%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : HWV003-2 : TPTP v8.1.2. Released v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n021.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 01:59:55 EDT 2023

% Result   : Unsatisfiable 172.91s 174.85s
% Output   : CNFRefutation 173.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   40
%            Number of leaves      :   55
% Syntax   : Number of formulae    :  567 ( 545 unt;  20 typ;   0 def)
%            Number of atoms       :  549 ( 548 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    7 (   5   ~;   2   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   1 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   20 (  20 usr;  16 con; 0-2 aty)
%            Number of variables   :  284 (  49 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    or: ( $i * $i ) > $i ).

tff(decl_23,type,
    and: ( $i * $i ) > $i ).

tff(decl_24,type,
    ll0: $i ).

tff(decl_25,type,
    ll1: $i ).

tff(decl_26,type,
    not: $i > $i ).

tff(decl_27,type,
    xor: ( $i * $i ) > $i ).

tff(decl_28,type,
    a: $i ).

tff(decl_29,type,
    b: $i ).

tff(decl_30,type,
    cin: $i ).

tff(decl_31,type,
    sum_def: $i ).

tff(decl_32,type,
    carry_def: $i ).

tff(decl_33,type,
    t1: $i ).

tff(decl_34,type,
    t2: $i ).

tff(decl_35,type,
    t3: $i ).

tff(decl_36,type,
    t4: $i ).

tff(decl_37,type,
    t5: $i ).

tff(decl_38,type,
    t6: $i ).

tff(decl_39,type,
    t7: $i ).

tff(decl_40,type,
    sum: $i ).

tff(decl_41,type,
    carry: $i ).

cnf(t6,negated_conjecture,
    not(and(t4,t5)) = t6,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6) ).

cnf(and_commutative,axiom,
    and(X1,X2) = and(X2,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_commutative) ).

cnf(and_absorption,axiom,
    and(X1,or(X1,X2)) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_absorption) ).

cnf(or_commutative,axiom,
    or(X1,X2) = or(X2,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_commutative) ).

cnf(or_demorgan,axiom,
    not(or(X1,X2)) = and(not(X1),not(X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_demorgan) ).

cnf(or_absorption,axiom,
    or(X1,and(X1,X2)) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_absorption) ).

cnf(not_involution,axiom,
    not(not(X1)) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_involution) ).

cnf(t5,negated_conjecture,
    not(and(t4,cin)) = t5,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5) ).

cnf(and_associative,axiom,
    and(and(X1,X2),X3) = and(X1,and(X2,X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_associative) ).

cnf(sum,negated_conjecture,
    not(and(t6,t7)) = sum,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum) ).

cnf(and_distributive,axiom,
    or(X1,and(X2,X3)) = and(or(X1,X2),or(X1,X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_distributive) ).

cnf(t4,negated_conjecture,
    not(and(t2,t3)) = t4,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4) ).

cnf(or_complement,axiom,
    or(X1,not(X1)) = ll1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_complement) ).

cnf(or_associative,axiom,
    or(or(X1,X2),X3) = or(X1,or(X2,X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_associative) ).

cnf(or_boundedness,axiom,
    or(X1,ll1) = ll1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_boundedness) ).

cnf(t2,negated_conjecture,
    not(and(a,t1)) = t2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2) ).

cnf(and_identity,axiom,
    and(X1,ll1) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_identity) ).

cnf(xor_associative,axiom,
    xor(X1,xor(X2,X3)) = xor(xor(X1,X2),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_associative) ).

cnf(xor_definition,axiom,
    or(and(not(X1),X2),and(X1,not(X2))) = xor(X1,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_definition) ).

cnf(and_complement,axiom,
    and(X1,not(X1)) = ll0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_complement) ).

cnf(t1,negated_conjecture,
    not(and(a,b)) = t1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1) ).

cnf(or_identity,axiom,
    or(X1,ll0) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_identity) ).

cnf(t3,negated_conjecture,
    not(and(b,t1)) = t3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3) ).

cnf(ll1_inverse,axiom,
    not(ll1) = ll0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ll1_inverse) ).

cnf(and_boundedness,axiom,
    and(X1,ll0) = ll0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_boundedness) ).

cnf(ll0_inverse,axiom,
    not(ll0) = ll1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ll0_inverse) ).

cnf(carry,negated_conjecture,
    not(and(t1,t5)) = carry,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',carry) ).

cnf(and_idempotent,axiom,
    and(X1,X1) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_idempotent) ).

cnf(or_idempotent,axiom,
    or(X1,X1) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_idempotent) ).

cnf(or_distributive,axiom,
    and(X1,or(X2,X3)) = or(and(X1,X2),and(X1,X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_distributive) ).

cnf(t7,negated_conjecture,
    not(and(t5,cin)) = t7,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7) ).

cnf(and_demorgan,axiom,
    not(and(X1,X2)) = or(not(X1),not(X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_demorgan) ).

cnf(carry_def,negated_conjecture,
    or(and(cin,or(a,b)),and(not(cin),and(a,b))) = carry_def,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',carry_def) ).

cnf(sum_def,negated_conjecture,
    xor(xor(a,b),cin) = sum_def,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_def) ).

cnf(prove_circuit,negated_conjecture,
    ( sum != sum_def
    | carry != carry_def ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_circuit) ).

cnf(c_0_35,negated_conjecture,
    not(and(t4,t5)) = t6,
    t6 ).

cnf(c_0_36,axiom,
    and(X1,X2) = and(X2,X1),
    and_commutative ).

cnf(c_0_37,axiom,
    and(X1,or(X1,X2)) = X1,
    and_absorption ).

cnf(c_0_38,axiom,
    or(X1,X2) = or(X2,X1),
    or_commutative ).

cnf(c_0_39,axiom,
    not(or(X1,X2)) = and(not(X1),not(X2)),
    or_demorgan ).

cnf(c_0_40,axiom,
    or(X1,and(X1,X2)) = X1,
    or_absorption ).

cnf(c_0_41,axiom,
    not(not(X1)) = X1,
    not_involution ).

cnf(c_0_42,negated_conjecture,
    not(and(t5,t4)) = t6,
    inference(rw,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_43,negated_conjecture,
    not(and(t4,cin)) = t5,
    t5 ).

cnf(c_0_44,plain,
    and(X1,or(X2,X1)) = X1,
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_45,axiom,
    and(and(X1,X2),X3) = and(X1,and(X2,X3)),
    and_associative ).

cnf(c_0_46,plain,
    and(not(X1),not(and(X1,X2))) = not(X1),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_47,negated_conjecture,
    not(and(t6,t7)) = sum,
    sum ).

cnf(c_0_48,negated_conjecture,
    not(t6) = and(t5,t4),
    inference(spm,[status(thm)],[c_0_41,c_0_42]) ).

cnf(c_0_49,axiom,
    or(X1,and(X2,X3)) = and(or(X1,X2),or(X1,X3)),
    and_distributive ).

cnf(c_0_50,plain,
    or(X1,and(X2,X1)) = X1,
    inference(spm,[status(thm)],[c_0_40,c_0_36]) ).

cnf(c_0_51,negated_conjecture,
    not(and(cin,t4)) = t5,
    inference(rw,[status(thm)],[c_0_43,c_0_36]) ).

cnf(c_0_52,plain,
    and(X1,and(X2,X1)) = and(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_40]),c_0_45]) ).

cnf(c_0_53,negated_conjecture,
    and(t5,and(t4,sum)) = and(t5,t4),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_45]),c_0_48]) ).

cnf(c_0_54,negated_conjecture,
    not(and(t2,t3)) = t4,
    t4 ).

cnf(c_0_55,plain,
    or(X1,and(X2,and(X1,X3))) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_37]),c_0_45]) ).

cnf(c_0_56,negated_conjecture,
    and(t5,not(cin)) = not(cin),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_51]),c_0_36]) ).

cnf(c_0_57,negated_conjecture,
    and(t4,and(sum,and(t5,t4))) = and(t4,and(t5,sum)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_45]),c_0_45]),c_0_36]) ).

cnf(c_0_58,negated_conjecture,
    not(t4) = and(t2,t3),
    inference(spm,[status(thm)],[c_0_41,c_0_54]) ).

cnf(c_0_59,axiom,
    or(X1,not(X1)) = ll1,
    or_complement ).

cnf(c_0_60,axiom,
    or(or(X1,X2),X3) = or(X1,or(X2,X3)),
    or_associative ).

cnf(c_0_61,negated_conjecture,
    or(t5,and(X1,not(cin))) = t5,
    inference(spm,[status(thm)],[c_0_55,c_0_56]) ).

cnf(c_0_62,axiom,
    or(X1,ll1) = ll1,
    or_boundedness ).

cnf(c_0_63,negated_conjecture,
    and(t2,and(t3,not(and(t4,and(t5,sum))))) = and(t2,t3),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_57]),c_0_58]),c_0_45]),c_0_58]) ).

cnf(c_0_64,plain,
    and(X1,and(X2,X3)) = and(X3,and(X1,X2)),
    inference(spm,[status(thm)],[c_0_36,c_0_45]) ).

cnf(c_0_65,negated_conjecture,
    not(and(a,t1)) = t2,
    t2 ).

cnf(c_0_66,plain,
    or(X1,or(X2,and(not(X1),not(X2)))) = ll1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_39]),c_0_60]) ).

cnf(c_0_67,negated_conjecture,
    or(t5,and(not(cin),X1)) = t5,
    inference(spm,[status(thm)],[c_0_61,c_0_36]) ).

cnf(c_0_68,axiom,
    and(X1,ll1) = X1,
    and_identity ).

cnf(c_0_69,axiom,
    xor(X1,xor(X2,X3)) = xor(xor(X1,X2),X3),
    xor_associative ).

cnf(c_0_70,axiom,
    or(and(not(X1),X2),and(X1,not(X2))) = xor(X1,X2),
    xor_definition ).

cnf(c_0_71,negated_conjecture,
    or(t4,and(t2,t3)) = ll1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_54]),c_0_38]) ).

cnf(c_0_72,plain,
    or(ll1,X1) = ll1,
    inference(spm,[status(thm)],[c_0_62,c_0_38]) ).

cnf(c_0_73,negated_conjecture,
    and(t2,and(t3,t6)) = and(t2,t3),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_36]),c_0_53]),c_0_42]) ).

cnf(c_0_74,negated_conjecture,
    not(t5) = and(cin,t4),
    inference(spm,[status(thm)],[c_0_41,c_0_51]) ).

cnf(c_0_75,negated_conjecture,
    not(t2) = and(a,t1),
    inference(spm,[status(thm)],[c_0_41,c_0_65]) ).

cnf(c_0_76,negated_conjecture,
    or(cin,t5) = ll1,
    inference(spm,[status(thm)],[c_0_66,c_0_67]) ).

cnf(c_0_77,plain,
    and(ll1,X1) = X1,
    inference(spm,[status(thm)],[c_0_68,c_0_36]) ).

cnf(c_0_78,axiom,
    and(X1,not(X1)) = ll0,
    and_complement ).

cnf(c_0_79,negated_conjecture,
    or(t6,and(t5,t4)) = ll1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_42]),c_0_38]) ).

cnf(c_0_80,plain,
    or(and(not(X1),or(and(not(X2),X3),and(X2,not(X3)))),and(X1,not(or(and(not(X2),X3),and(X2,not(X3)))))) = or(and(not(or(and(not(X1),X2),and(X1,not(X2)))),X3),and(or(and(not(X1),X2),and(X1,not(X2))),not(X3))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70]),c_0_70]),c_0_70]),c_0_70]) ).

cnf(c_0_81,plain,
    not(and(not(X1),not(X2))) = or(X1,X2),
    inference(spm,[status(thm)],[c_0_41,c_0_39]) ).

cnf(c_0_82,negated_conjecture,
    or(t4,or(and(t2,t3),X1)) = ll1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_71]),c_0_72]) ).

cnf(c_0_83,negated_conjecture,
    or(and(t2,t3),and(t3,t6)) = and(t3,t6),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_73]),c_0_38]) ).

cnf(c_0_84,negated_conjecture,
    and(cin,and(t4,t6)) = and(cin,t4),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_42]),c_0_74]),c_0_45]),c_0_74]) ).

cnf(c_0_85,negated_conjecture,
    or(t5,and(cin,t4)) = ll1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_51]),c_0_38]) ).

cnf(c_0_86,negated_conjecture,
    and(a,and(t1,t4)) = and(a,t1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_54]),c_0_75]),c_0_45]),c_0_75]) ).

cnf(c_0_87,negated_conjecture,
    not(and(a,b)) = t1,
    t1 ).

cnf(c_0_88,negated_conjecture,
    or(cin,and(t5,X1)) = or(cin,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_76]),c_0_77]) ).

cnf(c_0_89,negated_conjecture,
    and(t5,and(t4,t6)) = ll0,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_42]),c_0_45]) ).

cnf(c_0_90,axiom,
    or(X1,ll0) = X1,
    or_identity ).

cnf(c_0_91,negated_conjecture,
    or(t6,or(and(t5,t4),X1)) = ll1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_79]),c_0_72]) ).

cnf(c_0_92,negated_conjecture,
    or(and(t5,t4),and(t4,sum)) = and(t4,sum),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_53]),c_0_38]) ).

cnf(c_0_93,negated_conjecture,
    not(and(b,t1)) = t3,
    t3 ).

cnf(c_0_94,plain,
    or(and(X1,and(not(and(X2,not(X3))),not(and(not(X2),X3)))),and(not(X1),or(and(X2,not(X3)),and(not(X2),X3)))) = or(and(not(and(X1,not(X2))),and(not(and(not(X1),X2)),X3)),and(or(and(X1,not(X2)),and(not(X1),X2)),not(X3))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_38]),c_0_38]),c_0_39]),c_0_38]),c_0_38]),c_0_39]),c_0_45]),c_0_38]) ).

cnf(c_0_95,axiom,
    not(ll1) = ll0,
    ll1_inverse ).

cnf(c_0_96,axiom,
    and(X1,ll0) = ll0,
    and_boundedness ).

cnf(c_0_97,axiom,
    not(ll0) = ll1,
    ll0_inverse ).

cnf(c_0_98,plain,
    or(X1,not(X2)) = not(and(not(X1),X2)),
    inference(spm,[status(thm)],[c_0_81,c_0_41]) ).

cnf(c_0_99,plain,
    or(X1,or(X2,or(X1,and(X2,X3)))) = or(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_49]),c_0_60]) ).

cnf(c_0_100,negated_conjecture,
    or(t4,and(t3,t6)) = ll1,
    inference(spm,[status(thm)],[c_0_82,c_0_83]) ).

cnf(c_0_101,negated_conjecture,
    and(t4,and(t6,and(cin,t4))) = and(t4,and(cin,t6)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_84]),c_0_45]),c_0_45]),c_0_36]) ).

cnf(c_0_102,negated_conjecture,
    or(t5,or(and(cin,t4),X1)) = ll1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_85]),c_0_72]) ).

cnf(c_0_103,negated_conjecture,
    or(and(cin,t4),and(t4,t6)) = and(t4,t6),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_84]),c_0_38]) ).

cnf(c_0_104,negated_conjecture,
    and(t1,and(t4,and(a,t1))) = and(t1,and(a,t4)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_86]),c_0_45]),c_0_45]),c_0_36]) ).

cnf(c_0_105,negated_conjecture,
    not(t1) = and(a,b),
    inference(spm,[status(thm)],[c_0_41,c_0_87]) ).

cnf(c_0_106,negated_conjecture,
    or(cin,and(t4,t6)) = cin,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_90]) ).

cnf(c_0_107,negated_conjecture,
    or(t6,and(t4,sum)) = ll1,
    inference(spm,[status(thm)],[c_0_91,c_0_92]) ).

cnf(c_0_108,negated_conjecture,
    and(t3,not(b)) = not(b),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_93]),c_0_36]) ).

cnf(c_0_109,plain,
    and(not(and(X1,not(X2))),not(and(not(X1),X2))) = or(and(X1,X2),and(not(X1),not(X2))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_96]),c_0_97]),c_0_68]),c_0_41]),c_0_96]),c_0_68]),c_0_68]),c_0_96]),c_0_90]),c_0_77]),c_0_98]),c_0_97]),c_0_77]) ).

cnf(c_0_110,plain,
    and(X1,and(X2,X3)) = and(X2,and(X1,X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_36]),c_0_45]) ).

cnf(c_0_111,negated_conjecture,
    or(t4,t3) = ll1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_62]),c_0_62]) ).

cnf(c_0_112,negated_conjecture,
    and(t2,and(t3,not(and(t4,and(cin,t6))))) = and(t2,t3),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_101]),c_0_58]),c_0_45]),c_0_58]) ).

cnf(c_0_113,negated_conjecture,
    or(t5,and(t4,t6)) = ll1,
    inference(spm,[status(thm)],[c_0_102,c_0_103]) ).

cnf(c_0_114,negated_conjecture,
    and(a,and(b,not(and(t1,and(a,t4))))) = and(a,b),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_104]),c_0_105]),c_0_45]),c_0_105]) ).

cnf(c_0_115,negated_conjecture,
    and(t4,t6) = and(cin,t4),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_106]),c_0_45]),c_0_36]),c_0_64]),c_0_36]),c_0_84]) ).

cnf(c_0_116,plain,
    and(or(X1,X2),or(X3,X1)) = or(X1,and(X2,X3)),
    inference(spm,[status(thm)],[c_0_49,c_0_38]) ).

cnf(c_0_117,negated_conjecture,
    or(t4,t6) = ll1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_107]),c_0_62]),c_0_62]),c_0_38]) ).

cnf(c_0_118,negated_conjecture,
    not(and(t1,t5)) = carry,
    carry ).

cnf(c_0_119,negated_conjecture,
    and(t2,and(t4,t3)) = ll0,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_54]),c_0_45]),c_0_36]) ).

cnf(c_0_120,plain,
    and(ll0,X1) = ll0,
    inference(spm,[status(thm)],[c_0_96,c_0_36]) ).

cnf(c_0_121,negated_conjecture,
    or(t3,and(X1,not(b))) = t3,
    inference(spm,[status(thm)],[c_0_55,c_0_108]) ).

cnf(c_0_122,axiom,
    and(X1,X1) = X1,
    and_idempotent ).

cnf(c_0_123,negated_conjecture,
    or(and(t6,or(and(X1,not(X2)),and(not(X1),X2))),and(t5,and(t4,or(and(X1,X2),and(not(X1),not(X2)))))) = or(and(not(and(t6,X1)),and(not(and(t5,and(t4,not(X1)))),X2)),and(or(and(t6,X1),and(t5,and(t4,not(X1)))),not(X2))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_42]),c_0_45]),c_0_45]),c_0_45]),c_0_109]),c_0_38]),c_0_110]),c_0_38]) ).

cnf(c_0_124,negated_conjecture,
    and(t4,and(t2,t3)) = ll0,
    inference(spm,[status(thm)],[c_0_78,c_0_58]) ).

cnf(c_0_125,negated_conjecture,
    or(t4,and(X1,t3)) = or(t4,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_111]),c_0_68]) ).

cnf(c_0_126,negated_conjecture,
    or(t4,t2) = ll1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_71]),c_0_62]),c_0_62]) ).

cnf(c_0_127,axiom,
    or(X1,X1) = X1,
    or_idempotent ).

cnf(c_0_128,negated_conjecture,
    and(t5,and(t2,t3)) = and(t2,t3),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_64]),c_0_36]),c_0_84]),c_0_51]),c_0_36]),c_0_64]),c_0_36]) ).

cnf(c_0_129,negated_conjecture,
    or(t5,t4) = ll1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_113]),c_0_62]),c_0_62]) ).

cnf(c_0_130,negated_conjecture,
    and(a,and(b,t2)) = and(a,b),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_64]),c_0_36]),c_0_86]),c_0_65]) ).

cnf(c_0_131,axiom,
    and(X1,or(X2,X3)) = or(and(X1,X2),and(X1,X3)),
    or_distributive ).

cnf(c_0_132,negated_conjecture,
    or(t2,and(a,t1)) = ll1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_65]),c_0_38]) ).

cnf(c_0_133,negated_conjecture,
    not(and(t5,cin)) = t7,
    t7 ).

cnf(c_0_134,negated_conjecture,
    or(t6,and(cin,t4)) = t6,
    inference(spm,[status(thm)],[c_0_50,c_0_115]) ).

cnf(c_0_135,negated_conjecture,
    or(t6,and(X1,t4)) = or(t6,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_68]) ).

cnf(c_0_136,negated_conjecture,
    or(t1,and(a,b)) = ll1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_87]),c_0_38]) ).

cnf(c_0_137,negated_conjecture,
    and(a,and(b,carry)) = and(a,b),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_118]),c_0_105]),c_0_45]),c_0_105]) ).

cnf(c_0_138,negated_conjecture,
    and(t2,and(t4,and(t3,X1))) = ll0,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_119]),c_0_120]),c_0_45]) ).

cnf(c_0_139,negated_conjecture,
    or(t3,and(not(b),X1)) = t3,
    inference(spm,[status(thm)],[c_0_121,c_0_36]) ).

cnf(c_0_140,negated_conjecture,
    or(and(t5,or(and(X1,not(X2)),and(not(X1),X2))),and(cin,and(t4,or(and(X1,X2),and(not(X1),not(X2)))))) = or(and(not(and(t5,X1)),and(not(and(cin,and(t4,not(X1)))),X2)),and(or(and(t5,X1),and(cin,and(t4,not(X1)))),not(X2))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_51]),c_0_45]),c_0_45]),c_0_45]),c_0_109]),c_0_38]),c_0_110]),c_0_38]) ).

cnf(c_0_141,plain,
    and(X1,and(X1,X2)) = and(X1,X2),
    inference(spm,[status(thm)],[c_0_45,c_0_122]) ).

cnf(c_0_142,negated_conjecture,
    or(and(cin,t4),and(t2,t3)) = t6,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_54]),c_0_122]),c_0_58]),c_0_122]),c_0_125]),c_0_126]),c_0_68]),c_0_58]),c_0_54]),c_0_45]),c_0_36]),c_0_64]),c_0_36]),c_0_124]),c_0_127]),c_0_96]),c_0_96]),c_0_90]),c_0_36]),c_0_115]),c_0_51]),c_0_58]),c_0_124]),c_0_96]),c_0_97]),c_0_77]),c_0_128]),c_0_36]),c_0_115]),c_0_58]),c_0_124]),c_0_96]),c_0_90]),c_0_54]),c_0_45]),c_0_122]),c_0_38]) ).

cnf(c_0_143,negated_conjecture,
    or(t5,and(X1,t4)) = or(t5,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_129]),c_0_68]) ).

cnf(c_0_144,plain,
    or(ll0,X1) = X1,
    inference(spm,[status(thm)],[c_0_90,c_0_38]) ).

cnf(c_0_145,negated_conjecture,
    or(and(a,b),and(b,t2)) = and(b,t2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_130]),c_0_38]) ).

cnf(c_0_146,plain,
    or(and(X1,X2),and(X2,X3)) = and(X2,or(X1,X3)),
    inference(spm,[status(thm)],[c_0_131,c_0_36]) ).

cnf(c_0_147,negated_conjecture,
    or(a,t2) = ll1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_132]),c_0_62]),c_0_62]),c_0_38]) ).

cnf(c_0_148,negated_conjecture,
    not(and(cin,t5)) = t7,
    inference(rw,[status(thm)],[c_0_133,c_0_36]) ).

cnf(c_0_149,negated_conjecture,
    or(cin,t6) = t6,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_134,c_0_135]),c_0_38]) ).

cnf(c_0_150,axiom,
    not(and(X1,X2)) = or(not(X1),not(X2)),
    and_demorgan ).

cnf(c_0_151,negated_conjecture,
    or(t1,or(and(a,b),X1)) = ll1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_136]),c_0_72]) ).

cnf(c_0_152,negated_conjecture,
    or(and(a,b),and(b,carry)) = and(b,carry),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_137]),c_0_38]) ).

cnf(c_0_153,plain,
    and(or(X1,X2),or(X2,X3)) = or(X2,and(X1,X3)),
    inference(spm,[status(thm)],[c_0_49,c_0_38]) ).

cnf(c_0_154,negated_conjecture,
    and(t2,and(t4,not(b))) = ll0,
    inference(spm,[status(thm)],[c_0_138,c_0_108]) ).

cnf(c_0_155,negated_conjecture,
    or(b,t3) = ll1,
    inference(spm,[status(thm)],[c_0_66,c_0_139]) ).

cnf(c_0_156,negated_conjecture,
    or(and(cin,t4),and(t5,t4)) = t4,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_128]),c_0_54]),c_0_74]),c_0_45]),c_0_124]),c_0_96]),c_0_90]),c_0_141]),c_0_74]),c_0_54]),c_0_45]),c_0_122]),c_0_38]),c_0_142]),c_0_115]),c_0_141]),c_0_122]),c_0_74]),c_0_74]),c_0_52]),c_0_36]),c_0_141]),c_0_51]),c_0_128]),c_0_45]),c_0_124]),c_0_96]),c_0_122]),c_0_74]),c_0_52]),c_0_36]),c_0_141]),c_0_143]),c_0_38]),c_0_76]),c_0_54]),c_0_77]),c_0_144]),c_0_38]) ).

cnf(c_0_157,negated_conjecture,
    and(b,t2) = b,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_145,c_0_146]),c_0_147]),c_0_68]) ).

cnf(c_0_158,negated_conjecture,
    and(t7,not(cin)) = not(cin),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_148]),c_0_36]) ).

cnf(c_0_159,negated_conjecture,
    and(t5,and(t4,not(cin))) = and(t5,t4),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_149]),c_0_48]),c_0_48]),c_0_36]),c_0_45]) ).

cnf(c_0_160,plain,
    or(and(X1,X2),and(X3,X1)) = and(X1,or(X2,X3)),
    inference(spm,[status(thm)],[c_0_131,c_0_36]) ).

cnf(c_0_161,plain,
    or(not(X1),X2) = not(and(X1,not(X2))),
    inference(spm,[status(thm)],[c_0_150,c_0_41]) ).

cnf(c_0_162,negated_conjecture,
    or(t1,and(b,carry)) = ll1,
    inference(spm,[status(thm)],[c_0_151,c_0_152]) ).

cnf(c_0_163,negated_conjecture,
    and(t1,not(and(b,t2))) = not(and(b,t2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_145]),c_0_87]) ).

cnf(c_0_164,negated_conjecture,
    or(t6,and(t4,X1)) = or(t6,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_117]),c_0_77]) ).

cnf(c_0_165,negated_conjecture,
    and(t4,and(t2,not(b))) = ll0,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_154]),c_0_96]),c_0_45]),c_0_36]) ).

cnf(c_0_166,negated_conjecture,
    or(b,and(X1,t3)) = or(b,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_155]),c_0_68]) ).

cnf(c_0_167,negated_conjecture,
    and(t2,t3) = and(t5,t6),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_156]),c_0_58]),c_0_51]),c_0_42]) ).

cnf(c_0_168,negated_conjecture,
    or(b,t2) = t2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_157]),c_0_38]) ).

cnf(c_0_169,negated_conjecture,
    or(t4,and(t3,X1)) = or(t4,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_111]),c_0_77]) ).

cnf(c_0_170,negated_conjecture,
    not(t3) = and(b,t1),
    inference(spm,[status(thm)],[c_0_41,c_0_93]) ).

cnf(c_0_171,negated_conjecture,
    or(t7,and(X1,not(cin))) = t7,
    inference(spm,[status(thm)],[c_0_55,c_0_158]) ).

cnf(c_0_172,negated_conjecture,
    and(t4,not(cin)) = and(t5,t4),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_159]),c_0_160]),c_0_161]),c_0_74]),c_0_141]),c_0_51]),c_0_36]) ).

cnf(c_0_173,plain,
    and(X1,and(not(X1),X2)) = ll0,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_78]),c_0_120]) ).

cnf(c_0_174,negated_conjecture,
    or(b,t1) = ll1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_162]),c_0_62]),c_0_62]),c_0_38]) ).

cnf(c_0_175,negated_conjecture,
    and(t1,not(b)) = not(b),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_163,c_0_157]),c_0_157]) ).

cnf(c_0_176,negated_conjecture,
    or(t6,and(t2,not(b))) = t6,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_165]),c_0_90]) ).

cnf(c_0_177,negated_conjecture,
    or(b,and(t5,t6)) = t2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_167]),c_0_168]) ).

cnf(c_0_178,negated_conjecture,
    not(and(t5,t6)) = t4,
    inference(rw,[status(thm)],[c_0_54,c_0_167]) ).

cnf(c_0_179,negated_conjecture,
    or(t4,and(b,t1)) = t4,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_78]),c_0_90]),c_0_170]) ).

cnf(c_0_180,negated_conjecture,
    or(and(a,t1),and(t1,t4)) = and(t1,t4),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_86]),c_0_38]) ).

cnf(c_0_181,negated_conjecture,
    or(t7,and(t5,t4)) = t7,
    inference(spm,[status(thm)],[c_0_171,c_0_172]) ).

cnf(c_0_182,plain,
    and(X1,and(X2,not(X1))) = ll0,
    inference(spm,[status(thm)],[c_0_173,c_0_36]) ).

cnf(c_0_183,negated_conjecture,
    or(t5,and(t4,X1)) = or(t5,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_129]),c_0_77]) ).

cnf(c_0_184,negated_conjecture,
    or(t7,and(not(cin),X1)) = t7,
    inference(spm,[status(thm)],[c_0_171,c_0_36]) ).

cnf(c_0_185,negated_conjecture,
    or(t2,or(and(a,t1),X1)) = ll1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_132]),c_0_72]) ).

cnf(c_0_186,negated_conjecture,
    or(b,and(t1,X1)) = or(b,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_174]),c_0_77]) ).

cnf(c_0_187,negated_conjecture,
    and(t1,and(t5,carry)) = ll0,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_118]),c_0_45]) ).

cnf(c_0_188,negated_conjecture,
    and(t4,and(a,and(t1,and(a,t4)))) = and(t4,and(a,t1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_104]),c_0_45]),c_0_45]),c_0_141]),c_0_45]),c_0_45]),c_0_122]) ).

cnf(c_0_189,negated_conjecture,
    and(a,not(b)) = and(a,t1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_168]),c_0_75]),c_0_75]),c_0_36]),c_0_45]),c_0_175]) ).

cnf(c_0_190,plain,
    or(and(X1,or(and(X1,X2),and(not(X1),not(X2)))),and(not(X1),or(and(X1,not(X2)),and(not(X1),X2)))) = X2,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_78]),c_0_41]),c_0_41]),c_0_41]),c_0_41]),c_0_41]),c_0_78]),c_0_97]),c_0_97]),c_0_41]),c_0_78]),c_0_127]),c_0_109]),c_0_77]),c_0_77]),c_0_120]),c_0_90]) ).

cnf(c_0_191,negated_conjecture,
    and(a,and(b,t1)) = ll0,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_87]),c_0_45]) ).

cnf(c_0_192,negated_conjecture,
    or(a,and(t2,X1)) = or(a,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_147]),c_0_77]) ).

cnf(c_0_193,negated_conjecture,
    and(t2,and(t6,not(b))) = and(t2,not(b)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_176]),c_0_45]),c_0_36]) ).

cnf(c_0_194,plain,
    and(X1,not(and(X1,not(X2)))) = and(X1,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_78]),c_0_161]),c_0_144]) ).

cnf(c_0_195,negated_conjecture,
    and(t4,not(b)) = and(a,t1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_177]),c_0_75]),c_0_178]),c_0_36]) ).

cnf(c_0_196,negated_conjecture,
    or(a,t1) = ll1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_136]),c_0_62]),c_0_62]),c_0_38]) ).

cnf(c_0_197,negated_conjecture,
    and(b,and(t1,t4)) = and(b,t1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_179]),c_0_45]) ).

cnf(c_0_198,negated_conjecture,
    and(t1,or(a,t4)) = and(t1,t4),
    inference(rw,[status(thm)],[c_0_180,c_0_146]) ).

cnf(c_0_199,plain,
    or(X1,or(X2,X3)) = or(X2,or(X1,X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_38]),c_0_60]) ).

cnf(c_0_200,negated_conjecture,
    and(t5,and(t4,t7)) = and(t5,t4),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_181]),c_0_45]) ).

cnf(c_0_201,negated_conjecture,
    and(cin,or(t5,t7)) = cin,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_56]),c_0_41]),c_0_36]),c_0_74]),c_0_45]),c_0_182]),c_0_90]),c_0_52]),c_0_36]),c_0_74]),c_0_41]),c_0_45]),c_0_36]),c_0_141]),c_0_161]),c_0_51]),c_0_148]),c_0_131]),c_0_183]),c_0_122]),c_0_74]),c_0_74]),c_0_52]),c_0_36]),c_0_141]),c_0_51]),c_0_56]),c_0_45]),c_0_182]),c_0_122]),c_0_74]),c_0_52]),c_0_36]),c_0_141]),c_0_143]),c_0_38]),c_0_76]),c_0_41]),c_0_77]),c_0_144]) ).

cnf(c_0_202,negated_conjecture,
    or(cin,t7) = ll1,
    inference(spm,[status(thm)],[c_0_66,c_0_184]) ).

cnf(c_0_203,negated_conjecture,
    or(t2,and(t1,t4)) = ll1,
    inference(spm,[status(thm)],[c_0_185,c_0_180]) ).

cnf(c_0_204,negated_conjecture,
    or(b,and(t5,carry)) = b,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_186,c_0_187]),c_0_90]) ).

cnf(c_0_205,negated_conjecture,
    and(t2,and(t3,not(and(t4,and(a,t1))))) = and(t2,t3),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_188]),c_0_58]),c_0_45]),c_0_58]) ).

cnf(c_0_206,negated_conjecture,
    or(t3,and(a,t1)) = t3,
    inference(spm,[status(thm)],[c_0_121,c_0_189]) ).

cnf(c_0_207,negated_conjecture,
    not(b) = and(t1,t3),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_175]),c_0_105]),c_0_41]),c_0_45]),c_0_122]),c_0_161]),c_0_87]),c_0_93]),c_0_105]),c_0_41]),c_0_36]),c_0_105]),c_0_45]),c_0_78]),c_0_96]),c_0_90]),c_0_45]),c_0_141]),c_0_191]),c_0_90]) ).

cnf(c_0_208,negated_conjecture,
    or(a,and(t6,not(b))) = not(and(b,not(a))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_193]),c_0_192]),c_0_98]),c_0_36]) ).

cnf(c_0_209,negated_conjecture,
    and(t2,not(a)) = not(a),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_65]),c_0_36]) ).

cnf(c_0_210,negated_conjecture,
    and(a,t2) = and(a,b),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_189]),c_0_65]) ).

cnf(c_0_211,negated_conjecture,
    and(t1,not(a)) = not(a),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_87]),c_0_36]) ).

cnf(c_0_212,negated_conjecture,
    or(a,and(X1,t2)) = or(a,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_147]),c_0_68]) ).

cnf(c_0_213,negated_conjecture,
    and(t4,t2) = and(b,t4),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_195]),c_0_65]),c_0_36]) ).

cnf(c_0_214,negated_conjecture,
    or(a,and(t1,X1)) = or(a,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_196]),c_0_77]) ).

cnf(c_0_215,negated_conjecture,
    and(t1,or(b,t4)) = and(t1,t4),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_197]),c_0_160]),c_0_38]) ).

cnf(c_0_216,negated_conjecture,
    or(a,or(b,t4)) = or(b,t4),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_186,c_0_198]),c_0_186]),c_0_199]) ).

cnf(c_0_217,negated_conjecture,
    or(and(cin,or(a,b)),and(not(cin),and(a,b))) = carry_def,
    carry_def ).

cnf(c_0_218,negated_conjecture,
    or(sum,and(t6,t7)) = ll1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_47]),c_0_38]) ).

cnf(c_0_219,negated_conjecture,
    and(t4,or(t5,t7)) = and(t4,t7),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_200]),c_0_160]),c_0_38]) ).

cnf(c_0_220,negated_conjecture,
    or(t5,t7) = ll1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_201]),c_0_60]),c_0_38]),c_0_202]),c_0_62]) ).

cnf(c_0_221,negated_conjecture,
    or(t1,t2) = ll1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_203]),c_0_62]),c_0_62]),c_0_38]) ).

cnf(c_0_222,negated_conjecture,
    and(not(b),not(and(t5,carry))) = not(b),
    inference(spm,[status(thm)],[c_0_39,c_0_204]) ).

cnf(c_0_223,negated_conjecture,
    and(t5,and(t2,t6)) = and(t5,t6),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_205,c_0_64]),c_0_86]),c_0_65]),c_0_36]),c_0_167]),c_0_110]),c_0_167]) ).

cnf(c_0_224,negated_conjecture,
    and(a,and(t1,t3)) = and(a,t1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_206]),c_0_45]) ).

cnf(c_0_225,negated_conjecture,
    and(t1,and(t4,t3)) = and(a,t1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_195,c_0_207]),c_0_110]) ).

cnf(c_0_226,negated_conjecture,
    and(a,not(and(b,not(a)))) = a,
    inference(spm,[status(thm)],[c_0_37,c_0_208]) ).

cnf(c_0_227,negated_conjecture,
    not(a) = and(t1,t2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_209]),c_0_75]),c_0_41]),c_0_45]),c_0_36]),c_0_141]),c_0_161]),c_0_65]),c_0_210]),c_0_87]),c_0_36]),c_0_75]),c_0_41]),c_0_36]),c_0_210]),c_0_75]),c_0_45]),c_0_211]),c_0_78]),c_0_90]),c_0_45]),c_0_64]),c_0_191]),c_0_96]),c_0_90]) ).

cnf(c_0_228,negated_conjecture,
    and(b,and(t1,t2)) = and(b,t1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_206]),c_0_170]),c_0_170]),c_0_65]),c_0_45]) ).

cnf(c_0_229,negated_conjecture,
    or(a,and(b,t4)) = or(a,t4),
    inference(spm,[status(thm)],[c_0_212,c_0_213]) ).

cnf(c_0_230,negated_conjecture,
    or(b,t4) = or(a,t4),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_215]),c_0_214]),c_0_216]) ).

cnf(c_0_231,plain,
    or(X1,or(X1,X2)) = or(X1,X2),
    inference(spm,[status(thm)],[c_0_60,c_0_127]) ).

cnf(c_0_232,negated_conjecture,
    or(a,and(t3,t6)) = or(a,t3),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_73]),c_0_192]) ).

cnf(c_0_233,negated_conjecture,
    or(and(a,and(b,not(cin))),and(cin,or(a,b))) = carry_def,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_217,c_0_36]),c_0_45]),c_0_38]) ).

cnf(c_0_234,negated_conjecture,
    or(a,and(t5,t3)) = or(a,t3),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_112]),c_0_192]),c_0_64]),c_0_36]),c_0_115]),c_0_141]),c_0_51]),c_0_36]) ).

cnf(c_0_235,plain,
    or(and(X1,and(not(and(X1,X2)),or(X1,X2))),and(not(X1),or(and(X1,X2),and(not(X1),not(X2))))) = not(X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_122]),c_0_41]),c_0_41]),c_0_41]),c_0_122]),c_0_41]),c_0_41]),c_0_122]),c_0_59]),c_0_81]),c_0_36]),c_0_38]),c_0_64]),c_0_182]),c_0_77]),c_0_98]),c_0_97]),c_0_77]) ).

cnf(c_0_236,negated_conjecture,
    or(t6,sum) = ll1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_218]),c_0_62]),c_0_62]),c_0_38]) ).

cnf(c_0_237,negated_conjecture,
    not(sum) = and(t6,t7),
    inference(spm,[status(thm)],[c_0_41,c_0_47]) ).

cnf(c_0_238,negated_conjecture,
    and(t5,and(t4,and(t6,X1))) = ll0,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_89]),c_0_120]),c_0_45]) ).

cnf(c_0_239,negated_conjecture,
    and(t4,t7) = t4,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_219,c_0_220]),c_0_68]) ).

cnf(c_0_240,negated_conjecture,
    or(t1,and(t2,X1)) = or(t1,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_221]),c_0_77]) ).

cnf(c_0_241,negated_conjecture,
    or(t3,and(b,t1)) = ll1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_93]),c_0_38]) ).

cnf(c_0_242,negated_conjecture,
    or(t3,and(b,X1)) = or(t3,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_155]),c_0_77]) ).

cnf(c_0_243,negated_conjecture,
    or(t4,and(t5,X1)) = or(t4,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_129]),c_0_77]) ).

cnf(c_0_244,negated_conjecture,
    and(t5,and(carry,not(b))) = ll0,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_222]),c_0_41]),c_0_36]),c_0_78]),c_0_36]),c_0_45]) ).

cnf(c_0_245,negated_conjecture,
    or(and(a,t1),and(t5,t6)) = t3,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_167]),c_0_75]),c_0_170]),c_0_45]),c_0_52]),c_0_36]),c_0_191]),c_0_90]),c_0_110]),c_0_223]),c_0_75]),c_0_170]),c_0_64]),c_0_36]),c_0_157]),c_0_36]),c_0_75]),c_0_45]),c_0_224]),c_0_44]),c_0_38]) ).

cnf(c_0_246,negated_conjecture,
    or(a,and(t4,t3)) = a,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_225]),c_0_40]) ).

cnf(c_0_247,negated_conjecture,
    and(a,t3) = a,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_226,c_0_227]),c_0_228]),c_0_93]) ).

cnf(c_0_248,negated_conjecture,
    or(a,t4) = or(a,b),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_229]),c_0_199]),c_0_230]),c_0_231]),c_0_231]) ).

cnf(c_0_249,negated_conjecture,
    or(a,t3) = t3,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_207]),c_0_64]),c_0_36]),c_0_110]),c_0_214]),c_0_232]),c_0_227]),c_0_228]),c_0_93]) ).

cnf(c_0_250,negated_conjecture,
    or(a,and(t5,carry)) = a,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_187]),c_0_90]) ).

cnf(c_0_251,negated_conjecture,
    or(and(a,and(b,not(cin))),and(cin,and(or(a,b),X1))) = and(carry_def,or(and(a,and(b,not(cin))),X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_233]),c_0_45]) ).

cnf(c_0_252,plain,
    and(X1,or(X2,or(X3,X1))) = X1,
    inference(spm,[status(thm)],[c_0_44,c_0_60]) ).

cnf(c_0_253,negated_conjecture,
    or(a,or(t5,t3)) = or(a,t5),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_234]),c_0_199]),c_0_231]) ).

cnf(c_0_254,negated_conjecture,
    or(t4,and(t6,X1)) = or(t4,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_117]),c_0_77]) ).

cnf(c_0_255,negated_conjecture,
    and(t6,not(and(t6,sum))) = and(t6,t7),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_236]),c_0_68]),c_0_48]),c_0_48]),c_0_237]),c_0_45]),c_0_238]),c_0_90]),c_0_45]),c_0_238]),c_0_90]),c_0_237]) ).

cnf(c_0_256,negated_conjecture,
    or(t4,t7) = t7,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_239]),c_0_38]) ).

cnf(c_0_257,negated_conjecture,
    or(t5,t6) = ll1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_79]),c_0_62]),c_0_62]),c_0_38]) ).

cnf(c_0_258,negated_conjecture,
    or(carry,and(t1,t5)) = ll1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_118]),c_0_38]) ).

cnf(c_0_259,negated_conjecture,
    or(t1,and(t5,t6)) = or(t1,t3),
    inference(spm,[status(thm)],[c_0_240,c_0_167]) ).

cnf(c_0_260,negated_conjecture,
    or(t1,t3) = ll1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_241,c_0_242]),c_0_38]) ).

cnf(c_0_261,negated_conjecture,
    or(t4,and(carry,not(b))) = t4,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_243,c_0_244]),c_0_90]) ).

cnf(c_0_262,negated_conjecture,
    and(b,t4) = and(b,t1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_245]),c_0_170]),c_0_65]),c_0_178]),c_0_36]),c_0_213]) ).

cnf(c_0_263,negated_conjecture,
    and(t5,and(t3,t6)) = and(t5,t6),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_167]),c_0_36]),c_0_167]),c_0_110]) ).

cnf(c_0_264,negated_conjecture,
    and(t4,t3) = and(a,t4),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_246]),c_0_45]),c_0_36]),c_0_247]),c_0_36]) ).

cnf(c_0_265,negated_conjecture,
    or(b,and(t3,X1)) = or(b,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_155]),c_0_77]) ).

cnf(c_0_266,plain,
    or(X1,or(and(X1,X2),X3)) = or(X1,X3),
    inference(spm,[status(thm)],[c_0_60,c_0_40]) ).

cnf(c_0_267,negated_conjecture,
    or(b,and(X1,t1)) = or(b,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_174]),c_0_68]) ).

cnf(c_0_268,negated_conjecture,
    and(t1,or(a,b)) = and(t1,t4),
    inference(rw,[status(thm)],[c_0_198,c_0_248]) ).

cnf(c_0_269,negated_conjecture,
    or(cin,and(carry,not(b))) = cin,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_244]),c_0_90]) ).

cnf(c_0_270,negated_conjecture,
    or(t3,and(a,X1)) = t3,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_249]),c_0_37]) ).

cnf(c_0_271,negated_conjecture,
    and(a,and(t5,carry)) = and(t5,carry),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_250]),c_0_45]),c_0_36]),c_0_110]) ).

cnf(c_0_272,negated_conjecture,
    and(cin,and(carry_def,or(a,b))) = and(cin,or(a,b)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_233]),c_0_45]),c_0_36]) ).

cnf(c_0_273,negated_conjecture,
    and(carry_def,or(a,b)) = carry_def,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_251,c_0_122]),c_0_233]),c_0_38]),c_0_60]),c_0_55]) ).

cnf(c_0_274,negated_conjecture,
    and(t3,or(a,t5)) = t3,
    inference(spm,[status(thm)],[c_0_252,c_0_253]) ).

cnf(c_0_275,negated_conjecture,
    not(and(t5,and(t6,sum))) = t7,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_254,c_0_255]),c_0_254]),c_0_256]),c_0_98]),c_0_58]),c_0_167]),c_0_45]),c_0_141]) ).

cnf(c_0_276,negated_conjecture,
    not(t7) = and(cin,t5),
    inference(spm,[status(thm)],[c_0_41,c_0_148]) ).

cnf(c_0_277,negated_conjecture,
    or(t5,and(t6,X1)) = or(t5,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_257]),c_0_77]) ).

cnf(c_0_278,negated_conjecture,
    and(t6,and(t7,sum)) = ll0,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_47]),c_0_45]) ).

cnf(c_0_279,negated_conjecture,
    or(t1,carry) = ll1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_258]),c_0_62]),c_0_62]),c_0_38]) ).

cnf(c_0_280,negated_conjecture,
    or(t1,and(t5,t6)) = ll1,
    inference(rw,[status(thm)],[c_0_259,c_0_260]) ).

cnf(c_0_281,negated_conjecture,
    and(a,and(b,and(t1,X1))) = ll0,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_191]),c_0_120]),c_0_45]) ).

cnf(c_0_282,negated_conjecture,
    and(t4,and(carry,not(b))) = and(carry,not(b)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_261]),c_0_45]),c_0_36]),c_0_110]) ).

cnf(c_0_283,negated_conjecture,
    and(t1,t4) = t4,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_262]),c_0_207]),c_0_58]),c_0_167]),c_0_45]),c_0_110]),c_0_263]),c_0_146]),c_0_177]),c_0_228]),c_0_207]),c_0_58]),c_0_167]),c_0_36]),c_0_207]),c_0_110]),c_0_264]),c_0_64]),c_0_36]),c_0_86]),c_0_45]),c_0_146]),c_0_265]),c_0_266]),c_0_267]),c_0_38]),c_0_268]) ).

cnf(c_0_284,negated_conjecture,
    or(t6,and(cin,X1)) = t6,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_149]),c_0_37]) ).

cnf(c_0_285,negated_conjecture,
    and(cin,and(carry,not(b))) = and(carry,not(b)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_269]),c_0_45]),c_0_36]),c_0_110]) ).

cnf(c_0_286,negated_conjecture,
    or(t3,and(t5,carry)) = t3,
    inference(spm,[status(thm)],[c_0_270,c_0_271]) ).

cnf(c_0_287,negated_conjecture,
    or(t1,and(t5,t3)) = or(t1,t3),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_240,c_0_112]),c_0_240]),c_0_64]),c_0_36]),c_0_115]),c_0_141]),c_0_51]),c_0_36]) ).

cnf(c_0_288,negated_conjecture,
    or(t5,and(cin,X1)) = or(t5,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_76]),c_0_77]) ).

cnf(c_0_289,negated_conjecture,
    and(cin,or(a,b)) = and(cin,carry_def),
    inference(rw,[status(thm)],[c_0_272,c_0_273]) ).

cnf(c_0_290,plain,
    or(X1,or(X2,X3)) = or(X3,or(X1,X2)),
    inference(spm,[status(thm)],[c_0_38,c_0_60]) ).

cnf(c_0_291,negated_conjecture,
    or(a,or(b,t5)) = ll1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_265,c_0_274]),c_0_155]),c_0_199]) ).

cnf(c_0_292,negated_conjecture,
    and(t5,and(t6,sum)) = and(cin,t5),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_275]),c_0_276]) ).

cnf(c_0_293,plain,
    and(X1,and(or(X1,X2),X3)) = and(X1,X3),
    inference(spm,[status(thm)],[c_0_45,c_0_37]) ).

cnf(c_0_294,plain,
    and(or(X1,X2),and(not(X1),not(X2))) = ll0,
    inference(spm,[status(thm)],[c_0_78,c_0_39]) ).

cnf(c_0_295,negated_conjecture,
    and(cin,and(t5,t7)) = ll0,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_148]),c_0_45]) ).

cnf(c_0_296,negated_conjecture,
    or(t5,and(t7,sum)) = t5,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_277,c_0_278]),c_0_90]) ).

cnf(c_0_297,negated_conjecture,
    or(carry,and(t1,X1)) = or(carry,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_279]),c_0_77]) ).

cnf(c_0_298,negated_conjecture,
    and(t1,not(and(t1,and(t5,t6)))) = t4,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_280]),c_0_68]),c_0_105]),c_0_105]),c_0_178]),c_0_45]),c_0_262]),c_0_191]),c_0_90]),c_0_45]),c_0_281]),c_0_90]),c_0_178]) ).

cnf(c_0_299,negated_conjecture,
    not(carry) = and(t1,t5),
    inference(spm,[status(thm)],[c_0_41,c_0_118]) ).

cnf(c_0_300,negated_conjecture,
    or(t2,and(b,X1)) = t2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_168]),c_0_37]) ).

cnf(c_0_301,negated_conjecture,
    and(b,and(t5,carry)) = and(t5,carry),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_204]),c_0_45]),c_0_36]),c_0_110]) ).

cnf(c_0_302,negated_conjecture,
    and(t1,and(t4,and(t3,carry))) = and(t1,and(t3,carry)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_282,c_0_207]),c_0_64]),c_0_36]),c_0_110]),c_0_110]),c_0_207]),c_0_64]),c_0_36]),c_0_110]) ).

cnf(c_0_303,negated_conjecture,
    and(t1,and(t4,X1)) = and(t4,X1),
    inference(spm,[status(thm)],[c_0_45,c_0_283]) ).

cnf(c_0_304,negated_conjecture,
    or(t6,and(carry,not(b))) = t6,
    inference(spm,[status(thm)],[c_0_284,c_0_285]) ).

cnf(c_0_305,negated_conjecture,
    or(t6,and(t5,X1)) = or(t6,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_257]),c_0_77]) ).

cnf(c_0_306,negated_conjecture,
    and(t5,and(t3,carry)) = and(t5,carry),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_286]),c_0_45]),c_0_36]) ).

cnf(c_0_307,negated_conjecture,
    or(t1,or(t5,t3)) = or(t1,t5),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_287]),c_0_199]),c_0_231]) ).

cnf(c_0_308,negated_conjecture,
    or(t4,and(X1,t2)) = or(t4,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_126]),c_0_68]) ).

cnf(c_0_309,negated_conjecture,
    or(t5,carry_def) = ll1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_288,c_0_289]),c_0_288]),c_0_290]),c_0_38]),c_0_199]),c_0_291]) ).

cnf(c_0_310,plain,
    and(not(X1),and(X1,X2)) = ll0,
    inference(spm,[status(thm)],[c_0_173,c_0_41]) ).

cnf(c_0_311,negated_conjecture,
    or(cin,and(t6,sum)) = cin,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_292]),c_0_40]) ).

cnf(c_0_312,negated_conjecture,
    and(cin,and(t6,X1)) = and(cin,X1),
    inference(spm,[status(thm)],[c_0_293,c_0_149]) ).

cnf(c_0_313,negated_conjecture,
    or(sum,and(t6,X1)) = or(sum,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_236]),c_0_77]) ).

cnf(c_0_314,plain,
    and(not(X1),and(not(X2),or(X1,X2))) = ll0,
    inference(rw,[status(thm)],[c_0_294,c_0_64]) ).

cnf(c_0_315,negated_conjecture,
    and(cin,and(t5,and(t7,X1))) = ll0,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_295]),c_0_120]),c_0_45]) ).

cnf(c_0_316,negated_conjecture,
    and(t5,and(t7,sum)) = and(t7,sum),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_296]),c_0_45]),c_0_36]),c_0_110]) ).

cnf(c_0_317,negated_conjecture,
    not(and(t1,and(t5,t6))) = or(t4,carry),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_297,c_0_298]),c_0_38]),c_0_98]),c_0_299]),c_0_45]),c_0_110]),c_0_141]),c_0_141]) ).

cnf(c_0_318,negated_conjecture,
    or(t2,and(t5,carry)) = t2,
    inference(spm,[status(thm)],[c_0_300,c_0_301]) ).

cnf(c_0_319,negated_conjecture,
    and(not(a),not(and(t5,carry))) = not(a),
    inference(spm,[status(thm)],[c_0_39,c_0_250]) ).

cnf(c_0_320,negated_conjecture,
    and(t4,and(t3,carry)) = and(t1,and(t3,carry)),
    inference(rw,[status(thm)],[c_0_302,c_0_303]) ).

cnf(c_0_321,negated_conjecture,
    or(t6,and(t1,and(t3,carry))) = t6,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_304,c_0_207]),c_0_64]),c_0_36]),c_0_110]) ).

cnf(c_0_322,negated_conjecture,
    or(t6,and(t3,carry)) = or(carry,t6),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_305,c_0_306]),c_0_305]),c_0_38]) ).

cnf(c_0_323,negated_conjecture,
    and(t3,or(t1,t5)) = t3,
    inference(spm,[status(thm)],[c_0_252,c_0_307]) ).

cnf(c_0_324,negated_conjecture,
    and(b,and(t2,X1)) = and(b,X1),
    inference(spm,[status(thm)],[c_0_45,c_0_157]) ).

cnf(c_0_325,negated_conjecture,
    and(b,and(t1,t3)) = ll0,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_93]),c_0_45]) ).

cnf(c_0_326,negated_conjecture,
    or(t4,and(a,b)) = or(a,t4),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_308,c_0_210]),c_0_38]) ).

cnf(c_0_327,negated_conjecture,
    or(carry_def,and(t5,X1)) = or(carry_def,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_309]),c_0_77]) ).

cnf(c_0_328,negated_conjecture,
    and(cin,t7) = and(cin,t4),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_76]),c_0_148]),c_0_68]),c_0_74]),c_0_310]),c_0_90]),c_0_36]),c_0_45]),c_0_56]),c_0_78]),c_0_90]),c_0_74]) ).

cnf(c_0_329,negated_conjecture,
    and(t6,sum) = and(cin,sum),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_311]),c_0_45]),c_0_36]),c_0_110]),c_0_312]) ).

cnf(c_0_330,negated_conjecture,
    or(t7,sum) = ll1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_218,c_0_313]),c_0_38]) ).

cnf(c_0_331,negated_conjecture,
    and(cin,and(t5,and(t6,t7))) = ll0,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_314,c_0_181]),c_0_276]),c_0_42]),c_0_45]) ).

cnf(c_0_332,negated_conjecture,
    and(cin,and(t7,sum)) = ll0,
    inference(spm,[status(thm)],[c_0_315,c_0_316]) ).

cnf(c_0_333,negated_conjecture,
    and(t7,not(and(cin,t7))) = not(cin),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_158]),c_0_276]),c_0_41]),c_0_45]),c_0_36]),c_0_141]),c_0_161]),c_0_148]),c_0_276]),c_0_41]),c_0_36]),c_0_276]),c_0_45]),c_0_56]),c_0_78]),c_0_90]),c_0_45]),c_0_64]),c_0_36]),c_0_295]),c_0_96]),c_0_90]) ).

cnf(c_0_334,negated_conjecture,
    and(t1,or(t4,carry)) = t4,
    inference(rw,[status(thm)],[c_0_298,c_0_317]) ).

cnf(c_0_335,negated_conjecture,
    or(a,or(t4,carry)) = or(t4,carry),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_297,c_0_198]),c_0_297]),c_0_290]),c_0_38]),c_0_199]),c_0_38]) ).

cnf(c_0_336,plain,
    or(and(X1,or(and(X2,not(X3)),and(not(X2),X3))),and(not(X1),or(and(X2,X3),and(not(X2),not(X3))))) = or(and(not(and(X1,X2)),and(or(X1,X2),X3)),and(or(and(X1,X2),and(not(X1),not(X2))),not(X3))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_41]),c_0_109]),c_0_38]),c_0_81]),c_0_110]),c_0_38]) ).

cnf(c_0_337,negated_conjecture,
    and(a,and(t1,not(and(t5,carry)))) = and(a,t1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_318]),c_0_75]),c_0_75]),c_0_45]) ).

cnf(c_0_338,negated_conjecture,
    and(t5,and(carry,not(a))) = ll0,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_319]),c_0_41]),c_0_36]),c_0_78]),c_0_36]),c_0_45]) ).

cnf(c_0_339,negated_conjecture,
    or(carry,t6) = t6,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_320]),c_0_321]),c_0_322]) ).

cnf(c_0_340,negated_conjecture,
    or(t5,carry) = ll1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_258,c_0_297]),c_0_38]) ).

cnf(c_0_341,negated_conjecture,
    or(t1,t5) = ll1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_323]),c_0_170]),c_0_39]),c_0_105]),c_0_74]),c_0_45]),c_0_45]),c_0_37]),c_0_170]),c_0_39]),c_0_105]),c_0_74]),c_0_45]),c_0_170]),c_0_45]),c_0_37]),c_0_44]),c_0_241]) ).

cnf(c_0_342,plain,
    or(and(X1,not(and(X2,X1))),and(not(X1),or(and(X2,X1),and(not(X2),not(X1))))) = not(X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_122]),c_0_41]),c_0_41]),c_0_122]),c_0_78]),c_0_96]),c_0_41]),c_0_122]),c_0_41]),c_0_41]),c_0_81]),c_0_36]),c_0_44]),c_0_36]),c_0_36]),c_0_161]),c_0_78]),c_0_97]),c_0_68]),c_0_144]) ).

cnf(c_0_343,negated_conjecture,
    and(cin,and(t5,t4)) = ll0,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_51]),c_0_45]),c_0_36]) ).

cnf(c_0_344,negated_conjecture,
    and(b,and(t5,t6)) = and(b,t3),
    inference(spm,[status(thm)],[c_0_324,c_0_167]) ).

cnf(c_0_345,negated_conjecture,
    and(b,t3) = and(a,b),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_174]),c_0_93]),c_0_68]),c_0_207]),c_0_207]),c_0_105]),c_0_45]),c_0_146]),c_0_265]),c_0_50]),c_0_36]),c_0_45]),c_0_64]),c_0_325]),c_0_96]),c_0_90]),c_0_105]) ).

cnf(c_0_346,negated_conjecture,
    or(t4,and(a,b)) = or(a,b),
    inference(rw,[status(thm)],[c_0_326,c_0_248]) ).

cnf(c_0_347,negated_conjecture,
    or(carry_def,and(cin,t4)) = carry_def,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_327,c_0_78]),c_0_90]),c_0_74]) ).

cnf(c_0_348,negated_conjecture,
    and(cin,not(and(cin,sum))) = and(cin,t4),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_312,c_0_255]),c_0_312]),c_0_328]),c_0_329]) ).

cnf(c_0_349,negated_conjecture,
    and(cin,and(t5,sum)) = and(cin,t5),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_292,c_0_329]),c_0_110]) ).

cnf(c_0_350,negated_conjecture,
    and(sum,and(t5,and(t4,and(t5,sum)))) = and(sum,and(t5,t4)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_57]),c_0_45]),c_0_45]),c_0_141]),c_0_45]),c_0_45]),c_0_122]) ).

cnf(c_0_351,negated_conjecture,
    or(cin,and(t7,X1)) = or(cin,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_202]),c_0_77]) ).

cnf(c_0_352,negated_conjecture,
    and(t7,not(and(t7,sum))) = and(t6,t7),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_330]),c_0_68]),c_0_276]),c_0_276]),c_0_237]),c_0_45]),c_0_331]),c_0_90]),c_0_45]),c_0_316]),c_0_332]),c_0_90]),c_0_237]) ).

cnf(c_0_353,negated_conjecture,
    or(cin,and(X1,t7)) = or(cin,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_202]),c_0_68]) ).

cnf(c_0_354,negated_conjecture,
    not(cin) = and(t5,t7),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_333,c_0_328]),c_0_51]),c_0_36]) ).

cnf(c_0_355,negated_conjecture,
    or(t4,carry) = or(a,b),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_334]),c_0_248]),c_0_335]) ).

cnf(c_0_356,plain,
    or(and(X1,not(and(X1,X2))),and(not(X1),or(and(X1,X2),and(not(X1),not(X2))))) = not(X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_122]),c_0_41]),c_0_122]),c_0_41]),c_0_41]),c_0_122]),c_0_59]),c_0_68]),c_0_41]),c_0_36]),c_0_110]),c_0_109]),c_0_36]),c_0_38]),c_0_336]),c_0_36]),c_0_37]),c_0_36]),c_0_36]),c_0_36]),c_0_78]),c_0_96]),c_0_144]) ).

cnf(c_0_357,negated_conjecture,
    and(t1,not(and(t5,carry))) = t1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_337]),c_0_160]),c_0_161]),c_0_45]),c_0_338]),c_0_97]),c_0_68]) ).

cnf(c_0_358,negated_conjecture,
    or(t1,and(X1,carry)) = or(t1,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_279]),c_0_68]) ).

cnf(c_0_359,negated_conjecture,
    and(carry,t6) = carry,
    inference(spm,[status(thm)],[c_0_37,c_0_339]) ).

cnf(c_0_360,negated_conjecture,
    and(t1,and(X1,t4)) = and(X1,t4),
    inference(spm,[status(thm)],[c_0_110,c_0_283]) ).

cnf(c_0_361,negated_conjecture,
    or(carry,and(t5,X1)) = or(carry,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_340]),c_0_77]) ).

cnf(c_0_362,negated_conjecture,
    or(t1,t6) = ll1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_283]),c_0_38]),c_0_117]),c_0_38]) ).

cnf(c_0_363,negated_conjecture,
    and(a,and(b,and(cin,t4))) = ll0,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_341]),c_0_95]),c_0_105]),c_0_74]),c_0_45]) ).

cnf(c_0_364,negated_conjecture,
    and(t5,and(t6,or(a,b))) = and(a,b),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_342,c_0_283]),c_0_58]),c_0_167]),c_0_64]),c_0_36]),c_0_115]),c_0_64]),c_0_36]),c_0_343]),c_0_58]),c_0_167]),c_0_105]),c_0_58]),c_0_167]),c_0_45]),c_0_344]),c_0_345]),c_0_141]),c_0_346]),c_0_45]),c_0_144]),c_0_105]) ).

cnf(c_0_365,negated_conjecture,
    or(carry,and(a,b)) = carry,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_297,c_0_78]),c_0_90]),c_0_105]) ).

cnf(c_0_366,negated_conjecture,
    or(t7,and(t4,X1)) = t7,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_256]),c_0_37]) ).

cnf(c_0_367,negated_conjecture,
    or(carry_def,and(t3,carry)) = or(carry,carry_def),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_327,c_0_306]),c_0_327]),c_0_38]) ).

cnf(c_0_368,negated_conjecture,
    and(t5,not(carry_def)) = not(carry_def),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_347]),c_0_51]),c_0_36]) ).

cnf(c_0_369,negated_conjecture,
    not(and(cin,sum)) = t7,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_348]),c_0_161]),c_0_51]),c_0_45]),c_0_36]),c_0_349]),c_0_148]) ).

cnf(c_0_370,negated_conjecture,
    and(t6,and(t7,not(and(sum,and(t5,t4))))) = and(t6,t7),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_350]),c_0_237]),c_0_45]),c_0_237]) ).

cnf(c_0_371,negated_conjecture,
    not(and(t7,sum)) = t6,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_351,c_0_352]),c_0_353]),c_0_149]),c_0_98]),c_0_354]),c_0_45]),c_0_141]),c_0_316]) ).

cnf(c_0_372,negated_conjecture,
    or(and(t1,or(and(X1,X2),and(not(X1),not(X2)))),and(a,and(b,or(and(X1,not(X2)),and(not(X1),X2))))) = or(and(not(and(a,and(b,X1))),and(not(and(t1,not(X1))),X2)),and(or(and(a,and(b,X1)),and(t1,not(X1))),not(X2))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_105]),c_0_45]),c_0_45]),c_0_45]),c_0_109]),c_0_110]),c_0_38]) ).

cnf(c_0_373,negated_conjecture,
    and(carry,or(a,b)) = carry,
    inference(spm,[status(thm)],[c_0_44,c_0_355]) ).

cnf(c_0_374,negated_conjecture,
    and(t5,carry) = and(a,b),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_356,c_0_357]),c_0_105]),c_0_64]),c_0_191]),c_0_105]),c_0_105]),c_0_41]),c_0_45]),c_0_301]),c_0_271]),c_0_358]),c_0_341]),c_0_68]),c_0_144]),c_0_41]) ).

cnf(c_0_375,negated_conjecture,
    and(t1,and(t5,or(a,b))) = and(t5,t4),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_356,c_0_359]),c_0_299]),c_0_64]),c_0_187]),c_0_299]),c_0_299]),c_0_48]),c_0_45]),c_0_141]),c_0_360]),c_0_361]),c_0_38]),c_0_355]),c_0_45]),c_0_144]),c_0_48]) ).

cnf(c_0_376,negated_conjecture,
    and(a,and(b,and(t5,t4))) = ll0,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_362]),c_0_95]),c_0_105]),c_0_48]),c_0_45]) ).

cnf(c_0_377,negated_conjecture,
    and(t1,carry) = and(cin,t4),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_356,c_0_118]),c_0_105]),c_0_105]),c_0_74]),c_0_45]),c_0_363]),c_0_90]),c_0_45]),c_0_281]),c_0_90]),c_0_74]) ).

cnf(c_0_378,negated_conjecture,
    or(X1,and(t1,t5)) = not(and(carry,not(X1))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_118]),c_0_36]) ).

cnf(c_0_379,negated_conjecture,
    or(and(cin,t4),X1) = not(and(t5,not(X1))),
    inference(spm,[status(thm)],[c_0_81,c_0_51]) ).

cnf(c_0_380,negated_conjecture,
    or(carry,and(t6,or(a,b))) = carry,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_361,c_0_364]),c_0_365]) ).

cnf(c_0_381,negated_conjecture,
    and(carry,and(t6,X1)) = and(carry,X1),
    inference(spm,[status(thm)],[c_0_293,c_0_339]) ).

cnf(c_0_382,negated_conjecture,
    or(t7,and(X1,t4)) = t7,
    inference(spm,[status(thm)],[c_0_366,c_0_36]) ).

cnf(c_0_383,negated_conjecture,
    or(t7,and(a,t1)) = t7,
    inference(spm,[status(thm)],[c_0_366,c_0_195]) ).

cnf(c_0_384,negated_conjecture,
    and(not(carry_def),not(and(t3,carry))) = and(t1,not(carry_def)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_367]),c_0_39]),c_0_299]),c_0_45]),c_0_368]) ).

cnf(c_0_385,negated_conjecture,
    and(cin,sum) = and(cin,t5),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_369]),c_0_276]) ).

cnf(c_0_386,negated_conjecture,
    or(and(t5,t4),and(t6,sum)) = sum,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_370]),c_0_47]),c_0_64]),c_0_53]),c_0_42]),c_0_36]),c_0_40]),c_0_36]),c_0_141]),c_0_48]),c_0_48]),c_0_64]),c_0_53]),c_0_42]),c_0_36]),c_0_47]),c_0_45]),c_0_53]),c_0_44]),c_0_64]),c_0_53]),c_0_42]),c_0_36]),c_0_47]),c_0_38]) ).

cnf(c_0_387,negated_conjecture,
    and(t7,sum) = and(t5,t4),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_371]),c_0_48]) ).

cnf(c_0_388,negated_conjecture,
    and(cin,and(t5,t6)) = and(cin,t5),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_181]),c_0_276]),c_0_276]),c_0_42]),c_0_45]) ).

cnf(c_0_389,negated_conjecture,
    not(and(t5,or(a,b))) = and(t1,t6),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_372,c_0_373]),c_0_299]),c_0_39]),c_0_227]),c_0_207]),c_0_45]),c_0_64]),c_0_36]),c_0_167]),c_0_141]),c_0_45]),c_0_110]),c_0_141]),c_0_141]),c_0_297]),c_0_361]),c_0_339]),c_0_39]),c_0_227]),c_0_207]),c_0_45]),c_0_64]),c_0_36]),c_0_167]),c_0_141]),c_0_110]),c_0_110]),c_0_359]),c_0_374]),c_0_64]),c_0_191]),c_0_299]),c_0_45]),c_0_375]),c_0_144]),c_0_376]),c_0_90]),c_0_137]),c_0_87]),c_0_299]),c_0_141]),c_0_118]),c_0_373]),c_0_377]),c_0_137]),c_0_299]),c_0_141]),c_0_378]),c_0_87]),c_0_36]),c_0_377]),c_0_51]),c_0_39]),c_0_227]),c_0_207]),c_0_45]),c_0_64]),c_0_36]),c_0_167]),c_0_141]),c_0_110]),c_0_141]),c_0_379]),c_0_317]),c_0_355]) ).

cnf(c_0_390,negated_conjecture,
    xor(xor(a,b),cin) = sum_def,
    sum_def ).

cnf(c_0_391,negated_conjecture,
    not(and(t6,or(a,b))) = and(t1,t5),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_380]),c_0_381]),c_0_373]),c_0_299]),c_0_45]),c_0_374]),c_0_64]),c_0_191]),c_0_96]),c_0_299]),c_0_381]),c_0_373]),c_0_299]),c_0_45]),c_0_297]),c_0_361]),c_0_98]),c_0_299]),c_0_45]),c_0_364]),c_0_64]),c_0_191]),c_0_97]),c_0_68]),c_0_144]) ).

cnf(c_0_392,negated_conjecture,
    or(a,and(X1,t1)) = or(a,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_196]),c_0_68]) ).

cnf(c_0_393,negated_conjecture,
    or(a,or(b,carry)) = or(t4,carry),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_297,c_0_268]),c_0_297]),c_0_38]),c_0_290]),c_0_38]),c_0_199]) ).

cnf(c_0_394,negated_conjecture,
    or(t7,and(b,t1)) = t7,
    inference(spm,[status(thm)],[c_0_382,c_0_262]) ).

cnf(c_0_395,negated_conjecture,
    and(a,and(t1,t7)) = and(a,t1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_383]),c_0_45]) ).

cnf(c_0_396,negated_conjecture,
    not(and(t1,not(carry_def))) = or(carry,carry_def),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_384]),c_0_367]) ).

cnf(c_0_397,negated_conjecture,
    or(t6,and(t1,X1)) = or(t6,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_362]),c_0_77]) ).

cnf(c_0_398,negated_conjecture,
    and(t1,not(and(t1,carry))) = and(t1,t5),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_279]),c_0_68]),c_0_105]),c_0_105]),c_0_299]),c_0_45]),c_0_281]),c_0_90]),c_0_45]),c_0_281]),c_0_90]),c_0_299]) ).

cnf(c_0_399,negated_conjecture,
    or(t6,and(X1,t5)) = or(t6,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_257]),c_0_68]) ).

cnf(c_0_400,negated_conjecture,
    or(carry,and(cin,t4)) = carry,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_361,c_0_78]),c_0_90]),c_0_74]) ).

cnf(c_0_401,negated_conjecture,
    and(t6,sum) = and(cin,t5),
    inference(rw,[status(thm)],[c_0_329,c_0_385]) ).

cnf(c_0_402,negated_conjecture,
    or(and(cin,sum),and(t5,t4)) = sum,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_386,c_0_329]),c_0_38]) ).

cnf(c_0_403,negated_conjecture,
    and(t5,or(cin,t4)) = and(t5,sum),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_349]),c_0_354]),c_0_45]),c_0_146]),c_0_351]),c_0_98]),c_0_354]),c_0_45]),c_0_110]),c_0_387]),c_0_141]),c_0_141]),c_0_42]),c_0_388]),c_0_354]),c_0_354]),c_0_45]),c_0_110]),c_0_387]),c_0_141]),c_0_141]),c_0_45]),c_0_146]),c_0_351]),c_0_266]),c_0_88]) ).

cnf(c_0_404,negated_conjecture,
    and(t5,or(a,b)) = not(and(t1,t6)),
    inference(spm,[status(thm)],[c_0_41,c_0_389]) ).

cnf(c_0_405,negated_conjecture,
    or(and(not(or(and(not(a),b),and(a,not(b)))),cin),and(or(and(not(a),b),and(a,not(b))),not(cin))) = sum_def,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_390,c_0_70]),c_0_70]) ).

cnf(c_0_406,negated_conjecture,
    and(t6,or(a,b)) = carry,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_391]),c_0_118]) ).

cnf(c_0_407,negated_conjecture,
    or(t2,and(t4,X1)) = or(t2,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_126]),c_0_77]) ).

cnf(c_0_408,negated_conjecture,
    and(t1,and(t2,or(a,b))) = and(b,t1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_356,c_0_247]),c_0_78]),c_0_227]),c_0_227]),c_0_170]),c_0_45]),c_0_64]),c_0_36]),c_0_157]),c_0_36]),c_0_52]),c_0_36]),c_0_392]),c_0_45]),c_0_144]),c_0_170]) ).

cnf(c_0_409,negated_conjecture,
    or(carry,and(X1,t1)) = or(carry,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_279]),c_0_68]) ).

cnf(c_0_410,negated_conjecture,
    or(a,or(b,carry)) = or(a,b),
    inference(rw,[status(thm)],[c_0_393,c_0_355]) ).

cnf(c_0_411,negated_conjecture,
    and(b,and(t1,t7)) = and(b,t1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_394]),c_0_45]) ).

cnf(c_0_412,negated_conjecture,
    and(t1,or(a,t7)) = and(t1,t7),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_395]),c_0_160]),c_0_38]) ).

cnf(c_0_413,plain,
    and(X1,and(X2,and(X1,or(X2,X3)))) = and(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_131]),c_0_45]) ).

cnf(c_0_414,negated_conjecture,
    and(t1,or(carry,carry_def)) = and(t1,carry_def),
    inference(spm,[status(thm)],[c_0_194,c_0_396]) ).

cnf(c_0_415,negated_conjecture,
    not(and(t5,and(t4,carry))) = ll1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_397,c_0_398]),c_0_399]),c_0_38]),c_0_362]),c_0_98]),c_0_48]),c_0_45]),c_0_110]),c_0_303]) ).

cnf(c_0_416,negated_conjecture,
    or(t5,and(X1,carry)) = or(X1,t5),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_340]),c_0_68]) ).

cnf(c_0_417,negated_conjecture,
    and(cin,and(t4,carry)) = and(cin,t4),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_400]),c_0_45]) ).

cnf(c_0_418,negated_conjecture,
    or(t7,and(X1,t5)) = or(t7,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_220]),c_0_68]) ).

cnf(c_0_419,negated_conjecture,
    and(a,and(b,cin)) = and(carry,sum),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_381,c_0_401]),c_0_64]),c_0_36]),c_0_110]),c_0_374]),c_0_64]),c_0_36]),c_0_110]) ).

cnf(c_0_420,negated_conjecture,
    and(t5,sum) = sum,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_402,c_0_385]),c_0_146]),c_0_403]) ).

cnf(c_0_421,negated_conjecture,
    and(t1,not(and(t1,t6))) = and(t5,t4),
    inference(rw,[status(thm)],[c_0_375,c_0_404]) ).

cnf(c_0_422,negated_conjecture,
    or(cin,and(t4,sum)) = or(cin,t4),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_53]),c_0_88]) ).

cnf(c_0_423,negated_conjecture,
    or(and(not(cin),or(and(a,not(b)),and(b,not(a)))),and(not(and(a,not(b))),and(cin,not(and(b,not(a)))))) = sum_def,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_405,c_0_38]),c_0_38]),c_0_38]),c_0_39]),c_0_36]),c_0_36]),c_0_36]),c_0_45]),c_0_36]) ).

cnf(c_0_424,negated_conjecture,
    and(cin,carry_def) = and(cin,carry),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_312,c_0_406]),c_0_289]) ).

cnf(c_0_425,negated_conjecture,
    or(t2,t7) = ll1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_407,c_0_239]),c_0_38]),c_0_126]) ).

cnf(c_0_426,negated_conjecture,
    or(carry,and(t2,or(a,b))) = or(b,carry),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_297,c_0_408]),c_0_409]),c_0_38]) ).

cnf(c_0_427,negated_conjecture,
    or(b,and(a,carry)) = or(b,carry),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_410]),c_0_116]),c_0_36]) ).

cnf(c_0_428,negated_conjecture,
    and(t1,or(b,t7)) = and(t1,t7),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_411]),c_0_160]),c_0_38]) ).

cnf(c_0_429,negated_conjecture,
    or(a,or(b,t7)) = or(b,t7),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_186,c_0_412]),c_0_186]),c_0_199]) ).

cnf(c_0_430,negated_conjecture,
    and(t1,and(carry,carry_def)) = and(t1,carry),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_413,c_0_414]),c_0_110]),c_0_141]) ).

cnf(c_0_431,negated_conjecture,
    or(t3,and(t4,X1)) = or(t3,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_111]),c_0_77]) ).

cnf(c_0_432,negated_conjecture,
    not(and(t4,carry)) = t5,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_415]),c_0_416]),c_0_38]),c_0_129]),c_0_122]),c_0_68]),c_0_74]),c_0_74]),c_0_45]),c_0_45]),c_0_288]),c_0_183]),c_0_266]),c_0_288]),c_0_183]),c_0_98]),c_0_74]),c_0_45]),c_0_141]),c_0_417]),c_0_51]) ).

cnf(c_0_433,plain,
    or(X1,or(X2,X1)) = or(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_37]),c_0_60]) ).

cnf(c_0_434,negated_conjecture,
    or(t1,t7) = not(and(carry,sum)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_418,c_0_378]),c_0_276]),c_0_64]),c_0_36]),c_0_110]),c_0_374]),c_0_64]),c_0_36]),c_0_110]),c_0_419]),c_0_38]) ).

cnf(c_0_435,negated_conjecture,
    and(t5,and(X1,sum)) = and(X1,sum),
    inference(spm,[status(thm)],[c_0_110,c_0_420]) ).

cnf(c_0_436,negated_conjecture,
    and(t6,not(and(t1,t6))) = and(a,b),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_342,c_0_421]),c_0_42]),c_0_41]),c_0_105]),c_0_41]),c_0_45]),c_0_281]),c_0_90]),c_0_45]),c_0_64]),c_0_115]),c_0_64]),c_0_36]),c_0_343]),c_0_96]),c_0_90]),c_0_105]),c_0_36]) ).

cnf(c_0_437,negated_conjecture,
    and(cin,t6) = cin,
    inference(spm,[status(thm)],[c_0_37,c_0_149]) ).

cnf(c_0_438,negated_conjecture,
    and(not(cin),not(and(t4,sum))) = and(t2,and(t3,not(cin))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_422]),c_0_39]),c_0_58]),c_0_36]),c_0_45]) ).

cnf(c_0_439,negated_conjecture,
    and(not(cin),and(sum_def,or(and(a,not(b)),and(b,not(a))))) = and(not(cin),or(and(a,not(b)),and(b,not(a)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_423]),c_0_45]),c_0_36]) ).

cnf(c_0_440,negated_conjecture,
    or(t3,and(t5,t6)) = t3,
    inference(spm,[status(thm)],[c_0_50,c_0_167]) ).

cnf(c_0_441,negated_conjecture,
    and(a,t4) = and(a,t1),
    inference(rw,[status(thm)],[c_0_86,c_0_283]) ).

cnf(c_0_442,negated_conjecture,
    or(carry_def,and(cin,carry)) = carry_def,
    inference(spm,[status(thm)],[c_0_50,c_0_424]) ).

cnf(c_0_443,negated_conjecture,
    or(t7,and(t2,X1)) = or(t7,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_425]),c_0_77]) ).

cnf(c_0_444,negated_conjecture,
    and(t2,or(b,carry)) = and(t2,or(a,b)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_426]),c_0_45]),c_0_153]),c_0_427]) ).

cnf(c_0_445,negated_conjecture,
    or(b,t7) = or(a,t7),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_428]),c_0_214]),c_0_429]) ).

cnf(c_0_446,negated_conjecture,
    or(a,or(carry,t7)) = or(carry,t7),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_297,c_0_412]),c_0_297]),c_0_199]) ).

cnf(c_0_447,negated_conjecture,
    and(t1,and(carry,carry_def)) = and(cin,t4),
    inference(rw,[status(thm)],[c_0_430,c_0_377]) ).

cnf(c_0_448,negated_conjecture,
    or(t3,t7) = ll1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_431,c_0_239]),c_0_38]),c_0_111]) ).

cnf(c_0_449,plain,
    or(X1,and(not(X2),not(X3))) = not(and(not(X1),or(X2,X3))),
    inference(spm,[status(thm)],[c_0_81,c_0_81]) ).

cnf(c_0_450,negated_conjecture,
    and(t5,and(t7,not(and(cin,carry)))) = and(t5,t7),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_424]),c_0_354]),c_0_45]),c_0_354]) ).

cnf(c_0_451,negated_conjecture,
    and(t4,carry) = and(cin,t4),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_432]),c_0_74]) ).

cnf(c_0_452,negated_conjecture,
    not(and(cin,and(carry,sum))) = not(and(carry,sum)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_433,c_0_434]),c_0_98]),c_0_276]),c_0_45]),c_0_435]),c_0_38]),c_0_434]) ).

cnf(c_0_453,negated_conjecture,
    and(cin,not(and(t1,t6))) = and(carry,sum),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_312,c_0_436]),c_0_64]),c_0_36]),c_0_110]),c_0_419]) ).

cnf(c_0_454,negated_conjecture,
    and(cin,and(X1,t6)) = and(X1,cin),
    inference(spm,[status(thm)],[c_0_110,c_0_437]) ).

cnf(c_0_455,negated_conjecture,
    not(and(t2,and(t3,not(cin)))) = or(cin,t4),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_438]),c_0_422]) ).

cnf(c_0_456,negated_conjecture,
    and(sum_def,and(not(cin),or(and(a,not(b)),and(b,not(a))))) = and(not(cin),or(and(a,not(b)),and(b,not(a)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_439,c_0_64]),c_0_36]) ).

cnf(c_0_457,negated_conjecture,
    and(b,and(X1,t2)) = and(X1,b),
    inference(spm,[status(thm)],[c_0_110,c_0_157]) ).

cnf(c_0_458,negated_conjecture,
    or(and(a,t1),and(b,t1)) = t4,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_440]),c_0_110]),c_0_263]),c_0_178]),c_0_264]),c_0_441]),c_0_64]),c_0_36]),c_0_247]),c_0_36]),c_0_170]),c_0_110]),c_0_263]),c_0_170]),c_0_178]),c_0_45]),c_0_283]),c_0_262]),c_0_44]),c_0_178]) ).

cnf(c_0_459,negated_conjecture,
    or(t6,and(t4,t7)) = ll1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_305,c_0_200]),c_0_135]),c_0_38]),c_0_257]) ).

cnf(c_0_460,negated_conjecture,
    or(t7,and(cin,X1)) = or(t7,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_202]),c_0_77]) ).

cnf(c_0_461,negated_conjecture,
    and(cin,and(carry,carry_def)) = and(cin,carry),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_442]),c_0_45]) ).

cnf(c_0_462,negated_conjecture,
    or(carry,t7) = or(a,t7),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_443,c_0_444]),c_0_443]),c_0_290]),c_0_38]),c_0_199]),c_0_445]),c_0_231]),c_0_290]),c_0_38]),c_0_445]),c_0_199]),c_0_446]) ).

cnf(c_0_463,negated_conjecture,
    or(and(cin,t4),and(carry,carry_def)) = and(carry,carry_def),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_447]),c_0_38]) ).

cnf(c_0_464,negated_conjecture,
    or(t7,and(X1,t3)) = or(t7,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_448]),c_0_68]) ).

cnf(c_0_465,plain,
    and(not(and(X1,not(X2))),not(and(not(X1),X2))) = not(and(not(and(X1,X2)),or(X1,X2))),
    inference(rw,[status(thm)],[c_0_109,c_0_449]) ).

cnf(c_0_466,negated_conjecture,
    and(t7,not(and(cin,carry))) = and(t5,t7),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_450]),c_0_160]),c_0_161]),c_0_74]),c_0_45]),c_0_64]),c_0_36]),c_0_110]),c_0_451]),c_0_141]),c_0_141]),c_0_51]),c_0_36]) ).

cnf(c_0_467,negated_conjecture,
    not(and(t5,t7)) = cin,
    inference(spm,[status(thm)],[c_0_41,c_0_354]) ).

cnf(c_0_468,negated_conjecture,
    and(cin,and(carry,sum)) = and(carry,sum),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_452]),c_0_41]) ).

cnf(c_0_469,negated_conjecture,
    and(cin,not(and(carry,sum))) = and(cin,t1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_453]),c_0_454]),c_0_36]) ).

cnf(c_0_470,negated_conjecture,
    and(not(cin),or(cin,t4)) = and(t4,and(sum,not(cin))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_438]),c_0_455]),c_0_36]),c_0_45]) ).

cnf(c_0_471,negated_conjecture,
    and(t5,and(t4,and(t7,sum_def))) = and(t5,t4),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_456,c_0_354]),c_0_207]),c_0_224]),c_0_227]),c_0_457]),c_0_36]),c_0_45]),c_0_110]),c_0_110]),c_0_354]),c_0_207]),c_0_224]),c_0_227]),c_0_457]),c_0_36]),c_0_45]),c_0_458]),c_0_36]),c_0_110]),c_0_458]),c_0_36]),c_0_239]) ).

cnf(c_0_472,negated_conjecture,
    or(t6,t7) = ll1,
    inference(rw,[status(thm)],[c_0_459,c_0_164]) ).

cnf(c_0_473,negated_conjecture,
    or(t7,and(carry,carry_def)) = or(a,t7),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_460,c_0_461]),c_0_460]),c_0_38]),c_0_462]) ).

cnf(c_0_474,negated_conjecture,
    and(cin,and(t5,t2)) = and(cin,t5),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_383]),c_0_276]),c_0_276]),c_0_65]),c_0_45]) ).

cnf(c_0_475,negated_conjecture,
    and(t5,not(and(carry,carry_def))) = not(and(carry,carry_def)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_463]),c_0_51]) ).

cnf(c_0_476,negated_conjecture,
    or(t7,and(a,b)) = or(a,t7),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_464,c_0_345]),c_0_38]),c_0_445]) ).

cnf(c_0_477,negated_conjecture,
    or(X1,and(a,b)) = not(and(t1,not(X1))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_87]),c_0_36]) ).

cnf(c_0_478,negated_conjecture,
    not(and(t5,or(a,t7))) = and(cin,t1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_465,c_0_466]),c_0_467]),c_0_276]),c_0_45]),c_0_110]),c_0_374]),c_0_64]),c_0_36]),c_0_110]),c_0_419]),c_0_468]),c_0_469]),c_0_64]),c_0_36]),c_0_328]),c_0_64]),c_0_36]),c_0_110]),c_0_451]),c_0_141]),c_0_51]),c_0_460]),c_0_38]),c_0_462]) ).

cnf(c_0_479,negated_conjecture,
    and(t1,and(t5,and(carry,X1))) = ll0,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_187]),c_0_120]),c_0_45]) ).

cnf(c_0_480,negated_conjecture,
    and(t4,and(sum,not(cin))) = and(t5,t4),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_343]),c_0_42]),c_0_36]),c_0_144]),c_0_182]),c_0_42]),c_0_437]),c_0_36]),c_0_45]),c_0_172]),c_0_141]),c_0_88]),c_0_470]),c_0_144]) ).

cnf(c_0_481,negated_conjecture,
    or(t6,and(t7,sum_def)) = ll1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_305,c_0_471]),c_0_135]),c_0_38]),c_0_257]),c_0_164]) ).

cnf(c_0_482,negated_conjecture,
    or(t6,and(t7,X1)) = or(t6,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_472]),c_0_77]) ).

cnf(c_0_483,plain,
    or(and(not(X1),not(X2)),X3) = not(and(or(X1,X2),not(X3))),
    inference(spm,[status(thm)],[c_0_81,c_0_81]) ).

cnf(c_0_484,negated_conjecture,
    and(cin,not(and(carry,carry_def))) = and(cin,and(t1,t5)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_473]),c_0_39]),c_0_227]),c_0_276]),c_0_45]),c_0_64]),c_0_36]),c_0_110]),c_0_474]),c_0_110]),c_0_276]),c_0_45]),c_0_475]) ).

cnf(c_0_485,negated_conjecture,
    not(and(cin,and(t1,t5))) = or(a,t7),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_476,c_0_477]),c_0_276]),c_0_110]) ).

cnf(c_0_486,negated_conjecture,
    and(t5,or(a,t7)) = not(and(cin,t1)),
    inference(spm,[status(thm)],[c_0_41,c_0_478]) ).

cnf(c_0_487,negated_conjecture,
    or(t3,and(t1,X1)) = or(t3,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_260]),c_0_77]) ).

cnf(c_0_488,negated_conjecture,
    and(t1,and(carry,sum)) = ll0,
    inference(spm,[status(thm)],[c_0_479,c_0_435]) ).

cnf(c_0_489,negated_conjecture,
    or(t2,and(t1,X1)) = or(t2,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_221]),c_0_77]) ).

cnf(c_0_490,plain,
    and(X1,not(and(not(X2),X1))) = and(X1,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_78]),c_0_90]),c_0_98]) ).

cnf(c_0_491,negated_conjecture,
    and(not(cin),or(cin,t4)) = and(t5,t4),
    inference(rw,[status(thm)],[c_0_470,c_0_480]) ).

cnf(c_0_492,negated_conjecture,
    or(t1,and(X1,t2)) = or(t1,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_221]),c_0_68]) ).

cnf(c_0_493,negated_conjecture,
    and(t4,or(t5,sum)) = and(t4,sum),
    inference(rw,[status(thm)],[c_0_92,c_0_146]) ).

cnf(c_0_494,negated_conjecture,
    or(t5,sum) = t5,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_288,c_0_385]),c_0_50]) ).

cnf(c_0_495,negated_conjecture,
    or(t6,sum_def) = ll1,
    inference(rw,[status(thm)],[c_0_481,c_0_482]) ).

cnf(c_0_496,plain,
    not(and(not(and(X1,and(not(and(X1,and(X2,X3))),or(and(X1,X2),X3)))),or(X1,and(not(and(X1,and(X2,X3))),or(and(X1,X2),X3))))) = not(and(not(and(X1,and(not(and(X1,X2)),X3))),or(and(X1,not(and(X1,X2))),X3))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_46]),c_0_81]),c_0_41]),c_0_45]),c_0_41]),c_0_45]),c_0_41]),c_0_41]),c_0_41]),c_0_36]),c_0_483]),c_0_36]),c_0_449]),c_0_141]),c_0_110]),c_0_141]),c_0_98]),c_0_36]),c_0_449]) ).

cnf(c_0_497,negated_conjecture,
    or(t5,and(X1,t1)) = or(t5,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_341]),c_0_68]) ).

cnf(c_0_498,negated_conjecture,
    and(cin,or(a,t7)) = and(cin,carry),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_484]),c_0_485]),c_0_461]) ).

cnf(c_0_499,negated_conjecture,
    or(cin,or(X1,t7)) = ll1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_202]),c_0_62]) ).

cnf(c_0_500,negated_conjecture,
    and(t5,not(and(cin,t1))) = not(and(cin,t1)),
    inference(spm,[status(thm)],[c_0_141,c_0_486]) ).

cnf(c_0_501,negated_conjecture,
    and(cin,not(and(cin,t1))) = and(carry,sum),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_469]),c_0_468]) ).

cnf(c_0_502,negated_conjecture,
    or(t5,and(X1,sum)) = t5,
    inference(spm,[status(thm)],[c_0_55,c_0_420]) ).

cnf(c_0_503,negated_conjecture,
    or(t3,and(carry,sum)) = t3,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_487,c_0_488]),c_0_90]) ).

cnf(c_0_504,negated_conjecture,
    or(t2,and(carry,sum)) = t2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_489,c_0_488]),c_0_90]) ).

cnf(c_0_505,negated_conjecture,
    and(t6,or(cin,t4)) = cin,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_490,c_0_491]),c_0_42]),c_0_36]),c_0_36]),c_0_37]) ).

cnf(c_0_506,negated_conjecture,
    or(t1,and(b,t4)) = or(t1,t4),
    inference(spm,[status(thm)],[c_0_492,c_0_213]) ).

cnf(c_0_507,plain,
    or(and(X1,or(and(X1,not(X2)),and(not(X1),X2))),and(not(X1),or(and(X1,X2),and(not(X1),not(X2))))) = not(X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_122]),c_0_41]),c_0_41]),c_0_41]),c_0_122]),c_0_41]),c_0_122]),c_0_109]),c_0_38]),c_0_173]),c_0_38]),c_0_98]),c_0_36]),c_0_78]),c_0_97]),c_0_77]),c_0_98]),c_0_97]),c_0_77]) ).

cnf(c_0_508,negated_conjecture,
    and(not(and(not(cin),or(and(a,not(b)),and(b,not(a))))),not(and(not(and(a,not(b))),and(cin,not(and(b,not(a))))))) = not(sum_def),
    inference(spm,[status(thm)],[c_0_39,c_0_423]) ).

cnf(c_0_509,negated_conjecture,
    and(t4,sum) = and(t5,t4),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_493,c_0_494]),c_0_36]) ).

cnf(c_0_510,negated_conjecture,
    and(t5,and(t4,not(sum_def))) = ll0,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_495]),c_0_95]),c_0_48]),c_0_45]) ).

cnf(c_0_511,negated_conjecture,
    not(and(t5,not(and(carry,sum)))) = and(cin,carry),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_496,c_0_485]),c_0_38]),c_0_497]),c_0_38]),c_0_76]),c_0_68]),c_0_498]),c_0_38]),c_0_497]),c_0_38]),c_0_76]),c_0_68]),c_0_499]),c_0_68]),c_0_41]),c_0_36]),c_0_500]),c_0_501]),c_0_501]),c_0_38]),c_0_502]),c_0_36]) ).

cnf(c_0_512,negated_conjecture,
    and(t4,or(t7,X1)) = t4,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_239]),c_0_40]) ).

cnf(c_0_513,negated_conjecture,
    and(t4,and(t2,and(t3,X1))) = ll0,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_138,c_0_64]),c_0_45]),c_0_64]) ).

cnf(c_0_514,negated_conjecture,
    and(t3,and(carry,sum)) = and(carry,sum),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_503]),c_0_45]),c_0_36]),c_0_110]) ).

cnf(c_0_515,negated_conjecture,
    and(t2,and(carry,sum)) = and(carry,sum),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_504]),c_0_45]),c_0_36]),c_0_110]) ).

cnf(c_0_516,negated_conjecture,
    and(carry,or(cin,t4)) = and(cin,carry),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_381,c_0_505]),c_0_36]) ).

cnf(c_0_517,negated_conjecture,
    or(b,and(carry,sum)) = b,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_186,c_0_488]),c_0_90]) ).

cnf(c_0_518,negated_conjecture,
    or(a,and(carry,sum)) = a,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_488]),c_0_90]) ).

cnf(c_0_519,negated_conjecture,
    or(t1,and(t5,X1)) = or(t1,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_341]),c_0_77]) ).

cnf(c_0_520,negated_conjecture,
    and(t5,or(cin,t4)) = sum,
    inference(rw,[status(thm)],[c_0_403,c_0_420]) ).

cnf(c_0_521,negated_conjecture,
    or(t1,t4) = t1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_506,c_0_262]),c_0_50]) ).

cnf(c_0_522,negated_conjecture,
    and(not(and(a,and(b,not(cin)))),not(and(cin,or(a,b)))) = not(carry_def),
    inference(spm,[status(thm)],[c_0_39,c_0_233]) ).

cnf(c_0_523,negated_conjecture,
    or(and(t5,t4),and(t6,not(sum_def))) = t7,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_507,c_0_508]),c_0_354]),c_0_207]),c_0_224]),c_0_227]),c_0_457]),c_0_36]),c_0_458]),c_0_45]),c_0_36]),c_0_239]),c_0_354]),c_0_207]),c_0_224]),c_0_227]),c_0_457]),c_0_36]),c_0_458]),c_0_45]),c_0_36]),c_0_239]),c_0_64]),c_0_36]),c_0_207]),c_0_224]),c_0_65]),c_0_227]),c_0_457]),c_0_36]),c_0_93]),c_0_167]),c_0_454]),c_0_36]),c_0_148]),c_0_45]),c_0_239]),c_0_354]),c_0_207]),c_0_224]),c_0_227]),c_0_457]),c_0_36]),c_0_458]),c_0_45]),c_0_36]),c_0_239]),c_0_42]),c_0_64]),c_0_36]),c_0_207]),c_0_224]),c_0_65]),c_0_227]),c_0_457]),c_0_36]),c_0_93]),c_0_167]),c_0_454]),c_0_36]),c_0_64]),c_0_36]),c_0_437]),c_0_36]),c_0_160]),c_0_38]),c_0_403]),c_0_420]),c_0_45]),c_0_509]),c_0_141]),c_0_354]),c_0_207]),c_0_224]),c_0_227]),c_0_457]),c_0_36]),c_0_458]),c_0_45]),c_0_36]),c_0_239]),c_0_42]),c_0_45]),c_0_354]),c_0_207]),c_0_224]),c_0_227]),c_0_457]),c_0_36]),c_0_458]),c_0_64]),c_0_36]),c_0_207]),c_0_224]),c_0_65]),c_0_227]),c_0_457]),c_0_36]),c_0_93]),c_0_167]),c_0_454]),c_0_36]),c_0_64]),c_0_36]),c_0_64]),c_0_36]),c_0_343]),c_0_96]),c_0_98]),c_0_97]),c_0_77]),c_0_64]),c_0_36]),c_0_207]),c_0_224]),c_0_65]),c_0_227]),c_0_457]),c_0_36]),c_0_93]),c_0_167]),c_0_454]),c_0_36]),c_0_148]) ).

cnf(c_0_524,negated_conjecture,
    not(and(t5,and(t4,sum_def))) = t6,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_305,c_0_510]),c_0_90]),c_0_164]),c_0_98]),c_0_48]),c_0_45]) ).

cnf(c_0_525,negated_conjecture,
    or(and(carry,or(and(X1,not(X2)),and(not(X1),X2))),and(t1,and(t5,or(and(X1,X2),and(not(X1),not(X2)))))) = or(and(not(and(carry,X1)),and(not(and(t1,and(t5,not(X1)))),X2)),and(or(and(carry,X1),and(t1,and(t5,not(X1)))),not(X2))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_118]),c_0_45]),c_0_45]),c_0_45]),c_0_109]),c_0_38]),c_0_110]),c_0_38]) ).

cnf(c_0_526,negated_conjecture,
    and(t5,not(and(carry,sum))) = not(and(cin,carry)),
    inference(spm,[status(thm)],[c_0_41,c_0_511]) ).

cnf(c_0_527,negated_conjecture,
    and(t4,not(and(carry,sum))) = t4,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_512,c_0_378]),c_0_276]),c_0_64]),c_0_36]),c_0_110]),c_0_374]),c_0_64]),c_0_36]),c_0_110]),c_0_419]) ).

cnf(c_0_528,negated_conjecture,
    or(X1,and(cin,t4)) = not(and(t5,not(X1))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_51]),c_0_36]) ).

cnf(c_0_529,negated_conjecture,
    and(t4,and(carry,sum)) = ll0,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_513,c_0_514]),c_0_515]) ).

cnf(c_0_530,negated_conjecture,
    and(t1,and(t5,not(and(cin,carry)))) = and(t1,t5),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_516]),c_0_299]),c_0_45]),c_0_299]) ).

cnf(c_0_531,negated_conjecture,
    and(t1,not(and(carry,sum))) = t1,
    inference(spm,[status(thm)],[c_0_37,c_0_434]) ).

cnf(c_0_532,negated_conjecture,
    and(b,and(carry,sum)) = and(carry,sum),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_517]),c_0_45]),c_0_36]),c_0_110]) ).

cnf(c_0_533,negated_conjecture,
    and(a,and(carry,sum)) = and(carry,sum),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_518]),c_0_45]),c_0_36]),c_0_110]) ).

cnf(c_0_534,negated_conjecture,
    or(t1,and(carry,X1)) = or(t1,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_279]),c_0_77]) ).

cnf(c_0_535,negated_conjecture,
    or(t1,sum) = or(cin,t1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_519,c_0_520]),c_0_199]),c_0_521]) ).

cnf(c_0_536,negated_conjecture,
    and(not(and(cin,carry_def)),not(and(a,and(b,not(cin))))) = not(carry_def),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_522,c_0_289]),c_0_36]) ).

cnf(c_0_537,negated_conjecture,
    not(and(a,and(b,not(X1)))) = or(X1,t1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_105]),c_0_36]),c_0_45]) ).

cnf(c_0_538,negated_conjecture,
    and(t6,sum_def) = and(cin,t5),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_523]),c_0_276]),c_0_42]),c_0_194]) ).

cnf(c_0_539,negated_conjecture,
    and(t5,and(t4,sum_def)) = and(t5,t4),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_524]),c_0_48]) ).

cnf(c_0_540,negated_conjecture,
    not(and(carry,not(and(cin,carry)))) = or(cin,t1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_525,c_0_526]),c_0_41]),c_0_435]),c_0_74]),c_0_45]),c_0_527]),c_0_528]),c_0_526]),c_0_41]),c_0_52]),c_0_36]),c_0_74]),c_0_41]),c_0_45]),c_0_529]),c_0_96]),c_0_90]),c_0_530]),c_0_378]),c_0_36]),c_0_374]),c_0_87]),c_0_74]),c_0_64]),c_0_36]),c_0_343]),c_0_96]),c_0_97]),c_0_77]),c_0_531]),c_0_36]),c_0_374]),c_0_74]),c_0_64]),c_0_36]),c_0_343]),c_0_96]),c_0_90]),c_0_41]),c_0_45]),c_0_532]),c_0_533]),c_0_534]),c_0_535]) ).

cnf(c_0_541,negated_conjecture,
    and(not(and(cin,carry)),or(cin,t1)) = not(carry_def),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_536,c_0_424]),c_0_537]) ).

cnf(c_0_542,negated_conjecture,
    ( sum != sum_def
    | carry != carry_def ),
    prove_circuit ).

cnf(c_0_543,negated_conjecture,
    sum_def = sum,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_538]),c_0_48]),c_0_45]),c_0_510]),c_0_90]),c_0_64]),c_0_36]),c_0_437]),c_0_36]),c_0_48]),c_0_48]),c_0_45]),c_0_539]),c_0_44]),c_0_146]),c_0_403]),c_0_420]) ).

cnf(c_0_544,negated_conjecture,
    not(carry_def) = and(t1,t5),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_342,c_0_540]),c_0_541]),c_0_41]),c_0_299]),c_0_41]),c_0_45]),c_0_110]),c_0_374]),c_0_64]),c_0_36]),c_0_110]),c_0_419]),c_0_488]),c_0_90]),c_0_182]),c_0_90]),c_0_299]) ).

cnf(c_0_545,negated_conjecture,
    carry_def != carry,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_542,c_0_543])]) ).

cnf(c_0_546,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_544]),c_0_118]),c_0_545]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : HWV003-2 : TPTP v8.1.2. Released v2.7.0.
% 0.13/0.14  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n021.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Aug 29 16:23:29 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.21/0.58  start to proof: theBenchmark
% 172.91/174.85  % Version  : CSE_E---1.5
% 172.91/174.85  % Problem  : theBenchmark.p
% 172.91/174.85  % Proof found
% 172.91/174.85  % SZS status Theorem for theBenchmark.p
% 172.91/174.85  % SZS output start Proof
% See solution above
% 173.10/174.88  % Total time : 172.353000 s
% 173.10/174.88  % SZS output end Proof
% 173.10/174.88  % Total time : 172.364000 s
%------------------------------------------------------------------------------