%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : KLE109+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n013.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 05:26:10 EDT 2023

% Result   : Theorem 43.32s 43.39s
% Output   : CNFRefutation 43.40s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)

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

tff(decl_23,type,
    zero: $i ).

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

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

tff(decl_26,type,
    leq: ( $i * $i ) > $o ).

tff(decl_27,type,
    antidomain: $i > $i ).

tff(decl_28,type,
    domain: $i > $i ).

tff(decl_29,type,
    coantidomain: $i > $i ).

tff(decl_30,type,
    codomain: $i > $i ).

tff(decl_31,type,
    c: $i > $i ).

tff(decl_32,type,
    domain_difference: ( $i * $i ) > $i ).

tff(decl_33,type,
    forward_diamond: ( $i * $i ) > $i ).

tff(decl_34,type,
    backward_diamond: ( $i * $i ) > $i ).

tff(decl_35,type,
    forward_box: ( $i * $i ) > $i ).

tff(decl_36,type,
    backward_box: ( $i * $i ) > $i ).

tff(decl_37,type,
    esk1_0: $i ).

tff(decl_38,type,
    esk2_0: $i ).

fof(left_distributivity,axiom,
    ! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).

fof(domain1,axiom,
    ! [X4] : multiplication(antidomain(X4),X4) = zero,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain1) ).

fof(additive_identity,axiom,
    ! [X1] : addition(X1,zero) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).

fof(additive_commutativity,axiom,
    ! [X1,X2] : addition(X1,X2) = addition(X2,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).

fof(domain3,axiom,
    ! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain3) ).

fof(right_distributivity,axiom,
    ! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).

fof(multiplicative_right_identity,axiom,
    ! [X1] : multiplication(X1,one) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).

fof(multiplicative_left_identity,axiom,
    ! [X1] : multiplication(one,X1) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).

fof(additive_associativity,axiom,
    ! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).

fof(additive_idempotence,axiom,
    ! [X1] : addition(X1,X1) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).

fof(codomain3,axiom,
    ! [X4] : addition(coantidomain(coantidomain(X4)),coantidomain(X4)) = one,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',codomain3) ).

fof(codomain1,axiom,
    ! [X4] : multiplication(X4,coantidomain(X4)) = zero,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',codomain1) ).

fof(multiplicative_associativity,axiom,
    ! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).

fof(left_annihilation,axiom,
    ! [X1] : multiplication(zero,X1) = zero,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).

fof(domain2,axiom,
    ! [X4,X5] : addition(antidomain(multiplication(X4,X5)),antidomain(multiplication(X4,antidomain(antidomain(X5))))) = antidomain(multiplication(X4,antidomain(antidomain(X5)))),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain2) ).

fof(codomain2,axiom,
    ! [X4,X5] : addition(coantidomain(multiplication(X4,X5)),coantidomain(multiplication(coantidomain(coantidomain(X4)),X5))) = coantidomain(multiplication(coantidomain(coantidomain(X4)),X5)),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',codomain2) ).

fof(right_annihilation,axiom,
    ! [X1] : multiplication(X1,zero) = zero,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).

fof(complement,axiom,
    ! [X4] : c(X4) = antidomain(domain(X4)),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax',complement) ).

fof(domain4,axiom,
    ! [X4] : domain(X4) = antidomain(antidomain(X4)),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain4) ).

fof(goals,conjecture,
    ! [X4,X5] : addition(forward_diamond(X4,backward_box(X4,domain(X5))),domain(X5)) = domain(X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

fof(forward_diamond,axiom,
    ! [X4,X5] : forward_diamond(X4,X5) = domain(multiplication(X4,domain(X5))),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax',forward_diamond) ).

fof(backward_box,axiom,
    ! [X4,X5] : backward_box(X4,X5) = c(backward_diamond(X4,c(X5))),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax',backward_box) ).

fof(backward_diamond,axiom,
    ! [X4,X5] : backward_diamond(X4,X5) = codomain(multiplication(codomain(X5),X4)),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax',backward_diamond) ).

fof(codomain4,axiom,
    ! [X4] : codomain(X4) = coantidomain(coantidomain(X4)),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',codomain4) ).

fof(c_0_24,plain,
    ! [X21,X22,X23] : multiplication(addition(X21,X22),X23) = addition(multiplication(X21,X23),multiplication(X22,X23)),
    inference(variable_rename,[status(thm)],[left_distributivity]) ).

fof(c_0_25,plain,
    ! [X28] : multiplication(antidomain(X28),X28) = zero,
    inference(variable_rename,[status(thm)],[domain1]) ).

fof(c_0_26,plain,
    ! [X11] : addition(X11,zero) = X11,
    inference(variable_rename,[status(thm)],[additive_identity]) ).

cnf(c_0_27,plain,
    multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_28,plain,
    multiplication(antidomain(X1),X1) = zero,
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_29,plain,
    addition(X1,zero) = X1,
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

fof(c_0_30,plain,
    ! [X6,X7] : addition(X6,X7) = addition(X7,X6),
    inference(variable_rename,[status(thm)],[additive_commutativity]) ).

fof(c_0_31,plain,
    ! [X31] : addition(antidomain(antidomain(X31)),antidomain(X31)) = one,
    inference(variable_rename,[status(thm)],[domain3]) ).

fof(c_0_32,plain,
    ! [X18,X19,X20] : multiplication(X18,addition(X19,X20)) = addition(multiplication(X18,X19),multiplication(X18,X20)),
    inference(variable_rename,[status(thm)],[right_distributivity]) ).

fof(c_0_33,plain,
    ! [X16] : multiplication(X16,one) = X16,
    inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).

cnf(c_0_34,plain,
    multiplication(addition(X1,antidomain(X2)),X2) = multiplication(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).

cnf(c_0_35,plain,
    addition(X1,X2) = addition(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_36,plain,
    addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

fof(c_0_37,plain,
    ! [X17] : multiplication(one,X17) = X17,
    inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).

fof(c_0_38,plain,
    ! [X8,X9,X10] : addition(X10,addition(X9,X8)) = addition(addition(X10,X9),X8),
    inference(variable_rename,[status(thm)],[additive_associativity]) ).

fof(c_0_39,plain,
    ! [X12] : addition(X12,X12) = X12,
    inference(variable_rename,[status(thm)],[additive_idempotence]) ).

cnf(c_0_40,plain,
    multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_41,plain,
    multiplication(X1,one) = X1,
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_42,plain,
    multiplication(addition(antidomain(X1),X2),X1) = multiplication(X2,X1),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_43,plain,
    addition(antidomain(X1),antidomain(antidomain(X1))) = one,
    inference(rw,[status(thm)],[c_0_36,c_0_35]) ).

cnf(c_0_44,plain,
    multiplication(one,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

fof(c_0_45,plain,
    ! [X36] : addition(coantidomain(coantidomain(X36)),coantidomain(X36)) = one,
    inference(variable_rename,[status(thm)],[codomain3]) ).

fof(c_0_46,plain,
    ! [X33] : multiplication(X33,coantidomain(X33)) = zero,
    inference(variable_rename,[status(thm)],[codomain1]) ).

fof(c_0_47,plain,
    ! [X13,X14,X15] : multiplication(X13,multiplication(X14,X15)) = multiplication(multiplication(X13,X14),X15),
    inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).

fof(c_0_48,plain,
    ! [X25] : multiplication(zero,X25) = zero,
    inference(variable_rename,[status(thm)],[left_annihilation]) ).

cnf(c_0_49,plain,
    addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_50,plain,
    addition(X1,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_51,plain,
    addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_35]) ).

cnf(c_0_52,plain,
    multiplication(antidomain(antidomain(X1)),X1) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).

cnf(c_0_53,plain,
    addition(coantidomain(coantidomain(X1)),coantidomain(X1)) = one,
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

cnf(c_0_54,plain,
    multiplication(X1,coantidomain(X1)) = zero,
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

cnf(c_0_55,plain,
    multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[c_0_47]) ).

cnf(c_0_56,plain,
    multiplication(zero,X1) = zero,
    inference(split_conjunct,[status(thm)],[c_0_48]) ).

fof(c_0_57,plain,
    ! [X29,X30] : addition(antidomain(multiplication(X29,X30)),antidomain(multiplication(X29,antidomain(antidomain(X30))))) = antidomain(multiplication(X29,antidomain(antidomain(X30)))),
    inference(variable_rename,[status(thm)],[domain2]) ).

cnf(c_0_58,plain,
    antidomain(one) = zero,
    inference(spm,[status(thm)],[c_0_41,c_0_28]) ).

cnf(c_0_59,plain,
    addition(zero,X1) = X1,
    inference(spm,[status(thm)],[c_0_29,c_0_35]) ).

cnf(c_0_60,plain,
    addition(X1,addition(X1,X2)) = addition(X1,X2),
    inference(spm,[status(thm)],[c_0_49,c_0_50]) ).

cnf(c_0_61,plain,
    multiplication(antidomain(antidomain(X1)),addition(X1,one)) = addition(X1,antidomain(antidomain(X1))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_35]) ).

cnf(c_0_62,plain,
    addition(coantidomain(X1),coantidomain(coantidomain(X1))) = one,
    inference(rw,[status(thm)],[c_0_53,c_0_35]) ).

cnf(c_0_63,plain,
    multiplication(X1,addition(X2,coantidomain(X1))) = multiplication(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_54]),c_0_29]) ).

cnf(c_0_64,plain,
    multiplication(antidomain(X1),multiplication(X1,X2)) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_28]),c_0_56]) ).

cnf(c_0_65,plain,
    addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,antidomain(antidomain(X2))))) = antidomain(multiplication(X1,antidomain(antidomain(X2)))),
    inference(split_conjunct,[status(thm)],[c_0_57]) ).

cnf(c_0_66,plain,
    antidomain(zero) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_58]),c_0_59]) ).

cnf(c_0_67,plain,
    addition(one,antidomain(X1)) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_43]),c_0_35]) ).

cnf(c_0_68,plain,
    multiplication(antidomain(antidomain(X1)),addition(one,X1)) = addition(X1,antidomain(antidomain(X1))),
    inference(spm,[status(thm)],[c_0_61,c_0_35]) ).

cnf(c_0_69,plain,
    addition(one,coantidomain(X1)) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_62]),c_0_35]) ).

cnf(c_0_70,plain,
    multiplication(X1,addition(coantidomain(X1),X2)) = multiplication(X1,X2),
    inference(spm,[status(thm)],[c_0_63,c_0_35]) ).

cnf(c_0_71,plain,
    multiplication(antidomain(antidomain(antidomain(X1))),X1) = zero,
    inference(spm,[status(thm)],[c_0_64,c_0_52]) ).

cnf(c_0_72,plain,
    antidomain(multiplication(X1,antidomain(antidomain(coantidomain(X1))))) = one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_54]),c_0_66]),c_0_67]) ).

cnf(c_0_73,plain,
    addition(coantidomain(X1),addition(coantidomain(coantidomain(X1)),X2)) = addition(one,X2),
    inference(spm,[status(thm)],[c_0_49,c_0_62]) ).

cnf(c_0_74,plain,
    addition(coantidomain(X1),antidomain(antidomain(coantidomain(X1)))) = antidomain(antidomain(coantidomain(X1))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_41]) ).

cnf(c_0_75,plain,
    multiplication(addition(X1,X2),coantidomain(X2)) = multiplication(X1,coantidomain(X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_54]),c_0_29]) ).

cnf(c_0_76,plain,
    multiplication(X1,coantidomain(coantidomain(X1))) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_62]),c_0_41]) ).

fof(c_0_77,plain,
    ! [X34,X35] : addition(coantidomain(multiplication(X34,X35)),coantidomain(multiplication(coantidomain(coantidomain(X34)),X35))) = coantidomain(multiplication(coantidomain(coantidomain(X34)),X35)),
    inference(variable_rename,[status(thm)],[codomain2]) ).

cnf(c_0_78,plain,
    multiplication(antidomain(antidomain(antidomain(X1))),multiplication(X1,X2)) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_71]),c_0_56]) ).

cnf(c_0_79,plain,
    coantidomain(one) = zero,
    inference(spm,[status(thm)],[c_0_44,c_0_54]) ).

cnf(c_0_80,plain,
    multiplication(X1,antidomain(antidomain(coantidomain(X1)))) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_72]),c_0_44]) ).

cnf(c_0_81,plain,
    multiplication(antidomain(X1),addition(X2,X1)) = multiplication(antidomain(X1),X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_28]),c_0_29]) ).

cnf(c_0_82,plain,
    addition(coantidomain(X1),antidomain(antidomain(coantidomain(coantidomain(X1))))) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_67]) ).

cnf(c_0_83,plain,
    coantidomain(coantidomain(coantidomain(X1))) = coantidomain(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_62]),c_0_44]),c_0_76]) ).

cnf(c_0_84,plain,
    addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_44]),c_0_35]) ).

cnf(c_0_85,plain,
    addition(coantidomain(multiplication(X1,X2)),coantidomain(multiplication(coantidomain(coantidomain(X1)),X2))) = coantidomain(multiplication(coantidomain(coantidomain(X1)),X2)),
    inference(split_conjunct,[status(thm)],[c_0_77]) ).

cnf(c_0_86,plain,
    multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(X1))))),X1) = zero,
    inference(spm,[status(thm)],[c_0_78,c_0_52]) ).

cnf(c_0_87,plain,
    coantidomain(zero) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_79]),c_0_59]) ).

cnf(c_0_88,plain,
    multiplication(X1,addition(antidomain(antidomain(coantidomain(X1))),X2)) = multiplication(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_80]),c_0_59]) ).

cnf(c_0_89,plain,
    antidomain(antidomain(antidomain(X1))) = antidomain(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_43]),c_0_41]),c_0_52]) ).

cnf(c_0_90,plain,
    addition(antidomain(antidomain(coantidomain(X1))),coantidomain(coantidomain(X1))) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_35]) ).

cnf(c_0_91,plain,
    multiplication(addition(X1,one),coantidomain(coantidomain(X1))) = addition(X1,coantidomain(coantidomain(X1))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_76]),c_0_35]) ).

cnf(c_0_92,plain,
    coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(X1))))))),X1)) = one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87]),c_0_69]) ).

cnf(c_0_93,plain,
    multiplication(X1,antidomain(coantidomain(X1))) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_43]),c_0_41]),c_0_89]) ).

cnf(c_0_94,plain,
    multiplication(coantidomain(coantidomain(X1)),antidomain(coantidomain(X1))) = antidomain(coantidomain(X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_90]),c_0_44]) ).

cnf(c_0_95,plain,
    multiplication(addition(one,X1),coantidomain(coantidomain(X1))) = addition(X1,coantidomain(coantidomain(X1))),
    inference(spm,[status(thm)],[c_0_91,c_0_35]) ).

cnf(c_0_96,plain,
    multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(X1))))))),X1) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_92]),c_0_41]) ).

cnf(c_0_97,plain,
    coantidomain(coantidomain(X1)) = antidomain(coantidomain(X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_83]),c_0_94]) ).

cnf(c_0_98,plain,
    addition(antidomain(X1),addition(antidomain(antidomain(X1)),X2)) = addition(one,X2),
    inference(spm,[status(thm)],[c_0_49,c_0_43]) ).

cnf(c_0_99,plain,
    addition(antidomain(X1),coantidomain(coantidomain(antidomain(X1)))) = coantidomain(coantidomain(antidomain(X1))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_67]),c_0_44]) ).

cnf(c_0_100,plain,
    multiplication(antidomain(coantidomain(antidomain(X1))),X1) = zero,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_97]),c_0_89]),c_0_89]) ).

cnf(c_0_101,plain,
    addition(antidomain(X1),coantidomain(coantidomain(antidomain(antidomain(X1))))) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_69]) ).

cnf(c_0_102,plain,
    multiplication(coantidomain(X1),antidomain(coantidomain(coantidomain(X1)))) = antidomain(coantidomain(coantidomain(X1))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_82]),c_0_44]) ).

cnf(c_0_103,plain,
    multiplication(addition(antidomain(coantidomain(antidomain(X1))),X2),X1) = multiplication(X2,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_100]),c_0_59]) ).

cnf(c_0_104,plain,
    addition(antidomain(X1),antidomain(coantidomain(antidomain(antidomain(X1))))) = one,
    inference(rw,[status(thm)],[c_0_101,c_0_97]) ).

cnf(c_0_105,plain,
    antidomain(antidomain(coantidomain(X1))) = coantidomain(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_102,c_0_93]),c_0_97]) ).

cnf(c_0_106,plain,
    addition(antidomain(antidomain(X1)),coantidomain(coantidomain(antidomain(X1)))) = one,
    inference(spm,[status(thm)],[c_0_101,c_0_89]) ).

cnf(c_0_107,plain,
    addition(X1,addition(X2,X1)) = addition(X2,X1),
    inference(spm,[status(thm)],[c_0_60,c_0_35]) ).

cnf(c_0_108,plain,
    addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
    inference(spm,[status(thm)],[c_0_35,c_0_49]) ).

cnf(c_0_109,plain,
    multiplication(coantidomain(antidomain(X1)),X1) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_44]),c_0_105]),c_0_97]),c_0_105]) ).

cnf(c_0_110,plain,
    multiplication(coantidomain(antidomain(X1)),antidomain(antidomain(X1))) = coantidomain(antidomain(X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_106]),c_0_41]) ).

cnf(c_0_111,plain,
    multiplication(antidomain(addition(X1,X2)),X2) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_107]),c_0_28]) ).

cnf(c_0_112,plain,
    multiplication(antidomain(addition(X1,X2)),addition(X2,addition(X3,X1))) = multiplication(antidomain(addition(X1,X2)),X3),
    inference(spm,[status(thm)],[c_0_81,c_0_108]) ).

cnf(c_0_113,plain,
    addition(antidomain(antidomain(X1)),antidomain(coantidomain(antidomain(X1)))) = one,
    inference(rw,[status(thm)],[c_0_106,c_0_97]) ).

cnf(c_0_114,plain,
    coantidomain(antidomain(X1)) = antidomain(antidomain(X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_89]),c_0_110]) ).

cnf(c_0_115,plain,
    multiplication(antidomain(addition(X1,X2)),addition(X2,one)) = antidomain(addition(X1,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_111]),c_0_29]) ).

cnf(c_0_116,plain,
    multiplication(antidomain(addition(antidomain(X1),X2)),antidomain(antidomain(X1))) = antidomain(addition(antidomain(X1),X2)),
    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_113]),c_0_114]),c_0_89]),c_0_115]),c_0_114]),c_0_89]) ).

cnf(c_0_117,plain,
    multiplication(antidomain(addition(X1,X2)),X1) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_60]),c_0_28]) ).

cnf(c_0_118,plain,
    addition(one,addition(coantidomain(X1),X2)) = addition(one,X2),
    inference(spm,[status(thm)],[c_0_49,c_0_69]) ).

cnf(c_0_119,plain,
    addition(antidomain(antidomain(X1)),antidomain(addition(antidomain(X1),X2))) = antidomain(antidomain(X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_116]),c_0_35]),c_0_67]),c_0_44]) ).

cnf(c_0_120,plain,
    antidomain(multiplication(antidomain(addition(X1,X2)),antidomain(antidomain(X1)))) = one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_117]),c_0_66]),c_0_67]) ).

cnf(c_0_121,plain,
    addition(X1,addition(X2,addition(X3,X1))) = addition(X2,addition(X3,X1)),
    inference(spm,[status(thm)],[c_0_60,c_0_108]) ).

cnf(c_0_122,plain,
    addition(one,addition(X1,coantidomain(X2))) = addition(one,X1),
    inference(spm,[status(thm)],[c_0_118,c_0_35]) ).

cnf(c_0_123,plain,
    addition(antidomain(antidomain(X1)),antidomain(addition(X2,antidomain(X1)))) = antidomain(antidomain(X1)),
    inference(spm,[status(thm)],[c_0_119,c_0_107]) ).

cnf(c_0_124,plain,
    multiplication(X1,coantidomain(addition(X2,X1))) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_107]),c_0_54]) ).

cnf(c_0_125,plain,
    multiplication(antidomain(addition(X1,X2)),antidomain(antidomain(X1))) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_120]),c_0_44]) ).

cnf(c_0_126,plain,
    multiplication(X1,coantidomain(addition(X1,X2))) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_60]),c_0_54]) ).

fof(c_0_127,plain,
    ! [X24] : multiplication(X24,zero) = zero,
    inference(variable_rename,[status(thm)],[right_annihilation]) ).

cnf(c_0_128,plain,
    addition(coantidomain(X1),addition(antidomain(coantidomain(X1)),X2)) = addition(one,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_121]),c_0_122]),c_0_97]),c_0_108]) ).

cnf(c_0_129,plain,
    addition(antidomain(X1),antidomain(antidomain(addition(X2,antidomain(X1))))) = antidomain(antidomain(addition(X2,antidomain(X1)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_123]),c_0_89]),c_0_35]) ).

cnf(c_0_130,plain,
    multiplication(addition(X1,addition(X2,X3)),coantidomain(addition(X3,X1))) = multiplication(X2,coantidomain(addition(X3,X1))),
    inference(spm,[status(thm)],[c_0_75,c_0_108]) ).

cnf(c_0_131,plain,
    multiplication(addition(X1,one),coantidomain(addition(X2,X1))) = coantidomain(addition(X2,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_124]),c_0_29]) ).

cnf(c_0_132,plain,
    multiplication(antidomain(addition(X1,X2)),addition(antidomain(antidomain(X1)),X3)) = multiplication(antidomain(addition(X1,X2)),X3),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_125]),c_0_59]) ).

cnf(c_0_133,plain,
    coantidomain(multiplication(coantidomain(coantidomain(X1)),coantidomain(addition(X1,X2)))) = one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_126]),c_0_87]),c_0_69]) ).

cnf(c_0_134,plain,
    multiplication(addition(X1,one),coantidomain(addition(X1,X2))) = coantidomain(addition(X1,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_126]),c_0_29]) ).

cnf(c_0_135,plain,
    addition(coantidomain(multiplication(X1,multiplication(X2,X3))),coantidomain(multiplication(coantidomain(coantidomain(multiplication(X1,X2))),X3))) = coantidomain(multiplication(coantidomain(coantidomain(multiplication(X1,X2))),X3)),
    inference(spm,[status(thm)],[c_0_85,c_0_55]) ).

cnf(c_0_136,plain,
    multiplication(X1,zero) = zero,
    inference(split_conjunct,[status(thm)],[c_0_127]) ).

cnf(c_0_137,plain,
    addition(coantidomain(X1),antidomain(antidomain(addition(X2,antidomain(coantidomain(X1)))))) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_67]) ).

cnf(c_0_138,plain,
    multiplication(antidomain(antidomain(X1)),coantidomain(addition(antidomain(X1),X2))) = coantidomain(addition(antidomain(X1),X2)),
    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_130,c_0_113]),c_0_114]),c_0_89]),c_0_131]),c_0_114]),c_0_89]) ).

cnf(c_0_139,plain,
    multiplication(antidomain(addition(X1,X2)),antidomain(X1)) = antidomain(addition(X1,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_104]),c_0_41]),c_0_89]),c_0_114]),c_0_89]) ).

cnf(c_0_140,plain,
    multiplication(coantidomain(coantidomain(X1)),coantidomain(addition(X1,X2))) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_133]),c_0_41]) ).

cnf(c_0_141,plain,
    multiplication(addition(one,X1),coantidomain(addition(X1,X2))) = coantidomain(addition(X1,X2)),
    inference(spm,[status(thm)],[c_0_134,c_0_35]) ).

cnf(c_0_142,plain,
    coantidomain(multiplication(coantidomain(coantidomain(multiplication(X1,antidomain(X2)))),X2)) = one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_28]),c_0_136]),c_0_87]),c_0_69]) ).

cnf(c_0_143,plain,
    addition(antidomain(coantidomain(X1)),antidomain(antidomain(addition(X2,coantidomain(X1))))) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_97]),c_0_105]) ).

cnf(c_0_144,plain,
    addition(antidomain(antidomain(X1)),coantidomain(addition(antidomain(X1),X2))) = antidomain(antidomain(X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_138]),c_0_35]),c_0_69]),c_0_41]) ).

cnf(c_0_145,plain,
    multiplication(antidomain(addition(X1,X2)),antidomain(antidomain(X2))) = zero,
    inference(spm,[status(thm)],[c_0_125,c_0_107]) ).

cnf(c_0_146,plain,
    addition(antidomain(X1),antidomain(addition(X1,X2))) = antidomain(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_139]),c_0_35]),c_0_67]),c_0_44]) ).

cnf(c_0_147,plain,
    multiplication(antidomain(coantidomain(X1)),coantidomain(addition(X1,X2))) = zero,
    inference(rw,[status(thm)],[c_0_140,c_0_97]) ).

cnf(c_0_148,plain,
    multiplication(antidomain(coantidomain(X1)),coantidomain(addition(X2,coantidomain(X1)))) = coantidomain(addition(X2,coantidomain(X1))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_73]),c_0_141]),c_0_97]) ).

cnf(c_0_149,plain,
    multiplication(coantidomain(coantidomain(multiplication(X1,antidomain(X2)))),X2) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_142]),c_0_41]) ).

cnf(c_0_150,plain,
    addition(antidomain(antidomain(X1)),antidomain(coantidomain(addition(antidomain(X1),X2)))) = one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_89]),c_0_35]) ).

cnf(c_0_151,plain,
    antidomain(addition(X1,antidomain(X1))) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_116]),c_0_35]) ).

cnf(c_0_152,plain,
    addition(antidomain(antidomain(X1)),antidomain(antidomain(addition(X2,antidomain(X1))))) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_114]),c_0_89]) ).

cnf(c_0_153,plain,
    addition(antidomain(X1),antidomain(addition(X2,X1))) = antidomain(X1),
    inference(spm,[status(thm)],[c_0_146,c_0_107]) ).

cnf(c_0_154,plain,
    coantidomain(addition(X1,coantidomain(X1))) = zero,
    inference(spm,[status(thm)],[c_0_147,c_0_148]) ).

cnf(c_0_155,plain,
    multiplication(antidomain(coantidomain(multiplication(X1,antidomain(X2)))),X2) = zero,
    inference(rw,[status(thm)],[c_0_149,c_0_97]) ).

cnf(c_0_156,plain,
    multiplication(X1,addition(coantidomain(addition(X1,X2)),X3)) = multiplication(X1,X3),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_126]),c_0_59]) ).

cnf(c_0_157,plain,
    addition(coantidomain(X1),antidomain(coantidomain(X1))) = one,
    inference(rw,[status(thm)],[c_0_62,c_0_97]) ).

cnf(c_0_158,plain,
    addition(antidomain(antidomain(X1)),antidomain(coantidomain(addition(X2,antidomain(X1))))) = one,
    inference(spm,[status(thm)],[c_0_150,c_0_107]) ).

cnf(c_0_159,plain,
    addition(antidomain(X1),antidomain(multiplication(X1,addition(X2,antidomain(X2))))) = antidomain(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_65,c_0_151]),c_0_66]),c_0_41]),c_0_66]),c_0_41]),c_0_35]) ).

cnf(c_0_160,plain,
    multiplication(antidomain(multiplication(X1,X2)),multiplication(X1,antidomain(antidomain(X2)))) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_65]),c_0_28]) ).

cnf(c_0_161,plain,
    multiplication(antidomain(addition(X1,X2)),multiplication(X2,X3)) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_111]),c_0_56]) ).

cnf(c_0_162,plain,
    multiplication(X1,multiplication(coantidomain(coantidomain(X1)),X2)) = multiplication(X1,X2),
    inference(spm,[status(thm)],[c_0_55,c_0_76]) ).

cnf(c_0_163,plain,
    multiplication(X1,multiplication(X2,coantidomain(multiplication(X1,X2)))) = zero,
    inference(spm,[status(thm)],[c_0_54,c_0_55]) ).

cnf(c_0_164,plain,
    multiplication(antidomain(multiplication(addition(X1,X2),X3)),multiplication(X1,X3)) = zero,
    inference(spm,[status(thm)],[c_0_117,c_0_27]) ).

cnf(c_0_165,plain,
    addition(antidomain(X1),antidomain(antidomain(addition(X2,X1)))) = one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_89]),c_0_35]) ).

cnf(c_0_166,plain,
    addition(coantidomain(X1),coantidomain(multiplication(addition(X2,coantidomain(X2)),X1))) = coantidomain(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_85,c_0_154]),c_0_87]),c_0_44]),c_0_87]),c_0_44]),c_0_35]) ).

cnf(c_0_167,plain,
    multiplication(antidomain(coantidomain(multiplication(X1,multiplication(X2,antidomain(X3))))),X3) = zero,
    inference(spm,[status(thm)],[c_0_155,c_0_55]) ).

cnf(c_0_168,plain,
    multiplication(X1,antidomain(coantidomain(addition(X1,X2)))) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_157]),c_0_41]) ).

cnf(c_0_169,plain,
    addition(antidomain(X1),antidomain(antidomain(multiplication(X1,addition(X2,antidomain(X2)))))) = one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_159]),c_0_114]),c_0_89]),c_0_35]) ).

cnf(c_0_170,plain,
    multiplication(antidomain(addition(X1,X2)),antidomain(antidomain(multiplication(X2,X3)))) = zero,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_161]),c_0_66]),c_0_44]) ).

cnf(c_0_171,plain,
    multiplication(X1,multiplication(X2,coantidomain(multiplication(antidomain(coantidomain(X1)),X2)))) = zero,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_163]),c_0_136]),c_0_97]) ).

cnf(c_0_172,plain,
    multiplication(antidomain(X1),multiplication(antidomain(X2),X1)) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_104]),c_0_44]) ).

cnf(c_0_173,plain,
    addition(coantidomain(X1),antidomain(coantidomain(multiplication(addition(X2,coantidomain(X2)),X1)))) = one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_105]),c_0_35]) ).

cnf(c_0_174,plain,
    multiplication(antidomain(coantidomain(multiplication(X1,X2))),coantidomain(addition(X2,X3))) = zero,
    inference(spm,[status(thm)],[c_0_167,c_0_168]) ).

cnf(c_0_175,plain,
    multiplication(antidomain(addition(X1,X2)),addition(X1,one)) = antidomain(addition(X1,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_117]),c_0_29]) ).

cnf(c_0_176,plain,
    multiplication(antidomain(X1),multiplication(coantidomain(X2),X1)) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_157]),c_0_44]) ).

cnf(c_0_177,plain,
    multiplication(addition(antidomain(addition(X1,X2)),X3),X1) = multiplication(X3,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_117]),c_0_59]) ).

cnf(c_0_178,plain,
    addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,antidomain(antidomain(addition(X2,coantidomain(X1))))))) = antidomain(multiplication(X1,antidomain(antidomain(addition(X2,coantidomain(X1)))))),
    inference(spm,[status(thm)],[c_0_65,c_0_63]) ).

cnf(c_0_179,plain,
    multiplication(antidomain(antidomain(multiplication(X1,addition(X2,antidomain(X2))))),X1) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_169]),c_0_44]) ).

cnf(c_0_180,plain,
    antidomain(addition(X1,antidomain(multiplication(X1,X2)))) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_116]),c_0_35]) ).

cnf(c_0_181,plain,
    multiplication(X1,multiplication(antidomain(X2),coantidomain(X1))) = zero,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_172]),c_0_87]),c_0_41]) ).

cnf(c_0_182,plain,
    addition(coantidomain(multiplication(X1,X2)),coantidomain(multiplication(antidomain(coantidomain(addition(X1,antidomain(X2)))),X2))) = coantidomain(multiplication(antidomain(coantidomain(addition(X1,antidomain(X2)))),X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_34]),c_0_97]),c_0_97]) ).

cnf(c_0_183,plain,
    multiplication(X1,antidomain(coantidomain(multiplication(addition(X2,coantidomain(X2)),X1)))) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_173]),c_0_41]) ).

cnf(c_0_184,plain,
    coantidomain(addition(X1,coantidomain(multiplication(X2,X1)))) = zero,
    inference(spm,[status(thm)],[c_0_174,c_0_148]) ).

cnf(c_0_185,plain,
    addition(multiplication(X1,multiplication(X2,X3)),multiplication(X4,X3)) = multiplication(addition(multiplication(X1,X2),X4),X3),
    inference(spm,[status(thm)],[c_0_27,c_0_55]) ).

cnf(c_0_186,plain,
    multiplication(antidomain(addition(X1,X2)),addition(one,X1)) = antidomain(addition(X1,X2)),
    inference(spm,[status(thm)],[c_0_175,c_0_35]) ).

cnf(c_0_187,plain,
    addition(antidomain(X1),antidomain(addition(antidomain(antidomain(X1)),X2))) = antidomain(X1),
    inference(spm,[status(thm)],[c_0_119,c_0_89]) ).

cnf(c_0_188,plain,
    multiplication(antidomain(X1),multiplication(coantidomain(X2),multiplication(X1,X3))) = zero,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_176]),c_0_56]),c_0_55]) ).

cnf(c_0_189,plain,
    multiplication(antidomain(antidomain(addition(X1,X2))),X1) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_104]),c_0_44]),c_0_114]),c_0_89]) ).

cnf(c_0_190,plain,
    antidomain(multiplication(X1,addition(X2,antidomain(X2)))) = antidomain(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(spm,[status(thm)],[c_0_178,c_0_179]),c_0_114]),c_0_89]),c_0_180]),c_0_66]),c_0_41]),c_0_89]),c_0_159]),c_0_114]),c_0_89]),c_0_180]),c_0_66]),c_0_41]),c_0_89]) ).

cnf(c_0_191,plain,
    multiplication(X1,addition(multiplication(antidomain(X2),coantidomain(X1)),X3)) = multiplication(X1,X3),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_181]),c_0_59]) ).

cnf(c_0_192,plain,
    coantidomain(multiplication(addition(X1,coantidomain(X1)),X2)) = coantidomain(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_182,c_0_183]),c_0_105]),c_0_184]),c_0_66]),c_0_44]),c_0_114]),c_0_105]),c_0_166]),c_0_105]),c_0_184]),c_0_66]),c_0_44]),c_0_114]),c_0_105]) ).

cnf(c_0_193,plain,
    multiplication(addition(multiplication(antidomain(multiplication(X1,X2)),X1),X3),X2) = multiplication(X3,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_28]),c_0_59]) ).

cnf(c_0_194,plain,
    antidomain(multiplication(X1,antidomain(antidomain(addition(coantidomain(X1),coantidomain(addition(X1,X2))))))) = one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_126]),c_0_66]),c_0_67]),c_0_35]) ).

cnf(c_0_195,plain,
    multiplication(antidomain(addition(X1,antidomain(X2))),antidomain(antidomain(X2))) = antidomain(addition(X1,antidomain(X2))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_98]),c_0_186]) ).

cnf(c_0_196,plain,
    addition(antidomain(coantidomain(X1)),antidomain(addition(coantidomain(X1),X2))) = antidomain(coantidomain(X1)),
    inference(spm,[status(thm)],[c_0_119,c_0_105]) ).

cnf(c_0_197,plain,
    multiplication(X1,antidomain(coantidomain(addition(X2,X1)))) = X1,
    inference(spm,[status(thm)],[c_0_168,c_0_107]) ).

cnf(c_0_198,plain,
    addition(antidomain(X1),antidomain(addition(X2,antidomain(antidomain(X1))))) = antidomain(X1),
    inference(spm,[status(thm)],[c_0_187,c_0_107]) ).

cnf(c_0_199,plain,
    multiplication(antidomain(addition(X1,X2)),multiplication(coantidomain(X3),X1)) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_189]),c_0_89]) ).

cnf(c_0_200,plain,
    antidomain(multiplication(X1,antidomain(multiplication(antidomain(X2),coantidomain(X1))))) = antidomain(X1),
    inference(spm,[status(thm)],[c_0_190,c_0_191]) ).

cnf(c_0_201,plain,
    coantidomain(multiplication(coantidomain(multiplication(antidomain(multiplication(X1,X2)),X1)),X2)) = coantidomain(X2),
    inference(spm,[status(thm)],[c_0_192,c_0_193]) ).

cnf(c_0_202,plain,
    multiplication(X1,antidomain(antidomain(addition(coantidomain(X1),coantidomain(addition(X1,X2)))))) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_194]),c_0_44]) ).

cnf(c_0_203,plain,
    multiplication(coantidomain(X1),antidomain(antidomain(addition(coantidomain(X1),X2)))) = coantidomain(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_195,c_0_196]),c_0_105]),c_0_105]) ).

cnf(c_0_204,plain,
    multiplication(coantidomain(X1),coantidomain(X1)) = coantidomain(X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_62]),c_0_41]) ).

cnf(c_0_205,plain,
    multiplication(antidomain(addition(X1,antidomain(antidomain(X2)))),antidomain(X2)) = antidomain(addition(X1,antidomain(antidomain(X2)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_197,c_0_198]),c_0_114]),c_0_89]) ).

cnf(c_0_206,plain,
    multiplication(antidomain(addition(X1,X2)),antidomain(antidomain(multiplication(coantidomain(X3),X1)))) = zero,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_199]),c_0_66]),c_0_44]) ).

cnf(c_0_207,plain,
    antidomain(multiplication(coantidomain(X1),antidomain(multiplication(antidomain(X2),antidomain(coantidomain(X1)))))) = antidomain(coantidomain(X1)),
    inference(spm,[status(thm)],[c_0_200,c_0_97]) ).

cnf(c_0_208,plain,
    multiplication(antidomain(X1),addition(multiplication(X1,X2),X3)) = multiplication(antidomain(X1),X3),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_64]),c_0_59]) ).

cnf(c_0_209,plain,
    antidomain(addition(coantidomain(X1),coantidomain(addition(X1,X2)))) = antidomain(coantidomain(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_201,c_0_202]),c_0_66]),c_0_44]),c_0_203]),c_0_97]),c_0_114]),c_0_89]) ).

cnf(c_0_210,plain,
    multiplication(coantidomain(X1),addition(coantidomain(X1),X2)) = multiplication(coantidomain(X1),addition(X2,one)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_204]),c_0_51]) ).

cnf(c_0_211,plain,
    coantidomain(addition(one,X1)) = zero,
    inference(spm,[status(thm)],[c_0_44,c_0_126]) ).

cnf(c_0_212,plain,
    multiplication(X1,addition(multiplication(X2,coantidomain(multiplication(X1,X2))),X3)) = multiplication(X1,X3),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_163]),c_0_59]) ).

cnf(c_0_213,plain,
    multiplication(antidomain(coantidomain(multiplication(X1,X2))),multiplication(X3,coantidomain(multiplication(X1,multiplication(X2,X3))))) = zero,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_135]),c_0_54]),c_0_55]),c_0_97]) ).

cnf(c_0_214,plain,
    multiplication(X1,multiplication(coantidomain(X2),coantidomain(X1))) = zero,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_176]),c_0_87]),c_0_41]) ).

cnf(c_0_215,plain,
    addition(multiplication(X1,X2),addition(multiplication(X3,X2),X4)) = addition(multiplication(addition(X1,X3),X2),X4),
    inference(spm,[status(thm)],[c_0_49,c_0_27]) ).

cnf(c_0_216,plain,
    multiplication(coantidomain(X1),addition(X2,coantidomain(X1))) = multiplication(coantidomain(X1),addition(X2,one)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_204]),c_0_35]),c_0_51]) ).

cnf(c_0_217,plain,
    antidomain(addition(X1,antidomain(multiplication(coantidomain(X2),X1)))) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_205,c_0_206]),c_0_89]) ).

cnf(c_0_218,plain,
    antidomain(multiplication(antidomain(antidomain(X1)),antidomain(multiplication(antidomain(X2),antidomain(X1))))) = antidomain(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_114]),c_0_89]),c_0_89]) ).

cnf(c_0_219,plain,
    antidomain(multiplication(antidomain(X1),antidomain(multiplication(X1,X2)))) = antidomain(antidomain(X1)),
    inference(spm,[status(thm)],[c_0_190,c_0_208]) ).

cnf(c_0_220,plain,
    multiplication(antidomain(antidomain(X1)),multiplication(X1,X2)) = multiplication(X1,X2),
    inference(spm,[status(thm)],[c_0_55,c_0_52]) ).

cnf(c_0_221,plain,
    addition(coantidomain(X1),coantidomain(addition(X1,X2))) = coantidomain(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_52,c_0_209]),c_0_105]),c_0_210]),c_0_35]),c_0_69]),c_0_41]) ).

cnf(c_0_222,plain,
    multiplication(addition(X1,one),X1) = multiplication(X1,addition(X1,one)),
    inference(spm,[status(thm)],[c_0_51,c_0_84]) ).

cnf(c_0_223,plain,
    coantidomain(addition(X1,addition(X2,one))) = zero,
    inference(spm,[status(thm)],[c_0_211,c_0_108]) ).

cnf(c_0_224,plain,
    antidomain(multiplication(X1,antidomain(multiplication(X2,coantidomain(multiplication(X1,X2)))))) = antidomain(X1),
    inference(spm,[status(thm)],[c_0_190,c_0_212]) ).

cnf(c_0_225,plain,
    multiplication(antidomain(coantidomain(multiplication(X1,coantidomain(X2)))),coantidomain(X1)) = zero,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_213,c_0_214]),c_0_87]),c_0_41]) ).

cnf(c_0_226,plain,
    addition(antidomain(X1),antidomain(antidomain(addition(X1,X2)))) = one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_146]),c_0_89]),c_0_35]) ).

cnf(c_0_227,plain,
    addition(X1,addition(X2,addition(X1,X3))) = addition(X2,addition(X1,X3)),
    inference(spm,[status(thm)],[c_0_60,c_0_108]) ).

cnf(c_0_228,plain,
    addition(X1,addition(multiplication(X2,X1),X3)) = addition(multiplication(addition(one,X2),X1),X3),
    inference(spm,[status(thm)],[c_0_215,c_0_44]) ).

cnf(c_0_229,plain,
    addition(X1,multiplication(coantidomain(X2),addition(X1,one))) = addition(X1,coantidomain(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_84,c_0_216]),c_0_49]),c_0_51]),c_0_49]),c_0_50]),c_0_35]),c_0_69]),c_0_44]) ).

cnf(c_0_230,plain,
    antidomain(addition(X1,antidomain(multiplication(antidomain(coantidomain(X2)),X1)))) = zero,
    inference(spm,[status(thm)],[c_0_217,c_0_97]) ).

cnf(c_0_231,plain,
    multiplication(antidomain(antidomain(addition(X1,X2))),X2) = X2,
    inference(spm,[status(thm)],[c_0_189,c_0_107]) ).

cnf(c_0_232,plain,
    antidomain(multiplication(antidomain(antidomain(multiplication(X1,X2))),antidomain(antidomain(X1)))) = antidomain(multiplication(X1,X2)),
    inference(spm,[status(thm)],[c_0_218,c_0_219]) ).

cnf(c_0_233,plain,
    multiplication(antidomain(antidomain(X1)),addition(one,multiplication(X1,X2))) = addition(antidomain(antidomain(X1)),multiplication(X1,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_220]),c_0_35]) ).

cnf(c_0_234,plain,
    addition(coantidomain(X1),antidomain(coantidomain(addition(X1,X2)))) = one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_221]),c_0_105]),c_0_35]) ).

cnf(c_0_235,plain,
    addition(multiplication(X1,X2),multiplication(X2,addition(X2,one))) = multiplication(addition(X1,addition(X2,one)),X2),
    inference(spm,[status(thm)],[c_0_27,c_0_222]) ).

cnf(c_0_236,plain,
    coantidomain(multiplication(addition(X1,addition(X2,one)),X3)) = coantidomain(X3),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_223]),c_0_29]) ).

cnf(c_0_237,plain,
    multiplication(antidomain(X1),antidomain(antidomain(multiplication(antidomain(X2),X1)))) = zero,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_172]),c_0_66]),c_0_44]) ).

cnf(c_0_238,plain,
    antidomain(multiplication(antidomain(coantidomain(multiplication(X1,coantidomain(X2)))),antidomain(coantidomain(X1)))) = coantidomain(multiplication(X1,coantidomain(X2))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_224,c_0_225]),c_0_87]),c_0_41]),c_0_105]) ).

cnf(c_0_239,plain,
    multiplication(X1,multiplication(coantidomain(X1),X2)) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_54]),c_0_56]) ).

cnf(c_0_240,plain,
    multiplication(coantidomain(coantidomain(antidomain(antidomain(X1)))),X1) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_101]),c_0_44]) ).

cnf(c_0_241,plain,
    addition(antidomain(X1),antidomain(antidomain(addition(X2,addition(X1,X3))))) = one,
    inference(spm,[status(thm)],[c_0_226,c_0_227]) ).

cnf(c_0_242,plain,
    addition(X1,addition(multiplication(coantidomain(X2),X1),X3)) = addition(X1,X3),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_228,c_0_229]),c_0_50]),c_0_41]),c_0_69]),c_0_44]) ).

cnf(c_0_243,plain,
    antidomain(addition(X1,antidomain(multiplication(antidomain(X2),X1)))) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_230,c_0_114]),c_0_89]) ).

cnf(c_0_244,plain,
    multiplication(antidomain(X1),antidomain(addition(X2,X1))) = antidomain(addition(X2,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_231,c_0_153]),c_0_89]) ).

cnf(c_0_245,plain,
    antidomain(addition(antidomain(antidomain(X1)),multiplication(X1,X2))) = antidomain(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_232,c_0_233]),c_0_89]),c_0_189]),c_0_89]) ).

cnf(c_0_246,plain,
    addition(antidomain(coantidomain(X1)),coantidomain(multiplication(X2,X1))) = one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_234,c_0_235]),c_0_236]),c_0_35]) ).

cnf(c_0_247,plain,
    multiplication(coantidomain(X1),antidomain(coantidomain(multiplication(X1,coantidomain(X2))))) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_237,c_0_238]),c_0_105]) ).

cnf(c_0_248,plain,
    multiplication(coantidomain(antidomain(antidomain(X1))),X1) = zero,
    inference(spm,[status(thm)],[c_0_239,c_0_240]) ).

cnf(c_0_249,plain,
    addition(antidomain(multiplication(coantidomain(X1),X2)),antidomain(antidomain(addition(X2,X3)))) = one,
    inference(spm,[status(thm)],[c_0_241,c_0_242]) ).

cnf(c_0_250,plain,
    addition(coantidomain(X1),coantidomain(multiplication(X1,addition(X2,one)))) = coantidomain(X1),
    inference(spm,[status(thm)],[c_0_221,c_0_51]) ).

cnf(c_0_251,plain,
    multiplication(addition(multiplication(antidomain(X1),coantidomain(X2)),X3),X1) = multiplication(X3,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_176]),c_0_59]) ).

cnf(c_0_252,plain,
    antidomain(multiplication(X1,addition(X2,antidomain(multiplication(antidomain(X3),X2))))) = antidomain(X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_243]),c_0_29]) ).

cnf(c_0_253,plain,
    multiplication(antidomain(X1),addition(X1,X2)) = multiplication(antidomain(X1),X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_28]),c_0_59]) ).

cnf(c_0_254,plain,
    multiplication(antidomain(multiplication(X1,X2)),antidomain(X1)) = antidomain(X1),
    inference(spm,[status(thm)],[c_0_244,c_0_245]) ).

cnf(c_0_255,plain,
    multiplication(coantidomain(multiplication(X1,antidomain(X2))),X2) = X2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_246]),c_0_44]) ).

cnf(c_0_256,plain,
    multiplication(coantidomain(X1),antidomain(coantidomain(multiplication(X1,antidomain(coantidomain(X2)))))) = zero,
    inference(spm,[status(thm)],[c_0_247,c_0_97]) ).

cnf(c_0_257,plain,
    multiplication(addition(coantidomain(antidomain(antidomain(X1))),X2),X1) = multiplication(X2,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_248]),c_0_59]) ).

cnf(c_0_258,plain,
    addition(coantidomain(X1),antidomain(multiplication(coantidomain(X2),coantidomain(X1)))) = one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_249,c_0_250]),c_0_105]),c_0_35]) ).

cnf(c_0_259,plain,
    coantidomain(multiplication(coantidomain(multiplication(antidomain(X1),coantidomain(X2))),X1)) = coantidomain(X1),
    inference(spm,[status(thm)],[c_0_192,c_0_251]) ).

cnf(c_0_260,plain,
    antidomain(multiplication(antidomain(X1),antidomain(multiplication(antidomain(X2),X1)))) = antidomain(antidomain(X1)),
    inference(spm,[status(thm)],[c_0_252,c_0_253]) ).

cnf(c_0_261,plain,
    multiplication(X1,multiplication(X2,antidomain(coantidomain(multiplication(X1,X2))))) = multiplication(X1,X2),
    inference(spm,[status(thm)],[c_0_55,c_0_93]) ).

cnf(c_0_262,plain,
    multiplication(antidomain(X1),antidomain(coantidomain(multiplication(X2,antidomain(X1))))) = antidomain(coantidomain(multiplication(X2,antidomain(X1)))),
    inference(spm,[status(thm)],[c_0_254,c_0_255]) ).

cnf(c_0_263,plain,
    multiplication(coantidomain(X1),antidomain(coantidomain(multiplication(X1,antidomain(X2))))) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_256,c_0_114]),c_0_89]) ).

cnf(c_0_264,plain,
    multiplication(antidomain(multiplication(coantidomain(X1),antidomain(X2))),X2) = X2,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_257,c_0_258]),c_0_44]),c_0_114]),c_0_89]) ).

cnf(c_0_265,plain,
    coantidomain(multiplication(coantidomain(multiplication(antidomain(X1),coantidomain(X2))),antidomain(antidomain(X1)))) = antidomain(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_259,c_0_89]),c_0_114]),c_0_89]) ).

cnf(c_0_266,plain,
    antidomain(multiplication(antidomain(X1),antidomain(multiplication(coantidomain(X2),X1)))) = antidomain(antidomain(X1)),
    inference(spm,[status(thm)],[c_0_260,c_0_105]) ).

cnf(c_0_267,plain,
    multiplication(X1,antidomain(coantidomain(multiplication(X1,antidomain(X2))))) = multiplication(X1,antidomain(X2)),
    inference(spm,[status(thm)],[c_0_261,c_0_262]) ).

cnf(c_0_268,plain,
    multiplication(addition(X1,X2),multiplication(coantidomain(X2),X3)) = multiplication(X1,multiplication(coantidomain(X2),X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_239]),c_0_29]) ).

cnf(c_0_269,plain,
    antidomain(multiplication(coantidomain(X1),coantidomain(multiplication(X1,antidomain(X2))))) = antidomain(coantidomain(X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_224,c_0_263]),c_0_87]),c_0_41]),c_0_105]) ).

cnf(c_0_270,plain,
    multiplication(antidomain(multiplication(antidomain(X1),antidomain(X2))),X2) = X2,
    inference(spm,[status(thm)],[c_0_264,c_0_265]) ).

cnf(c_0_271,plain,
    antidomain(multiplication(antidomain(antidomain(multiplication(coantidomain(X1),X2))),antidomain(antidomain(X2)))) = antidomain(multiplication(coantidomain(X1),X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_260,c_0_266]),c_0_89]) ).

cnf(c_0_272,plain,
    multiplication(X1,antidomain(coantidomain(multiplication(coantidomain(X1),coantidomain(X2))))) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_247]),c_0_136]) ).

cnf(c_0_273,plain,
    multiplication(X1,antidomain(coantidomain(multiplication(X1,coantidomain(X2))))) = multiplication(X1,coantidomain(X2)),
    inference(spm,[status(thm)],[c_0_267,c_0_105]) ).

cnf(c_0_274,plain,
    coantidomain(multiplication(antidomain(coantidomain(X1)),X2)) = coantidomain(multiplication(X1,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_268]),c_0_162]),c_0_97]) ).

cnf(c_0_275,plain,
    multiplication(addition(X1,X2),coantidomain(X1)) = multiplication(X2,coantidomain(X1)),
    inference(spm,[status(thm)],[c_0_75,c_0_35]) ).

cnf(c_0_276,plain,
    multiplication(coantidomain(X1),coantidomain(multiplication(X2,X1))) = coantidomain(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_253,c_0_246]),c_0_41]),c_0_105]),c_0_105]) ).

cnf(c_0_277,plain,
    antidomain(multiplication(antidomain(coantidomain(X1)),coantidomain(multiplication(coantidomain(X1),antidomain(X2))))) = coantidomain(X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_269,c_0_97]),c_0_105]) ).

cnf(c_0_278,plain,
    multiplication(antidomain(multiplication(coantidomain(X1),X2)),antidomain(X2)) = antidomain(X2),
    inference(spm,[status(thm)],[c_0_270,c_0_271]) ).

cnf(c_0_279,plain,
    antidomain(multiplication(X1,coantidomain(multiplication(coantidomain(X1),coantidomain(X2))))) = antidomain(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_224,c_0_272]),c_0_87]),c_0_41]),c_0_105]) ).

cnf(c_0_280,plain,
    multiplication(antidomain(coantidomain(X1)),antidomain(coantidomain(multiplication(X1,coantidomain(X2))))) = multiplication(antidomain(coantidomain(X1)),coantidomain(X2)),
    inference(spm,[status(thm)],[c_0_273,c_0_274]) ).

cnf(c_0_281,plain,
    multiplication(coantidomain(multiplication(X1,X2)),coantidomain(X2)) = coantidomain(X2),
    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_275,c_0_246]),c_0_44]),c_0_114]),c_0_105]),c_0_114]),c_0_105]) ).

cnf(c_0_282,plain,
    multiplication(X1,coantidomain(multiplication(X2,coantidomain(X1)))) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_276]),c_0_97]),c_0_93]) ).

cnf(c_0_283,plain,
    antidomain(multiplication(coantidomain(X1),multiplication(antidomain(X2),coantidomain(X1)))) = antidomain(multiplication(coantidomain(X1),antidomain(X2))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_200,c_0_277]),c_0_55]) ).

cnf(c_0_284,plain,
    multiplication(antidomain(coantidomain(X1)),coantidomain(X2)) = antidomain(coantidomain(multiplication(X1,coantidomain(X2)))),
    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_278,c_0_279]),c_0_97]),c_0_274]),c_0_280]),c_0_97]),c_0_274]) ).

cnf(c_0_285,plain,
    multiplication(coantidomain(X1),antidomain(coantidomain(multiplication(X2,coantidomain(X1))))) = antidomain(coantidomain(multiplication(X2,coantidomain(X1)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_281,c_0_282]),c_0_97]),c_0_97]) ).

cnf(c_0_286,plain,
    multiplication(addition(one,X1),antidomain(coantidomain(X1))) = addition(X1,antidomain(coantidomain(X1))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_95,c_0_97]),c_0_97]) ).

cnf(c_0_287,plain,
    addition(coantidomain(X1),coantidomain(addition(antidomain(coantidomain(X1)),X2))) = coantidomain(X1),
    inference(spm,[status(thm)],[c_0_144,c_0_105]) ).

cnf(c_0_288,plain,
    antidomain(multiplication(coantidomain(X1),antidomain(coantidomain(X2)))) = coantidomain(multiplication(X2,coantidomain(X1))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_283,c_0_284]),c_0_285]),c_0_105]) ).

cnf(c_0_289,plain,
    addition(coantidomain(multiplication(X1,coantidomain(X2))),coantidomain(multiplication(antidomain(coantidomain(addition(X1,X2))),coantidomain(X2)))) = coantidomain(multiplication(antidomain(coantidomain(addition(X1,X2))),coantidomain(X2))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_75]),c_0_97]),c_0_97]) ).

cnf(c_0_290,plain,
    coantidomain(addition(antidomain(coantidomain(X1)),coantidomain(addition(X1,antidomain(coantidomain(X1)))))) = zero,
    inference(spm,[status(thm)],[c_0_184,c_0_286]) ).

cnf(c_0_291,plain,
    coantidomain(antidomain(coantidomain(X1))) = coantidomain(X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_97]),c_0_105]) ).

cnf(c_0_292,plain,
    addition(coantidomain(X1),coantidomain(addition(X2,antidomain(coantidomain(X1))))) = coantidomain(X1),
    inference(spm,[status(thm)],[c_0_287,c_0_107]) ).

cnf(c_0_293,plain,
    coantidomain(multiplication(coantidomain(X1),coantidomain(X2))) = antidomain(multiplication(coantidomain(X2),coantidomain(X1))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_288,c_0_97]),c_0_105]) ).

cnf(c_0_294,plain,
    coantidomain(addition(X1,antidomain(coantidomain(X1)))) = coantidomain(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(spm,[status(thm)],[c_0_289,c_0_290]),c_0_97]),c_0_197]),c_0_114]),c_0_105]),c_0_66]),c_0_97]),c_0_44]),c_0_291]),c_0_292]),c_0_66]),c_0_97]),c_0_44]),c_0_291]) ).

cnf(c_0_295,plain,
    multiplication(X1,antidomain(coantidomain(multiplication(coantidomain(X1),antidomain(X2))))) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_263]),c_0_136]) ).

cnf(c_0_296,plain,
    addition(antidomain(antidomain(X1)),antidomain(multiplication(X1,X2))) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_245]),c_0_35]) ).

cnf(c_0_297,plain,
    multiplication(coantidomain(X1),multiplication(coantidomain(X1),X2)) = multiplication(coantidomain(X1),X2),
    inference(spm,[status(thm)],[c_0_55,c_0_204]) ).

cnf(c_0_298,plain,
    antidomain(antidomain(multiplication(coantidomain(X1),coantidomain(X2)))) = multiplication(coantidomain(X2),coantidomain(X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_284,c_0_97]),c_0_105]),c_0_293]) ).

cnf(c_0_299,plain,
    multiplication(addition(X1,antidomain(coantidomain(X1))),multiplication(antidomain(X2),coantidomain(X1))) = zero,
    inference(spm,[status(thm)],[c_0_181,c_0_294]) ).

cnf(c_0_300,plain,
    coantidomain(multiplication(antidomain(X1),coantidomain(X2))) = antidomain(multiplication(coantidomain(X2),antidomain(X1))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_288,c_0_114]),c_0_89]) ).

cnf(c_0_301,plain,
    antidomain(multiplication(X1,coantidomain(multiplication(coantidomain(X1),antidomain(X2))))) = antidomain(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_224,c_0_295]),c_0_87]),c_0_41]),c_0_105]) ).

cnf(c_0_302,plain,
    multiplication(antidomain(coantidomain(X1)),antidomain(coantidomain(multiplication(X1,antidomain(X2))))) = multiplication(antidomain(coantidomain(X1)),antidomain(X2)),
    inference(spm,[status(thm)],[c_0_267,c_0_274]) ).

cnf(c_0_303,plain,
    multiplication(antidomain(addition(X1,X2)),antidomain(X2)) = antidomain(addition(X1,X2)),
    inference(spm,[status(thm)],[c_0_139,c_0_107]) ).

cnf(c_0_304,plain,
    addition(coantidomain(X1),antidomain(multiplication(coantidomain(X1),X2))) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_296,c_0_297]),c_0_105]) ).

cnf(c_0_305,plain,
    coantidomain(multiplication(antidomain(coantidomain(multiplication(antidomain(multiplication(X1,X2)),X1))),X2)) = one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_28]),c_0_87]),c_0_69]),c_0_97]) ).

cnf(c_0_306,plain,
    multiplication(coantidomain(X1),antidomain(coantidomain(X2))) = antidomain(coantidomain(multiplication(X2,coantidomain(X1)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_298,c_0_97]),c_0_284]),c_0_105]) ).

cnf(c_0_307,plain,
    coantidomain(multiplication(coantidomain(X1),multiplication(antidomain(X2),coantidomain(X1)))) = coantidomain(multiplication(antidomain(X2),coantidomain(X1))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_299]),c_0_66]),c_0_44]),c_0_294]) ).

cnf(c_0_308,plain,
    antidomain(antidomain(multiplication(coantidomain(X1),antidomain(X2)))) = multiplication(antidomain(X2),coantidomain(X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_284,c_0_114]),c_0_89]),c_0_300]) ).

cnf(c_0_309,plain,
    multiplication(antidomain(coantidomain(X1)),antidomain(X2)) = antidomain(coantidomain(multiplication(X1,antidomain(X2)))),
    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_278,c_0_301]),c_0_97]),c_0_274]),c_0_302]),c_0_97]),c_0_274]) ).

cnf(c_0_310,plain,
    coantidomain(multiplication(coantidomain(X1),antidomain(X2))) = antidomain(multiplication(antidomain(X2),coantidomain(X1))),
    inference(spm,[status(thm)],[c_0_293,c_0_265]) ).

cnf(c_0_311,plain,
    multiplication(X1,multiplication(antidomain(coantidomain(X1)),X2)) = multiplication(X1,X2),
    inference(spm,[status(thm)],[c_0_55,c_0_93]) ).

cnf(c_0_312,plain,
    multiplication(antidomain(X1),antidomain(multiplication(X1,X2))) = antidomain(X1),
    inference(spm,[status(thm)],[c_0_303,c_0_245]) ).

cnf(c_0_313,plain,
    multiplication(antidomain(addition(X1,X2)),addition(X3,X1)) = multiplication(antidomain(addition(X1,X2)),X3),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_117]),c_0_29]) ).

cnf(c_0_314,plain,
    multiplication(antidomain(multiplication(antidomain(X1),X2)),X1) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_257,c_0_304]),c_0_44]),c_0_114]),c_0_89]) ).

cnf(c_0_315,plain,
    multiplication(antidomain(coantidomain(multiplication(antidomain(multiplication(X1,X2)),X1))),X2) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_305]),c_0_41]) ).

cnf(c_0_316,plain,
    multiplication(antidomain(X1),coantidomain(X2)) = multiplication(coantidomain(X2),antidomain(X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_267,c_0_306]),c_0_55]),c_0_307]),c_0_300]),c_0_308]) ).

cnf(c_0_317,plain,
    antidomain(antidomain(multiplication(antidomain(X1),coantidomain(X2)))) = multiplication(coantidomain(X2),antidomain(X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_309,c_0_97]),c_0_105]),c_0_310]) ).

cnf(c_0_318,plain,
    multiplication(X1,antidomain(multiplication(coantidomain(X1),X2))) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_311,c_0_312]),c_0_93]) ).

cnf(c_0_319,plain,
    antidomain(multiplication(antidomain(addition(antidomain(X1),X2)),X1)) = antidomain(antidomain(addition(antidomain(X1),X2))),
    inference(spm,[status(thm)],[c_0_190,c_0_313]) ).

cnf(c_0_320,plain,
    antidomain(addition(X1,antidomain(multiplication(antidomain(X1),X2)))) = antidomain(antidomain(multiplication(antidomain(X1),X2))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_245,c_0_314]),c_0_89]),c_0_35]) ).

cnf(c_0_321,plain,
    multiplication(coantidomain(X1),multiplication(antidomain(multiplication(coantidomain(X1),X2)),X2)) = zero,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_315,c_0_316]),c_0_310]),c_0_317]),c_0_55]) ).

cnf(c_0_322,plain,
    multiplication(X1,multiplication(antidomain(multiplication(coantidomain(X1),X2)),X3)) = multiplication(X1,X3),
    inference(spm,[status(thm)],[c_0_55,c_0_318]) ).

cnf(c_0_323,plain,
    coantidomain(multiplication(antidomain(antidomain(X1)),multiplication(antidomain(X2),X1))) = coantidomain(multiplication(antidomain(X2),X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_172]),c_0_66]),c_0_44]),c_0_114]) ).

cnf(c_0_324,plain,
    antidomain(coantidomain(multiplication(antidomain(X1),antidomain(X2)))) = multiplication(antidomain(X1),antidomain(X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_309,c_0_114]),c_0_89]) ).

cnf(c_0_325,plain,
    antidomain(multiplication(antidomain(antidomain(multiplication(antidomain(antidomain(X1)),X2))),X1)) = antidomain(multiplication(antidomain(antidomain(X1)),X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_319,c_0_320]),c_0_89]) ).

cnf(c_0_326,plain,
    multiplication(X1,antidomain(coantidomain(multiplication(X2,antidomain(coantidomain(X1)))))) = multiplication(X1,antidomain(coantidomain(X2))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_306]),c_0_97]) ).

cnf(c_0_327,plain,
    coantidomain(multiplication(antidomain(multiplication(coantidomain(X1),X2)),X2)) = coantidomain(multiplication(X1,X2)),
    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_201,c_0_321]),c_0_66]),c_0_44]),c_0_97]),c_0_274]),c_0_322]) ).

cnf(c_0_328,plain,
    multiplication(antidomain(X1),antidomain(coantidomain(X2))) = antidomain(coantidomain(multiplication(X2,antidomain(X1)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_308,c_0_97]),c_0_309]),c_0_105]) ).

cnf(c_0_329,plain,
    coantidomain(multiplication(antidomain(X1),multiplication(antidomain(X2),antidomain(X1)))) = coantidomain(multiplication(antidomain(X2),antidomain(X1))),
    inference(spm,[status(thm)],[c_0_323,c_0_89]) ).

cnf(c_0_330,plain,
    coantidomain(multiplication(antidomain(X1),antidomain(X2))) = antidomain(multiplication(antidomain(X1),antidomain(X2))),
    inference(spm,[status(thm)],[c_0_114,c_0_324]) ).

cnf(c_0_331,plain,
    addition(antidomain(X1),antidomain(antidomain(antidomain(X1)))) = antidomain(antidomain(antidomain(X1))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_44]),c_0_44]) ).

cnf(c_0_332,plain,
    antidomain(multiplication(antidomain(antidomain(X1)),coantidomain(X2))) = antidomain(multiplication(coantidomain(X2),X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_325,c_0_317]),c_0_55]),c_0_52]) ).

cnf(c_0_333,plain,
    multiplication(X1,coantidomain(multiplication(X1,coantidomain(X2)))) = multiplication(X1,antidomain(coantidomain(X2))),
    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_326,c_0_327]),c_0_326]),c_0_114]),c_0_308]),c_0_284]),c_0_105]) ).

cnf(c_0_334,plain,
    antidomain(antidomain(multiplication(antidomain(X1),antidomain(X2)))) = multiplication(antidomain(X2),antidomain(X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_267,c_0_328]),c_0_55]),c_0_329]),c_0_330]) ).

cnf(c_0_335,plain,
    multiplication(antidomain(X1),antidomain(antidomain(X1))) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_331]),c_0_28]) ).

cnf(c_0_336,plain,
    multiplication(coantidomain(X1),antidomain(antidomain(X2))) = antidomain(antidomain(multiplication(coantidomain(X1),X2))),
    inference(spm,[status(thm)],[c_0_317,c_0_332]) ).

cnf(c_0_337,plain,
    multiplication(X1,coantidomain(multiplication(X1,antidomain(coantidomain(X2))))) = multiplication(X1,coantidomain(X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_333,c_0_333]),c_0_273]) ).

cnf(c_0_338,plain,
    antidomain(multiplication(antidomain(antidomain(X1)),antidomain(X2))) = antidomain(multiplication(antidomain(X2),X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_325,c_0_334]),c_0_55]),c_0_52]) ).

cnf(c_0_339,plain,
    multiplication(antidomain(X1),multiplication(antidomain(antidomain(X1)),X2)) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_335]),c_0_56]) ).

cnf(c_0_340,plain,
    coantidomain(multiplication(X1,antidomain(antidomain(X2)))) = antidomain(multiplication(antidomain(coantidomain(X1)),X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_332,c_0_97]),c_0_328]),c_0_105]) ).

cnf(c_0_341,plain,
    multiplication(X1,antidomain(antidomain(multiplication(antidomain(coantidomain(X1)),X2)))) = multiplication(X1,antidomain(antidomain(X2))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_336]),c_0_97]) ).

cnf(c_0_342,plain,
    multiplication(X1,coantidomain(multiplication(X1,antidomain(X2)))) = multiplication(X1,antidomain(antidomain(X2))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_337,c_0_114]),c_0_89]) ).

cnf(c_0_343,plain,
    multiplication(antidomain(X1),antidomain(antidomain(X2))) = antidomain(antidomain(multiplication(antidomain(X1),X2))),
    inference(spm,[status(thm)],[c_0_334,c_0_338]) ).

cnf(c_0_344,plain,
    antidomain(multiplication(antidomain(X1),antidomain(antidomain(multiplication(antidomain(antidomain(X1)),X2))))) = one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_339]),c_0_66]),c_0_67]) ).

cnf(c_0_345,plain,
    multiplication(X1,antidomain(multiplication(antidomain(coantidomain(X1)),X2))) = multiplication(X1,antidomain(X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_333,c_0_114]),c_0_340]),c_0_89]) ).

cnf(c_0_346,plain,
    multiplication(X1,antidomain(antidomain(addition(X2,coantidomain(X1))))) = multiplication(X1,antidomain(antidomain(X2))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_341,c_0_63]),c_0_341]),c_0_114]),c_0_105]) ).

cnf(c_0_347,plain,
    multiplication(antidomain(addition(X1,X2)),addition(X3,X2)) = multiplication(antidomain(addition(X1,X2)),X3),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_111]),c_0_29]) ).

fof(c_0_348,plain,
    ! [X38] : c(X38) = antidomain(domain(X38)),
    inference(variable_rename,[status(thm)],[complement]) ).

fof(c_0_349,plain,
    ! [X32] : domain(X32) = antidomain(antidomain(X32)),
    inference(variable_rename,[status(thm)],[domain4]) ).

cnf(c_0_350,plain,
    addition(multiplication(X1,X2),multiplication(X3,addition(X2,coantidomain(X1)))) = multiplication(addition(X1,X3),addition(X2,coantidomain(X1))),
    inference(spm,[status(thm)],[c_0_27,c_0_63]) ).

cnf(c_0_351,plain,
    multiplication(antidomain(X1),antidomain(multiplication(antidomain(X1),X2))) = multiplication(antidomain(X1),antidomain(X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_342,c_0_343]),c_0_114]),c_0_89]),c_0_89]) ).

cnf(c_0_352,plain,
    addition(antidomain(multiplication(antidomain(X1),X2)),antidomain(multiplication(antidomain(X1),antidomain(antidomain(addition(X2,X1)))))) = antidomain(multiplication(antidomain(X1),antidomain(antidomain(addition(X2,X1))))),
    inference(spm,[status(thm)],[c_0_65,c_0_81]) ).

cnf(c_0_353,plain,
    antidomain(addition(antidomain(antidomain(X1)),antidomain(addition(X1,antidomain(antidomain(X1)))))) = zero,
    inference(spm,[status(thm)],[c_0_180,c_0_68]) ).

cnf(c_0_354,plain,
    antidomain(multiplication(antidomain(X1),antidomain(antidomain(multiplication(X1,X2))))) = one,
    inference(spm,[status(thm)],[c_0_344,c_0_220]) ).

cnf(c_0_355,plain,
    multiplication(antidomain(antidomain(X1)),antidomain(X2)) = antidomain(antidomain(multiplication(antidomain(X2),X1))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_334,c_0_343]),c_0_89]) ).

cnf(c_0_356,plain,
    multiplication(X1,antidomain(addition(X2,coantidomain(X1)))) = multiplication(X1,antidomain(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_345,c_0_346]),c_0_309]),c_0_340]),c_0_89]),c_0_345]),c_0_114]),c_0_105]),c_0_89]) ).

cnf(c_0_357,plain,
    antidomain(multiplication(antidomain(addition(X1,antidomain(X2))),X2)) = antidomain(antidomain(addition(X1,antidomain(X2)))),
    inference(spm,[status(thm)],[c_0_190,c_0_347]) ).

fof(c_0_358,negated_conjecture,
    ~ ! [X4,X5] : addition(forward_diamond(X4,backward_box(X4,domain(X5))),domain(X5)) = domain(X5),
    inference(assume_negation,[status(cth)],[goals]) ).

fof(c_0_359,plain,
    ! [X41,X42] : forward_diamond(X41,X42) = domain(multiplication(X41,domain(X42))),
    inference(variable_rename,[status(thm)],[forward_diamond]) ).

fof(c_0_360,plain,
    ! [X47,X48] : backward_box(X47,X48) = c(backward_diamond(X47,c(X48))),
    inference(variable_rename,[status(thm)],[backward_box]) ).

cnf(c_0_361,plain,
    c(X1) = antidomain(domain(X1)),
    inference(split_conjunct,[status(thm)],[c_0_348]) ).

cnf(c_0_362,plain,
    domain(X1) = antidomain(antidomain(X1)),
    inference(split_conjunct,[status(thm)],[c_0_349]) ).

fof(c_0_363,plain,
    ! [X43,X44] : backward_diamond(X43,X44) = codomain(multiplication(codomain(X44),X43)),
    inference(variable_rename,[status(thm)],[backward_diamond]) ).

fof(c_0_364,plain,
    ! [X37] : codomain(X37) = coantidomain(coantidomain(X37)),
    inference(variable_rename,[status(thm)],[codomain4]) ).

cnf(c_0_365,plain,
    addition(multiplication(X1,X2),multiplication(coantidomain(X1),addition(X2,one))) = multiplication(addition(X1,coantidomain(X1)),addition(X2,coantidomain(X1))),
    inference(spm,[status(thm)],[c_0_350,c_0_216]) ).

cnf(c_0_366,plain,
    multiplication(antidomain(X1),antidomain(X2)) = antidomain(addition(X2,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_351,c_0_81]),c_0_351]),c_0_244]) ).

cnf(c_0_367,plain,
    antidomain(addition(X1,antidomain(antidomain(X1)))) = antidomain(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(spm,[status(thm)],[c_0_352,c_0_353]),c_0_231]),c_0_89]),c_0_66]),c_0_41]),c_0_89]),c_0_198]),c_0_66]),c_0_41]),c_0_89]) ).

cnf(c_0_368,plain,
    multiplication(antidomain(X1),antidomain(antidomain(multiplication(X1,X2)))) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_354]),c_0_44]) ).

cnf(c_0_369,plain,
    antidomain(addition(X1,antidomain(X2))) = antidomain(antidomain(multiplication(antidomain(X1),X2))),
    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_355,c_0_356]),c_0_355]),c_0_114]),c_0_89]),c_0_357]),c_0_89]) ).

fof(c_0_370,negated_conjecture,
    addition(forward_diamond(esk1_0,backward_box(esk1_0,domain(esk2_0))),domain(esk2_0)) != domain(esk2_0),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_358])])]) ).

cnf(c_0_371,plain,
    forward_diamond(X1,X2) = domain(multiplication(X1,domain(X2))),
    inference(split_conjunct,[status(thm)],[c_0_359]) ).

cnf(c_0_372,plain,
    backward_box(X1,X2) = c(backward_diamond(X1,c(X2))),
    inference(split_conjunct,[status(thm)],[c_0_360]) ).

cnf(c_0_373,plain,
    c(X1) = antidomain(antidomain(antidomain(X1))),
    inference(rw,[status(thm)],[c_0_361,c_0_362]) ).

cnf(c_0_374,plain,
    backward_diamond(X1,X2) = codomain(multiplication(codomain(X2),X1)),
    inference(split_conjunct,[status(thm)],[c_0_363]) ).

cnf(c_0_375,plain,
    codomain(X1) = coantidomain(coantidomain(X1)),
    inference(split_conjunct,[status(thm)],[c_0_364]) ).

cnf(c_0_376,plain,
    addition(antidomain(antidomain(X1)),antidomain(addition(X2,X1))) = addition(antidomain(X2),antidomain(antidomain(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(spm,[status(thm)],[c_0_365,c_0_366]),c_0_114]),c_0_35]),c_0_67]),c_0_41]),c_0_35]),c_0_114]),c_0_43]),c_0_114]),c_0_44]) ).

cnf(c_0_377,plain,
    antidomain(multiplication(X1,addition(X2,one))) = antidomain(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_367]),c_0_49]),c_0_35]),c_0_43]) ).

cnf(c_0_378,plain,
    addition(multiplication(X1,X2),addition(multiplication(X1,X3),X4)) = addition(multiplication(X1,addition(X2,X3)),X4),
    inference(spm,[status(thm)],[c_0_49,c_0_40]) ).

cnf(c_0_379,plain,
    addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_35]),c_0_49]) ).

cnf(c_0_380,plain,
    antidomain(addition(X1,multiplication(antidomain(X1),X2))) = antidomain(addition(X2,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_351,c_0_366]),c_0_35]),c_0_366]) ).

cnf(c_0_381,plain,
    multiplication(antidomain(X1),addition(antidomain(antidomain(multiplication(X1,X2))),X3)) = multiplication(antidomain(X1),X3),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_368]),c_0_59]) ).

cnf(c_0_382,plain,
    antidomain(addition(antidomain(X1),X2)) = antidomain(antidomain(multiplication(antidomain(X2),X1))),
    inference(spm,[status(thm)],[c_0_369,c_0_35]) ).

cnf(c_0_383,negated_conjecture,
    addition(forward_diamond(esk1_0,backward_box(esk1_0,domain(esk2_0))),domain(esk2_0)) != domain(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_370]) ).

cnf(c_0_384,plain,
    forward_diamond(X1,X2) = antidomain(antidomain(multiplication(X1,antidomain(antidomain(X2))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_371,c_0_362]),c_0_362]) ).

cnf(c_0_385,plain,
    backward_box(X1,X2) = antidomain(antidomain(antidomain(backward_diamond(X1,antidomain(antidomain(antidomain(X2))))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_372,c_0_373]),c_0_373]) ).

cnf(c_0_386,plain,
    backward_diamond(X1,X2) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(X2)),X1))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_374,c_0_375]),c_0_375]) ).

cnf(c_0_387,plain,
    addition(coantidomain(X1),antidomain(addition(X2,coantidomain(X1)))) = addition(antidomain(X2),coantidomain(X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_376,c_0_229]),c_0_377]),c_0_105]),c_0_377]),c_0_105]) ).

cnf(c_0_388,plain,
    addition(X1,addition(multiplication(X1,X2),X3)) = addition(multiplication(X1,addition(X2,one)),X3),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_378,c_0_41]),c_0_379]) ).

cnf(c_0_389,plain,
    antidomain(addition(X1,addition(multiplication(X1,X2),X3))) = antidomain(addition(X3,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_380,c_0_381]),c_0_380]),c_0_49]),c_0_382]),c_0_366]),c_0_89]),c_0_108]) ).

cnf(c_0_390,plain,
    multiplication(coantidomain(X1),antidomain(multiplication(antidomain(coantidomain(X1)),X2))) = coantidomain(X1),
    inference(spm,[status(thm)],[c_0_312,c_0_105]) ).

cnf(c_0_391,negated_conjecture,
    addition(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk2_0))))))),esk1_0))))))))))),antidomain(antidomain(esk2_0))) != antidomain(antidomain(esk2_0)),
    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_383,c_0_362]),c_0_362]),c_0_362]),c_0_384]),c_0_385]),c_0_386]) ).

cnf(c_0_392,plain,
    addition(coantidomain(X1),antidomain(addition(coantidomain(X1),X2))) = addition(antidomain(X2),coantidomain(X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_387,c_0_388]),c_0_389]),c_0_377]) ).

cnf(c_0_393,plain,
    addition(coantidomain(X1),antidomain(multiplication(antidomain(coantidomain(X1)),X2))) = antidomain(multiplication(antidomain(coantidomain(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_235,c_0_390]),c_0_35]),c_0_67]),c_0_41]),c_0_35]),c_0_67]),c_0_35]),c_0_69]),c_0_44]) ).

cnf(c_0_394,negated_conjecture,
    addition(antidomain(antidomain(esk2_0)),antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk2_0))))))),esk1_0)))))))))))) != antidomain(antidomain(esk2_0)),
    inference(rw,[status(thm)],[c_0_391,c_0_35]) ).

cnf(c_0_395,plain,
    addition(antidomain(X1),coantidomain(X2)) = antidomain(multiplication(antidomain(coantidomain(X2)),X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_392,c_0_380]),c_0_387]),c_0_35]),c_0_393]) ).

cnf(c_0_396,negated_conjecture,
    addition(antidomain(antidomain(esk2_0)),antidomain(antidomain(multiplication(esk1_0,antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(esk2_0))),esk1_0)))))))) != antidomain(antidomain(esk2_0)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_394,c_0_89]),c_0_89]),c_0_89]),c_0_89]) ).

cnf(c_0_397,plain,
    addition(antidomain(X1),antidomain(coantidomain(X2))) = antidomain(multiplication(coantidomain(X2),X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_395,c_0_97]),c_0_105]) ).

cnf(c_0_398,plain,
    multiplication(X1,antidomain(multiplication(X2,coantidomain(multiplication(X1,X2))))) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_341,c_0_224]),c_0_89]),c_0_93]),c_0_89]),c_0_274]) ).

cnf(c_0_399,negated_conjecture,
    addition(antidomain(antidomain(esk2_0)),antidomain(antidomain(multiplication(esk1_0,coantidomain(multiplication(antidomain(esk2_0),esk1_0)))))) != antidomain(antidomain(esk2_0)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_396,c_0_114]),c_0_114]),c_0_89]),c_0_97]),c_0_105]) ).

cnf(c_0_400,plain,
    addition(antidomain(X1),antidomain(X2)) = antidomain(multiplication(antidomain(antidomain(X2)),X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_397,c_0_114]),c_0_89]) ).

cnf(c_0_401,plain,
    antidomain(addition(X1,multiplication(X2,coantidomain(multiplication(antidomain(X1),X2))))) = antidomain(X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_398,c_0_366]),c_0_35]) ).

cnf(c_0_402,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_399,c_0_400]),c_0_89]),c_0_366]),c_0_401])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : KLE109+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n013.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 11:35:47 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 43.32/43.39  % Version  : CSE_E---1.5
% 43.32/43.39  % Problem  : theBenchmark.p
% 43.32/43.39  % Proof found
% 43.32/43.39  % SZS status Theorem for theBenchmark.p
% 43.32/43.39  % SZS output start Proof
% See solution above
% 43.40/43.41  % Total time : 42.810000 s
% 43.40/43.41  % SZS output end Proof
% 43.40/43.41  % Total time : 42.816000 s
%------------------------------------------------------------------------------