TSTP Solution File: KLE073+1 by Enigma---0.5.1
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%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : KLE073+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% 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 : 600s
% DateTime : Sun Jul 17 01:49:59 EDT 2022
% Result : Theorem 68.11s 10.04s
% Output : CNFRefutation 68.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 19
% Syntax : Number of formulae : 217 ( 217 unt; 0 def)
% Number of atoms : 217 ( 216 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 388 ( 47 sgn 64 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(domain3,axiom,
! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain3) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
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_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(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(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(codomain1,axiom,
! [X4] : multiplication(X4,coantidomain(X4)) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',codomain1) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
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_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(codomain3,axiom,
! [X4] : addition(coantidomain(coantidomain(X4)),coantidomain(X4)) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',codomain3) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
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(goals,conjecture,
! [X4,X5,X6] : domain(multiplication(X4,addition(domain(X5),domain(X6)))) = addition(domain(multiplication(X4,domain(X5))),domain(multiplication(X4,domain(X6)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(domain4,axiom,
! [X4] : domain(X4) = antidomain(antidomain(X4)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain4) ).
fof(c_0_19,plain,
! [X32] : addition(antidomain(antidomain(X32)),antidomain(X32)) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
fof(c_0_20,plain,
! [X7,X8] : addition(X7,X8) = addition(X8,X7),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_21,plain,
! [X17] : multiplication(X17,one) = X17,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_22,plain,
! [X29] : multiplication(antidomain(X29),X29) = zero,
inference(variable_rename,[status(thm)],[domain1]) ).
fof(c_0_23,plain,
! [X12] : addition(X12,zero) = X12,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_24,plain,
! [X9,X10,X11] : addition(X11,addition(X10,X9)) = addition(addition(X11,X10),X9),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_25,plain,
! [X13] : addition(X13,X13) = X13,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_26,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,plain,
multiplication(antidomain(X1),X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_33,plain,
! [X22,X23,X24] : multiplication(addition(X22,X23),X24) = addition(multiplication(X22,X24),multiplication(X23,X24)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_34,plain,
! [X30,X31] : addition(antidomain(multiplication(X30,X31)),antidomain(multiplication(X30,antidomain(antidomain(X31))))) = antidomain(multiplication(X30,antidomain(antidomain(X31)))),
inference(variable_rename,[status(thm)],[domain2]) ).
fof(c_0_35,plain,
! [X34] : multiplication(X34,coantidomain(X34)) = zero,
inference(variable_rename,[status(thm)],[codomain1]) ).
cnf(c_0_36,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_37,plain,
antidomain(one) = zero,
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_38,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_30,c_0_27]) ).
cnf(c_0_39,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_40,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,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_34]) ).
cnf(c_0_42,plain,
multiplication(X1,coantidomain(X1)) = zero,
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_43,plain,
antidomain(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
cnf(c_0_44,plain,
addition(one,antidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_36]),c_0_27]) ).
fof(c_0_45,plain,
! [X18] : multiplication(one,X18) = X18,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_46,plain,
! [X19,X20,X21] : multiplication(X19,addition(X20,X21)) = addition(multiplication(X19,X20),multiplication(X19,X21)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_47,plain,
multiplication(addition(X1,antidomain(X2)),X2) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_29]),c_0_30]) ).
cnf(c_0_48,plain,
antidomain(multiplication(X1,antidomain(antidomain(coantidomain(X1))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]),c_0_44]) ).
cnf(c_0_49,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_50,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_51,plain,
multiplication(addition(antidomain(X1),X2),X1) = multiplication(X2,X1),
inference(spm,[status(thm)],[c_0_47,c_0_27]) ).
cnf(c_0_52,plain,
multiplication(X1,antidomain(antidomain(coantidomain(X1)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_48]),c_0_49]) ).
cnf(c_0_53,plain,
multiplication(antidomain(X1),addition(X2,X1)) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_29]),c_0_30]) ).
cnf(c_0_54,plain,
multiplication(antidomain(antidomain(X1)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_36]),c_0_49]) ).
fof(c_0_55,plain,
! [X14,X15,X16] : multiplication(X14,multiplication(X15,X16)) = multiplication(multiplication(X14,X15),X16),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_56,plain,
multiplication(X1,addition(antidomain(antidomain(coantidomain(X1))),X2)) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_52]),c_0_38]) ).
cnf(c_0_57,plain,
antidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_36]),c_0_28]),c_0_54]) ).
cnf(c_0_58,plain,
multiplication(antidomain(addition(X1,X2)),X1) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_39]),c_0_29]) ).
fof(c_0_59,plain,
! [X37] : addition(coantidomain(coantidomain(X37)),coantidomain(X37)) = one,
inference(variable_rename,[status(thm)],[codomain3]) ).
cnf(c_0_60,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_61,plain,
multiplication(X1,antidomain(coantidomain(X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_36]),c_0_28]),c_0_57]) ).
cnf(c_0_62,plain,
multiplication(antidomain(multiplication(addition(X1,X2),X3)),multiplication(X1,X3)) = zero,
inference(spm,[status(thm)],[c_0_58,c_0_40]) ).
fof(c_0_63,plain,
! [X25] : multiplication(X25,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
cnf(c_0_64,plain,
multiplication(X1,addition(X2,coantidomain(X1))) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_42]),c_0_30]) ).
cnf(c_0_65,plain,
addition(coantidomain(coantidomain(X1)),coantidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_66,plain,
multiplication(X1,multiplication(antidomain(coantidomain(X1)),X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_67,plain,
multiplication(antidomain(X1),multiplication(antidomain(X2),X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_36]),c_0_49]) ).
cnf(c_0_68,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_69,plain,
multiplication(X1,addition(coantidomain(X1),X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_64,c_0_27]) ).
cnf(c_0_70,plain,
addition(coantidomain(X1),coantidomain(coantidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_65,c_0_27]) ).
cnf(c_0_71,plain,
multiplication(X1,multiplication(antidomain(X2),coantidomain(X1))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]) ).
cnf(c_0_72,plain,
multiplication(X1,coantidomain(coantidomain(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_28]) ).
fof(c_0_73,plain,
! [X26] : multiplication(zero,X26) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_74,plain,
multiplication(antidomain(X1),multiplication(coantidomain(X2),X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_70]),c_0_49]) ).
cnf(c_0_75,plain,
multiplication(coantidomain(antidomain(X1)),antidomain(X1)) = zero,
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_76,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_77,plain,
addition(X1,multiplication(antidomain(antidomain(X1)),X2)) = multiplication(antidomain(antidomain(X1)),addition(X1,X2)),
inference(spm,[status(thm)],[c_0_50,c_0_54]) ).
cnf(c_0_78,plain,
multiplication(antidomain(antidomain(coantidomain(coantidomain(X1)))),coantidomain(X1)) = zero,
inference(spm,[status(thm)],[c_0_74,c_0_61]) ).
cnf(c_0_79,plain,
multiplication(addition(X1,X2),coantidomain(X2)) = multiplication(X1,coantidomain(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_42]),c_0_30]) ).
cnf(c_0_80,plain,
multiplication(coantidomain(antidomain(X1)),multiplication(antidomain(X1),X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_75]),c_0_76]) ).
cnf(c_0_81,plain,
antidomain(antidomain(coantidomain(coantidomain(X1)))) = coantidomain(coantidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_30]),c_0_27]),c_0_70]),c_0_28]) ).
cnf(c_0_82,plain,
coantidomain(coantidomain(coantidomain(X1))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_70]),c_0_49]),c_0_72]) ).
cnf(c_0_83,plain,
multiplication(coantidomain(antidomain(antidomain(X1))),X1) = zero,
inference(spm,[status(thm)],[c_0_80,c_0_54]) ).
cnf(c_0_84,plain,
antidomain(antidomain(coantidomain(X1))) = coantidomain(X1),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
fof(c_0_85,plain,
! [X35,X36] : addition(coantidomain(multiplication(X35,X36)),coantidomain(multiplication(coantidomain(coantidomain(X35)),X36))) = coantidomain(multiplication(coantidomain(coantidomain(X35)),X36)),
inference(variable_rename,[status(thm)],[codomain2]) ).
cnf(c_0_86,plain,
coantidomain(one) = zero,
inference(spm,[status(thm)],[c_0_49,c_0_42]) ).
cnf(c_0_87,plain,
multiplication(addition(coantidomain(antidomain(antidomain(X1))),X2),X1) = multiplication(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_83]),c_0_38]) ).
cnf(c_0_88,plain,
addition(coantidomain(X1),antidomain(coantidomain(X1))) = one,
inference(spm,[status(thm)],[c_0_36,c_0_84]) ).
cnf(c_0_89,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_39,c_0_27]) ).
cnf(c_0_90,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_85]) ).
cnf(c_0_91,plain,
coantidomain(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_86]),c_0_38]) ).
cnf(c_0_92,plain,
addition(one,coantidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_70]),c_0_27]) ).
cnf(c_0_93,plain,
multiplication(antidomain(coantidomain(antidomain(antidomain(X1)))),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_49]) ).
cnf(c_0_94,plain,
multiplication(antidomain(coantidomain(coantidomain(X1))),coantidomain(X1)) = antidomain(coantidomain(coantidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_70]),c_0_28]) ).
cnf(c_0_95,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_28]),c_0_27]) ).
cnf(c_0_96,plain,
multiplication(antidomain(addition(X1,X2)),X2) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_89]),c_0_29]) ).
cnf(c_0_97,plain,
coantidomain(multiplication(coantidomain(coantidomain(antidomain(X1))),X1)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_29]),c_0_91]),c_0_92]) ).
cnf(c_0_98,plain,
antidomain(coantidomain(coantidomain(X1))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_84]),c_0_94]) ).
cnf(c_0_99,plain,
addition(antidomain(X1),addition(antidomain(antidomain(X1)),X2)) = addition(one,X2),
inference(spm,[status(thm)],[c_0_31,c_0_36]) ).
cnf(c_0_100,plain,
multiplication(antidomain(addition(X1,X2)),addition(X2,one)) = antidomain(addition(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_30]) ).
cnf(c_0_101,plain,
multiplication(coantidomain(coantidomain(antidomain(X1))),X1) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_97]),c_0_60]),c_0_28]) ).
cnf(c_0_102,plain,
coantidomain(coantidomain(X1)) = antidomain(coantidomain(X1)),
inference(spm,[status(thm)],[c_0_84,c_0_98]) ).
cnf(c_0_103,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_41,c_0_58]),c_0_43]),c_0_44]) ).
cnf(c_0_104,plain,
multiplication(antidomain(multiplication(X1,X2)),multiplication(X1,antidomain(antidomain(X2)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_41]),c_0_29]) ).
cnf(c_0_105,plain,
multiplication(antidomain(X1),multiplication(X1,X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_29]),c_0_76]) ).
cnf(c_0_106,plain,
multiplication(antidomain(addition(X1,X2)),multiplication(X2,X3)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_96]),c_0_76]) ).
cnf(c_0_107,plain,
multiplication(antidomain(addition(antidomain(antidomain(X1)),X2)),addition(one,X2)) = multiplication(antidomain(addition(antidomain(antidomain(X1)),X2)),antidomain(X1)),
inference(spm,[status(thm)],[c_0_53,c_0_99]) ).
cnf(c_0_108,plain,
multiplication(antidomain(addition(X1,X2)),addition(one,X2)) = antidomain(addition(X1,X2)),
inference(spm,[status(thm)],[c_0_100,c_0_27]) ).
cnf(c_0_109,plain,
multiplication(antidomain(coantidomain(antidomain(X1))),X1) = zero,
inference(rw,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_110,plain,
multiplication(antidomain(addition(X1,X2)),antidomain(antidomain(X1))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_103]),c_0_49]) ).
cnf(c_0_111,plain,
multiplication(antidomain(X1),antidomain(antidomain(multiplication(X1,X2)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_43]),c_0_49]) ).
cnf(c_0_112,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_104,c_0_106]),c_0_43]),c_0_49]) ).
cnf(c_0_113,plain,
multiplication(antidomain(addition(antidomain(antidomain(X1)),X2)),antidomain(X1)) = antidomain(addition(antidomain(antidomain(X1)),X2)),
inference(rw,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_114,plain,
multiplication(addition(antidomain(coantidomain(antidomain(X1))),X2),X1) = multiplication(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_109]),c_0_38]) ).
cnf(c_0_115,plain,
multiplication(antidomain(X1),coantidomain(antidomain(antidomain(X1)))) = coantidomain(antidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_36]),c_0_49]) ).
cnf(c_0_116,plain,
multiplication(antidomain(addition(X1,X2)),antidomain(antidomain(X2))) = zero,
inference(spm,[status(thm)],[c_0_110,c_0_89]) ).
cnf(c_0_117,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_50,c_0_111]),c_0_38]) ).
cnf(c_0_118,plain,
antidomain(addition(X1,antidomain(multiplication(X1,X2)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_57]),c_0_27]) ).
cnf(c_0_119,plain,
multiplication(coantidomain(antidomain(X1)),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_36]),c_0_49]),c_0_84]) ).
cnf(c_0_120,plain,
multiplication(addition(coantidomain(antidomain(X1)),X2),antidomain(X1)) = multiplication(X2,antidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_75]),c_0_38]) ).
cnf(c_0_121,plain,
addition(antidomain(X1),coantidomain(antidomain(antidomain(X1)))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_115]),c_0_27]),c_0_92]),c_0_28]) ).
cnf(c_0_122,plain,
antidomain(addition(X1,antidomain(X1))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_113]),c_0_57]),c_0_27]) ).
cnf(c_0_123,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_49]),c_0_27]) ).
cnf(c_0_124,plain,
multiplication(antidomain(X1),antidomain(multiplication(X1,X2))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_36]),c_0_28]),c_0_57]) ).
cnf(c_0_125,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_41,c_0_53]) ).
cnf(c_0_126,plain,
antidomain(addition(antidomain(X1),coantidomain(antidomain(X1)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_27]) ).
cnf(c_0_127,plain,
multiplication(antidomain(coantidomain(antidomain(X1))),antidomain(X1)) = antidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_88]),c_0_49]) ).
cnf(c_0_128,plain,
addition(antidomain(antidomain(X1)),coantidomain(antidomain(X1))) = antidomain(antidomain(X1)),
inference(spm,[status(thm)],[c_0_121,c_0_57]) ).
cnf(c_0_129,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_41,c_0_122]),c_0_43]),c_0_28]),c_0_43]),c_0_28]),c_0_27]) ).
cnf(c_0_130,plain,
addition(antidomain(X1),antidomain(multiplication(X1,X2))) = antidomain(multiplication(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_27]),c_0_44]),c_0_49]),c_0_27]) ).
cnf(c_0_131,plain,
addition(X1,addition(coantidomain(X2),multiplication(X2,X1))) = multiplication(addition(X2,one),addition(X1,coantidomain(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_64]),c_0_31]) ).
cnf(c_0_132,plain,
coantidomain(antidomain(X1)) = 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(spm,[status(thm)],[c_0_125,c_0_126]),c_0_127]),c_0_43]),c_0_28]),c_0_84]),c_0_128]),c_0_43]),c_0_28]),c_0_84]) ).
cnf(c_0_133,plain,
antidomain(multiplication(X1,addition(X2,antidomain(X2)))) = antidomain(X1),
inference(rw,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_134,plain,
antidomain(addition(X1,addition(X2,antidomain(addition(X1,X2))))) = zero,
inference(spm,[status(thm)],[c_0_122,c_0_31]) ).
cnf(c_0_135,plain,
multiplication(addition(X1,X2),coantidomain(X1)) = multiplication(X2,coantidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_42]),c_0_38]) ).
cnf(c_0_136,plain,
addition(antidomain(antidomain(X1)),antidomain(multiplication(X1,X2))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(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_131,c_0_124]),c_0_27]),c_0_132]),c_0_36]),c_0_27]),c_0_44]),c_0_27]),c_0_44]),c_0_132]),c_0_27]),c_0_49]) ).
cnf(c_0_137,plain,
multiplication(addition(antidomain(addition(X1,X2)),X3),X1) = multiplication(X3,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_58]),c_0_38]) ).
cnf(c_0_138,plain,
antidomain(multiplication(X1,addition(X2,addition(X3,antidomain(addition(X2,X3)))))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_31]),c_0_31]),c_0_30]) ).
cnf(c_0_139,plain,
multiplication(antidomain(X1),addition(X1,X2)) = multiplication(antidomain(X1),X2),
inference(spm,[status(thm)],[c_0_53,c_0_27]) ).
cnf(c_0_140,plain,
multiplication(antidomain(multiplication(X1,X2)),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(spm,[status(thm)],[c_0_135,c_0_136]),c_0_49]),c_0_132]),c_0_57]),c_0_132]),c_0_57]) ).
cnf(c_0_141,plain,
multiplication(antidomain(antidomain(addition(X1,X2))),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_36]),c_0_49]) ).
cnf(c_0_142,plain,
antidomain(multiplication(antidomain(X1),addition(X2,antidomain(addition(X1,X2))))) = antidomain(antidomain(X1)),
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_143,plain,
multiplication(X1,addition(multiplication(antidomain(X2),coantidomain(X1)),X3)) = multiplication(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_71]),c_0_38]) ).
cnf(c_0_144,plain,
multiplication(antidomain(X1),antidomain(addition(X1,X2))) = antidomain(addition(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_57]),c_0_57]) ).
cnf(c_0_145,plain,
antidomain(antidomain(addition(X1,multiplication(antidomain(X2),antidomain(antidomain(X1)))))) = antidomain(antidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_132]),c_0_144]) ).
cnf(c_0_146,plain,
multiplication(antidomain(antidomain(multiplication(addition(X1,X2),X3))),multiplication(X1,X3)) = multiplication(X1,X3),
inference(spm,[status(thm)],[c_0_141,c_0_40]) ).
cnf(c_0_147,plain,
multiplication(antidomain(antidomain(multiplication(X1,addition(X2,one)))),X1) = X1,
inference(spm,[status(thm)],[c_0_141,c_0_95]) ).
cnf(c_0_148,plain,
antidomain(addition(one,X1)) = zero,
inference(spm,[status(thm)],[c_0_28,c_0_58]) ).
cnf(c_0_149,plain,
antidomain(addition(X1,multiplication(antidomain(X2),antidomain(antidomain(X1))))) = antidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_145]),c_0_57]) ).
cnf(c_0_150,plain,
multiplication(antidomain(antidomain(X1)),multiplication(antidomain(X2),X1)) = multiplication(antidomain(X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_36]),c_0_49]) ).
cnf(c_0_151,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_41,c_0_64]) ).
cnf(c_0_152,plain,
multiplication(antidomain(antidomain(multiplication(X1,addition(one,X2)))),X1) = X1,
inference(spm,[status(thm)],[c_0_147,c_0_27]) ).
cnf(c_0_153,plain,
addition(antidomain(X1),antidomain(multiplication(X1,addition(one,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_41,c_0_148]),c_0_43]),c_0_28]),c_0_43]),c_0_28]),c_0_27]) ).
cnf(c_0_154,plain,
multiplication(antidomain(antidomain(X1)),multiplication(X1,X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_60,c_0_54]) ).
cnf(c_0_155,plain,
antidomain(addition(X1,antidomain(addition(antidomain(X1),X2)))) = antidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_113]),c_0_57]) ).
cnf(c_0_156,plain,
addition(antidomain(X1),antidomain(multiplication(antidomain(X2),X1))) = antidomain(multiplication(antidomain(X2),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_150]),c_0_57]) ).
cnf(c_0_157,plain,
multiplication(antidomain(X1),addition(X2,addition(X1,X3))) = multiplication(antidomain(X1),addition(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_53]),c_0_50]),c_0_31]) ).
cnf(c_0_158,plain,
multiplication(antidomain(antidomain(addition(X1,X2))),X2) = X2,
inference(spm,[status(thm)],[c_0_141,c_0_89]) ).
cnf(c_0_159,plain,
antidomain(multiplication(X1,addition(one,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_151,c_0_152]),c_0_132]),c_0_57]),c_0_118]),c_0_43]),c_0_28]),c_0_57]),c_0_153]),c_0_132]),c_0_57]),c_0_118]),c_0_43]),c_0_28]),c_0_57]) ).
cnf(c_0_160,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_95,c_0_154]),c_0_27]) ).
cnf(c_0_161,plain,
antidomain(addition(X1,antidomain(antidomain(multiplication(antidomain(X2),X1))))) = antidomain(X1),
inference(spm,[status(thm)],[c_0_155,c_0_156]) ).
cnf(c_0_162,plain,
antidomain(multiplication(antidomain(X1),addition(X2,antidomain(addition(X2,X1))))) = antidomain(antidomain(X1)),
inference(spm,[status(thm)],[c_0_138,c_0_157]) ).
cnf(c_0_163,plain,
addition(antidomain(X1),antidomain(addition(X2,X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_158]),c_0_57]),c_0_27]) ).
cnf(c_0_164,plain,
antidomain(addition(antidomain(antidomain(X1)),multiplication(X1,X2))) = antidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_160]),c_0_57]) ).
cnf(c_0_165,plain,
multiplication(antidomain(X1),antidomain(X1)) = antidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_36]),c_0_49]) ).
cnf(c_0_166,plain,
antidomain(addition(X1,antidomain(addition(X1,X2)))) = antidomain(addition(X1,antidomain(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_57]),c_0_31]),c_0_27]),c_0_163]) ).
cnf(c_0_167,plain,
antidomain(addition(X1,antidomain(antidomain(addition(X1,X2))))) = antidomain(addition(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_141]),c_0_57]),c_0_57]),c_0_27]) ).
cnf(c_0_168,plain,
multiplication(antidomain(X1),multiplication(antidomain(X1),X2)) = multiplication(antidomain(X1),X2),
inference(spm,[status(thm)],[c_0_60,c_0_165]) ).
cnf(c_0_169,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X3,X1)),
inference(spm,[status(thm)],[c_0_31,c_0_27]) ).
cnf(c_0_170,plain,
antidomain(addition(X1,antidomain(antidomain(X2)))) = antidomain(addition(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_166]),c_0_166]),c_0_167]) ).
cnf(c_0_171,plain,
multiplication(antidomain(X1),addition(multiplication(antidomain(X1),X2),X3)) = multiplication(antidomain(X1),addition(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_168]),c_0_50]) ).
cnf(c_0_172,plain,
addition(multiplication(X1,X2),addition(X3,multiplication(X1,X4))) = addition(X3,multiplication(X1,addition(X4,X2))),
inference(spm,[status(thm)],[c_0_169,c_0_50]) ).
cnf(c_0_173,plain,
antidomain(addition(X1,multiplication(X2,addition(X3,antidomain(X3))))) = antidomain(addition(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_133]),c_0_170]) ).
cnf(c_0_174,plain,
addition(X1,multiplication(antidomain(X2),addition(X1,X3))) = addition(multiplication(antidomain(X2),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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_171]),c_0_31]),c_0_172]),c_0_31]),c_0_89]),c_0_27]),c_0_44]),c_0_49]) ).
cnf(c_0_175,plain,
antidomain(addition(X1,multiplication(antidomain(X2),antidomain(X1)))) = antidomain(addition(X1,antidomain(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_174]),c_0_27]) ).
cnf(c_0_176,plain,
antidomain(multiplication(X1,multiplication(X2,addition(X3,antidomain(X3))))) = antidomain(multiplication(X1,X2)),
inference(spm,[status(thm)],[c_0_133,c_0_60]) ).
cnf(c_0_177,plain,
antidomain(addition(X1,antidomain(multiplication(antidomain(X2),antidomain(X1))))) = antidomain(addition(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_175]),c_0_166]),c_0_170]) ).
cnf(c_0_178,plain,
antidomain(multiplication(X1,antidomain(antidomain(X2)))) = antidomain(multiplication(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_53]),c_0_54]) ).
cnf(c_0_179,plain,
addition(antidomain(X1),antidomain(multiplication(antidomain(X1),X2))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_168]),c_0_57]) ).
cnf(c_0_180,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_27]),c_0_31]) ).
cnf(c_0_181,plain,
addition(X1,multiplication(antidomain(X2),addition(X3,X1))) = addition(multiplication(antidomain(X2),X3),X1),
inference(spm,[status(thm)],[c_0_174,c_0_27]) ).
cnf(c_0_182,plain,
antidomain(addition(antidomain(X1),X2)) = antidomain(antidomain(multiplication(antidomain(X2),X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_178]),c_0_156]) ).
cnf(c_0_183,plain,
multiplication(antidomain(addition(X1,X2)),antidomain(X1)) = antidomain(addition(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_141]),c_0_57]),c_0_57]) ).
cnf(c_0_184,plain,
multiplication(antidomain(multiplication(antidomain(X1),X2)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_179]),c_0_49]) ).
cnf(c_0_185,plain,
addition(X1,multiplication(addition(X2,one),X3)) = addition(X3,addition(X1,multiplication(X2,X3))),
inference(spm,[status(thm)],[c_0_180,c_0_123]) ).
cnf(c_0_186,plain,
antidomain(antidomain(multiplication(antidomain(multiplication(antidomain(X1),X2)),X2))) = antidomain(antidomain(multiplication(antidomain(antidomain(X1)),X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_181]),c_0_27]),c_0_182]),c_0_182]) ).
cnf(c_0_187,plain,
antidomain(multiplication(antidomain(antidomain(X1)),addition(X1,X2))) = antidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_77]),c_0_184]) ).
cnf(c_0_188,plain,
addition(X1,multiplication(antidomain(antidomain(X2)),addition(X2,X1))) = addition(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_77]),c_0_27]),c_0_44]),c_0_49]) ).
cnf(c_0_189,plain,
antidomain(multiplication(antidomain(multiplication(antidomain(X1),X2)),X2)) = antidomain(multiplication(antidomain(antidomain(X1)),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_186]),c_0_57]) ).
cnf(c_0_190,plain,
antidomain(multiplication(antidomain(antidomain(X1)),addition(X2,X1))) = antidomain(X1),
inference(spm,[status(thm)],[c_0_187,c_0_188]) ).
cnf(c_0_191,plain,
multiplication(antidomain(antidomain(multiplication(X1,addition(X2,X3)))),multiplication(X1,X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_141,c_0_50]) ).
cnf(c_0_192,plain,
antidomain(multiplication(antidomain(multiplication(antidomain(X1),X2)),addition(X2,X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_53]),c_0_190]) ).
cnf(c_0_193,plain,
multiplication(antidomain(X1),multiplication(antidomain(multiplication(X1,X2)),X3)) = multiplication(antidomain(X1),X3),
inference(spm,[status(thm)],[c_0_60,c_0_124]) ).
cnf(c_0_194,plain,
antidomain(addition(antidomain(antidomain(X1)),X2)) = antidomain(addition(X2,X1)),
inference(spm,[status(thm)],[c_0_170,c_0_27]) ).
fof(c_0_195,negated_conjecture,
~ ! [X4,X5,X6] : domain(multiplication(X4,addition(domain(X5),domain(X6)))) = addition(domain(multiplication(X4,domain(X5))),domain(multiplication(X4,domain(X6)))),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_196,plain,
multiplication(antidomain(multiplication(antidomain(X1),X2)),X2) = multiplication(antidomain(antidomain(X1)),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_191,c_0_192]),c_0_193]) ).
cnf(c_0_197,plain,
antidomain(antidomain(multiplication(antidomain(X1),antidomain(X2)))) = antidomain(addition(X1,X2)),
inference(rw,[status(thm)],[c_0_194,c_0_182]) ).
fof(c_0_198,negated_conjecture,
domain(multiplication(esk1_0,addition(domain(esk2_0),domain(esk3_0)))) != addition(domain(multiplication(esk1_0,domain(esk2_0))),domain(multiplication(esk1_0,domain(esk3_0)))),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_195])])]) ).
fof(c_0_199,plain,
! [X33] : domain(X33) = antidomain(antidomain(X33)),
inference(variable_rename,[status(thm)],[domain4]) ).
cnf(c_0_200,plain,
multiplication(antidomain(antidomain(multiplication(antidomain(X1),X2))),X2) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_196]),c_0_196]),c_0_57]) ).
cnf(c_0_201,plain,
antidomain(multiplication(antidomain(X1),antidomain(X2))) = antidomain(antidomain(addition(X1,X2))),
inference(spm,[status(thm)],[c_0_57,c_0_197]) ).
cnf(c_0_202,plain,
multiplication(antidomain(addition(X1,X2)),antidomain(X2)) = antidomain(addition(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_158]),c_0_57]),c_0_57]) ).
cnf(c_0_203,plain,
addition(multiplication(X1,X2),addition(multiplication(X1,X3),X4)) = addition(multiplication(X1,addition(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_31,c_0_50]) ).
cnf(c_0_204,negated_conjecture,
domain(multiplication(esk1_0,addition(domain(esk2_0),domain(esk3_0)))) != addition(domain(multiplication(esk1_0,domain(esk2_0))),domain(multiplication(esk1_0,domain(esk3_0)))),
inference(split_conjunct,[status(thm)],[c_0_198]) ).
cnf(c_0_205,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_199]) ).
cnf(c_0_206,plain,
multiplication(antidomain(X1),antidomain(X2)) = antidomain(addition(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_200,c_0_201]),c_0_57]),c_0_202]) ).
cnf(c_0_207,plain,
addition(multiplication(X1,X2),multiplication(addition(X1,X3),X4)) = addition(multiplication(X1,addition(X2,X4)),multiplication(X3,X4)),
inference(spm,[status(thm)],[c_0_203,c_0_40]) ).
cnf(c_0_208,negated_conjecture,
antidomain(antidomain(multiplication(esk1_0,addition(antidomain(antidomain(esk2_0)),antidomain(antidomain(esk3_0)))))) != addition(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0))))),antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk3_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)],[inference(rw,[status(thm)],[c_0_204,c_0_205]),c_0_205]),c_0_205]),c_0_205]),c_0_205]),c_0_205]),c_0_205]) ).
cnf(c_0_209,plain,
antidomain(addition(X1,multiplication(X2,antidomain(antidomain(X3))))) = antidomain(addition(X1,multiplication(X2,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_178]),c_0_206]) ).
cnf(c_0_210,plain,
addition(X1,multiplication(addition(X1,X2),antidomain(X3))) = addition(X1,multiplication(X2,antidomain(X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_44]),c_0_28]),c_0_28]) ).
cnf(c_0_211,negated_conjecture,
addition(antidomain(antidomain(multiplication(esk1_0,esk2_0))),antidomain(antidomain(multiplication(esk1_0,esk3_0)))) != antidomain(antidomain(multiplication(esk1_0,addition(antidomain(antidomain(esk2_0)),antidomain(antidomain(esk3_0)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_208,c_0_178]),c_0_178]) ).
cnf(c_0_212,plain,
antidomain(multiplication(X1,addition(X2,antidomain(antidomain(X3))))) = antidomain(multiplication(X1,addition(X2,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_209,c_0_50]),c_0_50]) ).
cnf(c_0_213,plain,
addition(antidomain(X1),antidomain(antidomain(multiplication(antidomain(X2),X1)))) = addition(antidomain(X1),antidomain(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_210,c_0_36]),c_0_49]),c_0_206]),c_0_182]) ).
cnf(c_0_214,negated_conjecture,
addition(antidomain(antidomain(multiplication(esk1_0,esk2_0))),antidomain(antidomain(multiplication(esk1_0,esk3_0)))) != antidomain(antidomain(multiplication(esk1_0,addition(esk2_0,esk3_0)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_211,c_0_212]),c_0_27]),c_0_212]),c_0_27]) ).
cnf(c_0_215,plain,
addition(antidomain(X1),antidomain(antidomain(X2))) = antidomain(multiplication(antidomain(X2),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_213,c_0_196]),c_0_213]),c_0_156]) ).
cnf(c_0_216,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_214,c_0_215]),c_0_206]),c_0_50]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : KLE073+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : enigmatic-eprover.py %s %d 1
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 16 09:59:45 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.44 # ENIGMATIC: Selected SinE mode:
% 0.18/0.44 # Parsing /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 # Filter: axfilter_auto 0 goes into file theBenchmark_axfilter_auto 0.p
% 0.18/0.44 # Filter: axfilter_auto 1 goes into file theBenchmark_axfilter_auto 1.p
% 0.18/0.44 # Filter: axfilter_auto 2 goes into file theBenchmark_axfilter_auto 2.p
% 68.11/10.04 # ENIGMATIC: Solved by autoschedule:
% 68.11/10.04 # No SInE strategy applied
% 68.11/10.04 # Trying AutoSched0 for 150 seconds
% 68.11/10.04 # AutoSched0-Mode selected heuristic G_E___100_C18_F1_PI_AE_Q4_CS_SP_PS_S0Y
% 68.11/10.04 # and selection function SelectMaxLComplexAvoidPosPred.
% 68.11/10.04 #
% 68.11/10.04 # Preprocessing time : 0.025 s
% 68.11/10.04 # Presaturation interreduction done
% 68.11/10.04
% 68.11/10.04 # Proof found!
% 68.11/10.04 # SZS status Theorem
% 68.11/10.04 # SZS output start CNFRefutation
% See solution above
% 68.11/10.04 # Training examples: 0 positive, 0 negative
% 68.11/10.04
% 68.11/10.04 # -------------------------------------------------
% 68.11/10.04 # User time : 7.302 s
% 68.11/10.04 # System time : 0.302 s
% 68.11/10.04 # Total time : 7.604 s
% 68.11/10.04 # Maximum resident set size: 7116 pages
% 68.11/10.04
%------------------------------------------------------------------------------