]) ).
cnf(refute_0_10,plain,
product(a6,a1) = a7,
inference(resolve,[$cnf( $equal(a7,product(a6,a1)) )],[knot_07,refute_0_9]) ).
cnf(refute_0_11,plain,
product(a3,a3) = a3,
inference(subst,[],[involutory_quandle:[bind(X,$fot(a3))]]) ).
cnf(refute_0_12,plain,
product(product(product(X_7,a3),a10),a10) = product(X_7,a3),
inference(subst,[],[involutory_quandle_01:[bind(X,$fot(product(X_7,a3))),bind(Y,$fot(a10))]]) ).
cnf(refute_0_13,plain,
product(product(X_3,a4),a3) = product(product(X_3,a3),product(a4,a3)),
inference(subst,[],[involutory_quandle_02:[bind(X,$fot(X_3)),bind(Y,$fot(a4)),bind(Z,$fot(a3))]]) ).
cnf(refute_0_14,plain,
product(product(a10,a3),a3) = a10,
inference(subst,[],[involutory_quandle_01:[bind(X,$fot(a10)),bind(Y,$fot(a3))]]) ).
cnf(refute_0_15,plain,
( a4 != product(a10,a3)
| product(a10,a3) = a4 ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(a4)),bind(Y0,$fot(product(a10,a3)))]]) ).
cnf(refute_0_16,plain,
product(a10,a3) = a4,
inference(resolve,[$cnf( $equal(a4,product(a10,a3)) )],[knot_10,refute_0_15]) ).
cnf(refute_0_17,plain,
( product(a10,a3) != a4
| product(product(a10,a3),a3) != a10
| product(a4,a3) = a10 ),
introduced(tautology,[equality,[$cnf( $equal(product(product(a10,a3),a3),a10) ),[0,0],$fot(a4)]]) ).
cnf(refute_0_18,plain,
( product(product(a10,a3),a3) != a10
| product(a4,a3) = a10 ),
inference(resolve,[$cnf( $equal(product(a10,a3),a4) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
product(a4,a3) = a10,
inference(resolve,[$cnf( $equal(product(product(a10,a3),a3),a10) )],[refute_0_14,refute_0_18]) ).
cnf(refute_0_20,plain,
( product(a4,a3) != a10
| product(product(X_3,a4),a3) != product(product(X_3,a3),product(a4,a3))
| product(product(X_3,a4),a3) = product(product(X_3,a3),a10) ),
introduced(tautology,[equality,[$cnf( $equal(product(product(X_3,a4),a3),product(product(X_3,a3),product(a4,a3))) ),[1,1],$fot(a10)]]) ).
cnf(refute_0_21,plain,
( product(product(X_3,a4),a3) != product(product(X_3,a3),product(a4,a3))
| product(product(X_3,a4),a3) = product(product(X_3,a3),a10) ),
inference(resolve,[$cnf( $equal(product(a4,a3),a10) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
product(product(X_3,a4),a3) = product(product(X_3,a3),a10),
inference(resolve,[$cnf( $equal(product(product(X_3,a4),a3),product(product(X_3,a3),product(a4,a3))) )],[refute_0_13,refute_0_21]) ).
cnf(refute_0_23,plain,
product(product(X_3,a2),a4) = product(product(X_3,a4),product(a2,a4)),
inference(subst,[],[involutory_quandle_02:[bind(X,$fot(X_3)),bind(Y,$fot(a2)),bind(Z,$fot(a4))]]) ).
cnf(refute_0_24,plain,
product(product(a3,a4),a4) = a3,
inference(subst,[],[involutory_quandle_01:[bind(X,$fot(a3)),bind(Y,$fot(a4))]]) ).
cnf(refute_0_25,plain,
( a2 != product(a3,a4)
| product(a3,a4) = a2 ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(a2)),bind(Y0,$fot(product(a3,a4)))]]) ).
cnf(refute_0_26,plain,
product(a3,a4) = a2,
inference(resolve,[$cnf( $equal(a2,product(a3,a4)) )],[knot_04,refute_0_25]) ).
cnf(refute_0_27,plain,
( product(a3,a4) != a2
| product(product(a3,a4),a4) != a3
| product(a2,a4) = a3 ),
introduced(tautology,[equality,[$cnf( $equal(product(product(a3,a4),a4),a3) ),[0,0],$fot(a2)]]) ).
cnf(refute_0_28,plain,
( product(product(a3,a4),a4) != a3
| product(a2,a4) = a3 ),
inference(resolve,[$cnf( $equal(product(a3,a4),a2) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
product(a2,a4) = a3,
inference(resolve,[$cnf( $equal(product(product(a3,a4),a4),a3) )],[refute_0_24,refute_0_28]) ).
cnf(refute_0_30,plain,
( product(a2,a4) != a3
| product(product(X_3,a2),a4) != product(product(X_3,a4),product(a2,a4))
| product(product(X_3,a2),a4) = product(product(X_3,a4),a3) ),
introduced(tautology,[equality,[$cnf( $equal(product(product(X_3,a2),a4),product(product(X_3,a4),product(a2,a4))) ),[1,1],$fot(a3)]]) ).
cnf(refute_0_31,plain,
( product(product(X_3,a2),a4) != product(product(X_3,a4),product(a2,a4))
| product(product(X_3,a2),a4) = product(product(X_3,a4),a3) ),
inference(resolve,[$cnf( $equal(product(a2,a4),a3) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
product(product(X_3,a2),a4) = product(product(X_3,a4),a3),
inference(resolve,[$cnf( $equal(product(product(X_3,a2),a4),product(product(X_3,a4),product(a2,a4))) )],[refute_0_23,refute_0_31]) ).
cnf(refute_0_33,plain,
( product(product(X_3,a2),a4) != product(product(X_3,a4),a3)
| product(product(X_3,a4),a3) = product(product(X_3,a2),a4) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(product(product(X_3,a2),a4))),bind(Y0,$fot(product(product(X_3,a4),a3)))]]) ).
cnf(refute_0_34,plain,
product(product(X_3,a4),a3) = product(product(X_3,a2),a4),
inference(resolve,[$cnf( $equal(product(product(X_3,a2),a4),product(product(X_3,a4),a3)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( product(product(X_3,a4),a3) != product(product(X_3,a2),a4)
| product(product(X_3,a4),a3) != product(product(X_3,a3),a10)
| product(product(X_3,a2),a4) = product(product(X_3,a3),a10) ),
introduced(tautology,[equality,[$cnf( $equal(product(product(X_3,a4),a3),product(product(X_3,a3),a10)) ),[0],$fot(product(product(X_3,a2),a4))]]) ).
cnf(refute_0_36,plain,
( product(product(X_3,a4),a3) != product(product(X_3,a3),a10)
| product(product(X_3,a2),a4) = product(product(X_3,a3),a10) ),
inference(resolve,[$cnf( $equal(product(product(X_3,a4),a3),product(product(X_3,a2),a4)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
product(product(X_3,a2),a4) = product(product(X_3,a3),a10),
inference(resolve,[$cnf( $equal(product(product(X_3,a4),a3),product(product(X_3,a3),a10)) )],[refute_0_22,refute_0_36]) ).
cnf(refute_0_38,plain,
product(product(X_7,a2),a4) = product(product(X_7,a3),a10),
inference(subst,[],[refute_0_37:[bind(X_3,$fot(X_7))]]) ).
cnf(refute_0_39,plain,
( product(product(X_7,a2),a4) != product(product(X_7,a3),a10)
| product(product(X_7,a3),a10) = product(product(X_7,a2),a4) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(product(product(X_7,a2),a4))),bind(Y0,$fot(product(product(X_7,a3),a10)))]]) ).
cnf(refute_0_40,plain,
product(product(X_7,a3),a10) = product(product(X_7,a2),a4),
inference(resolve,[$cnf( $equal(product(product(X_7,a2),a4),product(product(X_7,a3),a10)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( product(product(X_7,a3),a10) != product(product(X_7,a2),a4)
| product(product(product(X_7,a3),a10),a10) != product(X_7,a3)
| product(product(product(X_7,a2),a4),a10) = product(X_7,a3) ),
introduced(tautology,[equality,[$cnf( $equal(product(product(product(X_7,a3),a10),a10),product(X_7,a3)) ),[0,0],$fot(product(product(X_7,a2),a4))]]) ).
cnf(refute_0_42,plain,
( product(product(product(X_7,a3),a10),a10) != product(X_7,a3)
| product(product(product(X_7,a2),a4),a10) = product(X_7,a3) ),
inference(resolve,[$cnf( $equal(product(product(X_7,a3),a10),product(product(X_7,a2),a4)) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
product(product(product(X_7,a2),a4),a10) = product(X_7,a3),
inference(resolve,[$cnf( $equal(product(product(product(X_7,a3),a10),a10),product(X_7,a3)) )],[refute_0_12,refute_0_42]) ).
cnf(refute_0_44,plain,
product(product(X_7,a2),a2) = X_7,
inference(subst,[],[involutory_quandle_01:[bind(X,$fot(X_7)),bind(Y,$fot(a2))]]) ).
cnf(refute_0_45,plain,
product(product(product(X_7,a2),a2),a4) = product(product(product(X_7,a2),a2),a4),
introduced(tautology,[refl,[$fot(product(product(product(X_7,a2),a2),a4))]]) ).
cnf(refute_0_46,plain,
( product(product(X_7,a2),a2) != X_7
| product(product(product(X_7,a2),a2),a4) != product(product(product(X_7,a2),a2),a4)
| product(product(product(X_7,a2),a2),a4) = product(X_7,a4) ),
introduced(tautology,[equality,[$cnf( $equal(product(product(product(X_7,a2),a2),a4),product(product(product(X_7,a2),a2),a4)) ),[1,0],$fot(X_7)]]) ).
cnf(refute_0_47,plain,
( product(product(X_7,a2),a2) != X_7
| product(product(product(X_7,a2),a2),a4) = product(X_7,a4) ),
inference(resolve,[$cnf( $equal(product(product(product(X_7,a2),a2),a4),product(product(product(X_7,a2),a2),a4)) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
product(product(product(X_7,a2),a2),a4) = product(X_7,a4),
inference(resolve,[$cnf( $equal(product(product(X_7,a2),a2),X_7) )],[refute_0_44,refute_0_47]) ).
cnf(refute_0_49,plain,
product(product(X,a9),product(a1,a4)) = product(product(X,product(a1,a4)),product(a9,product(a1,a4))),
inference(subst,[],[involutory_quandle_02:[bind(Y,$fot(a9)),bind(Z,$fot(product(a1,a4)))]]) ).
cnf(refute_0_50,plain,
product(product(product(a4,a10),a9),a9) = product(a4,a10),
inference(subst,[],[involutory_quandle_01:[bind(X,$fot(product(a4,a10))),bind(Y,$fot(a9))]]) ).
cnf(refute_0_51,plain,
product(product(X_3,a10),a9) = product(product(X_3,a9),product(a10,a9)),
inference(subst,[],[involutory_quandle_02:[bind(X,$fot(X_3)),bind(Y,$fot(a10)),bind(Z,$fot(a9))]]) ).
cnf(refute_0_52,plain,
product(product(a8,a9),a9) = a8,
inference(subst,[],[involutory_quandle_01:[bind(X,$fot(a8)),bind(Y,$fot(a9))]]) ).
cnf(refute_0_53,plain,
( a10 != product(a8,a9)
| product(a8,a9) = a10 ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(a10)),bind(Y0,$fot(product(a8,a9)))]]) ).
cnf(refute_0_54,plain,
product(a8,a9) = a10,
inference(resolve,[$cnf( $equal(a10,product(a8,a9)) )],[knot_09,refute_0_53]) ).
cnf(refute_0_55,plain,
( product(a8,a9) != a10
| product(product(a8,a9),a9) != a8
| product(a10,a9) = a8 ),
introduced(tautology,[equality,[$cnf( $equal(product(product(a8,a9),a9),a8) ),[0,0],$fot(a10)]]) ).
cnf(refute_0_56,plain,
( product(product(a8,a9),a9) != a8
| product(a10,a9) = a8 ),
inference(resolve,[$cnf( $equal(product(a8,a9),a10) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
product(a10,a9) = a8,
inference(resolve,[$cnf( $equal(product(product(a8,a9),a9),a8) )],[refute_0_52,refute_0_56]) ).
cnf(refute_0_58,plain,
( product(a10,a9) != a8
| product(product(X_3,a10),a9) != product(product(X_3,a9),product(a10,a9))
| product(product(X_3,a10),a9) = product(product(X_3,a9),a8) ),
introduced(tautology,[equality,[$cnf( $equal(product(product(X_3,a10),a9),product(product(X_3,a9),product(a10,a9))) ),[1,1],$fot(a8)]]) ).
cnf(refute_0_59,plain,
( product(product(X_3,a10),a9) != product(product(X_3,a9),product(a10,a9))
| product(product(X_3,a10),a9) = product(product(X_3,a9),a8) ),
inference(resolve,[$cnf( $equal(product(a10,a9),a8) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
product(product(X_3,a10),a9) = product(product(X_3,a9),a8),
inference(resolve,[$cnf( $equal(product(product(X_3,a10),a9),product(product(X_3,a9),product(a10,a9))) )],[refute_0_51,refute_0_59]) ).
cnf(refute_0_61,plain,
product(product(a4,a10),a9) = product(product(a4,a9),a8),
inference(subst,[],[refute_0_60:[bind(X_3,$fot(a4))]]) ).
cnf(refute_0_62,plain,
product(product(X_3,a7),a4) = product(product(X_3,a4),product(a7,a4)),
inference(subst,[],[involutory_quandle_02:[bind(X,$fot(X_3)),bind(Y,$fot(a7)),bind(Z,$fot(a4))]]) ).
cnf(refute_0_63,plain,
( a8 != product(a7,a4)
| product(a7,a4) = a8 ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(a8)),bind(Y0,$fot(product(a7,a4)))]]) ).
cnf(refute_0_64,plain,
product(a7,a4) = a8,
inference(resolve,[$cnf( $equal(a8,product(a7,a4)) )],[knot_08,refute_0_63]) ).
cnf(refute_0_65,plain,
( product(a7,a4) != a8
| product(product(X_3,a7),a4) != product(product(X_3,a4),product(a7,a4))
| product(product(X_3,a7),a4) = product(product(X_3,a4),a8) ),
introduced(tautology,[equality,[$cnf( $equal(product(product(X_3,a7),a4),product(product(X_3,a4),product(a7,a4))) ),[1,1],$fot(a8)]]) ).
cnf(refute_0_66,plain,
( product(product(X_3,a7),a4) != product(product(X_3,a4),product(a7,a4))
| product(product(X_3,a7),a4) = product(product(X_3,a4),a8) ),
inference(resolve,[$cnf( $equal(product(a7,a4),a8) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
product(product(X_3,a7),a4) = product(product(X_3,a4),a8),
inference(resolve,[$cnf( $equal(product(product(X_3,a7),a4),product(product(X_3,a4),product(a7,a4))) )],[refute_0_62,refute_0_66]) ).
cnf(refute_0_68,plain,
product(product(a9,a7),a4) = product(product(a9,a4),a8),
inference(subst,[],[refute_0_67:[bind(X_3,$fot(a9))]]) ).
cnf(refute_0_69,plain,
( a1 != product(a9,a7)
| product(a9,a7) = a1 ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(a1)),bind(Y0,$fot(product(a9,a7)))]]) ).
cnf(refute_0_70,plain,
product(a9,a7) = a1,
inference(resolve,[$cnf( $equal(a1,product(a9,a7)) )],[knot,refute_0_69]) ).
cnf(refute_0_71,plain,
( product(a9,a7) != a1
| product(product(a9,a7),a4) != product(product(a9,a4),a8)
| product(a1,a4) = product(product(a9,a4),a8) ),
introduced(tautology,[equality,[$cnf( $equal(product(product(a9,a7),a4),product(product(a9,a4),a8)) ),[0,0],$fot(a1)]]) ).
cnf(refute_0_72,plain,
( product(product(a9,a7),a4) != product(product(a9,a4),a8)
| product(a1,a4) = product(product(a9,a4),a8) ),
inference(resolve,[$cnf( $equal(product(a9,a7),a1) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
product(a1,a4) = product(product(a9,a4),a8),
inference(resolve,[$cnf( $equal(product(product(a9,a7),a4),product(product(a9,a4),a8)) )],[refute_0_68,refute_0_72]) ).
cnf(refute_0_74,plain,
( a9 != product(a4,a8)
| product(a4,a8) = a9 ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(a9)),bind(Y0,$fot(product(a4,a8)))]]) ).
cnf(refute_0_75,plain,
product(a4,a8) = a9,
inference(resolve,[$cnf( $equal(a9,product(a4,a8)) )],[knot_11,refute_0_74]) ).
cnf(refute_0_76,plain,
product(a4,product(a4,a8)) = product(a4,product(a4,a8)),
introduced(tautology,[refl,[$fot(product(a4,product(a4,a8)))]]) ).
cnf(refute_0_77,plain,
( product(a4,a8) != a9
| product(a4,product(a4,a8)) != product(a4,product(a4,a8))
| product(a4,product(a4,a8)) = product(a4,a9) ),
introduced(tautology,[equality,[$cnf( $equal(product(a4,product(a4,a8)),product(a4,product(a4,a8))) ),[1,1],$fot(a9)]]) ).
cnf(refute_0_78,plain,
( product(a4,a8) != a9
| product(a4,product(a4,a8)) = product(a4,a9) ),
inference(resolve,[$cnf( $equal(product(a4,product(a4,a8)),product(a4,product(a4,a8))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
product(a4,product(a4,a8)) = product(a4,a9),
inference(resolve,[$cnf( $equal(product(a4,a8),a9) )],[refute_0_75,refute_0_78]) ).
cnf(refute_0_80,plain,
product(product(a9,X_4),a8) = product(product(a9,a8),product(X_4,a8)),
inference(subst,[],[involutory_quandle_02:[bind(X,$fot(a9)),bind(Y,$fot(X_4)),bind(Z,$fot(a8))]]) ).
cnf(refute_0_81,plain,
product(product(a4,a8),a8) = a4,
inference(subst,[],[involutory_quandle_01:[bind(X,$fot(a4)),bind(Y,$fot(a8))]]) ).
cnf(refute_0_82,plain,
( product(a4,a8) != a9
| product(product(a4,a8),a8) != a4
| product(a9,a8) = a4 ),
introduced(tautology,[equality,[$cnf( $equal(product(product(a4,a8),a8),a4) ),[0,0],$fot(a9)]]) ).
cnf(refute_0_83,plain,
( product(product(a4,a8),a8) != a4
| product(a9,a8) = a4 ),
inference(resolve,[$cnf( $equal(product(a4,a8),a9) )],[refute_0_75,refute_0_82]) ).
cnf(refute_0_84,plain,
product(a9,a8) = a4,
inference(resolve,[$cnf( $equal(product(product(a4,a8),a8),a4) )],[refute_0_81,refute_0_83]) ).
cnf(refute_0_85,plain,
( product(a9,a8) != a4
| product(product(a9,X_4),a8) != product(product(a9,a8),product(X_4,a8))
| product(product(a9,X_4),a8) = product(a4,product(X_4,a8)) ),
introduced(tautology,[equality,[$cnf( $equal(product(product(a9,X_4),a8),product(product(a9,a8),product(X_4,a8))) ),[1,0],$fot(a4)]]) ).
cnf(refute_0_86,plain,
( product(product(a9,X_4),a8) != product(product(a9,a8),product(X_4,a8))
| product(product(a9,X_4),a8) = product(a4,product(X_4,a8)) ),
inference(resolve,[$cnf( $equal(product(a9,a8),a4) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
product(product(a9,X_4),a8) = product(a4,product(X_4,a8)),
inference(resolve,[$cnf( $equal(product(product(a9,X_4),a8),product(product(a9,a8),product(X_4,a8))) )],[refute_0_80,refute_0_86]) ).
cnf(refute_0_88,plain,
product(product(a9,a4),a8) = product(a4,product(a4,a8)),
inference(subst,[],[refute_0_87:[bind(X_4,$fot(a4))]]) ).
cnf(refute_0_89,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_90,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_3,refute_0_89]) ).
cnf(refute_0_91,plain,
( product(a4,product(a4,a8)) != product(a4,a9)
| product(product(a9,a4),a8) != product(a4,product(a4,a8))
| product(product(a9,a4),a8) = product(a4,a9) ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(product(product(a9,a4),a8))),bind(Y0,$fot(product(a4,product(a4,a8)))),bind(Z0,$fot(product(a4,a9)))]]) ).
cnf(refute_0_92,plain,
( product(a4,product(a4,a8)) != product(a4,a9)
| product(product(a9,a4),a8) = product(a4,a9) ),
inference(resolve,[$cnf( $equal(product(product(a9,a4),a8),product(a4,product(a4,a8))) )],[refute_0_88,refute_0_91]) ).
cnf(refute_0_93,plain,
product(product(a9,a4),a8) = product(a4,a9),
inference(resolve,[$cnf( $equal(product(a4,product(a4,a8)),product(a4,a9)) )],[refute_0_79,refute_0_92]) ).
cnf(refute_0_94,plain,
( product(a1,a4) != product(product(a9,a4),a8)
| product(product(a9,a4),a8) != product(a4,a9)
| product(a1,a4) = product(a4,a9) ),
introduced(tautology,[equality,[$cnf( ~ $equal(product(a1,a4),product(a4,a9)) ),[0],$fot(product(product(a9,a4),a8))]]) ).
cnf(refute_0_95,plain,
( product(a1,a4) != product(product(a9,a4),a8)
| product(a1,a4) = product(a4,a9) ),
inference(resolve,[$cnf( $equal(product(product(a9,a4),a8),product(a4,a9)) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
product(a1,a4) = product(a4,a9),
inference(resolve,[$cnf( $equal(product(a1,a4),product(product(a9,a4),a8)) )],[refute_0_73,refute_0_95]) ).
cnf(refute_0_97,plain,
( product(a1,a4) != product(a4,a9)
| product(a4,a9) = product(a1,a4) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(product(a1,a4))),bind(Y0,$fot(product(a4,a9)))]]) ).
cnf(refute_0_98,plain,
product(a4,a9) = product(a1,a4),
inference(resolve,[$cnf( $equal(product(a1,a4),product(a4,a9)) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
( product(a4,a9) != product(a1,a4)
| product(product(a4,a10),a9) != product(product(a4,a9),a8)
| product(product(a4,a10),a9) = product(product(a1,a4),a8) ),
introduced(tautology,[equality,[$cnf( $equal(product(product(a4,a10),a9),product(product(a4,a9),a8)) ),[1,0],$fot(product(a1,a4))]]) ).
cnf(refute_0_100,plain,
( product(product(a4,a10),a9) != product(product(a4,a9),a8)
| product(product(a4,a10),a9) = product(product(a1,a4),a8) ),
inference(resolve,[$cnf( $equal(product(a4,a9),product(a1,a4)) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
product(product(a4,a10),a9) = product(product(a1,a4),a8),
inference(resolve,[$cnf( $equal(product(product(a4,a10),a9),product(product(a4,a9),a8)) )],[refute_0_61,refute_0_100]) ).
cnf(refute_0_102,plain,
product(product(a1,a7),a4) = product(product(a1,a4),a8),
inference(subst,[],[refute_0_67:[bind(X_3,$fot(a1))]]) ).
cnf(refute_0_103,plain,
product(product(a9,a7),a7) = a9,
inference(subst,[],[involutory_quandle_01:[bind(X,$fot(a9)),bind(Y,$fot(a7))]]) ).
cnf(refute_0_104,plain,
( product(a9,a7) != a1
| product(product(a9,a7),a7) != a9
| product(a1,a7) = a9 ),
introduced(tautology,[equality,[$cnf( $equal(product(product(a9,a7),a7),a9) ),[0,0],$fot(a1)]]) ).
cnf(refute_0_105,plain,
( product(product(a9,a7),a7) != a9
| product(a1,a7) = a9 ),
inference(resolve,[$cnf( $equal(product(a9,a7),a1) )],[refute_0_70,refute_0_104]) ).
cnf(refute_0_106,plain,
product(a1,a7) = a9,
inference(resolve,[$cnf( $equal(product(product(a9,a7),a7),a9) )],[refute_0_103,refute_0_105]) ).
cnf(refute_0_107,plain,
( product(a1,a7) != a9
| product(product(a1,a7),a4) != product(product(a1,a4),a8)
| product(a9,a4) = product(product(a1,a4),a8) ),
introduced(tautology,[equality,[$cnf( $equal(product(product(a1,a7),a4),product(product(a1,a4),a8)) ),[0,0],$fot(a9)]]) ).
cnf(refute_0_108,plain,
( product(product(a1,a7),a4) != product(product(a1,a4),a8)
| product(a9,a4) = product(product(a1,a4),a8) ),
inference(resolve,[$cnf( $equal(product(a1,a7),a9) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
product(a9,a4) = product(product(a1,a4),a8),
inference(resolve,[$cnf( $equal(product(product(a1,a7),a4),product(product(a1,a4),a8)) )],[refute_0_102,refute_0_108]) ).
cnf(refute_0_110,plain,
( product(a9,a4) != product(product(a1,a4),a8)
| product(product(a1,a4),a8) = product(a9,a4) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(product(a9,a4))),bind(Y0,$fot(product(product(a1,a4),a8)))]]) ).
cnf(refute_0_111,plain,
product(product(a1,a4),a8) = product(a9,a4),
inference(resolve,[$cnf( $equal(product(a9,a4),product(product(a1,a4),a8)) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
( product(product(a1,a4),a8) != product(a9,a4)
| product(product(a4,a10),a9) != product(product(a1,a4),a8)
| product(product(a4,a10),a9) = product(a9,a4) ),
introduced(tautology,[equality,[$cnf( $equal(product(product(a4,a10),a9),product(product(a1,a4),a8)) ),[1],$fot(product(a9,a4))]]) ).
cnf(refute_0_113,plain,
( product(product(a4,a10),a9) != product(product(a1,a4),a8)
| product(product(a4,a10),a9) = product(a9,a4) ),
inference(resolve,[$cnf( $equal(product(product(a1,a4),a8),product(a9,a4)) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
product(product(a4,a10),a9) = product(a9,a4),
inference(resolve,[$cnf( $equal(product(product(a4,a10),a9),product(product(a1,a4),a8)) )],[refute_0_101,refute_0_113]) ).
cnf(refute_0_115,plain,
( product(product(a4,a10),a9) != product(a9,a4)
| product(product(product(a4,a10),a9),a9) != product(a4,a10)
| product(product(a9,a4),a9) = product(a4,a10) ),
introduced(tautology,[equality,[$cnf( $equal(product(product(product(a4,a10),a9),a9),product(a4,a10)) ),[0,0],$fot(product(a9,a4))]]) ).
cnf(refute_0_116,plain,
( product(product(product(a4,a10),a9),a9) != product(a4,a10)
| product(product(a9,a4),a9) = product(a4,a10) ),
inference(resolve,[$cnf( $equal(product(product(a4,a10),a9),product(a9,a4)) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
product(product(a9,a4),a9) = product(a4,a10),
inference(resolve,[$cnf( $equal(product(product(product(a4,a10),a9),a9),product(a4,a10)) )],[refute_0_50,refute_0_116]) ).
cnf(refute_0_118,plain,
product(a9,product(a4,a9)) = product(a9,product(a4,a9)),
introduced(tautology,[refl,[$fot(product(a9,product(a4,a9)))]]) ).
cnf(refute_0_119,plain,
( product(a4,a9) != product(a1,a4)
| product(a9,product(a4,a9)) != product(a9,product(a4,a9))
| product(a9,product(a4,a9)) = product(a9,product(a1,a4)) ),
introduced(tautology,[equality,[$cnf( $equal(product(a9,product(a4,a9)),product(a9,product(a4,a9))) ),[1,1],$fot(product(a1,a4))]]) ).
cnf(refute_0_120,plain,
( product(a4,a9) != product(a1,a4)
| product(a9,product(a4,a9)) = product(a9,product(a1,a4)) ),
inference(resolve,[$cnf( $equal(product(a9,product(a4,a9)),product(a9,product(a4,a9))) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
product(a9,product(a4,a9)) = product(a9,product(a1,a4)),
inference(resolve,[$cnf( $equal(product(a4,a9),product(a1,a4)) )],[refute_0_98,refute_0_120]) ).
cnf(refute_0_122,plain,
product(product(X_5,X_4),X_5) = product(product(X_5,X_5),product(X_4,X_5)),
inference(subst,[],[involutory_quandle_02:[bind(X,$fot(X_5)),bind(Y,$fot(X_4)),bind(Z,$fot(X_5))]]) ).
cnf(refute_0_123,plain,
product(X_5,X_5) = X_5,
inference(subst,[],[involutory_quandle:[bind(X,$fot(X_5))]]) ).
cnf(refute_0_124,plain,
( product(X_5,X_5) != X_5
| product(product(X_5,X_4),X_5) != product(product(X_5,X_5),product(X_4,X_5))
| product(product(X_5,X_4),X_5) = product(X_5,product(X_4,X_5)) ),
introduced(tautology,[equality,[$cnf( $equal(product(product(X_5,X_4),X_5),product(product(X_5,X_5),product(X_4,X_5))) ),[1,0],$fot(X_5)]]) ).
cnf(refute_0_125,plain,
( product(product(X_5,X_4),X_5) != product(product(X_5,X_5),product(X_4,X_5))
| product(product(X_5,X_4),X_5) = product(X_5,product(X_4,X_5)) ),
inference(resolve,[$cnf( $equal(product(X_5,X_5),X_5) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
product(product(X_5,X_4),X_5) = product(X_5,product(X_4,X_5)),
inference(resolve,[$cnf( $equal(product(product(X_5,X_4),X_5),product(product(X_5,X_5),product(X_4,X_5))) )],[refute_0_122,refute_0_125]) ).
cnf(refute_0_127,plain,
product(product(a9,a4),a9) = product(a9,product(a4,a9)),
inference(subst,[],[refute_0_126:[bind(X_4,$fot(a4)),bind(X_5,$fot(a9))]]) ).
cnf(refute_0_128,plain,
( product(a9,product(a4,a9)) != product(a9,product(a1,a4))
| product(product(a9,a4),a9) != product(a9,product(a4,a9))
| product(product(a9,a4),a9) = product(a9,product(a1,a4)) ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(product(product(a9,a4),a9))),bind(Y0,$fot(product(a9,product(a4,a9)))),bind(Z0,$fot(product(a9,product(a1,a4))))]]) ).
cnf(refute_0_129,plain,
( product(a9,product(a4,a9)) != product(a9,product(a1,a4))
| product(product(a9,a4),a9) = product(a9,product(a1,a4)) ),
inference(resolve,[$cnf( $equal(product(product(a9,a4),a9),product(a9,product(a4,a9))) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
product(product(a9,a4),a9) = product(a9,product(a1,a4)),
inference(resolve,[$cnf( $equal(product(a9,product(a4,a9)),product(a9,product(a1,a4))) )],[refute_0_121,refute_0_129]) ).
cnf(refute_0_131,plain,
( product(product(a9,a4),a9) != product(a4,a10)
| product(product(a9,a4),a9) != product(a9,product(a1,a4))
| product(a9,product(a1,a4)) = product(a4,a10) ),
introduced(tautology,[equality,[$cnf( $equal(product(product(a9,a4),a9),product(a4,a10)) ),[0],$fot(product(a9,product(a1,a4)))]]) ).
cnf(refute_0_132,plain,
( product(product(a9,a4),a9) != product(a4,a10)
| product(a9,product(a1,a4)) = product(a4,a10) ),
inference(resolve,[$cnf( $equal(product(product(a9,a4),a9),product(a9,product(a1,a4))) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
product(a9,product(a1,a4)) = product(a4,a10),
inference(resolve,[$cnf( $equal(product(product(a9,a4),a9),product(a4,a10)) )],[refute_0_117,refute_0_132]) ).
cnf(refute_0_134,plain,
( product(a9,product(a1,a4)) != product(a4,a10)
| product(product(X,a9),product(a1,a4)) != product(product(X,product(a1,a4)),product(a9,product(a1,a4)))
| product(product(X,a9),product(a1,a4)) = product(product(X,product(a1,a4)),product(a4,a10)) ),
introduced(tautology,[equality,[$cnf( $equal(product(product(X,a9),product(a1,a4)),product(product(X,product(a1,a4)),product(a9,product(a1,a4)))) ),[1,1],$fot(product(a4,a10))]]) ).
cnf(refute_0_135,plain,
( product(product(X,a9),product(a1,a4)) != product(product(X,product(a1,a4)),product(a9,product(a1,a4)))
| product(product(X,a9),product(a1,a4)) = product(product(X,product(a1,a4)),product(a4,a10)) ),
inference(resolve,[$cnf( $equal(product(a9,product(a1,a4)),product(a4,a10)) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
product(product(X,a9),product(a1,a4)) = product(product(X,product(a1,a4)),product(a4,a10)),
inference(resolve,[$cnf( $equal(product(product(X,a9),product(a1,a4)),product(product(X,product(a1,a4)),product(a9,product(a1,a4)))) )],[refute_0_49,refute_0_135]) ).
cnf(refute_0_137,plain,
product(product(X,a4),a9) = product(product(X,a9),product(a4,a9)),
inference(subst,[],[involutory_quandle_02:[bind(Y,$fot(a4)),bind(Z,$fot(a9))]]) ).
cnf(refute_0_138,plain,
( product(a4,a9) != product(a1,a4)
| product(product(X,a4),a9) != product(product(X,a9),product(a4,a9))
| product(product(X,a4),a9) = product(product(X,a9),product(a1,a4)) ),
introduced(tautology,[equality,[$cnf( $equal(product(product(X,a4),a9),product(product(X,a9),product(a4,a9))) ),[1,1],$fot(product(a1,a4))]]) ).
cnf(refute_0_139,plain,
( product(product(X,a4),a9) != product(product(X,a9),product(a4,a9))
| product(product(X,a4),a9) = product(product(X,a9),product(a1,a4)) ),
inference(resolve,[$cnf( $equal(product(a4,a9),product(a1,a4)) )],[refute_0_98,refute_0_138]) ).
cnf(refute_0_140,plain,
product(product(X,a4),a9) = product(product(X,a9),product(a1,a4)),
inference(resolve,[$cnf( $equal(product(product(X,a4),a9),product(product(X,a9),product(a4,a9))) )],[refute_0_137,refute_0_139]) ).
cnf(refute_0_141,plain,
( product(product(X,a4),a9) != product(product(X,a9),product(a1,a4))
| product(product(X,a9),product(a1,a4)) = product(product(X,a4),a9) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(product(product(X,a4),a9))),bind(Y0,$fot(product(product(X,a9),product(a1,a4))))]]) ).
cnf(refute_0_142,plain,
product(product(X,a9),product(a1,a4)) = product(product(X,a4),a9),
inference(resolve,[$cnf( $equal(product(product(X,a4),a9),product(product(X,a9),product(a1,a4))) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
( product(product(X,a9),product(a1,a4)) != product(product(X,a4),a9)
| product(product(X,a9),product(a1,a4)) != product(product(X,product(a1,a4)),product(a4,a10))
| product(product(X,a4),a9) = product(product(X,product(a1,a4)),product(a4,a10)) ),
introduced(tautology,[equality,[$cnf( $equal(product(product(X,a9),product(a1,a4)),product(product(X,product(a1,a4)),product(a4,a10))) ),[0],$fot(product(product(X,a4),a9))]]) ).
cnf(refute_0_144,plain,
( product(product(X,a9),product(a1,a4)) != product(product(X,product(a1,a4)),product(a4,a10))
| product(product(X,a4),a9) = product(product(X,product(a1,a4)),product(a4,a10)) ),
inference(resolve,[$cnf( $equal(product(product(X,a9),product(a1,a4)),product(product(X,a4),a9)) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
product(product(X,a10),product(a1,a4)) = product(product(X,product(a1,a4)),product(a10,product(a1,a4))),
inference(subst,[],[involutory_quandle_02:[bind(Y,$fot(a10)),bind(Z,$fot(product(a1,a4)))]]) ).
cnf(refute_0_146,plain,
product(product(a10,a2),a4) = product(product(a10,a3),a10),
inference(subst,[],[refute_0_37:[bind(X_3,$fot(a10))]]) ).
cnf(refute_0_147,plain,
( product(a10,a3) != a4
| product(product(a10,a2),a4) != product(product(a10,a3),a10)
| product(product(a10,a2),a4) = product(a4,a10) ),
introduced(tautology,[equality,[$cnf( $equal(product(product(a10,a2),a4),product(product(a10,a3),a10)) ),[1,0],$fot(a4)]]) ).
cnf(refute_0_148,plain,
( product(product(a10,a2),a4) != product(product(a10,a3),a10)
| product(product(a10,a2),a4) = product(a4,a10) ),
inference(resolve,[$cnf( $equal(product(a10,a3),a4) )],[refute_0_16,refute_0_147]) ).
cnf(refute_0_149,plain,
product(product(a10,a2),a4) = product(a4,a10),
inference(resolve,[$cnf( $equal(product(product(a10,a2),a4),product(product(a10,a3),a10)) )],[refute_0_146,refute_0_148]) ).
cnf(refute_0_150,plain,
( product(product(a10,a2),a4) != product(a4,a10)
| product(product(a10,a2),a4) != product(product(a10,a3),a10)
| product(a4,a10) = product(product(a10,a3),a10) ),
introduced(tautology,[equality,[$cnf( $equal(product(product(a10,a2),a4),product(product(a10,a3),a10)) ),[0],$fot(product(a4,a10))]]) ).
cnf(refute_0_151,plain,
( product(product(a10,a2),a4) != product(product(a10,a3),a10)
| product(a4,a10) = product(product(a10,a3),a10) ),
inference(resolve,[$cnf( $equal(product(product(a10,a2),a4),product(a4,a10)) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
product(a4,a10) = product(product(a10,a3),a10),
inference(resolve,[$cnf( $equal(product(product(a10,a2),a4),product(product(a10,a3),a10)) )],[refute_0_146,refute_0_151]) ).
cnf(refute_0_153,plain,
product(product(a3,a2),a4) = product(product(a3,a3),a10),
inference(subst,[],[refute_0_37:[bind(X_3,$fot(a3))]]) ).
cnf(refute_0_154,plain,
( product(a3,a3) != a3
| product(product(a3,a2),a4) != product(product(a3,a3),a10)
| product(product(a3,a2),a4) = product(a3,a10) ),
introduced(tautology,[equality,[$cnf( $equal(product(product(a3,a2),a4),product(product(a3,a3),a10)) ),[1,0],$fot(a3)]]) ).
cnf(refute_0_155,plain,
( product(product(a3,a2),a4) != product(product(a3,a3),a10)
| product(product(a3,a2),a4) = product(a3,a10) ),
inference(resolve,[$cnf( $equal(product(a3,a3),a3) )],[refute_0_11,refute_0_154]) ).
cnf(refute_0_156,plain,
product(product(a3,a2),a4) = product(a3,a10),
inference(resolve,[$cnf( $equal(product(product(a3,a2),a4),product(product(a3,a3),a10)) )],[refute_0_153,refute_0_155]) ).
cnf(refute_0_157,plain,
product(product(a1,a2),a2) = a1,
inference(subst,[],[involutory_quandle_01:[bind(X,$fot(a1)),bind(Y,$fot(a2))]]) ).
cnf(refute_0_158,plain,
( a3 != product(a1,a2)
| product(a1,a2) = a3 ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(a3)),bind(Y0,$fot(product(a1,a2)))]]) ).
cnf(refute_0_159,plain,
product(a1,a2) = a3,
inference(resolve,[$cnf( $equal(a3,product(a1,a2)) )],[knot_03,refute_0_158]) ).
cnf(refute_0_160,plain,
( product(a1,a2) != a3
| product(product(a1,a2),a2) != a1
| product(a3,a2) = a1 ),
introduced(tautology,[equality,[$cnf( $equal(product(product(a1,a2),a2),a1) ),[0,0],$fot(a3)]]) ).
cnf(refute_0_161,plain,
( product(product(a1,a2),a2) != a1
| product(a3,a2) = a1 ),
inference(resolve,[$cnf( $equal(product(a1,a2),a3) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
product(a3,a2) = a1,
inference(resolve,[$cnf( $equal(product(product(a1,a2),a2),a1) )],[refute_0_157,refute_0_161]) ).
cnf(refute_0_163,plain,
( product(a3,a2) != a1
| product(product(a3,a2),a4) != product(product(a3,a3),a10)
| product(a1,a4) = product(product(a3,a3),a10) ),
introduced(tautology,[equality,[$cnf( $equal(product(product(a3,a2),a4),product(product(a3,a3),a10)) ),[0,0],$fot(a1)]]) ).
cnf(refute_0_164,plain,
( product(product(a3,a2),a4) != product(product(a3,a3),a10)
| product(a1,a4) = product(product(a3,a3),a10) ),
inference(resolve,[$cnf( $equal(product(a3,a2),a1) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
product(a1,a4) = product(product(a3,a3),a10),
inference(resolve,[$cnf( $equal(product(product(a3,a2),a4),product(product(a3,a3),a10)) )],[refute_0_153,refute_0_164]) ).
cnf(refute_0_166,plain,
product(a2,product(a2,a4)) = product(a2,product(a2,a4)),
introduced(tautology,[refl,[$fot(product(a2,product(a2,a4)))]]) ).
cnf(refute_0_167,plain,
( product(a2,a4) != a3
| product(a2,product(a2,a4)) != product(a2,product(a2,a4))
| product(a2,product(a2,a4)) = product(a2,a3) ),
introduced(tautology,[equality,[$cnf( $equal(product(a2,product(a2,a4)),product(a2,product(a2,a4))) ),[1,1],$fot(a3)]]) ).
cnf(refute_0_168,plain,
( product(a2,a4) != a3
| product(a2,product(a2,a4)) = product(a2,a3) ),
inference(resolve,[$cnf( $equal(product(a2,product(a2,a4)),product(a2,product(a2,a4))) )],[refute_0_166,refute_0_167]) ).
cnf(refute_0_169,plain,
product(a2,product(a2,a4)) = product(a2,a3),
inference(resolve,[$cnf( $equal(product(a2,a4),a3) )],[refute_0_29,refute_0_168]) ).
cnf(refute_0_170,plain,
product(product(a3,X_4),a4) = product(product(a3,a4),product(X_4,a4)),
inference(subst,[],[involutory_quandle_02:[bind(X,$fot(a3)),bind(Y,$fot(X_4)),bind(Z,$fot(a4))]]) ).
cnf(refute_0_171,plain,
( product(a3,a4) != a2
| product(product(a3,X_4),a4) != product(product(a3,a4),product(X_4,a4))
| product(product(a3,X_4),a4) = product(a2,product(X_4,a4)) ),
introduced(tautology,[equality,[$cnf( $equal(product(product(a3,X_4),a4),product(product(a3,a4),product(X_4,a4))) ),[1,0],$fot(a2)]]) ).
cnf(refute_0_172,plain,
( product(product(a3,X_4),a4) != product(product(a3,a4),product(X_4,a4))
| product(product(a3,X_4),a4) = product(a2,product(X_4,a4)) ),
inference(resolve,[$cnf( $equal(product(a3,a4),a2) )],[refute_0_26,refute_0_171]) ).
cnf(refute_0_173,plain,
product(product(a3,X_4),a4) = product(a2,product(X_4,a4)),
inference(resolve,[$cnf( $equal(product(product(a3,X_4),a4),product(product(a3,a4),product(X_4,a4))) )],[refute_0_170,refute_0_172]) ).
cnf(refute_0_174,plain,
product(product(a3,a2),a4) = product(a2,product(a2,a4)),
inference(subst,[],[refute_0_173:[bind(X_4,$fot(a2))]]) ).
cnf(refute_0_175,plain,
( product(product(X_3,a2),a4) != product(product(X_3,a3),a10)
| product(product(X_3,a3),a10) = product(product(X_3,a2),a4) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(product(product(X_3,a2),a4))),bind(Y0,$fot(product(product(X_3,a3),a10)))]]) ).
cnf(refute_0_176,plain,
product(product(X_3,a3),a10) = product(product(X_3,a2),a4),
inference(resolve,[$cnf( $equal(product(product(X_3,a2),a4),product(product(X_3,a3),a10)) )],[refute_0_37,refute_0_175]) ).
cnf(refute_0_177,plain,
product(product(a3,a3),a10) = product(product(a3,a2),a4),
inference(subst,[],[refute_0_176:[bind(X_3,$fot(a3))]]) ).
cnf(refute_0_178,plain,
( product(product(a3,a2),a4) != product(a2,product(a2,a4))
| product(product(a3,a3),a10) != product(product(a3,a2),a4)
| product(product(a3,a3),a10) = product(a2,product(a2,a4)) ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(product(product(a3,a3),a10))),bind(Y0,$fot(product(product(a3,a2),a4))),bind(Z0,$fot(product(a2,product(a2,a4))))]]) ).
cnf(refute_0_179,plain,
( product(product(a3,a2),a4) != product(a2,product(a2,a4))
| product(product(a3,a3),a10) = product(a2,product(a2,a4)) ),
inference(resolve,[$cnf( $equal(product(product(a3,a3),a10),product(product(a3,a2),a4)) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
product(product(a3,a3),a10) = product(a2,product(a2,a4)),
inference(resolve,[$cnf( $equal(product(product(a3,a2),a4),product(a2,product(a2,a4))) )],[refute_0_174,refute_0_179]) ).
cnf(refute_0_181,plain,
( product(a2,product(a2,a4)) != product(a2,a3)
| product(product(a3,a3),a10) != product(a2,product(a2,a4))
| product(product(a3,a3),a10) = product(a2,a3) ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(product(product(a3,a3),a10))),bind(Y0,$fot(product(a2,product(a2,a4)))),bind(Z0,$fot(product(a2,a3)))]]) ).
cnf(refute_0_182,plain,
( product(a2,product(a2,a4)) != product(a2,a3)
| product(product(a3,a3),a10) = product(a2,a3) ),
inference(resolve,[$cnf( $equal(product(product(a3,a3),a10),product(a2,product(a2,a4))) )],[refute_0_180,refute_0_181]) ).
cnf(refute_0_183,plain,
product(product(a3,a3),a10) = product(a2,a3),
inference(resolve,[$cnf( $equal(product(a2,product(a2,a4)),product(a2,a3)) )],[refute_0_169,refute_0_182]) ).
cnf(refute_0_184,plain,
( product(a1,a4) != product(product(a3,a3),a10)
| product(product(a3,a3),a10) != product(a2,a3)
| product(a1,a4) = product(a2,a3) ),
introduced(tautology,[equality,[$cnf( ~ $equal(product(a1,a4),product(a2,a3)) ),[0],$fot(product(product(a3,a3),a10))]]) ).
cnf(refute_0_185,plain,
( product(a1,a4) != product(product(a3,a3),a10)
| product(a1,a4) = product(a2,a3) ),
inference(resolve,[$cnf( $equal(product(product(a3,a3),a10),product(a2,a3)) )],[refute_0_183,refute_0_184]) ).
cnf(refute_0_186,plain,
product(a1,a4) = product(a2,a3),
inference(resolve,[$cnf( $equal(product(a1,a4),product(product(a3,a3),a10)) )],[refute_0_165,refute_0_185]) ).
cnf(refute_0_187,plain,
( product(a1,a4) != product(a2,a3)
| product(a2,a3) = product(a1,a4) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(product(a1,a4))),bind(Y0,$fot(product(a2,a3)))]]) ).
cnf(refute_0_188,plain,
product(a2,a3) = product(a1,a4),
inference(resolve,[$cnf( $equal(product(a1,a4),product(a2,a3)) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
( product(a2,a3) != product(a1,a4)
| product(a2,product(a2,a4)) != product(a2,a3)
| product(a2,product(a2,a4)) = product(a1,a4) ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(product(a2,product(a2,a4)))),bind(Y0,$fot(product(a2,a3))),bind(Z0,$fot(product(a1,a4)))]]) ).
cnf(refute_0_190,plain,
( product(a2,a3) != product(a1,a4)
| product(a2,product(a2,a4)) = product(a1,a4) ),
inference(resolve,[$cnf( $equal(product(a2,product(a2,a4)),product(a2,a3)) )],[refute_0_169,refute_0_189]) ).
cnf(refute_0_191,plain,
product(a2,product(a2,a4)) = product(a1,a4),
inference(resolve,[$cnf( $equal(product(a2,a3),product(a1,a4)) )],[refute_0_188,refute_0_190]) ).
cnf(refute_0_192,plain,
( product(a2,product(a2,a4)) != product(a1,a4)
| product(product(a3,a2),a4) != product(a2,product(a2,a4))
| product(product(a3,a2),a4) = product(a1,a4) ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(product(product(a3,a2),a4))),bind(Y0,$fot(product(a2,product(a2,a4)))),bind(Z0,$fot(product(a1,a4)))]]) ).
cnf(refute_0_193,plain,
( product(a2,product(a2,a4)) != product(a1,a4)
| product(product(a3,a2),a4) = product(a1,a4) ),
inference(resolve,[$cnf( $equal(product(product(a3,a2),a4),product(a2,product(a2,a4))) )],[refute_0_174,refute_0_192]) ).
cnf(refute_0_194,plain,
product(product(a3,a2),a4) = product(a1,a4),
inference(resolve,[$cnf( $equal(product(a2,product(a2,a4)),product(a1,a4)) )],[refute_0_191,refute_0_193]) ).
cnf(refute_0_195,plain,
( product(product(a3,a2),a4) != product(a1,a4)
| product(product(a3,a2),a4) != product(a3,a10)
| product(a1,a4) = product(a3,a10) ),
introduced(tautology,[equality,[$cnf( $equal(product(product(a3,a2),a4),product(a3,a10)) ),[0],$fot(product(a1,a4))]]) ).
cnf(refute_0_196,plain,
( product(product(a3,a2),a4) != product(a3,a10)
| product(a1,a4) = product(a3,a10) ),
inference(resolve,[$cnf( $equal(product(product(a3,a2),a4),product(a1,a4)) )],[refute_0_194,refute_0_195]) ).
cnf(refute_0_197,plain,
product(a1,a4) = product(a3,a10),
inference(resolve,[$cnf( $equal(product(product(a3,a2),a4),product(a3,a10)) )],[refute_0_156,refute_0_196]) ).
cnf(refute_0_198,plain,
( product(a1,a4) != product(a3,a10)
| product(a3,a10) = product(a1,a4) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(product(a1,a4))),bind(Y0,$fot(product(a3,a10)))]]) ).
cnf(refute_0_199,plain,
product(a3,a10) = product(a1,a4),
inference(resolve,[$cnf( $equal(product(a1,a4),product(a3,a10)) )],[refute_0_197,refute_0_198]) ).
cnf(refute_0_200,plain,
product(a10,product(a3,a10)) = product(a10,product(a3,a10)),
introduced(tautology,[refl,[$fot(product(a10,product(a3,a10)))]]) ).
cnf(refute_0_201,plain,
( product(a10,product(a3,a10)) != product(a10,product(a3,a10))
| product(a3,a10) != product(a1,a4)
| product(a10,product(a3,a10)) = product(a10,product(a1,a4)) ),
introduced(tautology,[equality,[$cnf( $equal(product(a10,product(a3,a10)),product(a10,product(a3,a10))) ),[1,1],$fot(product(a1,a4))]]) ).
cnf(refute_0_202,plain,
( product(a3,a10) != product(a1,a4)
| product(a10,product(a3,a10)) = product(a10,product(a1,a4)) ),
inference(resolve,[$cnf( $equal(product(a10,product(a3,a10)),product(a10,product(a3,a10))) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
product(a10,product(a3,a10)) = product(a10,product(a1,a4)),
inference(resolve,[$cnf( $equal(product(a3,a10),product(a1,a4)) )],[refute_0_199,refute_0_202]) ).
cnf(refute_0_204,plain,
product(product(a10,a3),a10) = product(a10,product(a3,a10)),
inference(subst,[],[refute_0_126:[bind(X_4,$fot(a3)),bind(X_5,$fot(a10))]]) ).
cnf(refute_0_205,plain,
( product(a10,product(a3,a10)) != product(a10,product(a1,a4))
| product(product(a10,a3),a10) != product(a10,product(a3,a10))
| product(product(a10,a3),a10) = product(a10,product(a1,a4)) ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(product(product(a10,a3),a10))),bind(Y0,$fot(product(a10,product(a3,a10)))),bind(Z0,$fot(product(a10,product(a1,a4))))]]) ).
cnf(refute_0_206,plain,
( product(a10,product(a3,a10)) != product(a10,product(a1,a4))
| product(product(a10,a3),a10) = product(a10,product(a1,a4)) ),
inference(resolve,[$cnf( $equal(product(product(a10,a3),a10),product(a10,product(a3,a10))) )],[refute_0_204,refute_0_205]) ).
cnf(refute_0_207,plain,
product(product(a10,a3),a10) = product(a10,product(a1,a4)),
inference(resolve,[$cnf( $equal(product(a10,product(a3,a10)),product(a10,product(a1,a4))) )],[refute_0_203,refute_0_206]) ).
cnf(refute_0_208,plain,
( product(a4,a10) != product(product(a10,a3),a10)
| product(product(a10,a3),a10) != product(a10,product(a1,a4))
| product(a4,a10) = product(a10,product(a1,a4)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(product(a4,a10),product(a10,product(a1,a4))) ),[0],$fot(product(product(a10,a3),a10))]]) ).
cnf(refute_0_209,plain,
( product(a4,a10) != product(product(a10,a3),a10)
| product(a4,a10) = product(a10,product(a1,a4)) ),
inference(resolve,[$cnf( $equal(product(product(a10,a3),a10),product(a10,product(a1,a4))) )],[refute_0_207,refute_0_208]) ).
cnf(refute_0_210,plain,
product(a4,a10) = product(a10,product(a1,a4)),
inference(resolve,[$cnf( $equal(product(a4,a10),product(product(a10,a3),a10)) )],[refute_0_152,refute_0_209]) ).
cnf(refute_0_211,plain,
( product(a4,a10) != product(a10,product(a1,a4))
| product(a10,product(a1,a4)) = product(a4,a10) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(product(a4,a10))),bind(Y0,$fot(product(a10,product(a1,a4))))]]) ).
cnf(refute_0_212,plain,
product(a10,product(a1,a4)) = product(a4,a10),
inference(resolve,[$cnf( $equal(product(a4,a10),product(a10,product(a1,a4))) )],[refute_0_210,refute_0_211]) ).
cnf(refute_0_213,plain,
( product(a10,product(a1,a4)) != product(a4,a10)
| product(product(X,a10),product(a1,a4)) != product(product(X,product(a1,a4)),product(a10,product(a1,a4)))
| product(product(X,a10),product(a1,a4)) = product(product(X,product(a1,a4)),product(a4,a10)) ),
introduced(tautology,[equality,[$cnf( $equal(product(product(X,a10),product(a1,a4)),product(product(X,product(a1,a4)),product(a10,product(a1,a4)))) ),[1,1],$fot(product(a4,a10))]]) ).
cnf(refute_0_214,plain,
( product(product(X,a10),product(a1,a4)) != product(product(X,product(a1,a4)),product(a10,product(a1,a4)))
| product(product(X,a10),product(a1,a4)) = product(product(X,product(a1,a4)),product(a4,a10)) ),
inference(resolve,[$cnf( $equal(product(a10,product(a1,a4)),product(a4,a10)) )],[refute_0_212,refute_0_213]) ).
cnf(refute_0_215,plain,
product(product(X,a10),product(a1,a4)) = product(product(X,product(a1,a4)),product(a4,a10)),
inference(resolve,[$cnf( $equal(product(product(X,a10),product(a1,a4)),product(product(X,product(a1,a4)),product(a10,product(a1,a4)))) )],[refute_0_145,refute_0_214]) ).
cnf(refute_0_216,plain,
product(product(X,a3),a10) = product(product(X,a10),product(a3,a10)),
inference(subst,[],[involutory_quandle_02:[bind(Y,$fot(a3)),bind(Z,$fot(a10))]]) ).
cnf(refute_0_217,plain,
( product(a3,a10) != product(a1,a4)
| product(product(X,a3),a10) != product(product(X,a10),product(a3,a10))
| product(product(X,a3),a10) = product(product(X,a10),product(a1,a4)) ),
introduced(tautology,[equality,[$cnf( $equal(product(product(X,a3),a10),product(product(X,a10),product(a3,a10))) ),[1,1],$fot(product(a1,a4))]]) ).
cnf(refute_0_218,plain,
( product(product(X,a3),a10) != product(product(X,a10),product(a3,a10))
| product(product(X,a3),a10) = product(product(X,a10),product(a1,a4)) ),
inference(resolve,[$cnf( $equal(product(a3,a10),product(a1,a4)) )],[refute_0_199,refute_0_217]) ).
cnf(refute_0_219,plain,
product(product(X,a3),a10) = product(product(X,a10),product(a1,a4)),
inference(resolve,[$cnf( $equal(product(product(X,a3),a10),product(product(X,a10),product(a3,a10))) )],[refute_0_216,refute_0_218]) ).
cnf(refute_0_220,plain,
product(product(X,a3),a10) = product(product(X,a2),a4),
inference(subst,[],[refute_0_176:[bind(X_3,$fot(X))]]) ).
cnf(refute_0_221,plain,
( product(product(X,a3),a10) != product(product(X,a10),product(a1,a4))
| product(product(X,a3),a10) != product(product(X,a2),a4)
| product(product(X,a2),a4) = product(product(X,a10),product(a1,a4)) ),
introduced(tautology,[equality,[$cnf( $equal(product(product(X,a3),a10),product(product(X,a10),product(a1,a4))) ),[0],$fot(product(product(X,a2),a4))]]) ).
cnf(refute_0_222,plain,
( product(product(X,a3),a10) != product(product(X,a10),product(a1,a4))
| product(product(X,a2),a4) = product(product(X,a10),product(a1,a4)) ),
inference(resolve,[$cnf( $equal(product(product(X,a3),a10),product(product(X,a2),a4)) )],[refute_0_220,refute_0_221]) ).
cnf(refute_0_223,plain,
product(product(X,a2),a4) = product(product(X,a10),product(a1,a4)),
inference(resolve,[$cnf( $equal(product(product(X,a3),a10),product(product(X,a10),product(a1,a4))) )],[refute_0_219,refute_0_222]) ).
cnf(refute_0_224,plain,
( product(product(X,a2),a4) != product(product(X,a10),product(a1,a4))
| product(product(X,a10),product(a1,a4)) = product(product(X,a2),a4) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(product(product(X,a2),a4))),bind(Y0,$fot(product(product(X,a10),product(a1,a4))))]]) ).
cnf(refute_0_225,plain,
product(product(X,a10),product(a1,a4)) = product(product(X,a2),a4),
inference(resolve,[$cnf( $equal(product(product(X,a2),a4),product(product(X,a10),product(a1,a4))) )],[refute_0_223,refute_0_224]) ).
cnf(refute_0_226,plain,
( product(product(X,a10),product(a1,a4)) != product(product(X,a2),a4)
| product(product(X,a10),product(a1,a4)) != product(product(X,product(a1,a4)),product(a4,a10))
| product(product(X,a2),a4) = product(product(X,product(a1,a4)),product(a4,a10)) ),
introduced(tautology,[equality,[$cnf( $equal(product(product(X,a10),product(a1,a4)),product(product(X,product(a1,a4)),product(a4,a10))) ),[0],$fot(product(product(X,a2),a4))]]) ).
cnf(refute_0_227,plain,
( product(product(X,a10),product(a1,a4)) != product(product(X,product(a1,a4)),product(a4,a10))
| product(product(X,a2),a4) = product(product(X,product(a1,a4)),product(a4,a10)) ),
inference(resolve,[$cnf( $equal(product(product(X,a10),product(a1,a4)),product(product(X,a2),a4)) )],[refute_0_225,refute_0_226]) ).
cnf(refute_0_228,plain,
product(product(X,a2),a4) = product(product(X,product(a1,a4)),product(a4,a10)),
inference(resolve,[$cnf( $equal(product(product(X,a10),product(a1,a4)),product(product(X,product(a1,a4)),product(a4,a10))) )],[refute_0_215,refute_0_227]) ).
cnf(refute_0_229,plain,
( product(product(X,a2),a4) != product(product(X,product(a1,a4)),product(a4,a10))
| product(product(X,product(a1,a4)),product(a4,a10)) = product(product(X,a2),a4) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(product(product(X,a2),a4))),bind(Y0,$fot(product(product(X,product(a1,a4)),product(a4,a10))))]]) ).
cnf(refute_0_230,plain,
product(product(X,product(a1,a4)),product(a4,a10)) = product(product(X,a2),a4),
inference(resolve,[$cnf( $equal(product(product(X,a2),a4),product(product(X,product(a1,a4)),product(a4,a10))) )],[refute_0_228,refute_0_229]) ).
cnf(refute_0_231,plain,
( product(product(X,a4),a9) != product(product(X,product(a1,a4)),product(a4,a10))
| product(product(X,product(a1,a4)),product(a4,a10)) != product(product(X,a2),a4)
| product(product(X,a4),a9) = product(product(X,a2),a4) ),
introduced(tautology,[equality,[$cnf( ~ $equal(product(product(X,a4),a9),product(product(X,a2),a4)) ),[0],$fot(product(product(X,product(a1,a4)),product(a4,a10)))]]) ).
cnf(refute_0_232,plain,
( product(product(X,a4),a9) != product(product(X,product(a1,a4)),product(a4,a10))
| product(product(X,a4),a9) = product(product(X,a2),a4) ),
inference(resolve,[$cnf( $equal(product(product(X,product(a1,a4)),product(a4,a10)),product(product(X,a2),a4)) )],[refute_0_230,refute_0_231]) ).
cnf(refute_0_233,plain,
( product(product(X,a9),product(a1,a4)) != product(product(X,product(a1,a4)),product(a4,a10))
| product(product(X,a4),a9) = product(product(X,a2),a4) ),
inference(resolve,[$cnf( $equal(product(product(X,a4),a9),product(product(X,product(a1,a4)),product(a4,a10))) )],[refute_0_144,refute_0_232]) ).
cnf(refute_0_234,plain,
product(product(X,a4),a9) = product(product(X,a2),a4),
inference(resolve,[$cnf( $equal(product(product(X,a9),product(a1,a4)),product(product(X,product(a1,a4)),product(a4,a10))) )],[refute_0_136,refute_0_233]) ).
cnf(refute_0_235,plain,
product(product(a9,product(a1,a4)),product(a1,a4)) = a9,
inference(subst,[],[involutory_quandle_01:[bind(X,$fot(a9)),bind(Y,$fot(product(a1,a4)))]]) ).
cnf(refute_0_236,plain,
( product(a9,product(a1,a4)) != product(a4,a10)
| product(product(a9,product(a1,a4)),product(a1,a4)) != a9
| product(product(a4,a10),product(a1,a4)) = a9 ),
introduced(tautology,[equality,[$cnf( $equal(product(product(a9,product(a1,a4)),product(a1,a4)),a9) ),[0,0],$fot(product(a4,a10))]]) ).
cnf(refute_0_237,plain,
( product(product(a9,product(a1,a4)),product(a1,a4)) != a9
| product(product(a4,a10),product(a1,a4)) = a9 ),
inference(resolve,[$cnf( $equal(product(a9,product(a1,a4)),product(a4,a10)) )],[refute_0_133,refute_0_236]) ).
cnf(refute_0_238,plain,
product(product(a4,a10),product(a1,a4)) = a9,
inference(resolve,[$cnf( $equal(product(product(a9,product(a1,a4)),product(a1,a4)),a9) )],[refute_0_235,refute_0_237]) ).
cnf(refute_0_239,plain,
product(a4,product(a2,a4)) = product(a4,product(a2,a4)),
introduced(tautology,[refl,[$fot(product(a4,product(a2,a4)))]]) ).
cnf(refute_0_240,plain,
( product(a2,a4) != a3
| product(a4,product(a2,a4)) != product(a4,product(a2,a4))
| product(a4,product(a2,a4)) = product(a4,a3) ),
introduced(tautology,[equality,[$cnf( $equal(product(a4,product(a2,a4)),product(a4,product(a2,a4))) ),[1,1],$fot(a3)]]) ).
cnf(refute_0_241,plain,
( product(a2,a4) != a3
| product(a4,product(a2,a4)) = product(a4,a3) ),
inference(resolve,[$cnf( $equal(product(a4,product(a2,a4)),product(a4,product(a2,a4))) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
product(a4,product(a2,a4)) = product(a4,a3),
inference(resolve,[$cnf( $equal(product(a2,a4),a3) )],[refute_0_29,refute_0_241]) ).
cnf(refute_0_243,plain,
( product(a4,a3) != a10
| product(a4,product(a2,a4)) != product(a4,a3)
| product(a4,product(a2,a4)) = a10 ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(product(a4,product(a2,a4)))),bind(Y0,$fot(product(a4,a3))),bind(Z0,$fot(a10))]]) ).
cnf(refute_0_244,plain,
( product(a4,a3) != a10
| product(a4,product(a2,a4)) = a10 ),
inference(resolve,[$cnf( $equal(product(a4,product(a2,a4)),product(a4,a3)) )],[refute_0_242,refute_0_243]) ).
cnf(refute_0_245,plain,
product(a4,product(a2,a4)) = a10,
inference(resolve,[$cnf( $equal(product(a4,a3),a10) )],[refute_0_19,refute_0_244]) ).
cnf(refute_0_246,plain,
product(product(a4,a2),a4) = product(a4,product(a2,a4)),
inference(subst,[],[refute_0_126:[bind(X_4,$fot(a2)),bind(X_5,$fot(a4))]]) ).
cnf(refute_0_247,plain,
product(product(a4,a10),product(a1,a4)) = product(product(a4,a2),a4),
inference(subst,[],[refute_0_225:[bind(X,$fot(a4))]]) ).
cnf(refute_0_248,plain,
( product(product(a4,a10),product(a1,a4)) != product(product(a4,a2),a4)
| product(product(a4,a2),a4) != product(a4,product(a2,a4))
| product(product(a4,a10),product(a1,a4)) = product(a4,product(a2,a4)) ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(product(product(a4,a10),product(a1,a4)))),bind(Y0,$fot(product(product(a4,a2),a4))),bind(Z0,$fot(product(a4,product(a2,a4))))]]) ).
cnf(refute_0_249,plain,
( product(product(a4,a2),a4) != product(a4,product(a2,a4))
| product(product(a4,a10),product(a1,a4)) = product(a4,product(a2,a4)) ),
inference(resolve,[$cnf( $equal(product(product(a4,a10),product(a1,a4)),product(product(a4,a2),a4)) )],[refute_0_247,refute_0_248]) ).
cnf(refute_0_250,plain,
product(product(a4,a10),product(a1,a4)) = product(a4,product(a2,a4)),
inference(resolve,[$cnf( $equal(product(product(a4,a2),a4),product(a4,product(a2,a4))) )],[refute_0_246,refute_0_249]) ).
cnf(refute_0_251,plain,
( product(a4,product(a2,a4)) != a10
| product(product(a4,a10),product(a1,a4)) != product(a4,product(a2,a4))
| product(product(a4,a10),product(a1,a4)) = a10 ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(product(product(a4,a10),product(a1,a4)))),bind(Y0,$fot(product(a4,product(a2,a4)))),bind(Z0,$fot(a10))]]) ).
cnf(refute_0_252,plain,
( product(a4,product(a2,a4)) != a10
| product(product(a4,a10),product(a1,a4)) = a10 ),
inference(resolve,[$cnf( $equal(product(product(a4,a10),product(a1,a4)),product(a4,product(a2,a4))) )],[refute_0_250,refute_0_251]) ).
cnf(refute_0_253,plain,
product(product(a4,a10),product(a1,a4)) = a10,
inference(resolve,[$cnf( $equal(product(a4,product(a2,a4)),a10) )],[refute_0_245,refute_0_252]) ).
cnf(refute_0_254,plain,
( product(product(a4,a10),product(a1,a4)) != a10
| product(product(a4,a10),product(a1,a4)) != a9
| a10 = a9 ),
introduced(tautology,[equality,[$cnf( $equal(product(product(a4,a10),product(a1,a4)),a9) ),[0],$fot(a10)]]) ).
cnf(refute_0_255,plain,
( product(product(a4,a10),product(a1,a4)) != a9
| a10 = a9 ),
inference(resolve,[$cnf( $equal(product(product(a4,a10),product(a1,a4)),a10) )],[refute_0_253,refute_0_254]) ).
cnf(refute_0_256,plain,
a10 = a9,
inference(resolve,[$cnf( $equal(product(product(a4,a10),product(a1,a4)),a9) )],[refute_0_238,refute_0_255]) ).
cnf(refute_0_257,plain,
( a10 != a9
| a9 = a10 ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(a10)),bind(Y0,$fot(a9))]]) ).
cnf(refute_0_258,plain,
a9 = a10,
inference(resolve,[$cnf( $equal(a10,a9) )],[refute_0_256,refute_0_257]) ).
cnf(refute_0_259,plain,
product(product(X,a4),a9) = product(product(X,a4),a9),
introduced(tautology,[refl,[$fot(product(product(X,a4),a9))]]) ).
cnf(refute_0_260,plain,
( a9 != a10
| product(product(X,a4),a9) != product(product(X,a4),a9)
| product(product(X,a4),a9) = product(product(X,a4),a10) ),
introduced(tautology,[equality,[$cnf( $equal(product(product(X,a4),a9),product(product(X,a4),a9)) ),[1,1],$fot(a10)]]) ).
cnf(refute_0_261,plain,
( a9 != a10
| product(product(X,a4),a9) = product(product(X,a4),a10) ),
inference(resolve,[$cnf( $equal(product(product(X,a4),a9),product(product(X,a4),a9)) )],[refute_0_259,refute_0_260]) ).
cnf(refute_0_262,plain,
product(product(X,a4),a9) = product(product(X,a4),a10),
inference(resolve,[$cnf( $equal(a9,a10) )],[refute_0_258,refute_0_261]) ).
cnf(refute_0_263,plain,
( product(product(X,a4),a9) != product(product(X,a2),a4)
| product(product(X,a4),a9) != product(product(X,a4),a10)
| product(product(X,a4),a10) = product(product(X,a2),a4) ),
introduced(tautology,[equality,[$cnf( $equal(product(product(X,a4),a9),product(product(X,a2),a4)) ),[0],$fot(product(product(X,a4),a10))]]) ).
cnf(refute_0_264,plain,
( product(product(X,a4),a9) != product(product(X,a2),a4)
| product(product(X,a4),a10) = product(product(X,a2),a4) ),
inference(resolve,[$cnf( $equal(product(product(X,a4),a9),product(product(X,a4),a10)) )],[refute_0_262,refute_0_263]) ).
cnf(refute_0_265,plain,
product(product(X,a4),a10) = product(product(X,a2),a4),
inference(resolve,[$cnf( $equal(product(product(X,a4),a9),product(product(X,a2),a4)) )],[refute_0_234,refute_0_264]) ).
cnf(refute_0_266,plain,
product(product(product(X_7,a2),a4),a10) = product(product(product(X_7,a2),a2),a4),
inference(subst,[],[refute_0_265:[bind(X,$fot(product(X_7,a2)))]]) ).
cnf(refute_0_267,plain,
( product(product(product(X_7,a2),a2),a4) != product(X_7,a4)
| product(product(product(X_7,a2),a4),a10) != product(product(product(X_7,a2),a2),a4)
| product(product(product(X_7,a2),a4),a10) = product(X_7,a4) ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(product(product(product(X_7,a2),a4),a10))),bind(Y0,$fot(product(product(product(X_7,a2),a2),a4))),bind(Z0,$fot(product(X_7,a4)))]]) ).
cnf(refute_0_268,plain,
( product(product(product(X_7,a2),a2),a4) != product(X_7,a4)
| product(product(product(X_7,a2),a4),a10) = product(X_7,a4) ),
inference(resolve,[$cnf( $equal(product(product(product(X_7,a2),a4),a10),product(product(product(X_7,a2),a2),a4)) )],[refute_0_266,refute_0_267]) ).
cnf(refute_0_269,plain,
product(product(product(X_7,a2),a4),a10) = product(X_7,a4),
inference(resolve,[$cnf( $equal(product(product(product(X_7,a2),a2),a4),product(X_7,a4)) )],[refute_0_48,refute_0_268]) ).
cnf(refute_0_270,plain,
( product(product(product(X_7,a2),a4),a10) != product(X_7,a3)
| product(product(product(X_7,a2),a4),a10) != product(X_7,a4)
| product(X_7,a4) = product(X_7,a3) ),
introduced(tautology,[equality,[$cnf( $equal(product(product(product(X_7,a2),a4),a10),product(X_7,a3)) ),[0],$fot(product(X_7,a4))]]) ).
cnf(refute_0_271,plain,
( product(product(product(X_7,a2),a4),a10) != product(X_7,a3)
| product(X_7,a4) = product(X_7,a3) ),
inference(resolve,[$cnf( $equal(product(product(product(X_7,a2),a4),a10),product(X_7,a4)) )],[refute_0_269,refute_0_270]) ).
cnf(refute_0_272,plain,
product(X_7,a4) = product(X_7,a3),
inference(resolve,[$cnf( $equal(product(product(product(X_7,a2),a4),a10),product(X_7,a3)) )],[refute_0_43,refute_0_271]) ).
cnf(refute_0_273,plain,
product(a3,a4) = product(a3,a3),
inference(subst,[],[refute_0_272:[bind(X_7,$fot(a3))]]) ).
cnf(refute_0_274,plain,
( product(a3,a3) != a3
| product(a3,a4) != product(a3,a3)
| product(a3,a4) = a3 ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(product(a3,a4))),bind(Y0,$fot(product(a3,a3))),bind(Z0,$fot(a3))]]) ).
cnf(refute_0_275,plain,
( product(a3,a3) != a3
| product(a3,a4) = a3 ),
inference(resolve,[$cnf( $equal(product(a3,a4),product(a3,a3)) )],[refute_0_273,refute_0_274]) ).
cnf(refute_0_276,plain,
product(a3,a4) = a3,
inference(resolve,[$cnf( $equal(product(a3,a3),a3) )],[refute_0_11,refute_0_275]) ).
cnf(refute_0_277,plain,
( a2 != product(a3,a4)
| product(a3,a4) != a3
| a2 = a3 ),
introduced(tautology,[equality,[$cnf( ~ $equal(a2,a3) ),[0],$fot(product(a3,a4))]]) ).
cnf(refute_0_278,plain,
( a2 != product(a3,a4)
| a2 = a3 ),
inference(resolve,[$cnf( $equal(product(a3,a4),a3) )],[refute_0_276,refute_0_277]) ).
cnf(refute_0_279,plain,
a2 = a3,
inference(resolve,[$cnf( $equal(a2,product(a3,a4)) )],[knot_04,refute_0_278]) ).
cnf(refute_0_280,plain,
product(a2,a2) = a2,
inference(subst,[],[involutory_quandle:[bind(X,$fot(a2))]]) ).
cnf(refute_0_281,plain,
( a2 != a3
| a3 = a2 ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(a2)),bind(Y0,$fot(a3))]]) ).
cnf(refute_0_282,plain,
a3 = a2,
inference(resolve,[$cnf( $equal(a2,a3) )],[refute_0_279,refute_0_281]) ).
cnf(refute_0_283,plain,
product(a3,a2) = product(a3,a2),
introduced(tautology,[refl,[$fot(product(a3,a2))]]) ).
cnf(refute_0_284,plain,
( a3 != a2
| product(a3,a2) != product(a3,a2)
| product(a3,a2) = product(a2,a2) ),
introduced(tautology,[equality,[$cnf( $equal(product(a3,a2),product(a3,a2)) ),[1,0],$fot(a2)]]) ).
cnf(refute_0_285,plain,
( a3 != a2
| product(a3,a2) = product(a2,a2) ),
inference(resolve,[$cnf( $equal(product(a3,a2),product(a3,a2)) )],[refute_0_283,refute_0_284]) ).
cnf(refute_0_286,plain,
product(a3,a2) = product(a2,a2),
inference(resolve,[$cnf( $equal(a3,a2) )],[refute_0_282,refute_0_285]) ).
cnf(refute_0_287,plain,
( product(a2,a2) != a2
| product(a3,a2) != product(a2,a2)
| product(a3,a2) = a2 ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(product(a3,a2))),bind(Y0,$fot(product(a2,a2))),bind(Z0,$fot(a2))]]) ).
cnf(refute_0_288,plain,
( product(a2,a2) != a2
| product(a3,a2) = a2 ),
inference(resolve,[$cnf( $equal(product(a3,a2),product(a2,a2)) )],[refute_0_286,refute_0_287]) ).
cnf(refute_0_289,plain,
product(a3,a2) = a2,
inference(resolve,[$cnf( $equal(product(a2,a2),a2) )],[refute_0_280,refute_0_288]) ).
cnf(refute_0_290,plain,
( product(a3,a2) != a1
| product(a3,a2) != a2
| a2 = a1 ),
introduced(tautology,[equality,[$cnf( $equal(product(a3,a2),a1) ),[0],$fot(a2)]]) ).
cnf(refute_0_291,plain,
( product(a3,a2) != a1
| a2 = a1 ),
inference(resolve,[$cnf( $equal(product(a3,a2),a2) )],[refute_0_289,refute_0_290]) ).
cnf(refute_0_292,plain,
a2 = a1,
inference(resolve,[$cnf( $equal(product(a3,a2),a1) )],[refute_0_162,refute_0_291]) ).
cnf(refute_0_293,plain,
( a2 != a1
| a2 != a3
| a1 = a3 ),
introduced(tautology,[equality,[$cnf( $equal(a2,a3) ),[0],$fot(a1)]]) ).
cnf(refute_0_294,plain,
( a2 != a3
| a1 = a3 ),
inference(resolve,[$cnf( $equal(a2,a1) )],[refute_0_292,refute_0_293]) ).
cnf(refute_0_295,plain,
a1 = a3,
inference(resolve,[$cnf( $equal(a2,a3) )],[refute_0_279,refute_0_294]) ).
cnf(refute_0_296,plain,
( a1 != a3
| a3 = a1 ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(a1)),bind(Y0,$fot(a3))]]) ).
cnf(refute_0_297,plain,
a3 = a1,
inference(resolve,[$cnf( $equal(a1,a3) )],[refute_0_295,refute_0_296]) ).
cnf(refute_0_298,plain,
product(a6,a3) = product(a6,a3),
introduced(tautology,[refl,[$fot(product(a6,a3))]]) ).
cnf(refute_0_299,plain,
( a3 != a1
| product(a6,a3) != product(a6,a3)
| product(a6,a3) = product(a6,a1) ),
introduced(tautology,[equality,[$cnf( $equal(product(a6,a3),product(a6,a3)) ),[1,1],$fot(a1)]]) ).
cnf(refute_0_300,plain,
( a3 != a1
| product(a6,a3) = product(a6,a1) ),
inference(resolve,[$cnf( $equal(product(a6,a3),product(a6,a3)) )],[refute_0_298,refute_0_299]) ).
cnf(refute_0_301,plain,
product(a6,a3) = product(a6,a1),
inference(resolve,[$cnf( $equal(a3,a1) )],[refute_0_297,refute_0_300]) ).
cnf(refute_0_302,plain,
( product(a6,a1) != a7
| product(a6,a3) != product(a6,a1)
| product(a6,a3) = a7 ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(product(a6,a3))),bind(Y0,$fot(product(a6,a1))),bind(Z0,$fot(a7))]]) ).
cnf(refute_0_303,plain,
( product(a6,a1) != a7
| product(a6,a3) = a7 ),
inference(resolve,[$cnf( $equal(product(a6,a3),product(a6,a1)) )],[refute_0_301,refute_0_302]) ).
cnf(refute_0_304,plain,
product(a6,a3) = a7,
inference(resolve,[$cnf( $equal(product(a6,a1),a7) )],[refute_0_10,refute_0_303]) ).
cnf(refute_0_305,plain,
product(a6,a4) = product(a6,a3),
inference(subst,[],[refute_0_272:[bind(X_7,$fot(a6))]]) ).
cnf(refute_0_306,plain,
( product(a6,a3) != a7
| product(a6,a4) != product(a6,a3)
| product(a6,a4) = a7 ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(product(a6,a4))),bind(Y0,$fot(product(a6,a3))),bind(Z0,$fot(a7))]]) ).
cnf(refute_0_307,plain,
( product(a6,a3) != a7
| product(a6,a4) = a7 ),
inference(resolve,[$cnf( $equal(product(a6,a4),product(a6,a3)) )],[refute_0_305,refute_0_306]) ).
cnf(refute_0_308,plain,
product(a6,a4) = a7,
inference(resolve,[$cnf( $equal(product(a6,a3),a7) )],[refute_0_304,refute_0_307]) ).
cnf(refute_0_309,plain,
( product(a6,a4) != a5
| product(a6,a4) != a7
| a7 = a5 ),
introduced(tautology,[equality,[$cnf( $equal(product(a6,a4),a5) ),[0],$fot(a7)]]) ).
cnf(refute_0_310,plain,
( product(a6,a4) != a5
| a7 = a5 ),
inference(resolve,[$cnf( $equal(product(a6,a4),a7) )],[refute_0_308,refute_0_309]) ).
cnf(refute_0_311,plain,
a7 = a5,
inference(resolve,[$cnf( $equal(product(a6,a4),a5) )],[refute_0_8,refute_0_310]) ).
cnf(refute_0_312,plain,
( a7 != a5
| a7 != product(a6,a1)
| a5 = product(a6,a1) ),
introduced(tautology,[equality,[$cnf( $equal(a7,product(a6,a1)) ),[0],$fot(a5)]]) ).
cnf(refute_0_313,plain,
( a7 != product(a6,a1)
| a5 = product(a6,a1) ),
inference(resolve,[$cnf( $equal(a7,a5) )],[refute_0_311,refute_0_312]) ).
cnf(refute_0_314,plain,
a5 = product(a6,a1),
inference(resolve,[$cnf( $equal(a7,product(a6,a1)) )],[knot_07,refute_0_313]) ).
cnf(refute_0_315,plain,
product(a10,a3) = product(a10,a3),
introduced(tautology,[refl,[$fot(product(a10,a3))]]) ).
cnf(refute_0_316,plain,
( a3 != a2
| product(a10,a3) != product(a10,a3)
| product(a10,a3) = product(a10,a2) ),
introduced(tautology,[equality,[$cnf( $equal(product(a10,a3),product(a10,a3)) ),[1,1],$fot(a2)]]) ).
cnf(refute_0_317,plain,
( a3 != a2
| product(a10,a3) = product(a10,a2) ),
inference(resolve,[$cnf( $equal(product(a10,a3),product(a10,a3)) )],[refute_0_315,refute_0_316]) ).
cnf(refute_0_318,plain,
product(a10,a3) = product(a10,a2),
inference(resolve,[$cnf( $equal(a3,a2) )],[refute_0_282,refute_0_317]) ).
cnf(refute_0_319,plain,
( a4 != product(a10,a3)
| product(a10,a3) != product(a10,a2)
| a4 = product(a10,a2) ),
introduced(tautology,[equality,[$cnf( ~ $equal(a4,product(a10,a2)) ),[0],$fot(product(a10,a3))]]) ).
cnf(refute_0_320,plain,
( a4 != product(a10,a3)
| a4 = product(a10,a2) ),
inference(resolve,[$cnf( $equal(product(a10,a3),product(a10,a2)) )],[refute_0_318,refute_0_319]) ).
cnf(refute_0_321,plain,
a4 = product(a10,a2),
inference(resolve,[$cnf( $equal(a4,product(a10,a3)) )],[knot_10,refute_0_320]) ).
cnf(refute_0_322,plain,
product(a10,a2) = product(a10,a2),
introduced(tautology,[refl,[$fot(product(a10,a2))]]) ).
cnf(refute_0_323,plain,
( a2 != a1
| product(a10,a2) != product(a10,a2)
| product(a10,a2) = product(a10,a1) ),
introduced(tautology,[equality,[$cnf( $equal(product(a10,a2),product(a10,a2)) ),[1,1],$fot(a1)]]) ).
cnf(refute_0_324,plain,
( a2 != a1
| product(a10,a2) = product(a10,a1) ),
inference(resolve,[$cnf( $equal(product(a10,a2),product(a10,a2)) )],[refute_0_322,refute_0_323]) ).
cnf(refute_0_325,plain,
product(a10,a2) = product(a10,a1),
inference(resolve,[$cnf( $equal(a2,a1) )],[refute_0_292,refute_0_324]) ).
cnf(refute_0_326,plain,
( a4 != product(a10,a2)
| product(a10,a2) != product(a10,a1)
| a4 = product(a10,a1) ),
introduced(tautology,[equality,[$cnf( ~ $equal(a4,product(a10,a1)) ),[0],$fot(product(a10,a2))]]) ).
cnf(refute_0_327,plain,
( a4 != product(a10,a2)
| a4 = product(a10,a1) ),
inference(resolve,[$cnf( $equal(product(a10,a2),product(a10,a1)) )],[refute_0_325,refute_0_326]) ).
cnf(refute_0_328,plain,
a4 = product(a10,a1),
inference(resolve,[$cnf( $equal(a4,product(a10,a2)) )],[refute_0_321,refute_0_327]) ).
cnf(refute_0_329,plain,
( a4 != product(a10,a1)
| product(a10,a1) = a4 ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(a4)),bind(Y0,$fot(product(a10,a1)))]]) ).
cnf(refute_0_330,plain,
product(a10,a1) = a4,
inference(resolve,[$cnf( $equal(a4,product(a10,a1)) )],[refute_0_328,refute_0_329]) ).
cnf(refute_0_331,plain,
product(a10,a10) = a10,
inference(subst,[],[involutory_quandle:[bind(X,$fot(a10))]]) ).
cnf(refute_0_332,plain,
product(a10,a9) = product(a10,a9),
introduced(tautology,[refl,[$fot(product(a10,a9))]]) ).
cnf(refute_0_333,plain,
( a9 != a10
| product(a10,a9) != product(a10,a9)
| product(a10,a9) = product(a10,a10) ),
introduced(tautology,[equality,[$cnf( $equal(product(a10,a9),product(a10,a9)) ),[1,1],$fot(a10)]]) ).
cnf(refute_0_334,plain,
( a9 != a10
| product(a10,a9) = product(a10,a10) ),
inference(resolve,[$cnf( $equal(product(a10,a9),product(a10,a9)) )],[refute_0_332,refute_0_333]) ).
cnf(refute_0_335,plain,
product(a10,a9) = product(a10,a10),
inference(resolve,[$cnf( $equal(a9,a10) )],[refute_0_258,refute_0_334]) ).
cnf(refute_0_336,plain,
( product(a10,a10) != a10
| product(a10,a9) != product(a10,a10)
| product(a10,a9) = a10 ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(product(a10,a9))),bind(Y0,$fot(product(a10,a10))),bind(Z0,$fot(a10))]]) ).
cnf(refute_0_337,plain,
( product(a10,a10) != a10
| product(a10,a9) = a10 ),
inference(resolve,[$cnf( $equal(product(a10,a9),product(a10,a10)) )],[refute_0_335,refute_0_336]) ).
cnf(refute_0_338,plain,
product(a10,a9) = a10,
inference(resolve,[$cnf( $equal(product(a10,a10),a10) )],[refute_0_331,refute_0_337]) ).
cnf(refute_0_339,plain,
( product(a10,a9) != a10
| product(a10,a9) != a8
| a10 = a8 ),
introduced(tautology,[equality,[$cnf( $equal(product(a10,a9),a8) ),[0],$fot(a10)]]) ).
cnf(refute_0_340,plain,
( product(a10,a9) != a8
| a10 = a8 ),
inference(resolve,[$cnf( $equal(product(a10,a9),a10) )],[refute_0_338,refute_0_339]) ).
cnf(refute_0_341,plain,
product(a7,a3) = product(a7,a3),
introduced(tautology,[refl,[$fot(product(a7,a3))]]) ).
cnf(refute_0_342,plain,
( a3 != a2
| product(a7,a3) != product(a7,a3)
| product(a7,a3) = product(a7,a2) ),
introduced(tautology,[equality,[$cnf( $equal(product(a7,a3),product(a7,a3)) ),[1,1],$fot(a2)]]) ).
cnf(refute_0_343,plain,
( a3 != a2
| product(a7,a3) = product(a7,a2) ),
inference(resolve,[$cnf( $equal(product(a7,a3),product(a7,a3)) )],[refute_0_341,refute_0_342]) ).
cnf(refute_0_344,plain,
product(a7,a3) = product(a7,a2),
inference(resolve,[$cnf( $equal(a3,a2) )],[refute_0_282,refute_0_343]) ).
cnf(refute_0_345,plain,
product(a7,a4) = product(a7,a3),
inference(subst,[],[refute_0_272:[bind(X_7,$fot(a7))]]) ).
cnf(refute_0_346,plain,
( product(a7,a3) != product(a7,a2)
| product(a7,a4) != product(a7,a3)
| product(a7,a4) = product(a7,a2) ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(product(a7,a4))),bind(Y0,$fot(product(a7,a3))),bind(Z0,$fot(product(a7,a2)))]]) ).
cnf(refute_0_347,plain,
( product(a7,a3) != product(a7,a2)
| product(a7,a4) = product(a7,a2) ),
inference(resolve,[$cnf( $equal(product(a7,a4),product(a7,a3)) )],[refute_0_345,refute_0_346]) ).
cnf(refute_0_348,plain,
product(a7,a4) = product(a7,a2),
inference(resolve,[$cnf( $equal(product(a7,a3),product(a7,a2)) )],[refute_0_344,refute_0_347]) ).
cnf(refute_0_349,plain,
( a8 != product(a7,a4)
| product(a7,a4) != product(a7,a2)
| a8 = product(a7,a2) ),
introduced(tautology,[equality,[$cnf( ~ $equal(a8,product(a7,a2)) ),[0],$fot(product(a7,a4))]]) ).
cnf(refute_0_350,plain,
( a8 != product(a7,a4)
| a8 = product(a7,a2) ),
inference(resolve,[$cnf( $equal(product(a7,a4),product(a7,a2)) )],[refute_0_348,refute_0_349]) ).
cnf(refute_0_351,plain,
a8 = product(a7,a2),
inference(resolve,[$cnf( $equal(a8,product(a7,a4)) )],[knot_08,refute_0_350]) ).
cnf(refute_0_352,plain,
product(product(a6,a1),a1) = a6,
inference(subst,[],[involutory_quandle_01:[bind(X,$fot(a6)),bind(Y,$fot(a1))]]) ).
cnf(refute_0_353,plain,
( product(a6,a1) != a7
| product(product(a6,a1),a1) != a6
| product(a7,a1) = a6 ),
introduced(tautology,[equality,[$cnf( $equal(product(product(a6,a1),a1),a6) ),[0,0],$fot(a7)]]) ).
cnf(refute_0_354,plain,
( product(product(a6,a1),a1) != a6
| product(a7,a1) = a6 ),
inference(resolve,[$cnf( $equal(product(a6,a1),a7) )],[refute_0_10,refute_0_353]) ).
cnf(refute_0_355,plain,
product(a7,a1) = a6,
inference(resolve,[$cnf( $equal(product(product(a6,a1),a1),a6) )],[refute_0_352,refute_0_354]) ).
cnf(refute_0_356,plain,
product(a7,a2) = product(a7,a2),
introduced(tautology,[refl,[$fot(product(a7,a2))]]) ).
cnf(refute_0_357,plain,
( a2 != a1
| product(a7,a2) != product(a7,a2)
| product(a7,a2) = product(a7,a1) ),
introduced(tautology,[equality,[$cnf( $equal(product(a7,a2),product(a7,a2)) ),[1,1],$fot(a1)]]) ).
cnf(refute_0_358,plain,
( a2 != a1
| product(a7,a2) = product(a7,a1) ),
inference(resolve,[$cnf( $equal(product(a7,a2),product(a7,a2)) )],[refute_0_356,refute_0_357]) ).
cnf(refute_0_359,plain,
product(a7,a2) = product(a7,a1),
inference(resolve,[$cnf( $equal(a2,a1) )],[refute_0_292,refute_0_358]) ).
cnf(refute_0_360,plain,
( product(a7,a1) != a6
| product(a7,a2) != product(a7,a1)
| product(a7,a2) = a6 ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(product(a7,a2))),bind(Y0,$fot(product(a7,a1))),bind(Z0,$fot(a6))]]) ).
cnf(refute_0_361,plain,
( product(a7,a1) != a6
| product(a7,a2) = a6 ),
inference(resolve,[$cnf( $equal(product(a7,a2),product(a7,a1)) )],[refute_0_359,refute_0_360]) ).
cnf(refute_0_362,plain,
product(a7,a2) = a6,
inference(resolve,[$cnf( $equal(product(a7,a1),a6) )],[refute_0_355,refute_0_361]) ).
cnf(refute_0_363,plain,
( a8 != product(a7,a2)
| product(a7,a2) != a6
| a8 = a6 ),
introduced(tautology,[equality,[$cnf( ~ $equal(a8,a6) ),[0],$fot(product(a7,a2))]]) ).
cnf(refute_0_364,plain,
( a8 != product(a7,a2)
| a8 = a6 ),
inference(resolve,[$cnf( $equal(product(a7,a2),a6) )],[refute_0_362,refute_0_363]) ).
cnf(refute_0_365,plain,
a8 = a6,
inference(resolve,[$cnf( $equal(a8,product(a7,a2)) )],[refute_0_351,refute_0_364]) ).
cnf(refute_0_366,plain,
( a10 != a8
| a8 != a6
| a10 = a6 ),
introduced(tautology,[equality,[$cnf( ~ $equal(a10,a6) ),[0],$fot(a8)]]) ).
cnf(refute_0_367,plain,
( a10 != a8
| a10 = a6 ),
inference(resolve,[$cnf( $equal(a8,a6) )],[refute_0_365,refute_0_366]) ).
cnf(refute_0_368,plain,
( product(a10,a9) != a8
| a10 = a6 ),
inference(resolve,[$cnf( $equal(a10,a8) )],[refute_0_340,refute_0_367]) ).
cnf(refute_0_369,plain,
a10 = a6,
inference(resolve,[$cnf( $equal(product(a10,a9),a8) )],[refute_0_57,refute_0_368]) ).
cnf(refute_0_370,plain,
( a10 != a6
| a6 = a10 ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(a10)),bind(Y0,$fot(a6))]]) ).
cnf(refute_0_371,plain,
a6 = a10,
inference(resolve,[$cnf( $equal(a10,a6) )],[refute_0_369,refute_0_370]) ).
cnf(refute_0_372,plain,
product(a6,a1) = product(a6,a1),
introduced(tautology,[refl,[$fot(product(a6,a1))]]) ).
cnf(refute_0_373,plain,
( a6 != a10
| product(a6,a1) != product(a6,a1)
| product(a6,a1) = product(a10,a1) ),
introduced(tautology,[equality,[$cnf( $equal(product(a6,a1),product(a6,a1)) ),[1,0],$fot(a10)]]) ).
cnf(refute_0_374,plain,
( a6 != a10
| product(a6,a1) = product(a10,a1) ),
inference(resolve,[$cnf( $equal(product(a6,a1),product(a6,a1)) )],[refute_0_372,refute_0_373]) ).
cnf(refute_0_375,plain,
product(a6,a1) = product(a10,a1),
inference(resolve,[$cnf( $equal(a6,a10) )],[refute_0_371,refute_0_374]) ).
cnf(refute_0_376,plain,
( product(a10,a1) != a4
| product(a6,a1) != product(a10,a1)
| product(a6,a1) = a4 ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(product(a6,a1))),bind(Y0,$fot(product(a10,a1))),bind(Z0,$fot(a4))]]) ).
cnf(refute_0_377,plain,
( product(a10,a1) != a4
| product(a6,a1) = a4 ),
inference(resolve,[$cnf( $equal(product(a6,a1),product(a10,a1)) )],[refute_0_375,refute_0_376]) ).
cnf(refute_0_378,plain,
product(a6,a1) = a4,
inference(resolve,[$cnf( $equal(product(a10,a1),a4) )],[refute_0_330,refute_0_377]) ).
cnf(refute_0_379,plain,
( a5 != product(a6,a1)
| product(a6,a1) != a4
| a5 = a4 ),
introduced(tautology,[equality,[$cnf( ~ $equal(a5,a4) ),[0],$fot(product(a6,a1))]]) ).
cnf(refute_0_380,plain,
( a5 != product(a6,a1)
| a5 = a4 ),
inference(resolve,[$cnf( $equal(product(a6,a1),a4) )],[refute_0_378,refute_0_379]) ).
cnf(refute_0_381,plain,
a5 = a4,
inference(resolve,[$cnf( $equal(a5,product(a6,a1)) )],[refute_0_314,refute_0_380]) ).
cnf(refute_0_382,plain,
product(a10,a7) = product(a10,a7),
introduced(tautology,[refl,[$fot(product(a10,a7))]]) ).
cnf(refute_0_383,plain,
( a7 != a5
| product(a10,a7) != product(a10,a7)
| product(a10,a7) = product(a10,a5) ),
introduced(tautology,[equality,[$cnf( $equal(product(a10,a7),product(a10,a7)) ),[1,1],$fot(a5)]]) ).
cnf(refute_0_384,plain,
( a7 != a5
| product(a10,a7) = product(a10,a5) ),
inference(resolve,[$cnf( $equal(product(a10,a7),product(a10,a7)) )],[refute_0_382,refute_0_383]) ).
cnf(refute_0_385,plain,
product(a10,a7) = product(a10,a5),
inference(resolve,[$cnf( $equal(a7,a5) )],[refute_0_311,refute_0_384]) ).
cnf(refute_0_386,plain,
product(a9,a7) = product(a9,a7),
introduced(tautology,[refl,[$fot(product(a9,a7))]]) ).
cnf(refute_0_387,plain,
( a9 != a10
| product(a9,a7) != product(a9,a7)
| product(a9,a7) = product(a10,a7) ),
introduced(tautology,[equality,[$cnf( $equal(product(a9,a7),product(a9,a7)) ),[1,0],$fot(a10)]]) ).
cnf(refute_0_388,plain,
( a9 != a10
| product(a9,a7) = product(a10,a7) ),
inference(resolve,[$cnf( $equal(product(a9,a7),product(a9,a7)) )],[refute_0_386,refute_0_387]) ).
cnf(refute_0_389,plain,
product(a9,a7) = product(a10,a7),
inference(resolve,[$cnf( $equal(a9,a10) )],[refute_0_258,refute_0_388]) ).
cnf(refute_0_390,plain,
( product(a10,a7) != product(a10,a5)
| product(a9,a7) != product(a10,a7)
| product(a9,a7) = product(a10,a5) ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(product(a9,a7))),bind(Y0,$fot(product(a10,a7))),bind(Z0,$fot(product(a10,a5)))]]) ).
cnf(refute_0_391,plain,
( product(a10,a7) != product(a10,a5)
| product(a9,a7) = product(a10,a5) ),
inference(resolve,[$cnf( $equal(product(a9,a7),product(a10,a7)) )],[refute_0_389,refute_0_390]) ).
cnf(refute_0_392,plain,
product(a9,a7) = product(a10,a5),
inference(resolve,[$cnf( $equal(product(a10,a7),product(a10,a5)) )],[refute_0_385,refute_0_391]) ).
cnf(refute_0_393,plain,
( a1 != product(a9,a7)
| product(a9,a7) != product(a10,a5)
| a1 = product(a10,a5) ),
introduced(tautology,[equality,[$cnf( ~ $equal(a1,product(a10,a5)) ),[0],$fot(product(a9,a7))]]) ).
cnf(refute_0_394,plain,
( a1 != product(a9,a7)
| a1 = product(a10,a5) ),
inference(resolve,[$cnf( $equal(product(a9,a7),product(a10,a5)) )],[refute_0_392,refute_0_393]) ).
cnf(refute_0_395,plain,
a1 = product(a10,a5),
inference(resolve,[$cnf( $equal(a1,product(a9,a7)) )],[knot,refute_0_394]) ).
cnf(refute_0_396,plain,
product(a10,a4) = product(a10,a3),
inference(subst,[],[refute_0_272:[bind(X_7,$fot(a10))]]) ).
cnf(refute_0_397,plain,
( product(a10,a3) != a4
| product(a10,a4) != product(a10,a3)
| product(a10,a4) = a4 ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(product(a10,a4))),bind(Y0,$fot(product(a10,a3))),bind(Z0,$fot(a4))]]) ).
cnf(refute_0_398,plain,
( product(a10,a3) != a4
| product(a10,a4) = a4 ),
inference(resolve,[$cnf( $equal(product(a10,a4),product(a10,a3)) )],[refute_0_396,refute_0_397]) ).
cnf(refute_0_399,plain,
product(a10,a4) = a4,
inference(resolve,[$cnf( $equal(product(a10,a3),a4) )],[refute_0_16,refute_0_398]) ).
cnf(refute_0_400,plain,
product(a10,a5) = product(a10,a5),
introduced(tautology,[refl,[$fot(product(a10,a5))]]) ).
cnf(refute_0_401,plain,
( a5 != a4
| product(a10,a5) != product(a10,a5)
| product(a10,a5) = product(a10,a4) ),
introduced(tautology,[equality,[$cnf( $equal(product(a10,a5),product(a10,a5)) ),[1,1],$fot(a4)]]) ).
cnf(refute_0_402,plain,
( a5 != a4
| product(a10,a5) = product(a10,a4) ),
inference(resolve,[$cnf( $equal(product(a10,a5),product(a10,a5)) )],[refute_0_400,refute_0_401]) ).
cnf(refute_0_403,plain,
product(a10,a5) = product(a10,a4),
inference(resolve,[$cnf( $equal(a5,a4) )],[refute_0_381,refute_0_402]) ).
cnf(refute_0_404,plain,
( product(a10,a4) != a4
| product(a10,a5) != product(a10,a4)
| product(a10,a5) = a4 ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(product(a10,a5))),bind(Y0,$fot(product(a10,a4))),bind(Z0,$fot(a4))]]) ).
cnf(refute_0_405,plain,
( product(a10,a4) != a4
| product(a10,a5) = a4 ),
inference(resolve,[$cnf( $equal(product(a10,a5),product(a10,a4)) )],[refute_0_403,refute_0_404]) ).
cnf(refute_0_406,plain,
product(a10,a5) = a4,
inference(resolve,[$cnf( $equal(product(a10,a4),a4) )],[refute_0_399,refute_0_405]) ).
cnf(refute_0_407,plain,
( a1 != product(a10,a5)
| product(a10,a5) != a4
| a1 = a4 ),
introduced(tautology,[equality,[$cnf( ~ $equal(a1,a4) ),[0],$fot(product(a10,a5))]]) ).
cnf(refute_0_408,plain,
( a1 != product(a10,a5)
| a1 = a4 ),
inference(resolve,[$cnf( $equal(product(a10,a5),a4) )],[refute_0_406,refute_0_407]) ).
cnf(refute_0_409,plain,
a1 = a4,
inference(resolve,[$cnf( $equal(a1,product(a10,a5)) )],[refute_0_395,refute_0_408]) ).
cnf(refute_0_410,plain,
( a1 != a4
| a4 = a1 ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(a1)),bind(Y0,$fot(a4))]]) ).
cnf(refute_0_411,plain,
a4 = a1,
inference(resolve,[$cnf( $equal(a1,a4) )],[refute_0_409,refute_0_410]) ).
cnf(refute_0_412,plain,
( a4 != a1
| a5 != a4
| a5 = a1 ),
introduced(tautology,[equality,[$cnf( $equal(a5,a4) ),[1],$fot(a1)]]) ).
cnf(refute_0_413,plain,
( a5 != a4
| a5 = a1 ),
inference(resolve,[$cnf( $equal(a4,a1) )],[refute_0_411,refute_0_412]) ).
cnf(refute_0_414,plain,
a5 = a1,
inference(resolve,[$cnf( $equal(a5,a4) )],[refute_0_381,refute_0_413]) ).
cnf(refute_0_415,plain,
tuple(a1,a1,a1,a1,a1,a1,a1,a1,a5) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a5),
introduced(tautology,[refl,[$fot(tuple(a1,a1,a1,a1,a1,a1,a1,a1,a5))]]) ).
cnf(refute_0_416,plain,
( a5 != a1
| tuple(a1,a1,a1,a1,a1,a1,a1,a1,a5) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a5)
| tuple(a1,a1,a1,a1,a1,a1,a1,a1,a5) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) ),
introduced(tautology,[equality,[$cnf( $equal(tuple(a1,a1,a1,a1,a1,a1,a1,a1,a5),tuple(a1,a1,a1,a1,a1,a1,a1,a1,a5)) ),[1,8],$fot(a1)]]) ).
cnf(refute_0_417,plain,
( a5 != a1
| tuple(a1,a1,a1,a1,a1,a1,a1,a1,a5) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) ),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a1,a1,a1,a1,a1,a5),tuple(a1,a1,a1,a1,a1,a1,a1,a1,a5)) )],[refute_0_415,refute_0_416]) ).
cnf(refute_0_418,plain,
tuple(a1,a1,a1,a1,a1,a1,a1,a1,a5) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1),
inference(resolve,[$cnf( $equal(a5,a1) )],[refute_0_414,refute_0_417]) ).
cnf(refute_0_419,plain,
tuple(a1,a1,a1,a1,a1,a1,a1,a4,a5) = tuple(a1,a1,a1,a1,a1,a1,a1,a4,a5),
introduced(tautology,[refl,[$fot(tuple(a1,a1,a1,a1,a1,a1,a1,a4,a5))]]) ).
cnf(refute_0_420,plain,
( a4 != a1
| tuple(a1,a1,a1,a1,a1,a1,a1,a4,a5) != tuple(a1,a1,a1,a1,a1,a1,a1,a4,a5)
| tuple(a1,a1,a1,a1,a1,a1,a1,a4,a5) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a5) ),
introduced(tautology,[equality,[$cnf( $equal(tuple(a1,a1,a1,a1,a1,a1,a1,a4,a5),tuple(a1,a1,a1,a1,a1,a1,a1,a4,a5)) ),[1,7],$fot(a1)]]) ).
cnf(refute_0_421,plain,
( a4 != a1
| tuple(a1,a1,a1,a1,a1,a1,a1,a4,a5) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a5) ),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a1,a1,a1,a1,a4,a5),tuple(a1,a1,a1,a1,a1,a1,a1,a4,a5)) )],[refute_0_419,refute_0_420]) ).
cnf(refute_0_422,plain,
tuple(a1,a1,a1,a1,a1,a1,a1,a4,a5) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a5),
inference(resolve,[$cnf( $equal(a4,a1) )],[refute_0_411,refute_0_421]) ).
cnf(refute_0_423,plain,
( tuple(a1,a1,a1,a1,a1,a1,a1,a1,a5) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)
| tuple(a1,a1,a1,a1,a1,a1,a1,a4,a5) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a5)
| tuple(a1,a1,a1,a1,a1,a1,a1,a4,a5) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(tuple(a1,a1,a1,a1,a1,a1,a1,a4,a5))),bind(Y0,$fot(tuple(a1,a1,a1,a1,a1,a1,a1,a1,a5))),bind(Z0,$fot(tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)))]]) ).
cnf(refute_0_424,plain,
( tuple(a1,a1,a1,a1,a1,a1,a1,a1,a5) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)
| tuple(a1,a1,a1,a1,a1,a1,a1,a4,a5) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) ),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a1,a1,a1,a1,a4,a5),tuple(a1,a1,a1,a1,a1,a1,a1,a1,a5)) )],[refute_0_422,refute_0_423]) ).
cnf(refute_0_425,plain,
tuple(a1,a1,a1,a1,a1,a1,a1,a4,a5) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a1,a1,a1,a1,a1,a5),tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)) )],[refute_0_418,refute_0_424]) ).
cnf(refute_0_426,plain,
tuple(a1,a1,a1,a1,a1,a1,a3,a4,a5) = tuple(a1,a1,a1,a1,a1,a1,a3,a4,a5),
introduced(tautology,[refl,[$fot(tuple(a1,a1,a1,a1,a1,a1,a3,a4,a5))]]) ).
cnf(refute_0_427,plain,
( a3 != a1
| tuple(a1,a1,a1,a1,a1,a1,a3,a4,a5) != tuple(a1,a1,a1,a1,a1,a1,a3,a4,a5)
| tuple(a1,a1,a1,a1,a1,a1,a3,a4,a5) = tuple(a1,a1,a1,a1,a1,a1,a1,a4,a5) ),
introduced(tautology,[equality,[$cnf( $equal(tuple(a1,a1,a1,a1,a1,a1,a3,a4,a5),tuple(a1,a1,a1,a1,a1,a1,a3,a4,a5)) ),[1,6],$fot(a1)]]) ).
cnf(refute_0_428,plain,
( a3 != a1
| tuple(a1,a1,a1,a1,a1,a1,a3,a4,a5) = tuple(a1,a1,a1,a1,a1,a1,a1,a4,a5) ),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a1,a1,a1,a3,a4,a5),tuple(a1,a1,a1,a1,a1,a1,a3,a4,a5)) )],[refute_0_426,refute_0_427]) ).
cnf(refute_0_429,plain,
tuple(a1,a1,a1,a1,a1,a1,a3,a4,a5) = tuple(a1,a1,a1,a1,a1,a1,a1,a4,a5),
inference(resolve,[$cnf( $equal(a3,a1) )],[refute_0_297,refute_0_428]) ).
cnf(refute_0_430,plain,
( tuple(a1,a1,a1,a1,a1,a1,a1,a4,a5) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)
| tuple(a1,a1,a1,a1,a1,a1,a3,a4,a5) != tuple(a1,a1,a1,a1,a1,a1,a1,a4,a5)
| tuple(a1,a1,a1,a1,a1,a1,a3,a4,a5) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(tuple(a1,a1,a1,a1,a1,a1,a3,a4,a5))),bind(Y0,$fot(tuple(a1,a1,a1,a1,a1,a1,a1,a4,a5))),bind(Z0,$fot(tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)))]]) ).
cnf(refute_0_431,plain,
( tuple(a1,a1,a1,a1,a1,a1,a1,a4,a5) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)
| tuple(a1,a1,a1,a1,a1,a1,a3,a4,a5) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) ),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a1,a1,a1,a3,a4,a5),tuple(a1,a1,a1,a1,a1,a1,a1,a4,a5)) )],[refute_0_429,refute_0_430]) ).
cnf(refute_0_432,plain,
tuple(a1,a1,a1,a1,a1,a1,a3,a4,a5) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a1,a1,a1,a1,a4,a5),tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)) )],[refute_0_425,refute_0_431]) ).
cnf(refute_0_433,plain,
tuple(a1,a1,a1,a1,a1,a2,a3,a4,a5) = tuple(a1,a1,a1,a1,a1,a2,a3,a4,a5),
introduced(tautology,[refl,[$fot(tuple(a1,a1,a1,a1,a1,a2,a3,a4,a5))]]) ).
cnf(refute_0_434,plain,
( a2 != a1
| tuple(a1,a1,a1,a1,a1,a2,a3,a4,a5) != tuple(a1,a1,a1,a1,a1,a2,a3,a4,a5)
| tuple(a1,a1,a1,a1,a1,a2,a3,a4,a5) = tuple(a1,a1,a1,a1,a1,a1,a3,a4,a5) ),
introduced(tautology,[equality,[$cnf( $equal(tuple(a1,a1,a1,a1,a1,a2,a3,a4,a5),tuple(a1,a1,a1,a1,a1,a2,a3,a4,a5)) ),[1,5],$fot(a1)]]) ).
cnf(refute_0_435,plain,
( a2 != a1
| tuple(a1,a1,a1,a1,a1,a2,a3,a4,a5) = tuple(a1,a1,a1,a1,a1,a1,a3,a4,a5) ),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a1,a1,a2,a3,a4,a5),tuple(a1,a1,a1,a1,a1,a2,a3,a4,a5)) )],[refute_0_433,refute_0_434]) ).
cnf(refute_0_436,plain,
tuple(a1,a1,a1,a1,a1,a2,a3,a4,a5) = tuple(a1,a1,a1,a1,a1,a1,a3,a4,a5),
inference(resolve,[$cnf( $equal(a2,a1) )],[refute_0_292,refute_0_435]) ).
cnf(refute_0_437,plain,
( tuple(a1,a1,a1,a1,a1,a1,a3,a4,a5) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)
| tuple(a1,a1,a1,a1,a1,a2,a3,a4,a5) != tuple(a1,a1,a1,a1,a1,a1,a3,a4,a5)
| tuple(a1,a1,a1,a1,a1,a2,a3,a4,a5) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(tuple(a1,a1,a1,a1,a1,a2,a3,a4,a5))),bind(Y0,$fot(tuple(a1,a1,a1,a1,a1,a1,a3,a4,a5))),bind(Z0,$fot(tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)))]]) ).
cnf(refute_0_438,plain,
( tuple(a1,a1,a1,a1,a1,a1,a3,a4,a5) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)
| tuple(a1,a1,a1,a1,a1,a2,a3,a4,a5) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) ),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a1,a1,a2,a3,a4,a5),tuple(a1,a1,a1,a1,a1,a1,a3,a4,a5)) )],[refute_0_436,refute_0_437]) ).
cnf(refute_0_439,plain,
tuple(a1,a1,a1,a1,a1,a2,a3,a4,a5) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a1,a1,a1,a3,a4,a5),tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)) )],[refute_0_432,refute_0_438]) ).
cnf(refute_0_440,plain,
( a5 != a1
| a7 != a5
| a7 = a1 ),
introduced(tautology,[equality,[$cnf( $equal(a7,a5) ),[1],$fot(a1)]]) ).
cnf(refute_0_441,plain,
( a7 != a5
| a7 = a1 ),
inference(resolve,[$cnf( $equal(a5,a1) )],[refute_0_414,refute_0_440]) ).
cnf(refute_0_442,plain,
a7 = a1,
inference(resolve,[$cnf( $equal(a7,a5) )],[refute_0_311,refute_0_441]) ).
cnf(refute_0_443,plain,
tuple(a1,a1,a1,a1,a7,a2,a3,a4,a5) = tuple(a1,a1,a1,a1,a7,a2,a3,a4,a5),
introduced(tautology,[refl,[$fot(tuple(a1,a1,a1,a1,a7,a2,a3,a4,a5))]]) ).
cnf(refute_0_444,plain,
( a7 != a1
| tuple(a1,a1,a1,a1,a7,a2,a3,a4,a5) != tuple(a1,a1,a1,a1,a7,a2,a3,a4,a5)
| tuple(a1,a1,a1,a1,a7,a2,a3,a4,a5) = tuple(a1,a1,a1,a1,a1,a2,a3,a4,a5) ),
introduced(tautology,[equality,[$cnf( $equal(tuple(a1,a1,a1,a1,a7,a2,a3,a4,a5),tuple(a1,a1,a1,a1,a7,a2,a3,a4,a5)) ),[1,4],$fot(a1)]]) ).
cnf(refute_0_445,plain,
( a7 != a1
| tuple(a1,a1,a1,a1,a7,a2,a3,a4,a5) = tuple(a1,a1,a1,a1,a1,a2,a3,a4,a5) ),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a1,a7,a2,a3,a4,a5),tuple(a1,a1,a1,a1,a7,a2,a3,a4,a5)) )],[refute_0_443,refute_0_444]) ).
cnf(refute_0_446,plain,
tuple(a1,a1,a1,a1,a7,a2,a3,a4,a5) = tuple(a1,a1,a1,a1,a1,a2,a3,a4,a5),
inference(resolve,[$cnf( $equal(a7,a1) )],[refute_0_442,refute_0_445]) ).
cnf(refute_0_447,plain,
( tuple(a1,a1,a1,a1,a1,a2,a3,a4,a5) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)
| tuple(a1,a1,a1,a1,a7,a2,a3,a4,a5) != tuple(a1,a1,a1,a1,a1,a2,a3,a4,a5)
| tuple(a1,a1,a1,a1,a7,a2,a3,a4,a5) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(tuple(a1,a1,a1,a1,a7,a2,a3,a4,a5))),bind(Y0,$fot(tuple(a1,a1,a1,a1,a1,a2,a3,a4,a5))),bind(Z0,$fot(tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)))]]) ).
cnf(refute_0_448,plain,
( tuple(a1,a1,a1,a1,a1,a2,a3,a4,a5) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)
| tuple(a1,a1,a1,a1,a7,a2,a3,a4,a5) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) ),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a1,a7,a2,a3,a4,a5),tuple(a1,a1,a1,a1,a1,a2,a3,a4,a5)) )],[refute_0_446,refute_0_447]) ).
cnf(refute_0_449,plain,
tuple(a1,a1,a1,a1,a7,a2,a3,a4,a5) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a1,a1,a2,a3,a4,a5),tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)) )],[refute_0_439,refute_0_448]) ).
cnf(refute_0_450,plain,
product(a5,a3) = product(a5,a3),
introduced(tautology,[refl,[$fot(product(a5,a3))]]) ).
cnf(refute_0_451,plain,
( a3 != a2
| product(a5,a3) != product(a5,a3)
| product(a5,a3) = product(a5,a2) ),
introduced(tautology,[equality,[$cnf( $equal(product(a5,a3),product(a5,a3)) ),[1,1],$fot(a2)]]) ).
cnf(refute_0_452,plain,
( a3 != a2
| product(a5,a3) = product(a5,a2) ),
inference(resolve,[$cnf( $equal(product(a5,a3),product(a5,a3)) )],[refute_0_450,refute_0_451]) ).
cnf(refute_0_453,plain,
product(a5,a3) = product(a5,a2),
inference(resolve,[$cnf( $equal(a3,a2) )],[refute_0_282,refute_0_452]) ).
cnf(refute_0_454,plain,
product(a5,a4) = product(a5,a3),
inference(subst,[],[refute_0_272:[bind(X_7,$fot(a5))]]) ).
cnf(refute_0_455,plain,
( product(a5,a3) != product(a5,a2)
| product(a5,a4) != product(a5,a3)
| product(a5,a4) = product(a5,a2) ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(product(a5,a4))),bind(Y0,$fot(product(a5,a3))),bind(Z0,$fot(product(a5,a2)))]]) ).
cnf(refute_0_456,plain,
( product(a5,a3) != product(a5,a2)
| product(a5,a4) = product(a5,a2) ),
inference(resolve,[$cnf( $equal(product(a5,a4),product(a5,a3)) )],[refute_0_454,refute_0_455]) ).
cnf(refute_0_457,plain,
product(a5,a4) = product(a5,a2),
inference(resolve,[$cnf( $equal(product(a5,a3),product(a5,a2)) )],[refute_0_453,refute_0_456]) ).
cnf(refute_0_458,plain,
( a6 != product(a5,a4)
| product(a5,a4) != product(a5,a2)
| a6 = product(a5,a2) ),
introduced(tautology,[equality,[$cnf( ~ $equal(a6,product(a5,a2)) ),[0],$fot(product(a5,a4))]]) ).
cnf(refute_0_459,plain,
( a6 != product(a5,a4)
| a6 = product(a5,a2) ),
inference(resolve,[$cnf( $equal(product(a5,a4),product(a5,a2)) )],[refute_0_457,refute_0_458]) ).
cnf(refute_0_460,plain,
a6 = product(a5,a2),
inference(resolve,[$cnf( $equal(a6,product(a5,a4)) )],[knot_06,refute_0_459]) ).
cnf(refute_0_461,plain,
product(a5,a2) = product(a5,a2),
introduced(tautology,[refl,[$fot(product(a5,a2))]]) ).
cnf(refute_0_462,plain,
( a2 != a1
| product(a5,a2) != product(a5,a2)
| product(a5,a2) = product(a5,a1) ),
introduced(tautology,[equality,[$cnf( $equal(product(a5,a2),product(a5,a2)) ),[1,1],$fot(a1)]]) ).
cnf(refute_0_463,plain,
( a2 != a1
| product(a5,a2) = product(a5,a1) ),
inference(resolve,[$cnf( $equal(product(a5,a2),product(a5,a2)) )],[refute_0_461,refute_0_462]) ).
cnf(refute_0_464,plain,
product(a5,a2) = product(a5,a1),
inference(resolve,[$cnf( $equal(a2,a1) )],[refute_0_292,refute_0_463]) ).
cnf(refute_0_465,plain,
( a6 != product(a5,a2)
| product(a5,a2) != product(a5,a1)
| a6 = product(a5,a1) ),
introduced(tautology,[equality,[$cnf( ~ $equal(a6,product(a5,a1)) ),[0],$fot(product(a5,a2))]]) ).
cnf(refute_0_466,plain,
( a6 != product(a5,a2)
| a6 = product(a5,a1) ),
inference(resolve,[$cnf( $equal(product(a5,a2),product(a5,a1)) )],[refute_0_464,refute_0_465]) ).
cnf(refute_0_467,plain,
a6 = product(a5,a1),
inference(resolve,[$cnf( $equal(a6,product(a5,a2)) )],[refute_0_460,refute_0_466]) ).
cnf(refute_0_468,plain,
( a6 != a10
| a6 != product(a5,a1)
| a10 = product(a5,a1) ),
introduced(tautology,[equality,[$cnf( $equal(a6,product(a5,a1)) ),[0],$fot(a10)]]) ).
cnf(refute_0_469,plain,
( a6 != product(a5,a1)
| a10 = product(a5,a1) ),
inference(resolve,[$cnf( $equal(a6,a10) )],[refute_0_371,refute_0_468]) ).
cnf(refute_0_470,plain,
a10 = product(a5,a1),
inference(resolve,[$cnf( $equal(a6,product(a5,a1)) )],[refute_0_467,refute_0_469]) ).
cnf(refute_0_471,plain,
product(a1,a1) = a1,
inference(subst,[],[involutory_quandle:[bind(X,$fot(a1))]]) ).
cnf(refute_0_472,plain,
product(a5,a1) = product(a5,a1),
introduced(tautology,[refl,[$fot(product(a5,a1))]]) ).
cnf(refute_0_473,plain,
( a5 != a1
| product(a5,a1) != product(a5,a1)
| product(a5,a1) = product(a1,a1) ),
introduced(tautology,[equality,[$cnf( $equal(product(a5,a1),product(a5,a1)) ),[1,0],$fot(a1)]]) ).
cnf(refute_0_474,plain,
( a5 != a1
| product(a5,a1) = product(a1,a1) ),
inference(resolve,[$cnf( $equal(product(a5,a1),product(a5,a1)) )],[refute_0_472,refute_0_473]) ).
cnf(refute_0_475,plain,
product(a5,a1) = product(a1,a1),
inference(resolve,[$cnf( $equal(a5,a1) )],[refute_0_414,refute_0_474]) ).
cnf(refute_0_476,plain,
( product(a1,a1) != a1
| product(a5,a1) != product(a1,a1)
| product(a5,a1) = a1 ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(product(a5,a1))),bind(Y0,$fot(product(a1,a1))),bind(Z0,$fot(a1))]]) ).
cnf(refute_0_477,plain,
( product(a1,a1) != a1
| product(a5,a1) = a1 ),
inference(resolve,[$cnf( $equal(product(a5,a1),product(a1,a1)) )],[refute_0_475,refute_0_476]) ).
cnf(refute_0_478,plain,
product(a5,a1) = a1,
inference(resolve,[$cnf( $equal(product(a1,a1),a1) )],[refute_0_471,refute_0_477]) ).
cnf(refute_0_479,plain,
( a10 != product(a5,a1)
| product(a5,a1) != a1
| a10 = a1 ),
introduced(tautology,[equality,[$cnf( ~ $equal(a10,a1) ),[0],$fot(product(a5,a1))]]) ).
cnf(refute_0_480,plain,
( a10 != product(a5,a1)
| a10 = a1 ),
inference(resolve,[$cnf( $equal(product(a5,a1),a1) )],[refute_0_478,refute_0_479]) ).
cnf(refute_0_481,plain,
a10 = a1,
inference(resolve,[$cnf( $equal(a10,product(a5,a1)) )],[refute_0_470,refute_0_480]) ).
cnf(refute_0_482,plain,
( a10 != a1
| a10 != a6
| a1 = a6 ),
introduced(tautology,[equality,[$cnf( $equal(a10,a6) ),[0],$fot(a1)]]) ).
cnf(refute_0_483,plain,
( a10 != a6
| a1 = a6 ),
inference(resolve,[$cnf( $equal(a10,a1) )],[refute_0_481,refute_0_482]) ).
cnf(refute_0_484,plain,
a1 = a6,
inference(resolve,[$cnf( $equal(a10,a6) )],[refute_0_369,refute_0_483]) ).
cnf(refute_0_485,plain,
( a1 != a6
| a6 = a1 ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(a1)),bind(Y0,$fot(a6))]]) ).
cnf(refute_0_486,plain,
a6 = a1,
inference(resolve,[$cnf( $equal(a1,a6) )],[refute_0_484,refute_0_485]) ).
cnf(refute_0_487,plain,
tuple(a1,a1,a1,a6,a7,a2,a3,a4,a5) = tuple(a1,a1,a1,a6,a7,a2,a3,a4,a5),
introduced(tautology,[refl,[$fot(tuple(a1,a1,a1,a6,a7,a2,a3,a4,a5))]]) ).
cnf(refute_0_488,plain,
( a6 != a1
| tuple(a1,a1,a1,a6,a7,a2,a3,a4,a5) != tuple(a1,a1,a1,a6,a7,a2,a3,a4,a5)
| tuple(a1,a1,a1,a6,a7,a2,a3,a4,a5) = tuple(a1,a1,a1,a1,a7,a2,a3,a4,a5) ),
introduced(tautology,[equality,[$cnf( $equal(tuple(a1,a1,a1,a6,a7,a2,a3,a4,a5),tuple(a1,a1,a1,a6,a7,a2,a3,a4,a5)) ),[1,3],$fot(a1)]]) ).
cnf(refute_0_489,plain,
( a6 != a1
| tuple(a1,a1,a1,a6,a7,a2,a3,a4,a5) = tuple(a1,a1,a1,a1,a7,a2,a3,a4,a5) ),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a6,a7,a2,a3,a4,a5),tuple(a1,a1,a1,a6,a7,a2,a3,a4,a5)) )],[refute_0_487,refute_0_488]) ).
cnf(refute_0_490,plain,
tuple(a1,a1,a1,a6,a7,a2,a3,a4,a5) = tuple(a1,a1,a1,a1,a7,a2,a3,a4,a5),
inference(resolve,[$cnf( $equal(a6,a1) )],[refute_0_486,refute_0_489]) ).
cnf(refute_0_491,plain,
( tuple(a1,a1,a1,a1,a7,a2,a3,a4,a5) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)
| tuple(a1,a1,a1,a6,a7,a2,a3,a4,a5) != tuple(a1,a1,a1,a1,a7,a2,a3,a4,a5)
| tuple(a1,a1,a1,a6,a7,a2,a3,a4,a5) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(tuple(a1,a1,a1,a6,a7,a2,a3,a4,a5))),bind(Y0,$fot(tuple(a1,a1,a1,a1,a7,a2,a3,a4,a5))),bind(Z0,$fot(tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)))]]) ).
cnf(refute_0_492,plain,
( tuple(a1,a1,a1,a1,a7,a2,a3,a4,a5) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)
| tuple(a1,a1,a1,a6,a7,a2,a3,a4,a5) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) ),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a6,a7,a2,a3,a4,a5),tuple(a1,a1,a1,a1,a7,a2,a3,a4,a5)) )],[refute_0_490,refute_0_491]) ).
cnf(refute_0_493,plain,
tuple(a1,a1,a1,a6,a7,a2,a3,a4,a5) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a1,a7,a2,a3,a4,a5),tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)) )],[refute_0_449,refute_0_492]) ).
cnf(refute_0_494,plain,
( a6 != a1
| a8 != a6
| a8 = a1 ),
introduced(tautology,[equality,[$cnf( $equal(a8,a6) ),[1],$fot(a1)]]) ).
cnf(refute_0_495,plain,
( a8 != a6
| a8 = a1 ),
inference(resolve,[$cnf( $equal(a6,a1) )],[refute_0_486,refute_0_494]) ).
cnf(refute_0_496,plain,
a8 = a1,
inference(resolve,[$cnf( $equal(a8,a6) )],[refute_0_365,refute_0_495]) ).
cnf(refute_0_497,plain,
tuple(a1,a1,a8,a6,a7,a2,a3,a4,a5) = tuple(a1,a1,a8,a6,a7,a2,a3,a4,a5),
introduced(tautology,[refl,[$fot(tuple(a1,a1,a8,a6,a7,a2,a3,a4,a5))]]) ).
cnf(refute_0_498,plain,
( a8 != a1
| tuple(a1,a1,a8,a6,a7,a2,a3,a4,a5) != tuple(a1,a1,a8,a6,a7,a2,a3,a4,a5)
| tuple(a1,a1,a8,a6,a7,a2,a3,a4,a5) = tuple(a1,a1,a1,a6,a7,a2,a3,a4,a5) ),
introduced(tautology,[equality,[$cnf( $equal(tuple(a1,a1,a8,a6,a7,a2,a3,a4,a5),tuple(a1,a1,a8,a6,a7,a2,a3,a4,a5)) ),[1,2],$fot(a1)]]) ).
cnf(refute_0_499,plain,
( a8 != a1
| tuple(a1,a1,a8,a6,a7,a2,a3,a4,a5) = tuple(a1,a1,a1,a6,a7,a2,a3,a4,a5) ),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a8,a6,a7,a2,a3,a4,a5),tuple(a1,a1,a8,a6,a7,a2,a3,a4,a5)) )],[refute_0_497,refute_0_498]) ).
cnf(refute_0_500,plain,
tuple(a1,a1,a8,a6,a7,a2,a3,a4,a5) = tuple(a1,a1,a1,a6,a7,a2,a3,a4,a5),
inference(resolve,[$cnf( $equal(a8,a1) )],[refute_0_496,refute_0_499]) ).
cnf(refute_0_501,plain,
( tuple(a1,a1,a1,a6,a7,a2,a3,a4,a5) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)
| tuple(a1,a1,a8,a6,a7,a2,a3,a4,a5) != tuple(a1,a1,a1,a6,a7,a2,a3,a4,a5)
| tuple(a1,a1,a8,a6,a7,a2,a3,a4,a5) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(tuple(a1,a1,a8,a6,a7,a2,a3,a4,a5))),bind(Y0,$fot(tuple(a1,a1,a1,a6,a7,a2,a3,a4,a5))),bind(Z0,$fot(tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)))]]) ).
cnf(refute_0_502,plain,
( tuple(a1,a1,a1,a6,a7,a2,a3,a4,a5) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)
| tuple(a1,a1,a8,a6,a7,a2,a3,a4,a5) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) ),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a8,a6,a7,a2,a3,a4,a5),tuple(a1,a1,a1,a6,a7,a2,a3,a4,a5)) )],[refute_0_500,refute_0_501]) ).
cnf(refute_0_503,plain,
tuple(a1,a1,a8,a6,a7,a2,a3,a4,a5) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a6,a7,a2,a3,a4,a5),tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)) )],[refute_0_493,refute_0_502]) ).
cnf(refute_0_504,plain,
( a10 != a1
| a10 != a9
| a1 = a9 ),
introduced(tautology,[equality,[$cnf( $equal(a10,a9) ),[0],$fot(a1)]]) ).
cnf(refute_0_505,plain,
( a10 != a9
| a1 = a9 ),
inference(resolve,[$cnf( $equal(a10,a1) )],[refute_0_481,refute_0_504]) ).
cnf(refute_0_506,plain,
a1 = a9,
inference(resolve,[$cnf( $equal(a10,a9) )],[refute_0_256,refute_0_505]) ).
cnf(refute_0_507,plain,
( a1 != a9
| a9 = a1 ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(a1)),bind(Y0,$fot(a9))]]) ).
cnf(refute_0_508,plain,
a9 = a1,
inference(resolve,[$cnf( $equal(a1,a9) )],[refute_0_506,refute_0_507]) ).
cnf(refute_0_509,plain,
tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5) = tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5),
introduced(tautology,[refl,[$fot(tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5))]]) ).
cnf(refute_0_510,plain,
( a9 != a1
| tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5) != tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5)
| tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5) = tuple(a1,a1,a8,a6,a7,a2,a3,a4,a5) ),
introduced(tautology,[equality,[$cnf( $equal(tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5),tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5)) ),[1,1],$fot(a1)]]) ).
cnf(refute_0_511,plain,
( a9 != a1
| tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5) = tuple(a1,a1,a8,a6,a7,a2,a3,a4,a5) ),
inference(resolve,[$cnf( $equal(tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5),tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5)) )],[refute_0_509,refute_0_510]) ).
cnf(refute_0_512,plain,
tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5) = tuple(a1,a1,a8,a6,a7,a2,a3,a4,a5),
inference(resolve,[$cnf( $equal(a9,a1) )],[refute_0_508,refute_0_511]) ).
cnf(refute_0_513,plain,
( tuple(a1,a1,a8,a6,a7,a2,a3,a4,a5) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)
| tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5) != tuple(a1,a1,a8,a6,a7,a2,a3,a4,a5)
| tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5))),bind(Y0,$fot(tuple(a1,a1,a8,a6,a7,a2,a3,a4,a5))),bind(Z0,$fot(tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)))]]) ).
cnf(refute_0_514,plain,
( tuple(a1,a1,a8,a6,a7,a2,a3,a4,a5) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)
| tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) ),
inference(resolve,[$cnf( $equal(tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5),tuple(a1,a1,a8,a6,a7,a2,a3,a4,a5)) )],[refute_0_512,refute_0_513]) ).
cnf(refute_0_515,plain,
tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a8,a6,a7,a2,a3,a4,a5),tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)) )],[refute_0_503,refute_0_514]) ).
cnf(refute_0_516,plain,
( tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) != tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6)
| tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)
| tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6) ),
introduced(tautology,[equality,[$cnf( $equal(tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5),tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)) ),[1],$fot(tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6))]]) ).
cnf(refute_0_517,plain,
( tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) != tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6)
| tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6) ),
inference(resolve,[$cnf( $equal(tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5),tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)) )],[refute_0_515,refute_0_516]) ).
cnf(refute_0_518,plain,
tuple(a1,a1,a1,a1,a1,a1,a1,a1,a6) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a6),
introduced(tautology,[refl,[$fot(tuple(a1,a1,a1,a1,a1,a1,a1,a1,a6))]]) ).
cnf(refute_0_519,plain,
( a6 != a1
| tuple(a1,a1,a1,a1,a1,a1,a1,a1,a6) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a6)
| tuple(a1,a1,a1,a1,a1,a1,a1,a1,a6) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) ),
introduced(tautology,[equality,[$cnf( $equal(tuple(a1,a1,a1,a1,a1,a1,a1,a1,a6),tuple(a1,a1,a1,a1,a1,a1,a1,a1,a6)) ),[1,8],$fot(a1)]]) ).
cnf(refute_0_520,plain,
( a6 != a1
| tuple(a1,a1,a1,a1,a1,a1,a1,a1,a6) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) ),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a1,a1,a1,a1,a1,a6),tuple(a1,a1,a1,a1,a1,a1,a1,a1,a6)) )],[refute_0_518,refute_0_519]) ).
cnf(refute_0_521,plain,
tuple(a1,a1,a1,a1,a1,a1,a1,a1,a6) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1),
inference(resolve,[$cnf( $equal(a6,a1) )],[refute_0_486,refute_0_520]) ).
cnf(refute_0_522,plain,
tuple(a1,a1,a1,a1,a1,a1,a1,a5,a6) = tuple(a1,a1,a1,a1,a1,a1,a1,a5,a6),
introduced(tautology,[refl,[$fot(tuple(a1,a1,a1,a1,a1,a1,a1,a5,a6))]]) ).
cnf(refute_0_523,plain,
( a5 != a1
| tuple(a1,a1,a1,a1,a1,a1,a1,a5,a6) != tuple(a1,a1,a1,a1,a1,a1,a1,a5,a6)
| tuple(a1,a1,a1,a1,a1,a1,a1,a5,a6) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a6) ),
introduced(tautology,[equality,[$cnf( $equal(tuple(a1,a1,a1,a1,a1,a1,a1,a5,a6),tuple(a1,a1,a1,a1,a1,a1,a1,a5,a6)) ),[1,7],$fot(a1)]]) ).
cnf(refute_0_524,plain,
( a5 != a1
| tuple(a1,a1,a1,a1,a1,a1,a1,a5,a6) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a6) ),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a1,a1,a1,a1,a5,a6),tuple(a1,a1,a1,a1,a1,a1,a1,a5,a6)) )],[refute_0_522,refute_0_523]) ).
cnf(refute_0_525,plain,
tuple(a1,a1,a1,a1,a1,a1,a1,a5,a6) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a6),
inference(resolve,[$cnf( $equal(a5,a1) )],[refute_0_414,refute_0_524]) ).
cnf(refute_0_526,plain,
( tuple(a1,a1,a1,a1,a1,a1,a1,a1,a6) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)
| tuple(a1,a1,a1,a1,a1,a1,a1,a5,a6) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a6)
| tuple(a1,a1,a1,a1,a1,a1,a1,a5,a6) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(tuple(a1,a1,a1,a1,a1,a1,a1,a5,a6))),bind(Y0,$fot(tuple(a1,a1,a1,a1,a1,a1,a1,a1,a6))),bind(Z0,$fot(tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)))]]) ).
cnf(refute_0_527,plain,
( tuple(a1,a1,a1,a1,a1,a1,a1,a1,a6) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)
| tuple(a1,a1,a1,a1,a1,a1,a1,a5,a6) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) ),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a1,a1,a1,a1,a5,a6),tuple(a1,a1,a1,a1,a1,a1,a1,a1,a6)) )],[refute_0_525,refute_0_526]) ).
cnf(refute_0_528,plain,
tuple(a1,a1,a1,a1,a1,a1,a1,a5,a6) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a1,a1,a1,a1,a1,a6),tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)) )],[refute_0_521,refute_0_527]) ).
cnf(refute_0_529,plain,
tuple(a1,a1,a1,a1,a1,a1,a4,a5,a6) = tuple(a1,a1,a1,a1,a1,a1,a4,a5,a6),
introduced(tautology,[refl,[$fot(tuple(a1,a1,a1,a1,a1,a1,a4,a5,a6))]]) ).
cnf(refute_0_530,plain,
( a4 != a1
| tuple(a1,a1,a1,a1,a1,a1,a4,a5,a6) != tuple(a1,a1,a1,a1,a1,a1,a4,a5,a6)
| tuple(a1,a1,a1,a1,a1,a1,a4,a5,a6) = tuple(a1,a1,a1,a1,a1,a1,a1,a5,a6) ),
introduced(tautology,[equality,[$cnf( $equal(tuple(a1,a1,a1,a1,a1,a1,a4,a5,a6),tuple(a1,a1,a1,a1,a1,a1,a4,a5,a6)) ),[1,6],$fot(a1)]]) ).
cnf(refute_0_531,plain,
( a4 != a1
| tuple(a1,a1,a1,a1,a1,a1,a4,a5,a6) = tuple(a1,a1,a1,a1,a1,a1,a1,a5,a6) ),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a1,a1,a1,a4,a5,a6),tuple(a1,a1,a1,a1,a1,a1,a4,a5,a6)) )],[refute_0_529,refute_0_530]) ).
cnf(refute_0_532,plain,
tuple(a1,a1,a1,a1,a1,a1,a4,a5,a6) = tuple(a1,a1,a1,a1,a1,a1,a1,a5,a6),
inference(resolve,[$cnf( $equal(a4,a1) )],[refute_0_411,refute_0_531]) ).
cnf(refute_0_533,plain,
( tuple(a1,a1,a1,a1,a1,a1,a1,a5,a6) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)
| tuple(a1,a1,a1,a1,a1,a1,a4,a5,a6) != tuple(a1,a1,a1,a1,a1,a1,a1,a5,a6)
| tuple(a1,a1,a1,a1,a1,a1,a4,a5,a6) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(tuple(a1,a1,a1,a1,a1,a1,a4,a5,a6))),bind(Y0,$fot(tuple(a1,a1,a1,a1,a1,a1,a1,a5,a6))),bind(Z0,$fot(tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)))]]) ).
cnf(refute_0_534,plain,
( tuple(a1,a1,a1,a1,a1,a1,a1,a5,a6) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)
| tuple(a1,a1,a1,a1,a1,a1,a4,a5,a6) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) ),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a1,a1,a1,a4,a5,a6),tuple(a1,a1,a1,a1,a1,a1,a1,a5,a6)) )],[refute_0_532,refute_0_533]) ).
cnf(refute_0_535,plain,
tuple(a1,a1,a1,a1,a1,a1,a4,a5,a6) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a1,a1,a1,a1,a5,a6),tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)) )],[refute_0_528,refute_0_534]) ).
cnf(refute_0_536,plain,
tuple(a1,a1,a1,a1,a1,a3,a4,a5,a6) = tuple(a1,a1,a1,a1,a1,a3,a4,a5,a6),
introduced(tautology,[refl,[$fot(tuple(a1,a1,a1,a1,a1,a3,a4,a5,a6))]]) ).
cnf(refute_0_537,plain,
( a3 != a1
| tuple(a1,a1,a1,a1,a1,a3,a4,a5,a6) != tuple(a1,a1,a1,a1,a1,a3,a4,a5,a6)
| tuple(a1,a1,a1,a1,a1,a3,a4,a5,a6) = tuple(a1,a1,a1,a1,a1,a1,a4,a5,a6) ),
introduced(tautology,[equality,[$cnf( $equal(tuple(a1,a1,a1,a1,a1,a3,a4,a5,a6),tuple(a1,a1,a1,a1,a1,a3,a4,a5,a6)) ),[1,5],$fot(a1)]]) ).
cnf(refute_0_538,plain,
( a3 != a1
| tuple(a1,a1,a1,a1,a1,a3,a4,a5,a6) = tuple(a1,a1,a1,a1,a1,a1,a4,a5,a6) ),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a1,a1,a3,a4,a5,a6),tuple(a1,a1,a1,a1,a1,a3,a4,a5,a6)) )],[refute_0_536,refute_0_537]) ).
cnf(refute_0_539,plain,
tuple(a1,a1,a1,a1,a1,a3,a4,a5,a6) = tuple(a1,a1,a1,a1,a1,a1,a4,a5,a6),
inference(resolve,[$cnf( $equal(a3,a1) )],[refute_0_297,refute_0_538]) ).
cnf(refute_0_540,plain,
( tuple(a1,a1,a1,a1,a1,a1,a4,a5,a6) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)
| tuple(a1,a1,a1,a1,a1,a3,a4,a5,a6) != tuple(a1,a1,a1,a1,a1,a1,a4,a5,a6)
| tuple(a1,a1,a1,a1,a1,a3,a4,a5,a6) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(tuple(a1,a1,a1,a1,a1,a3,a4,a5,a6))),bind(Y0,$fot(tuple(a1,a1,a1,a1,a1,a1,a4,a5,a6))),bind(Z0,$fot(tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)))]]) ).
cnf(refute_0_541,plain,
( tuple(a1,a1,a1,a1,a1,a1,a4,a5,a6) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)
| tuple(a1,a1,a1,a1,a1,a3,a4,a5,a6) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) ),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a1,a1,a3,a4,a5,a6),tuple(a1,a1,a1,a1,a1,a1,a4,a5,a6)) )],[refute_0_539,refute_0_540]) ).
cnf(refute_0_542,plain,
tuple(a1,a1,a1,a1,a1,a3,a4,a5,a6) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a1,a1,a1,a4,a5,a6),tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)) )],[refute_0_535,refute_0_541]) ).
cnf(refute_0_543,plain,
tuple(a1,a1,a1,a1,a8,a3,a4,a5,a6) = tuple(a1,a1,a1,a1,a8,a3,a4,a5,a6),
introduced(tautology,[refl,[$fot(tuple(a1,a1,a1,a1,a8,a3,a4,a5,a6))]]) ).
cnf(refute_0_544,plain,
( a8 != a1
| tuple(a1,a1,a1,a1,a8,a3,a4,a5,a6) != tuple(a1,a1,a1,a1,a8,a3,a4,a5,a6)
| tuple(a1,a1,a1,a1,a8,a3,a4,a5,a6) = tuple(a1,a1,a1,a1,a1,a3,a4,a5,a6) ),
introduced(tautology,[equality,[$cnf( $equal(tuple(a1,a1,a1,a1,a8,a3,a4,a5,a6),tuple(a1,a1,a1,a1,a8,a3,a4,a5,a6)) ),[1,4],$fot(a1)]]) ).
cnf(refute_0_545,plain,
( a8 != a1
| tuple(a1,a1,a1,a1,a8,a3,a4,a5,a6) = tuple(a1,a1,a1,a1,a1,a3,a4,a5,a6) ),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a1,a8,a3,a4,a5,a6),tuple(a1,a1,a1,a1,a8,a3,a4,a5,a6)) )],[refute_0_543,refute_0_544]) ).
cnf(refute_0_546,plain,
tuple(a1,a1,a1,a1,a8,a3,a4,a5,a6) = tuple(a1,a1,a1,a1,a1,a3,a4,a5,a6),
inference(resolve,[$cnf( $equal(a8,a1) )],[refute_0_496,refute_0_545]) ).
cnf(refute_0_547,plain,
( tuple(a1,a1,a1,a1,a1,a3,a4,a5,a6) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)
| tuple(a1,a1,a1,a1,a8,a3,a4,a5,a6) != tuple(a1,a1,a1,a1,a1,a3,a4,a5,a6)
| tuple(a1,a1,a1,a1,a8,a3,a4,a5,a6) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(tuple(a1,a1,a1,a1,a8,a3,a4,a5,a6))),bind(Y0,$fot(tuple(a1,a1,a1,a1,a1,a3,a4,a5,a6))),bind(Z0,$fot(tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)))]]) ).
cnf(refute_0_548,plain,
( tuple(a1,a1,a1,a1,a1,a3,a4,a5,a6) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)
| tuple(a1,a1,a1,a1,a8,a3,a4,a5,a6) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) ),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a1,a8,a3,a4,a5,a6),tuple(a1,a1,a1,a1,a1,a3,a4,a5,a6)) )],[refute_0_546,refute_0_547]) ).
cnf(refute_0_549,plain,
tuple(a1,a1,a1,a1,a8,a3,a4,a5,a6) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a1,a1,a3,a4,a5,a6),tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)) )],[refute_0_542,refute_0_548]) ).
cnf(refute_0_550,plain,
tuple(a1,a1,a1,a7,a8,a3,a4,a5,a6) = tuple(a1,a1,a1,a7,a8,a3,a4,a5,a6),
introduced(tautology,[refl,[$fot(tuple(a1,a1,a1,a7,a8,a3,a4,a5,a6))]]) ).
cnf(refute_0_551,plain,
( a7 != a1
| tuple(a1,a1,a1,a7,a8,a3,a4,a5,a6) != tuple(a1,a1,a1,a7,a8,a3,a4,a5,a6)
| tuple(a1,a1,a1,a7,a8,a3,a4,a5,a6) = tuple(a1,a1,a1,a1,a8,a3,a4,a5,a6) ),
introduced(tautology,[equality,[$cnf( $equal(tuple(a1,a1,a1,a7,a8,a3,a4,a5,a6),tuple(a1,a1,a1,a7,a8,a3,a4,a5,a6)) ),[1,3],$fot(a1)]]) ).
cnf(refute_0_552,plain,
( a7 != a1
| tuple(a1,a1,a1,a7,a8,a3,a4,a5,a6) = tuple(a1,a1,a1,a1,a8,a3,a4,a5,a6) ),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a7,a8,a3,a4,a5,a6),tuple(a1,a1,a1,a7,a8,a3,a4,a5,a6)) )],[refute_0_550,refute_0_551]) ).
cnf(refute_0_553,plain,
tuple(a1,a1,a1,a7,a8,a3,a4,a5,a6) = tuple(a1,a1,a1,a1,a8,a3,a4,a5,a6),
inference(resolve,[$cnf( $equal(a7,a1) )],[refute_0_442,refute_0_552]) ).
cnf(refute_0_554,plain,
( tuple(a1,a1,a1,a1,a8,a3,a4,a5,a6) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)
| tuple(a1,a1,a1,a7,a8,a3,a4,a5,a6) != tuple(a1,a1,a1,a1,a8,a3,a4,a5,a6)
| tuple(a1,a1,a1,a7,a8,a3,a4,a5,a6) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(tuple(a1,a1,a1,a7,a8,a3,a4,a5,a6))),bind(Y0,$fot(tuple(a1,a1,a1,a1,a8,a3,a4,a5,a6))),bind(Z0,$fot(tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)))]]) ).
cnf(refute_0_555,plain,
( tuple(a1,a1,a1,a1,a8,a3,a4,a5,a6) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)
| tuple(a1,a1,a1,a7,a8,a3,a4,a5,a6) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) ),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a7,a8,a3,a4,a5,a6),tuple(a1,a1,a1,a1,a8,a3,a4,a5,a6)) )],[refute_0_553,refute_0_554]) ).
cnf(refute_0_556,plain,
tuple(a1,a1,a1,a7,a8,a3,a4,a5,a6) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a1,a8,a3,a4,a5,a6),tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)) )],[refute_0_549,refute_0_555]) ).
cnf(refute_0_557,plain,
tuple(a1,a1,a9,a7,a8,a3,a4,a5,a6) = tuple(a1,a1,a9,a7,a8,a3,a4,a5,a6),
introduced(tautology,[refl,[$fot(tuple(a1,a1,a9,a7,a8,a3,a4,a5,a6))]]) ).
cnf(refute_0_558,plain,
( a9 != a1
| tuple(a1,a1,a9,a7,a8,a3,a4,a5,a6) != tuple(a1,a1,a9,a7,a8,a3,a4,a5,a6)
| tuple(a1,a1,a9,a7,a8,a3,a4,a5,a6) = tuple(a1,a1,a1,a7,a8,a3,a4,a5,a6) ),
introduced(tautology,[equality,[$cnf( $equal(tuple(a1,a1,a9,a7,a8,a3,a4,a5,a6),tuple(a1,a1,a9,a7,a8,a3,a4,a5,a6)) ),[1,2],$fot(a1)]]) ).
cnf(refute_0_559,plain,
( a9 != a1
| tuple(a1,a1,a9,a7,a8,a3,a4,a5,a6) = tuple(a1,a1,a1,a7,a8,a3,a4,a5,a6) ),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a9,a7,a8,a3,a4,a5,a6),tuple(a1,a1,a9,a7,a8,a3,a4,a5,a6)) )],[refute_0_557,refute_0_558]) ).
cnf(refute_0_560,plain,
tuple(a1,a1,a9,a7,a8,a3,a4,a5,a6) = tuple(a1,a1,a1,a7,a8,a3,a4,a5,a6),
inference(resolve,[$cnf( $equal(a9,a1) )],[refute_0_508,refute_0_559]) ).
cnf(refute_0_561,plain,
( tuple(a1,a1,a1,a7,a8,a3,a4,a5,a6) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)
| tuple(a1,a1,a9,a7,a8,a3,a4,a5,a6) != tuple(a1,a1,a1,a7,a8,a3,a4,a5,a6)
| tuple(a1,a1,a9,a7,a8,a3,a4,a5,a6) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(tuple(a1,a1,a9,a7,a8,a3,a4,a5,a6))),bind(Y0,$fot(tuple(a1,a1,a1,a7,a8,a3,a4,a5,a6))),bind(Z0,$fot(tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)))]]) ).
cnf(refute_0_562,plain,
( tuple(a1,a1,a1,a7,a8,a3,a4,a5,a6) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)
| tuple(a1,a1,a9,a7,a8,a3,a4,a5,a6) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) ),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a9,a7,a8,a3,a4,a5,a6),tuple(a1,a1,a1,a7,a8,a3,a4,a5,a6)) )],[refute_0_560,refute_0_561]) ).
cnf(refute_0_563,plain,
tuple(a1,a1,a9,a7,a8,a3,a4,a5,a6) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a7,a8,a3,a4,a5,a6),tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)) )],[refute_0_556,refute_0_562]) ).
cnf(refute_0_564,plain,
tuple(a1,a10,a9,a7,a8,a3,a4,a5,a6) = tuple(a1,a10,a9,a7,a8,a3,a4,a5,a6),
introduced(tautology,[refl,[$fot(tuple(a1,a10,a9,a7,a8,a3,a4,a5,a6))]]) ).
cnf(refute_0_565,plain,
( a10 != a1
| tuple(a1,a10,a9,a7,a8,a3,a4,a5,a6) != tuple(a1,a10,a9,a7,a8,a3,a4,a5,a6)
| tuple(a1,a10,a9,a7,a8,a3,a4,a5,a6) = tuple(a1,a1,a9,a7,a8,a3,a4,a5,a6) ),
introduced(tautology,[equality,[$cnf( $equal(tuple(a1,a10,a9,a7,a8,a3,a4,a5,a6),tuple(a1,a10,a9,a7,a8,a3,a4,a5,a6)) ),[1,1],$fot(a1)]]) ).
cnf(refute_0_566,plain,
( a10 != a1
| tuple(a1,a10,a9,a7,a8,a3,a4,a5,a6) = tuple(a1,a1,a9,a7,a8,a3,a4,a5,a6) ),
inference(resolve,[$cnf( $equal(tuple(a1,a10,a9,a7,a8,a3,a4,a5,a6),tuple(a1,a10,a9,a7,a8,a3,a4,a5,a6)) )],[refute_0_564,refute_0_565]) ).
cnf(refute_0_567,plain,
tuple(a1,a10,a9,a7,a8,a3,a4,a5,a6) = tuple(a1,a1,a9,a7,a8,a3,a4,a5,a6),
inference(resolve,[$cnf( $equal(a10,a1) )],[refute_0_481,refute_0_566]) ).
cnf(refute_0_568,plain,
( tuple(a1,a1,a9,a7,a8,a3,a4,a5,a6) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)
| tuple(a1,a10,a9,a7,a8,a3,a4,a5,a6) != tuple(a1,a1,a9,a7,a8,a3,a4,a5,a6)
| tuple(a1,a10,a9,a7,a8,a3,a4,a5,a6) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(tuple(a1,a10,a9,a7,a8,a3,a4,a5,a6))),bind(Y0,$fot(tuple(a1,a1,a9,a7,a8,a3,a4,a5,a6))),bind(Z0,$fot(tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)))]]) ).
cnf(refute_0_569,plain,
( tuple(a1,a1,a9,a7,a8,a3,a4,a5,a6) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)
| tuple(a1,a10,a9,a7,a8,a3,a4,a5,a6) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) ),
inference(resolve,[$cnf( $equal(tuple(a1,a10,a9,a7,a8,a3,a4,a5,a6),tuple(a1,a1,a9,a7,a8,a3,a4,a5,a6)) )],[refute_0_567,refute_0_568]) ).
cnf(refute_0_570,plain,
tuple(a1,a10,a9,a7,a8,a3,a4,a5,a6) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a9,a7,a8,a3,a4,a5,a6),tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)) )],[refute_0_563,refute_0_569]) ).
cnf(refute_0_571,plain,
tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
introduced(tautology,[refl,[$fot(tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6))]]) ).
cnf(refute_0_572,plain,
( a2 != a1
| tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6) != tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6)
| tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6) = tuple(a1,a10,a9,a7,a8,a3,a4,a5,a6) ),
introduced(tautology,[equality,[$cnf( $equal(tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6)) ),[1,0],$fot(a1)]]) ).
cnf(refute_0_573,plain,
( a2 != a1
| tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6) = tuple(a1,a10,a9,a7,a8,a3,a4,a5,a6) ),
inference(resolve,[$cnf( $equal(tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6)) )],[refute_0_571,refute_0_572]) ).
cnf(refute_0_574,plain,
tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6) = tuple(a1,a10,a9,a7,a8,a3,a4,a5,a6),
inference(resolve,[$cnf( $equal(a2,a1) )],[refute_0_292,refute_0_573]) ).
cnf(refute_0_575,plain,
( tuple(a1,a10,a9,a7,a8,a3,a4,a5,a6) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)
| tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6) != tuple(a1,a10,a9,a7,a8,a3,a4,a5,a6)
| tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6))),bind(Y0,$fot(tuple(a1,a10,a9,a7,a8,a3,a4,a5,a6))),bind(Z0,$fot(tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)))]]) ).
cnf(refute_0_576,plain,
( tuple(a1,a10,a9,a7,a8,a3,a4,a5,a6) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)
| tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) ),
inference(resolve,[$cnf( $equal(tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),tuple(a1,a10,a9,a7,a8,a3,a4,a5,a6)) )],[refute_0_574,refute_0_575]) ).
cnf(refute_0_577,plain,
tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1),
inference(resolve,[$cnf( $equal(tuple(a1,a10,a9,a7,a8,a3,a4,a5,a6),tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)) )],[refute_0_570,refute_0_576]) ).
cnf(refute_0_578,plain,
( tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)
| tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)
| tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6) ),
introduced(tautology,[equality,[$cnf( ~ $equal(tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1),tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6)) ),[1],$fot(tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1))]]) ).
cnf(refute_0_579,plain,
( tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)
| tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6) ),
inference(resolve,[$cnf( $equal(tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)) )],[refute_0_577,refute_0_578]) ).
cnf(refute_0_580,plain,
( tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)
| tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6) ),
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1),tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6)) )],[refute_0_579,refute_0_517]) ).
cnf(refute_0_581,plain,
tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) != tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1),
inference(resolve,[$cnf( $equal(tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5),tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6)) )],[refute_0_580,goal]) ).
cnf(refute_0_582,plain,
tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1),
introduced(tautology,[refl,[$fot(tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1))]]) ).
cnf(refute_0_583,plain,
$false,
inference(resolve,[$cnf( $equal(tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1),tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1)) )],[refute_0_582,refute_0_581]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : TOP049-1 : TPTP v8.1.0. Released v8.1.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun May 29 08:06:39 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.41 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.41
% 0.18/0.41 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.18/0.49
%------------------------------------------------------------------------------