TSTP Solution File: GRP695-1 by CSE

TSTP Solution File: GRP695-1 by CSE_E---1.5

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP695-1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n026.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 00:23:11 EDT 2023

% Result   : Unsatisfiable 23.27s 23.29s
% Output   : CNFRefutation 23.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   59
%            Number of leaves      :   25
% Syntax   : Number of formulae    :  524 ( 513 unt;  11 typ;   0 def)
%            Number of atoms       :  513 ( 512 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Maximal term depth    :    6 (   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    :   11 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :  809 (   0 sgn;   0   !;   0   ?;   0   :)

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

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

tff(decl_24,type,
    rd: ( $i * $i ) > $i ).

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

tff(decl_26,type,
    i: $i > $i ).

tff(decl_27,type,
    op_c: $i ).

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

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

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

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

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

cnf(c07,axiom,
    mult(X1,mult(X2,X3)) = mult(rd(mult(X1,X2),X1),mult(X1,X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c07) ).

cnf(c01,axiom,
    mult(X1,ld(X1,X2)) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c01) ).

cnf(c02,axiom,
    ld(X1,mult(X1,X2)) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c02) ).

cnf(c10,axiom,
    mult(X1,i(X1)) = unit,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c10) ).

cnf(c04,axiom,
    rd(mult(X1,X2),X2) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c04) ).

cnf(c09,axiom,
    mult(i(X1),X1) = unit,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c09) ).

cnf(c05,axiom,
    mult(X1,unit) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c05) ).

cnf(c03,axiom,
    mult(rd(X1,X2),X2) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c03) ).

cnf(c08,axiom,
    mult(mult(X1,X2),X3) = mult(mult(X1,X3),ld(X3,mult(X2,X3))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c08) ).

cnf(c06,axiom,
    mult(unit,X1) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c06) ).

cnf(c12,axiom,
    mult(op_d,op_d) = op_e,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c12) ).

cnf(c11,axiom,
    mult(op_c,mult(op_c,op_c)) = op_d,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c11) ).

cnf(c13,axiom,
    mult(op_e,op_e) = op_f,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c13) ).

cnf(goals,negated_conjecture,
    mult(a,mult(b,op_f)) != mult(mult(a,b),op_f),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

cnf(c_0_14,axiom,
    mult(X1,mult(X2,X3)) = mult(rd(mult(X1,X2),X1),mult(X1,X3)),
    c07 ).

cnf(c_0_15,axiom,
    mult(X1,ld(X1,X2)) = X2,
    c01 ).

cnf(c_0_16,axiom,
    ld(X1,mult(X1,X2)) = X2,
    c02 ).

cnf(c_0_17,axiom,
    mult(X1,i(X1)) = unit,
    c10 ).

cnf(c_0_18,axiom,
    rd(mult(X1,X2),X2) = X1,
    c04 ).

cnf(c_0_19,plain,
    mult(rd(mult(X1,X2),X1),X3) = mult(X1,mult(X2,ld(X1,X3))),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_20,axiom,
    mult(i(X1),X1) = unit,
    c09 ).

cnf(c_0_21,plain,
    i(X1) = ld(X1,unit),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_22,plain,
    rd(mult(X1,mult(X2,ld(X1,X3))),X3) = rd(mult(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_23,plain,
    mult(ld(X1,unit),X1) = unit,
    inference(rw,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_24,axiom,
    mult(X1,unit) = X1,
    c05 ).

cnf(c_0_25,axiom,
    mult(rd(X1,X2),X2) = X1,
    c03 ).

cnf(c_0_26,plain,
    rd(mult(X1,ld(ld(X1,X2),unit)),X1) = rd(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).

cnf(c_0_27,plain,
    mult(X1,ld(ld(X1,X2),unit)) = mult(rd(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_28,axiom,
    mult(mult(X1,X2),X3) = mult(mult(X1,X3),ld(X3,mult(X2,X3))),
    c08 ).

cnf(c_0_29,plain,
    ld(X1,mult(rd(X1,X2),X1)) = ld(ld(X1,X2),unit),
    inference(spm,[status(thm)],[c_0_16,c_0_27]) ).

cnf(c_0_30,plain,
    ld(ld(X1,unit),unit) = X1,
    inference(spm,[status(thm)],[c_0_16,c_0_23]) ).

cnf(c_0_31,plain,
    ld(mult(X1,X2),mult(mult(X1,X3),X2)) = ld(X2,mult(X3,X2)),
    inference(spm,[status(thm)],[c_0_16,c_0_28]) ).

cnf(c_0_32,axiom,
    mult(unit,X1) = X1,
    c06 ).

cnf(c_0_33,plain,
    mult(rd(X1,mult(rd(X1,X2),X1)),X1) = X2,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_29]),c_0_30]),c_0_15]) ).

cnf(c_0_34,plain,
    rd(X1,ld(X2,X1)) = X2,
    inference(spm,[status(thm)],[c_0_18,c_0_15]) ).

cnf(c_0_35,plain,
    ld(mult(ld(X1,unit),X2),X2) = ld(X2,mult(X1,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_23]),c_0_32]) ).

cnf(c_0_36,plain,
    ld(unit,X1) = X1,
    inference(spm,[status(thm)],[c_0_16,c_0_32]) ).

cnf(c_0_37,plain,
    ld(rd(X1,X2),X1) = X2,
    inference(spm,[status(thm)],[c_0_16,c_0_25]) ).

cnf(c_0_38,plain,
    rd(X1,mult(rd(X1,X2),X1)) = rd(X2,X1),
    inference(spm,[status(thm)],[c_0_18,c_0_33]) ).

cnf(c_0_39,plain,
    rd(X1,ld(X1,mult(X2,X1))) = mult(ld(X2,unit),X1),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_40,plain,
    ld(X1,mult(ld(X2,unit),X1)) = ld(mult(X2,X1),X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_35]),c_0_24]),c_0_36]),c_0_24]) ).

cnf(c_0_41,plain,
    ld(rd(X1,X2),X2) = mult(rd(X2,X1),X2),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_42,plain,
    mult(ld(rd(X1,X2),unit),X2) = rd(X2,ld(X2,X1)),
    inference(spm,[status(thm)],[c_0_39,c_0_25]) ).

cnf(c_0_43,plain,
    mult(X1,ld(mult(X2,X1),X1)) = mult(ld(X2,unit),X1),
    inference(spm,[status(thm)],[c_0_15,c_0_40]) ).

cnf(c_0_44,plain,
    mult(mult(rd(X1,X2),X3),X2) = mult(X1,ld(X2,mult(X3,X2))),
    inference(spm,[status(thm)],[c_0_28,c_0_25]) ).

cnf(c_0_45,plain,
    mult(rd(X1,mult(X2,X1)),X1) = ld(X2,X1),
    inference(spm,[status(thm)],[c_0_41,c_0_18]) ).

cnf(c_0_46,plain,
    ld(X1,rd(X1,ld(X1,X2))) = ld(X2,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_42]),c_0_25]) ).

cnf(c_0_47,plain,
    mult(ld(rd(X1,X2),unit),X2) = mult(X2,ld(X1,X2)),
    inference(spm,[status(thm)],[c_0_43,c_0_25]) ).

cnf(c_0_48,plain,
    rd(mult(X1,ld(X2,mult(X3,X2))),X2) = mult(rd(X1,X2),X3),
    inference(spm,[status(thm)],[c_0_18,c_0_44]) ).

cnf(c_0_49,plain,
    rd(unit,X1) = ld(X1,unit),
    inference(spm,[status(thm)],[c_0_18,c_0_23]) ).

cnf(c_0_50,plain,
    ld(ld(X1,mult(X2,X1)),unit) = ld(X1,ld(X2,X1)),
    inference(spm,[status(thm)],[c_0_29,c_0_45]) ).

cnf(c_0_51,plain,
    rd(X1,ld(X1,X2)) = mult(X1,ld(X2,X1)),
    inference(spm,[status(thm)],[c_0_15,c_0_46]) ).

cnf(c_0_52,plain,
    rd(mult(X1,ld(X2,X1)),X1) = ld(rd(X2,X1),unit),
    inference(spm,[status(thm)],[c_0_18,c_0_47]) ).

cnf(c_0_53,plain,
    mult(rd(ld(X1,ld(X2,X1)),X1),X2) = ld(X1,unit),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_23]),c_0_49]),c_0_50]) ).

cnf(c_0_54,plain,
    mult(mult(X1,ld(X2,X1)),ld(X1,X2)) = X1,
    inference(spm,[status(thm)],[c_0_25,c_0_51]) ).

cnf(c_0_55,plain,
    ld(rd(rd(X1,X2),X1),unit) = rd(mult(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_52,c_0_37]) ).

cnf(c_0_56,plain,
    rd(ld(X1,ld(X2,X1)),X1) = rd(ld(X1,unit),X2),
    inference(spm,[status(thm)],[c_0_18,c_0_53]) ).

cnf(c_0_57,plain,
    mult(X1,mult(X2,ld(X1,rd(rd(X1,X2),X1)))) = unit,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_32]),c_0_36]),c_0_19]) ).

cnf(c_0_58,plain,
    mult(mult(ld(X1,unit),X2),X1) = ld(X1,mult(X2,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_23]),c_0_32]) ).

cnf(c_0_59,plain,
    rd(ld(X1,unit),rd(X1,X2)) = rd(ld(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_56,c_0_37]) ).

cnf(c_0_60,plain,
    mult(X1,ld(X2,rd(rd(X2,X1),X2))) = ld(X2,unit),
    inference(spm,[status(thm)],[c_0_16,c_0_57]) ).

cnf(c_0_61,plain,
    rd(ld(X1,mult(X2,X1)),X1) = mult(ld(X1,unit),X2),
    inference(spm,[status(thm)],[c_0_18,c_0_58]) ).

cnf(c_0_62,plain,
    mult(rd(ld(X1,X2),X1),rd(X1,X2)) = ld(X1,unit),
    inference(spm,[status(thm)],[c_0_25,c_0_59]) ).

cnf(c_0_63,plain,
    ld(X1,rd(rd(X1,X2),X1)) = ld(X2,ld(X1,unit)),
    inference(spm,[status(thm)],[c_0_16,c_0_60]) ).

cnf(c_0_64,plain,
    mult(ld(X1,unit),rd(X2,X1)) = rd(ld(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_61,c_0_25]) ).

cnf(c_0_65,plain,
    mult(rd(X1,X2),rd(X2,mult(X2,X1))) = ld(X2,unit),
    inference(spm,[status(thm)],[c_0_62,c_0_16]) ).

cnf(c_0_66,plain,
    ld(ld(X1,X2),ld(X2,unit)) = ld(X2,rd(X1,X2)),
    inference(spm,[status(thm)],[c_0_63,c_0_34]) ).

cnf(c_0_67,plain,
    rd(rd(ld(X1,X2),X1),rd(X2,X1)) = ld(X1,unit),
    inference(spm,[status(thm)],[c_0_18,c_0_64]) ).

cnf(c_0_68,plain,
    ld(rd(X1,X2),ld(X2,unit)) = rd(X2,mult(X2,X1)),
    inference(spm,[status(thm)],[c_0_16,c_0_65]) ).

cnf(c_0_69,plain,
    mult(ld(X1,X2),ld(X2,rd(X1,X2))) = ld(X2,unit),
    inference(spm,[status(thm)],[c_0_15,c_0_66]) ).

cnf(c_0_70,plain,
    rd(rd(X1,ld(X1,unit)),X1) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_30]),c_0_34]),c_0_30]) ).

cnf(c_0_71,plain,
    rd(rd(X1,X2),rd(mult(X2,X1),X2)) = ld(X2,unit),
    inference(spm,[status(thm)],[c_0_67,c_0_16]) ).

cnf(c_0_72,plain,
    rd(X1,mult(X1,mult(X2,X1))) = ld(X2,ld(X1,unit)),
    inference(spm,[status(thm)],[c_0_68,c_0_18]) ).

cnf(c_0_73,plain,
    mult(ld(mult(X1,X2),X2),ld(X2,X1)) = ld(X2,unit),
    inference(spm,[status(thm)],[c_0_69,c_0_18]) ).

cnf(c_0_74,plain,
    rd(X1,ld(X1,unit)) = mult(X1,X1),
    inference(spm,[status(thm)],[c_0_25,c_0_70]) ).

cnf(c_0_75,plain,
    ld(ld(X1,unit),rd(X2,X1)) = rd(mult(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_37,c_0_71]) ).

cnf(c_0_76,plain,
    ld(ld(X1,ld(X2,unit)),X2) = mult(X2,mult(X1,X2)),
    inference(spm,[status(thm)],[c_0_37,c_0_72]) ).

cnf(c_0_77,plain,
    mult(rd(ld(X1,unit),X2),X1) = ld(X1,ld(X2,X1)),
    inference(spm,[status(thm)],[c_0_25,c_0_56]) ).

cnf(c_0_78,plain,
    rd(ld(X1,unit),ld(X1,X2)) = ld(mult(X2,X1),X1),
    inference(spm,[status(thm)],[c_0_18,c_0_73]) ).

cnf(c_0_79,plain,
    mult(X1,mult(ld(X1,X2),ld(X1,X3))) = mult(rd(X2,X1),X3),
    inference(spm,[status(thm)],[c_0_19,c_0_15]) ).

cnf(c_0_80,plain,
    mult(X1,mult(X2,ld(X1,unit))) = rd(mult(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_24,c_0_19]) ).

cnf(c_0_81,plain,
    mult(mult(X1,X1),ld(X1,unit)) = X1,
    inference(spm,[status(thm)],[c_0_25,c_0_74]) ).

cnf(c_0_82,plain,
    rd(mult(X1,mult(X2,X1)),X1) = ld(ld(X1,unit),X2),
    inference(spm,[status(thm)],[c_0_75,c_0_18]) ).

cnf(c_0_83,plain,
    ld(ld(X1,ld(X2,X1)),unit) = ld(X1,mult(X2,X1)),
    inference(spm,[status(thm)],[c_0_29,c_0_34]) ).

cnf(c_0_84,plain,
    ld(ld(X1,rd(X2,X1)),X1) = mult(X1,mult(ld(X2,X1),X1)),
    inference(spm,[status(thm)],[c_0_76,c_0_66]) ).

cnf(c_0_85,plain,
    ld(X1,mult(ld(X2,X3),X1)) = ld(mult(X2,X1),mult(X3,X1)),
    inference(spm,[status(thm)],[c_0_31,c_0_15]) ).

cnf(c_0_86,plain,
    ld(X1,ld(ld(X1,X2),X1)) = mult(ld(mult(X2,X1),X1),X1),
    inference(spm,[status(thm)],[c_0_77,c_0_78]) ).

cnf(c_0_87,plain,
    mult(rd(X1,X2),mult(X2,X3)) = mult(X2,mult(ld(X2,X1),X3)),
    inference(spm,[status(thm)],[c_0_79,c_0_16]) ).

cnf(c_0_88,plain,
    rd(mult(X1,mult(X2,X3)),mult(X1,X3)) = rd(mult(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_22,c_0_16]) ).

cnf(c_0_89,plain,
    ld(ld(X1,unit),X1) = mult(X1,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]) ).

cnf(c_0_90,plain,
    mult(ld(ld(X1,unit),X2),X1) = mult(X1,mult(X2,X1)),
    inference(spm,[status(thm)],[c_0_25,c_0_82]) ).

cnf(c_0_91,plain,
    ld(mult(ld(X1,X2),X2),unit) = ld(mult(X2,X2),X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_16]),c_0_85]),c_0_25]) ).

cnf(c_0_92,plain,
    mult(X1,mult(ld(mult(X2,X1),X1),X1)) = ld(ld(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_15,c_0_86]) ).

cnf(c_0_93,plain,
    mult(X1,mult(ld(X1,mult(X2,X1)),X3)) = mult(X2,mult(X1,X3)),
    inference(spm,[status(thm)],[c_0_87,c_0_18]) ).

cnf(c_0_94,plain,
    rd(mult(X1,rd(X2,X3)),X1) = rd(mult(X1,X2),mult(X1,X3)),
    inference(spm,[status(thm)],[c_0_88,c_0_25]) ).

cnf(c_0_95,plain,
    ld(mult(rd(X1,X2),X3),mult(X1,X3)) = ld(X3,mult(X2,X3)),
    inference(spm,[status(thm)],[c_0_31,c_0_25]) ).

cnf(c_0_96,plain,
    ld(X1,rd(mult(X1,X2),X1)) = mult(X2,ld(X1,unit)),
    inference(spm,[status(thm)],[c_0_16,c_0_80]) ).

cnf(c_0_97,plain,
    mult(ld(X1,unit),mult(X1,X1)) = X1,
    inference(spm,[status(thm)],[c_0_15,c_0_89]) ).

cnf(c_0_98,plain,
    mult(mult(X1,X1),X1) = mult(X1,mult(X1,X1)),
    inference(spm,[status(thm)],[c_0_90,c_0_89]) ).

cnf(c_0_99,plain,
    ld(mult(X1,X1),rd(X1,X2)) = ld(mult(X2,X1),unit),
    inference(spm,[status(thm)],[c_0_91,c_0_37]) ).

cnf(c_0_100,axiom,
    mult(op_d,op_d) = op_e,
    c12 ).

cnf(c_0_101,plain,
    ld(mult(X1,X1),X1) = ld(X1,unit),
    inference(spm,[status(thm)],[c_0_37,c_0_74]) ).

cnf(c_0_102,plain,
    ld(ld(X1,ld(X2,unit)),X1) = mult(X2,mult(X1,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_35]),c_0_93]) ).

cnf(c_0_103,plain,
    mult(rd(mult(X1,X2),mult(X1,X3)),X1) = mult(X1,rd(X2,X3)),
    inference(spm,[status(thm)],[c_0_25,c_0_94]) ).

cnf(c_0_104,plain,
    rd(mult(X1,X2),ld(X2,mult(X3,X2))) = mult(rd(X1,X3),X2),
    inference(spm,[status(thm)],[c_0_34,c_0_95]) ).

cnf(c_0_105,plain,
    ld(ld(X1,unit),mult(X1,X1)) = mult(X1,mult(X1,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_74]),c_0_30]),c_0_98]) ).

cnf(c_0_106,plain,
    rd(X1,mult(X1,X1)) = ld(X1,unit),
    inference(spm,[status(thm)],[c_0_34,c_0_89]) ).

cnf(c_0_107,plain,
    ld(op_e,rd(op_d,X1)) = ld(mult(X1,op_d),unit),
    inference(spm,[status(thm)],[c_0_99,c_0_100]) ).

cnf(c_0_108,plain,
    ld(op_e,op_d) = ld(op_d,unit),
    inference(spm,[status(thm)],[c_0_101,c_0_100]) ).

cnf(c_0_109,plain,
    ld(ld(X1,X2),X1) = mult(ld(X2,unit),mult(X1,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_102]),c_0_24]),c_0_24]),c_0_36]) ).

cnf(c_0_110,plain,
    ld(mult(X1,ld(X2,X1)),X1) = ld(X1,X2),
    inference(spm,[status(thm)],[c_0_37,c_0_51]) ).

cnf(c_0_111,plain,
    mult(X1,rd(X2,ld(X1,X3))) = mult(rd(mult(X1,X2),X3),X1),
    inference(spm,[status(thm)],[c_0_103,c_0_15]) ).

cnf(c_0_112,plain,
    rd(mult(X1,X2),ld(X2,X3)) = mult(rd(X1,rd(X3,X2)),X2),
    inference(spm,[status(thm)],[c_0_104,c_0_25]) ).

cnf(c_0_113,plain,
    rd(mult(X1,X1),mult(X1,mult(X1,X1))) = ld(X1,unit),
    inference(spm,[status(thm)],[c_0_34,c_0_105]) ).

cnf(c_0_114,axiom,
    mult(op_c,mult(op_c,op_c)) = op_d,
    c11 ).

cnf(c_0_115,plain,
    mult(X1,ld(mult(X1,X1),unit)) = ld(X1,unit),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_98]),c_0_18]),c_0_101]) ).

cnf(c_0_116,plain,
    rd(ld(X1,unit),X1) = ld(mult(X1,X1),unit),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_98]),c_0_106]),c_0_18]) ).

cnf(c_0_117,plain,
    mult(op_e,ld(mult(X1,op_d),unit)) = rd(op_d,X1),
    inference(spm,[status(thm)],[c_0_15,c_0_107]) ).

cnf(c_0_118,plain,
    mult(op_e,ld(op_d,unit)) = op_d,
    inference(spm,[status(thm)],[c_0_15,c_0_108]) ).

cnf(c_0_119,plain,
    rd(mult(X1,X2),mult(X1,ld(X3,X2))) = rd(mult(X1,X3),X1),
    inference(spm,[status(thm)],[c_0_88,c_0_15]) ).

cnf(c_0_120,plain,
    mult(mult(X1,X1),ld(mult(X2,X1),unit)) = rd(X1,X2),
    inference(spm,[status(thm)],[c_0_15,c_0_99]) ).

cnf(c_0_121,plain,
    rd(X1,mult(ld(X2,unit),mult(X1,X1))) = ld(X1,X2),
    inference(spm,[status(thm)],[c_0_34,c_0_109]) ).

cnf(c_0_122,plain,
    ld(X1,rd(X1,X2)) = ld(mult(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_110,c_0_37]) ).

cnf(c_0_123,plain,
    ld(X1,mult(rd(mult(X1,X2),X3),X1)) = rd(X2,ld(X1,X3)),
    inference(spm,[status(thm)],[c_0_16,c_0_111]) ).

cnf(c_0_124,plain,
    mult(rd(X1,rd(mult(X2,X3),X2)),X2) = rd(mult(X1,X2),X3),
    inference(spm,[status(thm)],[c_0_112,c_0_16]) ).

cnf(c_0_125,plain,
    rd(mult(op_c,op_c),op_d) = ld(op_c,unit),
    inference(spm,[status(thm)],[c_0_113,c_0_114]) ).

cnf(c_0_126,plain,
    mult(X1,ld(mult(X2,X1),mult(X3,X1))) = mult(ld(X2,X3),X1),
    inference(spm,[status(thm)],[c_0_15,c_0_85]) ).

cnf(c_0_127,plain,
    rd(ld(X1,unit),ld(mult(X1,X1),unit)) = X1,
    inference(spm,[status(thm)],[c_0_18,c_0_115]) ).

cnf(c_0_128,plain,
    ld(ld(mult(X1,X1),unit),ld(X1,unit)) = X1,
    inference(spm,[status(thm)],[c_0_37,c_0_116]) ).

cnf(c_0_129,plain,
    rd(mult(X1,ld(X2,X3)),X2) = mult(rd(X1,X2),rd(X3,X2)),
    inference(spm,[status(thm)],[c_0_48,c_0_25]) ).

cnf(c_0_130,plain,
    ld(mult(X1,X1),mult(X1,mult(X1,X1))) = X1,
    inference(spm,[status(thm)],[c_0_16,c_0_98]) ).

cnf(c_0_131,plain,
    rd(op_d,rd(X1,op_d)) = mult(op_e,ld(X1,unit)),
    inference(spm,[status(thm)],[c_0_117,c_0_25]) ).

cnf(c_0_132,plain,
    rd(mult(op_d,op_e),op_d) = op_e,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_118]),c_0_100]) ).

cnf(c_0_133,plain,
    ld(rd(mult(X1,X2),X1),mult(X1,X3)) = mult(X1,ld(X2,X3)),
    inference(spm,[status(thm)],[c_0_37,c_0_119]) ).

cnf(c_0_134,plain,
    rd(X1,rd(X2,X1)) = mult(mult(X1,X1),ld(X2,unit)),
    inference(spm,[status(thm)],[c_0_120,c_0_25]) ).

cnf(c_0_135,plain,
    rd(X1,mult(X2,mult(X1,X1))) = ld(X1,ld(X2,unit)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_37]),c_0_49]) ).

cnf(c_0_136,plain,
    ld(mult(X1,mult(rd(X1,X2),X1)),X1) = ld(X1,rd(X2,X1)),
    inference(spm,[status(thm)],[c_0_122,c_0_38]) ).

cnf(c_0_137,plain,
    ld(X1,rd(mult(mult(X1,X2),X1),X3)) = rd(X2,mult(X3,ld(X1,unit))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_96]) ).

cnf(c_0_138,plain,
    mult(ld(op_c,unit),op_d) = mult(op_c,op_c),
    inference(spm,[status(thm)],[c_0_25,c_0_125]) ).

cnf(c_0_139,plain,
    mult(ld(X1,rd(X2,X3)),X3) = mult(X3,ld(mult(X1,X3),X2)),
    inference(spm,[status(thm)],[c_0_126,c_0_25]) ).

cnf(c_0_140,plain,
    rd(X1,ld(mult(X1,X1),unit)) = mult(X1,mult(X1,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_127]),c_0_30]),c_0_98]),c_0_128]) ).

cnf(c_0_141,plain,
    rd(ld(X1,X2),X2) = rd(X2,mult(X1,X2)),
    inference(spm,[status(thm)],[c_0_38,c_0_34]) ).

cnf(c_0_142,plain,
    mult(rd(X1,mult(X1,X2)),X1) = mult(X1,ld(X2,unit)),
    inference(spm,[status(thm)],[c_0_27,c_0_16]) ).

cnf(c_0_143,plain,
    mult(ld(mult(X1,X2),unit),mult(X1,X1)) = ld(X2,X1),
    inference(spm,[status(thm)],[c_0_109,c_0_16]) ).

cnf(c_0_144,plain,
    mult(op_d,ld(mult(X1,op_d),op_e)) = mult(ld(X1,op_d),op_d),
    inference(spm,[status(thm)],[c_0_126,c_0_100]) ).

cnf(c_0_145,plain,
    rd(mult(X1,X2),mult(X2,X2)) = mult(rd(X1,mult(X2,X2)),X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_18]) ).

cnf(c_0_146,plain,
    ld(mult(op_e,ld(X1,unit)),op_d) = rd(X1,op_d),
    inference(spm,[status(thm)],[c_0_37,c_0_131]) ).

cnf(c_0_147,plain,
    mult(op_e,op_d) = mult(op_d,op_e),
    inference(spm,[status(thm)],[c_0_25,c_0_132]) ).

cnf(c_0_148,plain,
    ld(rd(mult(X1,X2),X1),X3) = mult(X1,ld(X2,ld(X1,X3))),
    inference(spm,[status(thm)],[c_0_133,c_0_15]) ).

cnf(c_0_149,plain,
    rd(mult(X1,mult(X1,ld(X2,X1))),X1) = rd(mult(X1,X1),X2),
    inference(spm,[status(thm)],[c_0_22,c_0_54]) ).

cnf(c_0_150,plain,
    rd(op_e,ld(op_d,X1)) = mult(mult(op_e,ld(X1,unit)),op_d),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_100]),c_0_134]),c_0_100]) ).

cnf(c_0_151,plain,
    ld(op_d,ld(X1,unit)) = rd(op_d,mult(X1,op_e)),
    inference(spm,[status(thm)],[c_0_135,c_0_100]) ).

cnf(c_0_152,plain,
    ld(X1,mult(rd(X2,X1),X3)) = mult(ld(X1,X2),ld(X1,X3)),
    inference(spm,[status(thm)],[c_0_16,c_0_79]) ).

cnf(c_0_153,plain,
    ld(ld(ld(X1,unit),rd(X1,X2)),unit) = rd(rd(X2,X1),X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_136]),c_0_15]),c_0_82]) ).

cnf(c_0_154,plain,
    ld(ld(op_c,unit),rd(op_c,X1)) = rd(op_d,mult(X1,op_c)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_81]),c_0_30]) ).

cnf(c_0_155,plain,
    rd(mult(X1,ld(mult(X2,X1),X3)),X1) = ld(X2,rd(X3,X1)),
    inference(spm,[status(thm)],[c_0_18,c_0_139]) ).

cnf(c_0_156,plain,
    mult(X1,ld(X2,ld(X1,unit))) = rd(rd(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_15,c_0_63]) ).

cnf(c_0_157,plain,
    ld(mult(X1,mult(X1,X1)),X1) = ld(mult(X1,X1),unit),
    inference(spm,[status(thm)],[c_0_37,c_0_140]) ).

cnf(c_0_158,plain,
    ld(op_c,mult(op_d,op_c)) = op_d,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_138]),c_0_98]),c_0_114]) ).

cnf(c_0_159,plain,
    mult(ld(X1,unit),ld(rd(X2,X1),unit)) = rd(X1,mult(X2,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_52]),c_0_16]),c_0_141]) ).

cnf(c_0_160,plain,
    rd(X1,unit) = X1,
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_161,plain,
    rd(mult(X1,ld(X2,unit)),X1) = rd(X1,mult(X1,X2)),
    inference(spm,[status(thm)],[c_0_18,c_0_142]) ).

cnf(c_0_162,plain,
    ld(ld(mult(X1,op_d),op_e),op_d) = mult(ld(op_e,X1),op_e),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_91]),c_0_100]),c_0_100]) ).

cnf(c_0_163,plain,
    mult(rd(rd(X1,X2),mult(X2,X2)),X2) = rd(X1,mult(X2,X2)),
    inference(spm,[status(thm)],[c_0_145,c_0_25]) ).

cnf(c_0_164,plain,
    ld(mult(rd(op_e,X1),op_e),op_d) = rd(ld(op_e,X1),op_d),
    inference(spm,[status(thm)],[c_0_146,c_0_27]) ).

cnf(c_0_165,axiom,
    mult(op_e,op_e) = op_f,
    c13 ).

cnf(c_0_166,plain,
    mult(mult(X1,op_e),op_d) = mult(mult(X1,op_d),op_e),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_147]),c_0_16]) ).

cnf(c_0_167,plain,
    mult(X1,ld(ld(X1,X2),ld(X1,X3))) = ld(rd(X2,X1),X3),
    inference(spm,[status(thm)],[c_0_148,c_0_15]) ).

cnf(c_0_168,plain,
    rd(mult(X1,X1),rd(X1,X2)) = rd(mult(X1,mult(X1,X2)),X1),
    inference(spm,[status(thm)],[c_0_149,c_0_37]) ).

cnf(c_0_169,plain,
    rd(op_e,rd(op_d,mult(X1,op_e))) = mult(mult(op_e,X1),op_d),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_151]),c_0_30]) ).

cnf(c_0_170,plain,
    mult(ld(X1,mult(X2,X1)),ld(X1,X3)) = ld(X1,mult(X2,X3)),
    inference(spm,[status(thm)],[c_0_152,c_0_18]) ).

cnf(c_0_171,plain,
    ld(rd(op_d,mult(X1,op_c)),unit) = rd(rd(X1,op_c),op_c),
    inference(spm,[status(thm)],[c_0_153,c_0_154]) ).

cnf(c_0_172,plain,
    rd(rd(rd(X1,mult(X2,X1)),X1),X1) = ld(X2,ld(mult(X1,X1),unit)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_116]) ).

cnf(c_0_173,plain,
    ld(mult(op_c,op_c),unit) = ld(op_d,op_c),
    inference(spm,[status(thm)],[c_0_157,c_0_114]) ).

cnf(c_0_174,plain,
    mult(mult(X1,op_c),op_d) = mult(mult(X1,op_d),op_c),
    inference(spm,[status(thm)],[c_0_28,c_0_158]) ).

cnf(c_0_175,plain,
    mult(rd(X1,X2),rd(X2,mult(X1,X2))) = rd(rd(X1,X2),X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_159]),c_0_160]),c_0_161]),c_0_25]) ).

cnf(c_0_176,plain,
    rd(rd(mult(X1,X2),X1),X1) = rd(X1,rd(mult(X1,X1),X2)),
    inference(spm,[status(thm)],[c_0_38,c_0_124]) ).

cnf(c_0_177,plain,
    mult(op_e,ld(op_f,rd(X1,op_d))) = rd(ld(op_e,X1),op_d),
    inference(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_162,c_0_163]),c_0_100]),c_0_41]),c_0_164]),c_0_100]),c_0_139]),c_0_165]) ).

cnf(c_0_178,plain,
    rd(mult(mult(X1,op_d),op_e),op_d) = mult(X1,op_e),
    inference(spm,[status(thm)],[c_0_18,c_0_166]) ).

cnf(c_0_179,plain,
    rd(mult(op_d,ld(op_e,X1)),op_d) = ld(op_d,rd(X1,op_d)),
    inference(spm,[status(thm)],[c_0_155,c_0_100]) ).

cnf(c_0_180,plain,
    ld(ld(X1,X2),ld(X1,X3)) = ld(X1,ld(rd(X2,X1),X3)),
    inference(spm,[status(thm)],[c_0_16,c_0_167]) ).

cnf(c_0_181,plain,
    rd(mult(op_d,mult(op_d,X1)),op_d) = rd(op_e,rd(op_d,X1)),
    inference(spm,[status(thm)],[c_0_168,c_0_100]) ).

cnf(c_0_182,plain,
    rd(op_e,rd(op_d,X1)) = mult(mult(op_e,rd(X1,op_e)),op_d),
    inference(spm,[status(thm)],[c_0_169,c_0_25]) ).

cnf(c_0_183,plain,
    mult(X1,rd(ld(X1,X2),X3)) = mult(rd(X2,mult(X1,X3)),X1),
    inference(spm,[status(thm)],[c_0_103,c_0_15]) ).

cnf(c_0_184,plain,
    rd(ld(X1,mult(X2,X3)),ld(X1,X3)) = ld(X1,mult(X2,X1)),
    inference(spm,[status(thm)],[c_0_18,c_0_170]) ).

cnf(c_0_185,plain,
    ld(X1,X1) = unit,
    inference(spm,[status(thm)],[c_0_16,c_0_24]) ).

cnf(c_0_186,plain,
    ld(op_e,ld(X1,unit)) = rd(op_e,mult(X1,op_f)),
    inference(spm,[status(thm)],[c_0_135,c_0_165]) ).

cnf(c_0_187,plain,
    ld(op_f,rd(op_e,X1)) = ld(mult(X1,op_e),unit),
    inference(spm,[status(thm)],[c_0_99,c_0_165]) ).

cnf(c_0_188,plain,
    rd(mult(X1,rd(X2,ld(X1,unit))),X1) = mult(X1,X2),
    inference(spm,[status(thm)],[c_0_80,c_0_25]) ).

cnf(c_0_189,plain,
    ld(rd(op_d,ld(X1,op_c)),unit) = ld(X1,ld(op_d,op_c)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_45]),c_0_172]),c_0_173]) ).

cnf(c_0_190,plain,
    mult(mult(rd(X1,op_c),op_d),op_c) = mult(X1,op_d),
    inference(spm,[status(thm)],[c_0_174,c_0_25]) ).

cnf(c_0_191,plain,
    mult(rd(rd(X1,X2),X1),X2) = mult(X1,ld(X2,ld(X1,X2))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_175]),c_0_45]) ).

cnf(c_0_192,plain,
    mult(rd(X1,rd(mult(X1,X1),X2)),X1) = rd(mult(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_25,c_0_176]) ).

cnf(c_0_193,plain,
    rd(rd(mult(X1,X2),X3),X2) = rd(X1,rd(mult(X2,X3),X2)),
    inference(spm,[status(thm)],[c_0_18,c_0_124]) ).

cnf(c_0_194,plain,
    ld(op_e,rd(ld(op_e,X1),op_d)) = ld(op_f,rd(X1,op_d)),
    inference(spm,[status(thm)],[c_0_16,c_0_177]) ).

cnf(c_0_195,plain,
    rd(mult(X1,op_e),op_d) = mult(rd(X1,op_d),op_e),
    inference(spm,[status(thm)],[c_0_178,c_0_25]) ).

cnf(c_0_196,plain,
    mult(mult(rd(X1,op_f),op_d),op_e) = mult(X1,ld(op_d,unit)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(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_75,c_0_179]),c_0_180]),c_0_49]),c_0_75]),c_0_96]),c_0_181]),c_0_182]),c_0_183]),c_0_165]),c_0_166]) ).

cnf(c_0_197,plain,
    rd(ld(X1,X2),ld(X1,X3)) = ld(X1,mult(rd(X2,X3),X1)),
    inference(spm,[status(thm)],[c_0_184,c_0_25]) ).

cnf(c_0_198,plain,
    ld(op_e,op_f) = op_e,
    inference(spm,[status(thm)],[c_0_16,c_0_165]) ).

cnf(c_0_199,plain,
    ld(rd(X1,X2),rd(X3,X2)) = rd(mult(X2,ld(X1,X3)),X2),
    inference(spm,[status(thm)],[c_0_155,c_0_25]) ).

cnf(c_0_200,plain,
    rd(op_f,op_e) = op_e,
    inference(spm,[status(thm)],[c_0_18,c_0_165]) ).

cnf(c_0_201,plain,
    ld(ld(mult(X1,X1),X2),unit) = mult(ld(X2,X1),X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_91]),c_0_185]),c_0_160]),c_0_36]) ).

cnf(c_0_202,plain,
    rd(op_e,mult(ld(X1,unit),op_f)) = ld(op_e,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_186,c_0_37]),c_0_49]) ).

cnf(c_0_203,plain,
    mult(ld(rd(X1,X2),X3),X2) = mult(X2,ld(X1,mult(X3,X2))),
    inference(spm,[status(thm)],[c_0_126,c_0_25]) ).

cnf(c_0_204,plain,
    mult(ld(mult(mult(X1,X2),X1),X1),X2) = ld(X1,unit),
    inference(spm,[status(thm)],[c_0_73,c_0_16]) ).

cnf(c_0_205,plain,
    mult(op_f,ld(mult(X1,op_e),unit)) = rd(op_e,X1),
    inference(spm,[status(thm)],[c_0_15,c_0_187]) ).

cnf(c_0_206,plain,
    ld(op_f,op_e) = ld(op_e,unit),
    inference(spm,[status(thm)],[c_0_101,c_0_165]) ).

cnf(c_0_207,plain,
    mult(X1,rd(X2,ld(X1,unit))) = mult(mult(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_25,c_0_188]) ).

cnf(c_0_208,plain,
    ld(ld(X1,ld(op_d,op_c)),unit) = rd(op_d,ld(X1,op_c)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_189]),c_0_185]),c_0_160]),c_0_36]) ).

cnf(c_0_209,plain,
    rd(mult(X1,op_d),op_c) = mult(rd(X1,op_c),op_d),
    inference(spm,[status(thm)],[c_0_18,c_0_190]) ).

cnf(c_0_210,plain,
    rd(X1,rd(mult(X2,X1),X2)) = mult(X1,rd(rd(X2,X1),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(spm,[status(thm)],[c_0_124,c_0_191]),c_0_41]),c_0_142]),c_0_16]),c_0_19]),c_0_156]),c_0_176]),c_0_192]),c_0_193]) ).

cnf(c_0_211,plain,
    mult(mult(X1,rd(X2,X3)),X3) = mult(mult(X1,X3),ld(X3,X2)),
    inference(spm,[status(thm)],[c_0_28,c_0_25]) ).

cnf(c_0_212,plain,
    ld(op_f,rd(mult(op_e,X1),op_d)) = ld(op_e,rd(X1,op_d)),
    inference(spm,[status(thm)],[c_0_194,c_0_16]) ).

cnf(c_0_213,plain,
    mult(rd(X1,op_d),ld(op_d,unit)) = mult(rd(X1,op_f),op_e),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_195,c_0_196]),c_0_129]),c_0_49]),c_0_18]) ).

cnf(c_0_214,plain,
    ld(op_e,mult(rd(X1,op_f),op_e)) = rd(ld(op_e,X1),op_e),
    inference(spm,[status(thm)],[c_0_197,c_0_198]) ).

cnf(c_0_215,plain,
    mult(rd(mult(X1,X1),X2),X1) = mult(X1,mult(X1,ld(X2,X1))),
    inference(spm,[status(thm)],[c_0_25,c_0_149]) ).

cnf(c_0_216,plain,
    rd(mult(op_e,ld(X1,op_f)),op_e) = mult(rd(op_e,X1),op_e),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_200]),c_0_41]) ).

cnf(c_0_217,plain,
    ld(ld(op_e,X1),unit) = mult(ld(X1,op_d),op_d),
    inference(spm,[status(thm)],[c_0_201,c_0_100]) ).

cnf(c_0_218,plain,
    ld(X1,mult(rd(X2,mult(X1,X3)),X1)) = rd(ld(X1,X2),X3),
    inference(spm,[status(thm)],[c_0_16,c_0_183]) ).

cnf(c_0_219,plain,
    rd(op_e,mult(op_f,ld(X1,op_f))) = ld(op_e,rd(X1,op_f)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_203]),c_0_32]) ).

cnf(c_0_220,plain,
    rd(ld(X1,unit),X2) = ld(mult(mult(X1,X2),X1),X1),
    inference(spm,[status(thm)],[c_0_18,c_0_204]) ).

cnf(c_0_221,plain,
    rd(op_e,rd(X1,op_e)) = mult(op_f,ld(X1,unit)),
    inference(spm,[status(thm)],[c_0_205,c_0_25]) ).

cnf(c_0_222,plain,
    mult(op_f,ld(op_e,unit)) = op_e,
    inference(spm,[status(thm)],[c_0_15,c_0_206]) ).

cnf(c_0_223,plain,
    rd(mult(mult(X1,X2),X1),rd(X2,ld(X1,unit))) = X1,
    inference(spm,[status(thm)],[c_0_18,c_0_207]) ).

cnf(c_0_224,plain,
    mult(rd(X1,ld(op_d,op_c)),X1) = mult(mult(rd(X1,op_c),op_d),X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_208]),c_0_111]),c_0_209]) ).

cnf(c_0_225,plain,
    mult(mult(X1,X2),ld(mult(X2,X1),X2)) = rd(mult(X1,X2),X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_210]),c_0_211]),c_0_122]) ).

cnf(c_0_226,plain,
    rd(X1,mult(X1,ld(X2,unit))) = rd(mult(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_38,c_0_142]) ).

cnf(c_0_227,plain,
    rd(X1,ld(X2,ld(X3,mult(X2,X1)))) = ld(X2,mult(X3,X2)),
    inference(spm,[status(thm)],[c_0_123,c_0_34]) ).

cnf(c_0_228,plain,
    rd(op_f,ld(op_e,X1)) = mult(mult(op_f,ld(X1,unit)),op_e),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_165]),c_0_134]),c_0_165]) ).

cnf(c_0_229,plain,
    ld(op_f,rd(mult(op_e,X1),op_e)) = rd(ld(op_e,X1),op_e),
    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_212,c_0_22]),c_0_108]),c_0_129]),c_0_49]),c_0_213]),c_0_214]) ).

cnf(c_0_230,plain,
    mult(op_e,mult(op_e,ld(X1,op_e))) = mult(rd(op_f,X1),op_e),
    inference(spm,[status(thm)],[c_0_215,c_0_165]) ).

cnf(c_0_231,plain,
    mult(ld(X1,op_f),ld(op_e,unit)) = mult(ld(X1,op_d),op_d),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_216]),c_0_29]),c_0_217]) ).

cnf(c_0_232,plain,
    mult(ld(X1,X2),ld(X1,unit)) = ld(X1,rd(X2,X1)),
    inference(spm,[status(thm)],[c_0_96,c_0_15]) ).

cnf(c_0_233,plain,
    ld(X1,ld(X1,unit)) = ld(mult(X1,X1),unit),
    inference(spm,[status(thm)],[c_0_16,c_0_115]) ).

cnf(c_0_234,plain,
    ld(mult(mult(op_e,ld(X1,op_f)),op_e),op_e) = ld(mult(op_e,op_f),X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_219]),c_0_139]),c_0_16]),c_0_206]),c_0_220]) ).

cnf(c_0_235,plain,
    mult(op_d,rd(op_d,mult(X1,op_e))) = ld(X1,unit),
    inference(spm,[status(thm)],[c_0_15,c_0_151]) ).

cnf(c_0_236,plain,
    ld(mult(op_f,ld(X1,unit)),op_e) = rd(X1,op_e),
    inference(spm,[status(thm)],[c_0_37,c_0_221]) ).

cnf(c_0_237,plain,
    rd(mult(op_e,op_f),op_e) = op_f,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_222]),c_0_165]) ).

cnf(c_0_238,plain,
    ld(X1,mult(mult(X1,X2),X1)) = rd(X2,ld(X1,unit)),
    inference(spm,[status(thm)],[c_0_37,c_0_223]) ).

cnf(c_0_239,plain,
    mult(mult(rd(X1,X2),X1),X1) = mult(X1,ld(X2,mult(X1,X1))),
    inference(spm,[status(thm)],[c_0_203,c_0_41]) ).

cnf(c_0_240,plain,
    rd(X1,ld(op_d,op_c)) = mult(rd(X1,op_c),op_d),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_224]),c_0_18]) ).

cnf(c_0_241,plain,
    mult(mult(X1,mult(X2,X2)),X2) = mult(mult(X1,X2),mult(X2,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_98]),c_0_16]) ).

cnf(c_0_242,plain,
    ld(mult(rd(X1,X2),X1),rd(X1,X2)) = rd(X2,mult(X1,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_175]),c_0_122]) ).

cnf(c_0_243,plain,
    ld(mult(mult(X1,X2),X1),mult(X1,X2)) = ld(mult(X2,X1),X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_225]),c_0_122]) ).

cnf(c_0_244,plain,
    ld(mult(X1,mult(X1,ld(X2,unit))),X1) = mult(X2,ld(X1,unit)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_226]),c_0_96]) ).

cnf(c_0_245,plain,
    ld(ld(X1,mult(X2,X1)),X3) = ld(X1,ld(X2,mult(X1,X3))),
    inference(spm,[status(thm)],[c_0_37,c_0_227]) ).

cnf(c_0_246,plain,
    rd(op_f,rd(op_e,mult(X1,op_f))) = mult(mult(op_f,X1),op_e),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_228,c_0_186]),c_0_30]) ).

cnf(c_0_247,plain,
    rd(op_e,mult(X1,op_e)) = ld(mult(op_f,X1),op_f),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_229,c_0_230]),c_0_18]),c_0_122]),c_0_16]),c_0_141]) ).

cnf(c_0_248,plain,
    mult(ld(op_f,unit),ld(op_e,X1)) = ld(mult(op_e,op_f),X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(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_120,c_0_231]),c_0_232]),c_0_49]),c_0_233]),c_0_165]),c_0_91]),c_0_100]),c_0_220]),c_0_234]) ).

cnf(c_0_249,plain,
    ld(op_e,mult(rd(op_f,X1),op_e)) = mult(op_e,ld(X1,op_e)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_197,c_0_198]),c_0_51]) ).

cnf(c_0_250,plain,
    ld(rd(X1,op_e),unit) = mult(op_d,rd(op_d,X1)),
    inference(spm,[status(thm)],[c_0_235,c_0_25]) ).

cnf(c_0_251,plain,
    rd(ld(X1,X2),mult(X2,X2)) = ld(mult(X2,X1),unit),
    inference(spm,[status(thm)],[c_0_18,c_0_143]) ).

cnf(c_0_252,plain,
    ld(mult(rd(op_f,X1),op_f),op_e) = rd(ld(op_f,X1),op_e),
    inference(spm,[status(thm)],[c_0_236,c_0_27]) ).

cnf(c_0_253,plain,
    mult(op_f,op_e) = mult(op_e,op_f),
    inference(spm,[status(thm)],[c_0_25,c_0_237]) ).

cnf(c_0_254,plain,
    rd(op_e,op_f) = ld(op_e,unit),
    inference(spm,[status(thm)],[c_0_106,c_0_165]) ).

cnf(c_0_255,plain,
    rd(ld(ld(X1,X2),unit),ld(X1,unit)) = ld(X2,mult(X1,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_238,c_0_27]),c_0_239]),c_0_16]) ).

cnf(c_0_256,plain,
    ld(mult(rd(X1,op_c),op_d),X1) = ld(op_d,op_c),
    inference(spm,[status(thm)],[c_0_37,c_0_240]) ).

cnf(c_0_257,plain,
    mult(mult(X1,X1),mult(X1,X1)) = mult(X1,mult(X1,mult(X1,X1))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_105]),c_0_98]),c_0_241]) ).

cnf(c_0_258,plain,
    mult(op_c,op_d) = mult(op_d,op_c),
    inference(spm,[status(thm)],[c_0_15,c_0_158]) ).

cnf(c_0_259,plain,
    rd(ld(X1,X2),mult(X2,ld(X1,X2))) = ld(mult(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_242,c_0_34]) ).

cnf(c_0_260,plain,
    mult(X1,ld(mult(X1,X2),X1)) = rd(X1,X2),
    inference(spm,[status(thm)],[c_0_51,c_0_16]) ).

cnf(c_0_261,plain,
    ld(mult(ld(X1,X2),X1),ld(X1,X2)) = ld(mult(X2,X1),X2),
    inference(spm,[status(thm)],[c_0_243,c_0_15]) ).

cnf(c_0_262,plain,
    rd(X1,mult(X2,ld(X3,ld(X2,X1)))) = rd(mult(X2,X3),X2),
    inference(spm,[status(thm)],[c_0_119,c_0_15]) ).

cnf(c_0_263,plain,
    ld(X1,ld(rd(mult(X2,X2),X1),mult(X2,X1))) = ld(X2,X1),
    inference(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_244,c_0_170]),c_0_24]),c_0_170]),c_0_180]),c_0_245]),c_0_24]),c_0_15]) ).

cnf(c_0_264,plain,
    ld(mult(rd(rd(X1,X2),X3),X2),X1) = ld(X2,mult(X3,X2)),
    inference(spm,[status(thm)],[c_0_95,c_0_25]) ).

cnf(c_0_265,plain,
    rd(op_f,rd(op_e,X1)) = mult(mult(op_f,rd(X1,op_f)),op_e),
    inference(spm,[status(thm)],[c_0_246,c_0_25]) ).

cnf(c_0_266,plain,
    ld(mult(op_f,rd(op_e,X1)),op_f) = rd(X1,op_e),
    inference(spm,[status(thm)],[c_0_38,c_0_247]) ).

cnf(c_0_267,plain,
    ld(mult(op_e,op_f),mult(op_e,X1)) = mult(ld(op_f,unit),X1),
    inference(spm,[status(thm)],[c_0_248,c_0_16]) ).

cnf(c_0_268,plain,
    mult(ld(op_e,unit),rd(op_f,X1)) = mult(op_d,rd(op_d,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_249]),c_0_52]),c_0_250]) ).

cnf(c_0_269,plain,
    ld(mult(X1,rd(X1,X2)),unit) = rd(X2,mult(X1,X1)),
    inference(spm,[status(thm)],[c_0_251,c_0_37]) ).

cnf(c_0_270,plain,
    ld(rd(op_f,X1),ld(op_e,unit)) = rd(X1,mult(op_e,op_f)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_252]),c_0_183]),c_0_253]),c_0_18]),c_0_254]) ).

cnf(c_0_271,plain,
    mult(mult(X1,op_f),op_e) = mult(mult(X1,op_e),op_f),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_253]),c_0_16]) ).

cnf(c_0_272,plain,
    ld(X1,mult(op_d,op_c)) = mult(ld(X1,op_c),op_d),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(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_255,c_0_256]),c_0_49]),c_0_138]),c_0_201]),c_0_240]),c_0_18]),c_0_49]),c_0_138]),c_0_49]),c_0_138]),c_0_257]),c_0_114]),c_0_258]) ).

cnf(c_0_273,plain,
    mult(ld(mult(X1,X2),X1),mult(X2,ld(X1,X2))) = ld(X1,X2),
    inference(spm,[status(thm)],[c_0_25,c_0_259]) ).

cnf(c_0_274,plain,
    mult(ld(X1,X2),ld(mult(X2,X1),X2)) = rd(ld(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_260,c_0_261]) ).

cnf(c_0_275,plain,
    rd(mult(rd(X1,X2),X1),X2) = rd(X1,mult(rd(X2,X1),X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_262,c_0_101]),c_0_27]),c_0_79]) ).

cnf(c_0_276,plain,
    mult(rd(X1,mult(X2,X1)),ld(X2,X1)) = ld(X2,ld(X2,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_34]),c_0_141]) ).

cnf(c_0_277,plain,
    ld(ld(rd(X1,X2),X3),X2) = mult(X2,ld(ld(X1,mult(X3,X2)),unit)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_203]),c_0_142]) ).

cnf(c_0_278,plain,
    ld(rd(mult(X1,X1),X2),mult(X1,X2)) = mult(X2,ld(X1,X2)),
    inference(spm,[status(thm)],[c_0_15,c_0_263]) ).

cnf(c_0_279,plain,
    ld(mult(X1,ld(X2,X1)),X2) = ld(X1,mult(X2,ld(X1,X2))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_264,c_0_106]),c_0_203]),c_0_32]),c_0_211]),c_0_25]) ).

cnf(c_0_280,plain,
    mult(mult(mult(op_f,rd(X1,op_f)),op_e),op_e) = mult(op_e,mult(op_e,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_230,c_0_37]),c_0_265]) ).

cnf(c_0_281,plain,
    mult(mult(op_f,rd(X1,op_f)),op_e) = mult(op_f,rd(X1,op_e)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_260,c_0_266]),c_0_265]) ).

cnf(c_0_282,plain,
    mult(op_e,mult(ld(op_f,unit),X1)) = ld(op_e,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_229]),c_0_25]),c_0_253]),c_0_267]) ).

cnf(c_0_283,plain,
    mult(rd(X1,op_e),ld(op_f,unit)) = rd(X1,mult(op_e,op_f)),
    inference(rw,[status(thm)],[inference(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_143,c_0_268]),c_0_269]),c_0_100]),c_0_232]),c_0_49]),c_0_233]),c_0_165]),c_0_270]) ).

cnf(c_0_284,plain,
    mult(mult(rd(X1,op_f),op_e),op_f) = mult(X1,op_e),
    inference(spm,[status(thm)],[c_0_271,c_0_25]) ).

cnf(c_0_285,plain,
    mult(X1,mult(ld(X1,op_c),op_d)) = mult(op_d,op_c),
    inference(spm,[status(thm)],[c_0_15,c_0_272]) ).

cnf(c_0_286,plain,
    mult(ld(X1,X2),rd(ld(X2,X1),X2)) = ld(mult(X1,X2),X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_273,c_0_261]),c_0_243]),c_0_15]),c_0_274]) ).

cnf(c_0_287,plain,
    ld(mult(mult(X1,X2),X2),mult(X1,X2)) = ld(mult(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_110,c_0_16]) ).

cnf(c_0_288,plain,
    rd(ld(X1,ld(X1,X2)),X2) = rd(ld(X1,X2),mult(X1,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_275,c_0_141]),c_0_276]),c_0_34]) ).

cnf(c_0_289,plain,
    rd(ld(X1,X2),mult(X1,X2)) = rd(X2,mult(X1,mult(X1,X2))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_275,c_0_45]),c_0_18]) ).

cnf(c_0_290,plain,
    mult(X1,mult(ld(mult(mult(X2,X1),X1),X2),X2)) = ld(X1,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_277,c_0_278]),c_0_110]),c_0_201]) ).

cnf(c_0_291,plain,
    ld(mult(X1,X2),rd(X1,X2)) = ld(mult(mult(X1,X2),X2),X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_279,c_0_16]),c_0_260]) ).

cnf(c_0_292,plain,
    mult(mult(op_e,op_f),ld(op_e,X1)) = mult(op_e,mult(op_e,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_280,c_0_281]),c_0_211]),c_0_253]) ).

cnf(c_0_293,plain,
    mult(op_e,rd(ld(op_f,X1),op_f)) = ld(op_e,rd(X1,op_f)),
    inference(spm,[status(thm)],[c_0_282,c_0_64]) ).

cnf(c_0_294,plain,
    ld(op_f,mult(mult(op_e,X1),op_e)) = ld(op_e,mult(X1,op_e)),
    inference(spm,[status(thm)],[c_0_31,c_0_165]) ).

cnf(c_0_295,plain,
    rd(mult(X1,op_e),mult(op_e,op_f)) = mult(X1,ld(op_f,unit)),
    inference(spm,[status(thm)],[c_0_283,c_0_18]) ).

cnf(c_0_296,plain,
    rd(mult(X1,op_e),op_f) = mult(rd(X1,op_f),op_e),
    inference(spm,[status(thm)],[c_0_18,c_0_284]) ).

cnf(c_0_297,plain,
    mult(rd(mult(op_e,X1),op_f),op_e) = mult(op_e,rd(X1,op_e)),
    inference(spm,[status(thm)],[c_0_103,c_0_165]) ).

cnf(c_0_298,plain,
    ld(op_f,mult(op_e,op_f)) = op_e,
    inference(spm,[status(thm)],[c_0_37,c_0_237]) ).

cnf(c_0_299,plain,
    rd(mult(op_d,op_c),mult(X1,op_d)) = rd(op_c,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_285]),c_0_15]) ).

cnf(c_0_300,plain,
    mult(X1,rd(X2,mult(mult(X2,X1),X2))) = rd(X1,mult(X2,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_286,c_0_122]),c_0_37]),c_0_141]),c_0_242]) ).

cnf(c_0_301,plain,
    mult(ld(mult(X1,mult(X2,X1)),X1),X2) = ld(mult(X2,X1),X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_273,c_0_287]),c_0_243]),c_0_15]) ).

cnf(c_0_302,plain,
    mult(rd(X1,mult(rd(X2,X1),X2)),X2) = mult(rd(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_25,c_0_275]) ).

cnf(c_0_303,plain,
    rd(ld(X1,ld(X1,X2)),X2) = rd(X2,mult(X1,mult(X1,X2))),
    inference(rw,[status(thm)],[c_0_288,c_0_289]) ).

cnf(c_0_304,plain,
    rd(X1,mult(X2,mult(X2,X1))) = ld(mult(mult(X1,X2),X2),X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_290]),c_0_289]),c_0_155]),c_0_291]) ).

cnf(c_0_305,plain,
    mult(op_e,mult(op_e,mult(op_e,X1))) = mult(mult(op_e,op_f),X1),
    inference(spm,[status(thm)],[c_0_292,c_0_16]) ).

cnf(c_0_306,plain,
    mult(mult(X1,ld(op_f,unit)),op_e) = rd(X1,op_e),
    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_293,c_0_294]),c_0_183]),c_0_295]),c_0_296]),c_0_297]),c_0_16]) ).

cnf(c_0_307,plain,
    mult(ld(op_f,unit),op_e) = ld(op_e,unit),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_298]),c_0_254]) ).

cnf(c_0_308,plain,
    rd(op_c,rd(X1,op_d)) = rd(mult(op_d,op_c),X1),
    inference(spm,[status(thm)],[c_0_299,c_0_25]) ).

cnf(c_0_309,plain,
    ld(mult(X1,op_d),mult(X1,op_c)) = ld(op_d,op_c),
    inference(spm,[status(thm)],[c_0_256,c_0_18]) ).

cnf(c_0_310,plain,
    mult(ld(X1,X2),rd(X1,mult(X2,X1))) = rd(X2,mult(X1,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_300,c_0_15]),c_0_141]) ).

cnf(c_0_311,plain,
    mult(ld(X1,rd(X2,X1)),rd(X1,X2)) = rd(X2,mult(X1,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_301,c_0_136]),c_0_242]) ).

cnf(c_0_312,plain,
    ld(mult(rd(X1,X2),X1),mult(X1,X2)) = ld(X1,mult(X2,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_302]),c_0_239]),c_0_16]) ).

cnf(c_0_313,plain,
    rd(ld(X1,ld(X1,X2)),X2) = ld(mult(mult(X2,X1),X1),X2),
    inference(rw,[status(thm)],[c_0_303,c_0_304]) ).

cnf(c_0_314,plain,
    ld(op_e,mult(mult(op_e,op_f),X1)) = mult(op_e,mult(op_e,X1)),
    inference(spm,[status(thm)],[c_0_16,c_0_305]) ).

cnf(c_0_315,plain,
    ld(mult(mult(X1,op_e),op_e),X1) = ld(op_f,unit),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_306]),c_0_291]),c_0_307]),c_0_233]),c_0_165]) ).

cnf(c_0_316,plain,
    ld(op_e,ld(op_e,X1)) = mult(ld(op_f,unit),X1),
    inference(spm,[status(thm)],[c_0_16,c_0_282]) ).

cnf(c_0_317,plain,
    rd(mult(X1,X2),ld(mult(X3,X2),X2)) = mult(rd(X1,ld(X3,unit)),X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_43]),c_0_18]) ).

cnf(c_0_318,plain,
    rd(mult(op_d,op_c),X1) = mult(op_d,rd(op_c,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_308]),c_0_103]),c_0_258]) ).

cnf(c_0_319,plain,
    mult(mult(X1,op_d),ld(op_d,op_c)) = mult(X1,op_c),
    inference(spm,[status(thm)],[c_0_15,c_0_309]) ).

cnf(c_0_320,plain,
    rd(rd(X1,X2),mult(X2,rd(X1,X2))) = rd(X1,mult(X2,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_310,c_0_25]),c_0_311]) ).

cnf(c_0_321,plain,
    rd(mult(X1,X2),ld(X1,mult(X2,X2))) = mult(rd(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_34,c_0_312]) ).

cnf(c_0_322,plain,
    rd(mult(op_e,X1),mult(mult(op_e,op_f),X1)) = ld(op_f,unit),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_313,c_0_314]),c_0_16]),c_0_315]) ).

cnf(c_0_323,plain,
    mult(ld(op_f,unit),mult(op_e,X1)) = ld(op_e,X1),
    inference(spm,[status(thm)],[c_0_316,c_0_16]) ).

cnf(c_0_324,plain,
    rd(mult(mult(X1,X2),ld(X2,X3)),X2) = mult(X1,rd(X3,X2)),
    inference(spm,[status(thm)],[c_0_18,c_0_211]) ).

cnf(c_0_325,plain,
    mult(rd(op_d,ld(X1,unit)),op_c) = mult(op_d,mult(X1,op_c)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_317,c_0_318]),c_0_34]) ).

cnf(c_0_326,plain,
    rd(mult(op_d,mult(X1,op_c)),op_c) = ld(ld(op_d,unit),X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_319]),c_0_82]) ).

cnf(c_0_327,plain,
    ld(rd(X1,mult(X2,X1)),rd(X1,X2)) = mult(X2,rd(X1,X2)),
    inference(spm,[status(thm)],[c_0_37,c_0_320]) ).

cnf(c_0_328,plain,
    rd(op_e,mult(op_d,ld(X1,op_d))) = rd(mult(op_d,X1),op_d),
    inference(spm,[status(thm)],[c_0_119,c_0_100]) ).

cnf(c_0_329,plain,
    rd(rd(X1,rd(ld(X1,unit),X2)),X1) = mult(X1,X2),
    inference(spm,[status(thm)],[c_0_156,c_0_37]) ).

cnf(c_0_330,plain,
    mult(ld(mult(op_e,X1),op_d),op_d) = ld(X1,unit),
    inference(spm,[status(thm)],[c_0_217,c_0_16]) ).

cnf(c_0_331,plain,
    rd(mult(X1,op_d),ld(X1,op_e)) = mult(rd(X1,op_d),X1),
    inference(spm,[status(thm)],[c_0_321,c_0_100]) ).

cnf(c_0_332,plain,
    ld(mult(op_e,X1),ld(op_e,X1)) = ld(X1,ld(op_f,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_322]),c_0_323]),c_0_31]),c_0_245]),c_0_24]) ).

cnf(c_0_333,plain,
    rd(X1,rd(X2,ld(X1,X3))) = mult(ld(rd(mult(X1,X2),X3),unit),X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_260,c_0_111]),c_0_43]) ).

cnf(c_0_334,plain,
    rd(mult(mult(X1,X2),X3),X2) = mult(X1,rd(mult(X2,X3),X2)),
    inference(spm,[status(thm)],[c_0_324,c_0_16]) ).

cnf(c_0_335,plain,
    rd(op_d,ld(X1,unit)) = ld(ld(op_d,unit),X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_325]),c_0_326]) ).

cnf(c_0_336,plain,
    ld(rd(X1,mult(ld(X2,X1),X1)),X2) = mult(ld(X2,X1),X2),
    inference(spm,[status(thm)],[c_0_327,c_0_34]) ).

cnf(c_0_337,plain,
    ld(ld(op_d,unit),ld(X1,unit)) = rd(op_e,mult(X1,op_d)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_328,c_0_35]),c_0_15]),c_0_82]) ).

cnf(c_0_338,plain,
    rd(X1,rd(ld(X1,unit),X2)) = mult(mult(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_25,c_0_329]) ).

cnf(c_0_339,plain,
    rd(ld(X1,unit),op_d) = ld(mult(op_e,X1),op_d),
    inference(spm,[status(thm)],[c_0_18,c_0_330]) ).

cnf(c_0_340,plain,
    mult(op_e,mult(op_f,ld(op_e,X1))) = mult(op_f,X1),
    inference(spm,[status(thm)],[c_0_19,c_0_237]) ).

cnf(c_0_341,plain,
    rd(op_d,ld(X1,ld(X1,op_e))) = ld(op_d,mult(X1,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_331]),c_0_239]),c_0_16]) ).

cnf(c_0_342,plain,
    ld(op_e,rd(X1,mult(op_e,X1))) = rd(X1,mult(op_f,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_332]),c_0_15]),c_0_141]),c_0_141]) ).

cnf(c_0_343,plain,
    rd(mult(X1,ld(X2,mult(X3,X1))),X1) = ld(rd(X2,X1),X3),
    inference(spm,[status(thm)],[c_0_18,c_0_203]) ).

cnf(c_0_344,plain,
    rd(mult(X1,X1),rd(X2,ld(X1,unit))) = mult(X1,ld(X2,unit)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_333,c_0_101]),c_0_334]),c_0_143]),c_0_41]),c_0_142]) ).

cnf(c_0_345,plain,
    rd(op_e,mult(X1,op_d)) = rd(op_d,X1),
    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_335,c_0_336]),c_0_36]),c_0_24]),c_0_36]),c_0_106]),c_0_337]) ).

cnf(c_0_346,plain,
    rd(X1,ld(mult(op_e,X1),op_d)) = mult(mult(X1,op_d),X1),
    inference(spm,[status(thm)],[c_0_338,c_0_339]) ).

cnf(c_0_347,plain,
    ld(op_e,mult(op_f,X1)) = mult(op_f,ld(op_e,X1)),
    inference(spm,[status(thm)],[c_0_16,c_0_340]) ).

cnf(c_0_348,plain,
    ld(X1,ld(X1,op_e)) = mult(ld(mult(X1,X1),unit),op_e),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_341]),c_0_109]),c_0_100]) ).

cnf(c_0_349,plain,
    mult(op_e,rd(X1,mult(op_f,X1))) = rd(X1,mult(op_e,X1)),
    inference(spm,[status(thm)],[c_0_15,c_0_342]) ).

cnf(c_0_350,plain,
    ld(X1,ld(rd(X2,X1),X3)) = mult(ld(X2,mult(X3,X1)),ld(X1,unit)),
    inference(spm,[status(thm)],[c_0_96,c_0_343]) ).

cnf(c_0_351,plain,
    mult(X1,ld(mult(X2,ld(X1,unit)),unit)) = rd(mult(X1,X1),X2),
    inference(spm,[status(thm)],[c_0_344,c_0_18]) ).

cnf(c_0_352,plain,
    mult(op_e,ld(X1,unit)) = rd(op_e,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_345,c_0_25]),c_0_134]),c_0_100]) ).

cnf(c_0_353,plain,
    rd(X1,mult(X2,ld(X1,unit))) = mult(X1,mult(X1,ld(X2,unit))),
    inference(spm,[status(thm)],[c_0_34,c_0_244]) ).

cnf(c_0_354,plain,
    ld(rd(op_d,X1),op_e) = mult(X1,op_d),
    inference(spm,[status(thm)],[c_0_37,c_0_345]) ).

cnf(c_0_355,plain,
    rd(X1,ld(mult(mult(X2,X1),X2),X2)) = mult(mult(X1,X1),X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_204]),c_0_30]) ).

cnf(c_0_356,plain,
    ld(mult(mult(X1,op_d),X1),X1) = ld(mult(op_e,X1),op_d),
    inference(spm,[status(thm)],[c_0_37,c_0_346]) ).

cnf(c_0_357,plain,
    rd(mult(op_e,ld(op_f,X1)),op_e) = ld(op_e,rd(X1,op_e)),
    inference(spm,[status(thm)],[c_0_155,c_0_165]) ).

cnf(c_0_358,plain,
    mult(op_f,ld(op_e,ld(op_f,X1))) = ld(op_e,X1),
    inference(spm,[status(thm)],[c_0_347,c_0_15]) ).

cnf(c_0_359,plain,
    ld(mult(mult(X1,rd(X1,X2)),X1),X1) = rd(ld(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_59,c_0_220]) ).

cnf(c_0_360,plain,
    mult(op_e,rd(op_e,mult(X1,op_f))) = ld(X1,unit),
    inference(spm,[status(thm)],[c_0_15,c_0_186]) ).

cnf(c_0_361,plain,
    rd(op_e,mult(X1,mult(X1,op_e))) = ld(mult(X1,X1),unit),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_289,c_0_348]),c_0_15]),c_0_18]),c_0_15]),c_0_289]) ).

cnf(c_0_362,plain,
    mult(rd(X1,mult(op_f,X1)),op_e) = rd(X1,mult(op_e,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_349]),c_0_15]),c_0_141]),c_0_340]) ).

cnf(c_0_363,plain,
    ld(mult(mult(X1,X2),ld(X2,X1)),X1) = mult(ld(X1,X2),ld(X2,unit)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_73]),c_0_15]),c_0_180]),c_0_350]),c_0_32]) ).

cnf(c_0_364,plain,
    mult(op_e,rd(op_e,X1)) = rd(op_f,X1),
    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_352]),c_0_165]) ).

cnf(c_0_365,plain,
    ld(mult(op_e,X1),op_e) = ld(X1,unit),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_354,c_0_355]),c_0_100]),c_0_356]),c_0_330]) ).

cnf(c_0_366,plain,
    ld(mult(op_e,rd(op_f,X1)),op_e) = rd(X1,op_f),
    inference(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_357,c_0_229]),c_0_183]),c_0_165]),c_0_18]),c_0_176]),c_0_165]),c_0_122]) ).

cnf(c_0_367,plain,
    rd(X1,ld(X2,mult(X3,X2))) = mult(rd(rd(X1,X2),X3),X2),
    inference(spm,[status(thm)],[c_0_34,c_0_264]) ).

cnf(c_0_368,plain,
    mult(op_e,rd(ld(op_f,X1),op_e)) = rd(ld(op_e,X1),op_e),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_358]),c_0_200]) ).

cnf(c_0_369,plain,
    ld(op_f,mult(mult(op_f,X1),op_f)) = mult(mult(X1,op_e),op_e),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_315]),c_0_238]) ).

cnf(c_0_370,plain,
    rd(ld(op_e,mult(X1,op_f)),op_e) = ld(op_e,mult(X1,op_e)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_359,c_0_360]),c_0_35]) ).

cnf(c_0_371,plain,
    ld(ld(mult(X1,X1),unit),op_e) = mult(X1,mult(X1,op_e)),
    inference(spm,[status(thm)],[c_0_37,c_0_361]) ).

cnf(c_0_372,plain,
    rd(op_d,op_e) = ld(op_d,unit),
    inference(spm,[status(thm)],[c_0_106,c_0_100]) ).

cnf(c_0_373,plain,
    rd(rd(X1,mult(op_e,X1)),op_e) = rd(X1,mult(op_f,X1)),
    inference(spm,[status(thm)],[c_0_18,c_0_362]) ).

cnf(c_0_374,plain,
    rd(X1,mult(op_e,X1)) = ld(op_e,unit),
    inference(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_363,c_0_364]),c_0_37]),c_0_25]),c_0_206]),c_0_122]),c_0_365]),c_0_159]) ).

cnf(c_0_375,plain,
    rd(op_f,mult(X1,op_f)) = ld(mult(op_e,X1),op_e),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_366,c_0_34]),c_0_141]) ).

cnf(c_0_376,plain,
    mult(rd(rd(op_e,X1),X2),X1) = mult(op_e,ld(X1,ld(X2,X1))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_352,c_0_245]),c_0_24]),c_0_367]) ).

cnf(c_0_377,plain,
    mult(mult(op_e,ld(mult(op_d,X1),unit)),op_d) = rd(op_e,X1),
    inference(spm,[status(thm)],[c_0_150,c_0_16]) ).

cnf(c_0_378,plain,
    mult(rd(op_e,mult(op_d,X1)),op_d) = mult(op_d,rd(op_d,X1)),
    inference(spm,[status(thm)],[c_0_103,c_0_100]) ).

cnf(c_0_379,plain,
    ld(op_e,mult(mult(op_f,X1),op_e)) = mult(op_e,mult(X1,op_e)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_368,c_0_369]),c_0_18]),c_0_370]) ).

cnf(c_0_380,plain,
    mult(ld(ld(X1,op_e),op_d),op_d) = ld(op_e,mult(X1,op_e)),
    inference(spm,[status(thm)],[c_0_83,c_0_217]) ).

cnf(c_0_381,plain,
    ld(mult(ld(X1,unit),X2),X1) = mult(mult(ld(X2,unit),X1),X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_61]),c_0_51]),c_0_43]) ).

cnf(c_0_382,plain,
    mult(ld(mult(X1,X1),unit),mult(X1,mult(X1,op_e))) = op_e,
    inference(spm,[status(thm)],[c_0_15,c_0_371]) ).

cnf(c_0_383,plain,
    mult(ld(op_d,unit),op_e) = op_d,
    inference(spm,[status(thm)],[c_0_25,c_0_372]) ).

cnf(c_0_384,plain,
    ld(rd(op_f,X1),unit) = rd(X1,op_f),
    inference(rw,[status(thm)],[c_0_366,c_0_365]) ).

cnf(c_0_385,plain,
    ld(rd(X1,mult(X2,X1)),ld(X2,rd(X1,X2))) = rd(X1,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_301,c_0_311]),c_0_175]),c_0_37]),c_0_15]) ).

cnf(c_0_386,plain,
    rd(X1,mult(op_f,X1)) = ld(op_f,unit),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_373,c_0_374]),c_0_116]),c_0_165]) ).

cnf(c_0_387,plain,
    mult(ld(mult(op_e,X1),op_e),op_f) = ld(X1,op_f),
    inference(spm,[status(thm)],[c_0_45,c_0_375]) ).

cnf(c_0_388,plain,
    mult(rd(op_e,X1),rd(X1,mult(X2,X1))) = rd(rd(op_e,X1),X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_376]),c_0_129]),c_0_141]) ).

cnf(c_0_389,plain,
    mult(op_d,rd(op_d,X1)) = rd(op_e,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_377,c_0_352]),c_0_378]) ).

cnf(c_0_390,plain,
    ld(X1,ld(op_e,unit)) = mult(ld(mult(op_f,X1),unit),op_e),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_379]),c_0_72]),c_0_43]) ).

cnf(c_0_391,plain,
    mult(ld(X1,unit),op_e) = ld(X1,op_e),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_345,c_0_380]),c_0_51]),c_0_43]),c_0_34]) ).

cnf(c_0_392,plain,
    ld(rd(X1,mult(X2,X1)),ld(X2,X1)) = X1,
    inference(spm,[status(thm)],[c_0_37,c_0_141]) ).

cnf(c_0_393,plain,
    rd(mult(X1,X2),mult(X2,mult(X1,X2))) = rd(X1,mult(X2,X1)),
    inference(spm,[status(thm)],[c_0_320,c_0_18]) ).

cnf(c_0_394,plain,
    mult(ld(mult(X1,op_e),X1),mult(X1,X1)) = ld(op_e,mult(X1,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_381,c_0_382]),c_0_143]) ).

cnf(c_0_395,plain,
    mult(ld(mult(mult(X1,X2),X1),X1),X1) = ld(X1,ld(X2,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_31]),c_0_50]) ).

cnf(c_0_396,plain,
    mult(op_d,rd(op_d,rd(op_e,X1))) = rd(mult(op_e,X1),op_e),
    inference(spm,[status(thm)],[c_0_55,c_0_250]) ).

cnf(c_0_397,plain,
    ld(ld(op_d,unit),op_e) = mult(op_d,op_e),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_383]),c_0_74]),c_0_100]),c_0_30]),c_0_147]) ).

cnf(c_0_398,plain,
    rd(X1,mult(X1,rd(X2,op_f))) = rd(mult(X1,op_f),mult(X1,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_384]),c_0_24]),c_0_94]) ).

cnf(c_0_399,plain,
    mult(X1,ld(op_f,unit)) = rd(X1,op_f),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_385,c_0_386]),c_0_180]),c_0_49]),c_0_75]),c_0_96]) ).

cnf(c_0_400,plain,
    mult(ld(X1,unit),op_f) = ld(X1,op_f),
    inference(rw,[status(thm)],[c_0_387,c_0_365]) ).

cnf(c_0_401,plain,
    ld(mult(rd(op_e,X1),X2),rd(op_e,X1)) = rd(X1,mult(X2,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_388]),c_0_122]) ).

cnf(c_0_402,plain,
    ld(rd(op_e,X1),unit) = rd(X1,op_e),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_269,c_0_389]),c_0_100]) ).

cnf(c_0_403,plain,
    mult(X1,ld(op_e,unit)) = rd(X1,op_e),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_365]),c_0_390]),c_0_391]),c_0_236]),c_0_96]) ).

cnf(c_0_404,plain,
    mult(ld(mult(X1,X2),X1),rd(X2,X1)) = ld(mult(X2,X1),X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_273,c_0_260]),c_0_243]) ).

cnf(c_0_405,plain,
    rd(rd(X1,X2),ld(mult(X1,X2),X1)) = X1,
    inference(spm,[status(thm)],[c_0_34,c_0_122]) ).

cnf(c_0_406,plain,
    ld(rd(X1,X2),rd(mult(X1,X2),X1)) = rd(mult(X2,X2),X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_312]),c_0_15]) ).

cnf(c_0_407,plain,
    mult(ld(X1,op_d),op_d) = ld(X1,op_e),
    inference(spm,[status(thm)],[c_0_354,c_0_34]) ).

cnf(c_0_408,plain,
    rd(op_e,op_d) = op_d,
    inference(spm,[status(thm)],[c_0_18,c_0_100]) ).

cnf(c_0_409,plain,
    ld(rd(X1,mult(X2,X1)),ld(X2,mult(X1,X2))) = mult(X1,X2),
    inference(spm,[status(thm)],[c_0_392,c_0_393]) ).

cnf(c_0_410,plain,
    rd(mult(X1,X1),mult(op_e,mult(X1,X1))) = ld(mult(X1,op_e),X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_394]),c_0_141]) ).

cnf(c_0_411,plain,
    ld(mult(X1,ld(op_d,unit)),unit) = ld(op_d,rd(op_e,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_395,c_0_396]),c_0_19]),c_0_108]),c_0_330]),c_0_37]) ).

cnf(c_0_412,plain,
    rd(op_e,ld(X1,ld(op_d,unit))) = mult(mult(op_d,op_e),X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_63]),c_0_55]),c_0_211]),c_0_147]),c_0_16]) ).

cnf(c_0_413,plain,
    mult(op_d,mult(op_d,op_e)) = op_f,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_397]),c_0_166]),c_0_100]),c_0_165]),c_0_147]) ).

cnf(c_0_414,plain,
    mult(op_d,mult(op_e,ld(op_d,X1))) = mult(op_e,X1),
    inference(spm,[status(thm)],[c_0_19,c_0_132]) ).

cnf(c_0_415,plain,
    rd(X1,mult(rd(X2,mult(X1,op_f)),X1)) = rd(mult(X1,op_f),X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_398,c_0_183]),c_0_15]) ).

cnf(c_0_416,plain,
    mult(rd(mult(X1,X2),mult(X2,op_f)),X2) = mult(X1,rd(X2,op_f)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_399]),c_0_183]),c_0_399]) ).

cnf(c_0_417,plain,
    ld(X1,ld(X2,mult(X1,op_f))) = mult(ld(X1,ld(X2,X1)),op_f),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_400,c_0_245]),c_0_24]),c_0_245]) ).

cnf(c_0_418,plain,
    rd(X1,mult(op_e,ld(mult(X2,X1),X1))) = mult(X2,rd(X1,op_e)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_244,c_0_401]),c_0_44]),c_0_85]),c_0_32]),c_0_402]) ).

cnf(c_0_419,plain,
    mult(rd(X1,X2),rd(X2,op_e)) = mult(rd(X1,mult(X2,op_e)),X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_403]),c_0_403]),c_0_183]) ).

cnf(c_0_420,plain,
    ld(ld(mult(X1,X2),X1),rd(X2,X1)) = mult(X2,rd(X2,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_404]),c_0_405]) ).

cnf(c_0_421,plain,
    rd(op_e,ld(X1,op_d)) = mult(op_d,X1),
    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_406,c_0_407]),c_0_141]),c_0_197]),c_0_408]),c_0_409]),c_0_100]) ).

cnf(c_0_422,plain,
    ld(mult(X1,op_e),X1) = ld(op_e,unit),
    inference(rw,[status(thm)],[c_0_410,c_0_374]) ).

cnf(c_0_423,plain,
    ld(ld(op_e,unit),X1) = ld(op_d,mult(mult(op_d,op_e),X1)),
    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_91,c_0_411]),c_0_412]),c_0_232]),c_0_49]),c_0_233]),c_0_100]) ).

cnf(c_0_424,plain,
    ld(X1,mult(X2,mult(X1,X3))) = mult(ld(X1,mult(X2,X1)),X3),
    inference(spm,[status(thm)],[c_0_170,c_0_16]) ).

cnf(c_0_425,plain,
    ld(op_d,op_f) = mult(op_d,op_e),
    inference(spm,[status(thm)],[c_0_16,c_0_413]) ).

cnf(c_0_426,plain,
    mult(op_e,mult(op_d,X1)) = mult(op_d,mult(op_e,X1)),
    inference(spm,[status(thm)],[c_0_414,c_0_16]) ).

cnf(c_0_427,plain,
    rd(X1,mult(X2,rd(X1,op_f))) = rd(mult(X1,op_f),mult(X2,X1)),
    inference(spm,[status(thm)],[c_0_415,c_0_416]) ).

cnf(c_0_428,plain,
    mult(X1,mult(ld(X1,ld(X2,X1)),op_f)) = ld(X2,mult(X1,op_f)),
    inference(spm,[status(thm)],[c_0_15,c_0_417]) ).

cnf(c_0_429,plain,
    rd(X1,mult(op_e,ld(X2,X1))) = mult(rd(X2,mult(X1,op_e)),X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_418,c_0_25]),c_0_419]) ).

cnf(c_0_430,plain,
    mult(mult(op_d,op_e),X1) = mult(op_d,mult(op_e,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(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_420,c_0_421]),c_0_422]),c_0_423]),c_0_424]),c_0_166]),c_0_100]),c_0_165]),c_0_425]),c_0_426]) ).

cnf(c_0_431,plain,
    rd(ld(X1,X2),rd(X2,op_f)) = rd(ld(X1,mult(X2,op_f)),X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_427]),c_0_218]) ).

cnf(c_0_432,plain,
    ld(rd(X1,X2),mult(X1,op_f)) = mult(X1,mult(ld(X1,X2),op_f)),
    inference(spm,[status(thm)],[c_0_428,c_0_37]) ).

cnf(c_0_433,plain,
    rd(mult(X1,op_e),ld(X1,op_f)) = mult(rd(X1,op_e),X1),
    inference(spm,[status(thm)],[c_0_321,c_0_165]) ).

cnf(c_0_434,plain,
    mult(op_e,ld(op_f,unit)) = ld(op_e,unit),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_253]),c_0_18]),c_0_206]) ).

cnf(c_0_435,plain,
    ld(mult(X1,mult(op_e,ld(X2,X1))),X1) = rd(ld(X1,X2),op_e),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_429]),c_0_218]) ).

cnf(c_0_436,plain,
    ld(ld(op_e,unit),X1) = mult(op_e,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_423,c_0_430]),c_0_16]) ).

cnf(c_0_437,plain,
    mult(ld(op_e,unit),X1) = ld(op_e,X1),
    inference(spm,[status(thm)],[c_0_45,c_0_374]) ).

cnf(c_0_438,plain,
    rd(mult(X1,mult(ld(X1,X2),op_f)),X1) = rd(X2,rd(X1,op_f)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_431,c_0_37]),c_0_432]) ).

cnf(c_0_439,plain,
    ld(mult(op_f,X1),op_f) = ld(X1,unit),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_391]),c_0_141]),c_0_247]) ).

cnf(c_0_440,plain,
    rd(op_e,ld(X1,ld(X1,op_f))) = ld(op_e,mult(X1,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_433]),c_0_239]),c_0_16]) ).

cnf(c_0_441,plain,
    ld(mult(X1,rd(X2,op_e)),X2) = mult(op_e,ld(mult(X1,X2),X2)),
    inference(spm,[status(thm)],[c_0_37,c_0_418]) ).

cnf(c_0_442,plain,
    rd(X1,mult(op_e,mult(op_e,X1))) = ld(op_f,unit),
    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_22,c_0_282]),c_0_288]),c_0_289]),c_0_434]),c_0_116]),c_0_165]) ).

cnf(c_0_443,plain,
    rd(ld(mult(X1,X2),X1),op_e) = ld(mult(X1,mult(op_e,X2)),X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_435,c_0_37]),c_0_122]) ).

cnf(c_0_444,plain,
    ld(mult(ld(X1,unit),X2),ld(X1,unit)) = rd(X1,mult(X2,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_56]),c_0_122]),c_0_15]),c_0_141]) ).

cnf(c_0_445,plain,
    mult(X1,ld(ld(X2,X1),ld(X1,X3))) = ld(ld(rd(X2,X1),unit),X3),
    inference(spm,[status(thm)],[c_0_148,c_0_52]) ).

cnf(c_0_446,plain,
    mult(X1,ld(ld(op_e,X1),X2)) = mult(mult(op_e,X1),ld(X1,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_436]),c_0_211]),c_0_437]) ).

cnf(c_0_447,plain,
    mult(rd(rd(X1,X2),rd(X2,X3)),X2) = rd(X1,ld(ld(X2,X3),unit)),
    inference(spm,[status(thm)],[c_0_367,c_0_29]) ).

cnf(c_0_448,plain,
    mult(rd(X1,rd(X2,op_f)),X2) = mult(X2,mult(ld(X2,X1),op_f)),
    inference(spm,[status(thm)],[c_0_25,c_0_438]) ).

cnf(c_0_449,plain,
    ld(ld(X1,op_f),unit) = ld(op_f,X1),
    inference(spm,[status(thm)],[c_0_110,c_0_439]) ).

cnf(c_0_450,plain,
    mult(ld(X1,unit),rd(mult(X1,X1),X2)) = ld(rd(X2,X1),unit),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_149]),c_0_16]),c_0_52]) ).

cnf(c_0_451,plain,
    rd(rd(ld(X1,X2),X1),ld(mult(X2,X1),X2)) = ld(X1,X2),
    inference(spm,[status(thm)],[c_0_405,c_0_261]) ).

cnf(c_0_452,plain,
    rd(ld(ld(X1,unit),X2),ld(X1,unit)) = mult(mult(X1,X2),X1),
    inference(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_64,c_0_35]),c_0_24]),c_0_36]),c_0_24]),c_0_207]),c_0_24]),c_0_24]) ).

cnf(c_0_453,plain,
    mult(rd(rd(X1,X2),rd(X3,X2)),X2) = rd(X1,ld(X2,X3)),
    inference(spm,[status(thm)],[c_0_112,c_0_25]) ).

cnf(c_0_454,plain,
    ld(ld(X1,op_e),unit) = ld(op_e,X1),
    inference(spm,[status(thm)],[c_0_110,c_0_365]) ).

cnf(c_0_455,plain,
    ld(X1,ld(X1,op_f)) = mult(ld(mult(X1,X1),unit),op_f),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_440]),c_0_109]),c_0_165]) ).

cnf(c_0_456,plain,
    ld(mult(rd(X1,mult(X2,op_e)),X2),X2) = mult(op_e,ld(X1,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_441,c_0_419]),c_0_25]) ).

cnf(c_0_457,plain,
    rd(rd(X1,op_e),op_e) = mult(X1,ld(op_f,unit)),
    inference(spm,[status(thm)],[c_0_18,c_0_306]) ).

cnf(c_0_458,plain,
    ld(ld(op_f,unit),X1) = mult(op_e,mult(op_e,X1)),
    inference(spm,[status(thm)],[c_0_37,c_0_442]) ).

cnf(c_0_459,plain,
    rd(X1,mult(mult(op_e,X1),ld(X1,X2))) = rd(rd(X1,X2),op_e),
    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_64]),c_0_68]),c_0_15]),c_0_444]),c_0_211]) ).

cnf(c_0_460,plain,
    mult(mult(op_e,X1),ld(X1,ld(X1,X2))) = ld(rd(X1,op_e),X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_445,c_0_446]),c_0_402]) ).

cnf(c_0_461,plain,
    mult(X1,mult(ld(X1,rd(X2,X1)),op_f)) = rd(X2,ld(op_f,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_447,c_0_448]),c_0_449]) ).

cnf(c_0_462,plain,
    ld(ld(X1,unit),ld(rd(X2,X1),unit)) = rd(mult(X1,X1),X2),
    inference(spm,[status(thm)],[c_0_16,c_0_450]) ).

cnf(c_0_463,plain,
    ld(ld(X1,unit),op_e) = mult(X1,op_e),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_451,c_0_352]),c_0_452]),c_0_37]),c_0_18]) ).

cnf(c_0_464,plain,
    rd(rd(X1,ld(X2,X3)),X2) = rd(rd(X1,X2),rd(X3,X2)),
    inference(spm,[status(thm)],[c_0_18,c_0_453]) ).

cnf(c_0_465,plain,
    mult(ld(X1,unit),mult(X1,X2)) = mult(X1,mult(ld(X1,unit),X2)),
    inference(spm,[status(thm)],[c_0_87,c_0_49]) ).

cnf(c_0_466,plain,
    mult(rd(X1,op_e),X1) = mult(X1,ld(op_e,X1)),
    inference(spm,[status(thm)],[c_0_27,c_0_454]) ).

cnf(c_0_467,plain,
    mult(rd(rd(X1,X2),X1),op_e) = mult(X1,ld(X2,ld(X1,op_e))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_391,c_0_148]),c_0_156]),c_0_148]) ).

cnf(c_0_468,plain,
    rd(op_f,mult(X1,mult(X1,op_f))) = ld(mult(X1,X1),unit),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_289,c_0_455]),c_0_15]),c_0_18]),c_0_15]),c_0_289]) ).

cnf(c_0_469,plain,
    ld(mult(X1,rd(X2,op_e)),X1) = mult(op_e,ld(mult(X1,X2),X1)),
    inference(spm,[status(thm)],[c_0_456,c_0_103]) ).

cnf(c_0_470,plain,
    rd(rd(X1,op_e),op_e) = rd(X1,op_f),
    inference(rw,[status(thm)],[c_0_457,c_0_399]) ).

cnf(c_0_471,plain,
    mult(op_e,mult(op_e,X1)) = mult(op_f,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_386]),c_0_458]) ).

cnf(c_0_472,plain,
    rd(X1,ld(rd(X1,op_e),X2)) = rd(mult(X1,ld(X2,X1)),op_e),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_459,c_0_460]),c_0_51]) ).

cnf(c_0_473,plain,
    rd(rd(X1,ld(op_f,X2)),X2) = rd(rd(X1,X2),rd(X2,op_f)),
    inference(spm,[status(thm)],[c_0_438,c_0_461]) ).

cnf(c_0_474,plain,
    mult(mult(op_e,X1),op_e) = mult(op_e,mult(X1,op_e)),
    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_462,c_0_374]),c_0_30]),c_0_463]),c_0_334]),c_0_82]),c_0_463]) ).

cnf(c_0_475,plain,
    rd(rd(X1,X2),ld(X2,unit)) = mult(X2,mult(ld(X2,unit),X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_464,c_0_238]),c_0_61]),c_0_49]),c_0_465]) ).

cnf(c_0_476,plain,
    ld(X1,ld(rd(X1,op_e),mult(X1,X2))) = ld(ld(op_e,X1),X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_245,c_0_466]),c_0_16]) ).

cnf(c_0_477,plain,
    mult(ld(mult(X1,X2),X1),ld(X1,op_e)) = ld(X2,ld(X1,op_e)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_467]),c_0_16]),c_0_122]) ).

cnf(c_0_478,plain,
    ld(ld(mult(X1,X1),unit),op_f) = mult(X1,mult(X1,op_f)),
    inference(spm,[status(thm)],[c_0_37,c_0_468]) ).

cnf(c_0_479,plain,
    mult(ld(X1,ld(X2,unit)),X2) = mult(X2,ld(mult(X1,X2),unit)),
    inference(spm,[status(thm)],[c_0_142,c_0_72]) ).

cnf(c_0_480,plain,
    ld(mult(X1,rd(X2,op_f)),X1) = mult(op_f,ld(mult(X1,X2),X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_469,c_0_470]),c_0_469]),c_0_471]) ).

cnf(c_0_481,plain,
    rd(mult(X1,op_e),ld(X1,X2)) = mult(X1,ld(rd(X2,op_e),X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(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_472,c_0_473]),c_0_206]),c_0_238]),c_0_474]),c_0_16]),c_0_254]),c_0_475]),c_0_437]),c_0_15]),c_0_206]),c_0_238]),c_0_474]),c_0_16]),c_0_206]),c_0_238]),c_0_474]),c_0_16]),c_0_334]),c_0_343]) ).

cnf(c_0_482,plain,
    ld(rd(X1,op_e),mult(X1,X2)) = mult(mult(op_e,X1),ld(X1,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_476]),c_0_446]) ).

cnf(c_0_483,plain,
    rd(mult(op_e,X1),op_e) = mult(op_e,rd(X1,op_e)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_327,c_0_374]),c_0_75]) ).

cnf(c_0_484,plain,
    mult(ld(op_e,X1),ld(mult(X1,X2),X1)) = rd(ld(op_e,X1),X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_477]),c_0_56]),c_0_454]),c_0_454]) ).

cnf(c_0_485,plain,
    mult(rd(X1,mult(op_e,op_f)),op_e) = mult(X1,ld(op_f,unit)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_283]),c_0_307]),c_0_233]),c_0_165]) ).

cnf(c_0_486,plain,
    mult(ld(mult(X1,X1),unit),mult(X1,mult(X1,op_f))) = op_f,
    inference(spm,[status(thm)],[c_0_15,c_0_478]) ).

cnf(c_0_487,plain,
    mult(rd(X1,mult(X2,X1)),mult(X2,mult(X1,X2))) = mult(X1,X2),
    inference(spm,[status(thm)],[c_0_25,c_0_393]) ).

cnf(c_0_488,plain,
    mult(X1,mult(ld(X1,unit),mult(X2,X1))) = rd(X2,ld(X1,unit)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_30]),c_0_90]),c_0_24]),c_0_465]) ).

cnf(c_0_489,plain,
    mult(mult(op_f,rd(X1,mult(X2,X1))),X1) = ld(rd(X2,op_f),X1),
    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_479,c_0_480]),c_0_444]),c_0_58]),c_0_245]),c_0_24]),c_0_15]) ).

cnf(c_0_490,plain,
    mult(rd(X1,X2),rd(X2,op_f)) = mult(rd(X1,mult(X2,op_f)),X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_399]),c_0_399]),c_0_183]) ).

cnf(c_0_491,plain,
    rd(rd(X1,X2),op_e) = mult(rd(X1,mult(op_f,X2)),op_e),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(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_481,c_0_482]),c_0_25]),c_0_459]),c_0_199]),c_0_483]),c_0_443]),c_0_87]),c_0_484]),c_0_183]),c_0_471]) ).

cnf(c_0_492,plain,
    mult(rd(X1,mult(op_e,op_f)),op_e) = rd(X1,op_f),
    inference(rw,[status(thm)],[c_0_485,c_0_399]) ).

cnf(c_0_493,plain,
    mult(ld(mult(X1,op_f),X1),mult(X1,X1)) = ld(op_f,mult(X1,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_381,c_0_486]),c_0_143]) ).

cnf(c_0_494,plain,
    mult(X1,mult(ld(X2,X1),ld(X1,X3))) = mult(ld(rd(X2,X1),unit),X3),
    inference(spm,[status(thm)],[c_0_19,c_0_52]) ).

cnf(c_0_495,plain,
    ld(ld(op_f,unit),X1) = mult(op_f,X1),
    inference(rw,[status(thm)],[c_0_458,c_0_471]) ).

cnf(c_0_496,plain,
    mult(mult(X1,op_e),op_e) = mult(X1,op_f),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_487,c_0_386]),c_0_465]),c_0_488]),c_0_238]),c_0_369]) ).

cnf(c_0_497,plain,
    ld(rd(rd(X1,X2),op_f),X1) = mult(mult(op_f,X1),ld(X1,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_489,c_0_38]),c_0_211]) ).

cnf(c_0_498,plain,
    rd(rd(X1,X2),op_f) = rd(X1,mult(op_f,X2)),
    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_254]),c_0_403]),c_0_18]),c_0_492]) ).

cnf(c_0_499,plain,
    rd(mult(X1,X1),mult(op_f,mult(X1,X1))) = ld(mult(X1,op_f),X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_493]),c_0_141]) ).

cnf(c_0_500,plain,
    mult(mult(X1,mult(ld(X1,X2),X1)),X1) = mult(X2,mult(X1,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_241,c_0_87]),c_0_25]) ).

cnf(c_0_501,plain,
    mult(X1,mult(mult(op_f,X1),ld(X1,X2))) = mult(mult(X1,op_f),X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_494,c_0_495]),c_0_220]),c_0_449]),c_0_369]),c_0_496]) ).

cnf(c_0_502,plain,
    mult(mult(op_f,X1),ld(X1,X2)) = mult(op_f,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_497,c_0_498]),c_0_37]) ).

cnf(c_0_503,plain,
    rd(ld(X1,X2),ld(mult(X2,X1),X2)) = mult(ld(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_34,c_0_261]) ).

cnf(c_0_504,plain,
    ld(mult(X1,op_f),X1) = ld(op_f,unit),
    inference(rw,[status(thm)],[c_0_499,c_0_386]) ).

cnf(c_0_505,plain,
    rd(mult(rd(X1,X2),X1),ld(ld(X1,X2),unit)) = X1,
    inference(spm,[status(thm)],[c_0_18,c_0_27]) ).

cnf(c_0_506,plain,
    rd(mult(X1,mult(X2,X2)),X2) = mult(X2,mult(ld(X2,X1),X2)),
    inference(spm,[status(thm)],[c_0_18,c_0_500]) ).

cnf(c_0_507,plain,
    mult(mult(X1,op_f),X2) = mult(X1,mult(op_f,X2)),
    inference(rw,[status(thm)],[c_0_501,c_0_502]) ).

cnf(c_0_508,plain,
    ld(op_f,mult(X1,op_f)) = mult(ld(op_f,X1),op_f),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_503,c_0_504]),c_0_197]),c_0_160]) ).

cnf(c_0_509,plain,
    mult(op_f,mult(ld(op_f,X1),op_f)) = mult(X1,op_f),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_505,c_0_504]),c_0_87]),c_0_16]),c_0_30]),c_0_506]) ).

cnf(c_0_510,negated_conjecture,
    mult(a,mult(b,op_f)) != mult(mult(a,b),op_f),
    goals ).

cnf(c_0_511,plain,
    mult(mult(X1,X2),op_f) = mult(X1,mult(X2,op_f)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_507]),c_0_508]),c_0_509]) ).

cnf(c_0_512,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_510,c_0_511])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : GRP695-1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n026.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Mon Aug 28 22:53:20 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.59  start to proof: theBenchmark
% 23.27/23.29  % Version  : CSE_E---1.5
% 23.27/23.29  % Problem  : theBenchmark.p
% 23.27/23.29  % Proof found
% 23.27/23.29  % SZS status Theorem for theBenchmark.p
% 23.27/23.29  % SZS output start Proof
% See solution above
% 23.27/23.32  % Total time : 22.699000 s
% 23.27/23.32  % SZS output end Proof
% 23.27/23.32  % Total time : 22.703000 s
%------------------------------------------------------------------------------