TSTP Solution File: KLE111+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : KLE111+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n023.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 05:26:23 EDT 2023
% Result : Theorem 24.74s 24.78s
% Output : CNFRefutation 24.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 41
% Syntax : Number of formulae : 394 ( 377 unt; 17 typ; 0 def)
% Number of atoms : 377 ( 376 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 20 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 13 >; 8 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 4 con; 0-2 aty)
% Number of variables : 690 ( 131 sgn; 78 !; 0 ?; 0 :)
% 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/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(domain1,axiom,
! [X4] : multiplication(antidomain(X4),X4) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain1) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(domain3,axiom,
! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(codomain3,axiom,
! [X4] : addition(coantidomain(coantidomain(X4)),coantidomain(X4)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain3) ).
fof(codomain1,axiom,
! [X4] : multiplication(X4,coantidomain(X4)) = zero,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/KLE001+4.ax',codomain2) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(complement,axiom,
! [X4] : c(X4) = antidomain(domain(X4)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+6.ax',complement) ).
fof(domain4,axiom,
! [X4] : domain(X4) = antidomain(antidomain(X4)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain4) ).
fof(forward_diamond,axiom,
! [X4,X5] : forward_diamond(X4,X5) = domain(multiplication(X4,domain(X5))),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+6.ax',forward_diamond) ).
fof(goals,conjecture,
! [X4,X5] : addition(backward_diamond(X4,forward_box(X4,domain(X5))),domain(X5)) = domain(X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(forward_box,axiom,
! [X4,X5] : forward_box(X4,X5) = c(forward_diamond(X4,c(X5))),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+6.ax',forward_box) ).
fof(backward_diamond,axiom,
! [X4,X5] : backward_diamond(X4,X5) = codomain(multiplication(codomain(X5),X4)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+6.ax',backward_diamond) ).
fof(codomain4,axiom,
! [X4] : codomain(X4) = coantidomain(coantidomain(X4)),
file('/export/starexec/sandbox/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(X1,X2)),X1) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_60]),c_0_28]) ).
cnf(c_0_117,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_118,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_116]),c_0_66]),c_0_67]) ).
cnf(c_0_119,plain,
addition(one,addition(coantidomain(X1),X2)) = addition(one,X2),
inference(spm,[status(thm)],[c_0_49,c_0_69]) ).
cnf(c_0_120,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_117]),c_0_35]),c_0_67]),c_0_44]) ).
cnf(c_0_121,plain,
multiplication(antidomain(addition(X1,X2)),antidomain(antidomain(X1))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_118]),c_0_44]) ).
cnf(c_0_122,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_123,plain,
! [X24] : multiplication(X24,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
cnf(c_0_124,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_125,plain,
addition(one,addition(X1,coantidomain(X2))) = addition(one,X1),
inference(spm,[status(thm)],[c_0_119,c_0_35]) ).
cnf(c_0_126,plain,
addition(antidomain(antidomain(X1)),antidomain(addition(X2,antidomain(X1)))) = antidomain(antidomain(X1)),
inference(spm,[status(thm)],[c_0_120,c_0_107]) ).
cnf(c_0_127,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_128,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_121]),c_0_59]) ).
cnf(c_0_129,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_122]),c_0_87]),c_0_69]) ).
cnf(c_0_130,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_122]),c_0_29]) ).
cnf(c_0_131,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_132,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_133,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_124]),c_0_125]),c_0_97]),c_0_108]) ).
cnf(c_0_134,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_126,c_0_126]),c_0_89]),c_0_35]) ).
cnf(c_0_135,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_136,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_127]),c_0_29]) ).
cnf(c_0_137,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_128,c_0_104]),c_0_41]),c_0_89]),c_0_114]),c_0_89]) ).
cnf(c_0_138,plain,
multiplication(coantidomain(coantidomain(X1)),coantidomain(addition(X1,X2))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_129]),c_0_41]) ).
cnf(c_0_139,plain,
multiplication(addition(one,X1),coantidomain(addition(X1,X2))) = coantidomain(addition(X1,X2)),
inference(spm,[status(thm)],[c_0_130,c_0_35]) ).
cnf(c_0_140,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_131,c_0_28]),c_0_132]),c_0_87]),c_0_69]) ).
cnf(c_0_141,plain,
addition(coantidomain(X1),antidomain(antidomain(addition(X2,antidomain(coantidomain(X1)))))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_67]) ).
cnf(c_0_142,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_135,c_0_113]),c_0_114]),c_0_89]),c_0_136]),c_0_114]),c_0_89]) ).
cnf(c_0_143,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_137]),c_0_35]),c_0_67]),c_0_44]) ).
cnf(c_0_144,plain,
multiplication(antidomain(coantidomain(X1)),coantidomain(addition(X1,X2))) = zero,
inference(rw,[status(thm)],[c_0_138,c_0_97]) ).
cnf(c_0_145,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_135,c_0_73]),c_0_139]),c_0_97]) ).
cnf(c_0_146,plain,
multiplication(coantidomain(coantidomain(multiplication(X1,antidomain(X2)))),X2) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_140]),c_0_41]) ).
cnf(c_0_147,plain,
addition(antidomain(coantidomain(X1)),antidomain(antidomain(addition(X2,coantidomain(X1))))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_97]),c_0_105]) ).
cnf(c_0_148,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_142]),c_0_35]),c_0_69]),c_0_41]) ).
cnf(c_0_149,plain,
multiplication(antidomain(addition(X1,X2)),antidomain(antidomain(X2))) = zero,
inference(spm,[status(thm)],[c_0_121,c_0_107]) ).
cnf(c_0_150,plain,
addition(antidomain(antidomain(X1)),antidomain(antidomain(addition(X2,antidomain(X1))))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_114]),c_0_89]) ).
cnf(c_0_151,plain,
addition(antidomain(X1),antidomain(addition(X2,X1))) = antidomain(X1),
inference(spm,[status(thm)],[c_0_143,c_0_107]) ).
cnf(c_0_152,plain,
coantidomain(addition(X1,coantidomain(X1))) = zero,
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_153,plain,
multiplication(antidomain(coantidomain(multiplication(X1,antidomain(X2)))),X2) = zero,
inference(rw,[status(thm)],[c_0_146,c_0_97]) ).
cnf(c_0_154,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_122]),c_0_59]) ).
cnf(c_0_155,plain,
addition(coantidomain(X1),antidomain(coantidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_62,c_0_97]) ).
cnf(c_0_156,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_147,c_0_148]),c_0_89]),c_0_35]) ).
cnf(c_0_157,plain,
antidomain(addition(X1,antidomain(X1))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_117]),c_0_35]) ).
cnf(c_0_158,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_159,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_160,plain,
addition(antidomain(X1),antidomain(antidomain(addition(X2,X1)))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_151]),c_0_89]),c_0_35]) ).
cnf(c_0_161,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_152]),c_0_87]),c_0_44]),c_0_87]),c_0_44]),c_0_35]) ).
cnf(c_0_162,plain,
multiplication(antidomain(coantidomain(multiplication(X1,multiplication(X2,antidomain(X3))))),X3) = zero,
inference(spm,[status(thm)],[c_0_153,c_0_55]) ).
cnf(c_0_163,plain,
multiplication(X1,antidomain(coantidomain(addition(X1,X2)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_155]),c_0_41]) ).
cnf(c_0_164,plain,
multiplication(antidomain(multiplication(addition(X1,X2),X3)),multiplication(X1,X3)) = zero,
inference(spm,[status(thm)],[c_0_116,c_0_27]) ).
cnf(c_0_165,plain,
addition(antidomain(antidomain(X1)),antidomain(coantidomain(addition(X2,antidomain(X1))))) = one,
inference(spm,[status(thm)],[c_0_156,c_0_107]) ).
cnf(c_0_166,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_157]),c_0_66]),c_0_41]),c_0_66]),c_0_41]),c_0_35]) ).
cnf(c_0_167,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_158,c_0_159]),c_0_66]),c_0_44]) ).
cnf(c_0_168,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_116]),c_0_59]) ).
cnf(c_0_169,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_160,c_0_161]),c_0_105]),c_0_35]) ).
cnf(c_0_170,plain,
multiplication(antidomain(coantidomain(multiplication(X1,X2))),coantidomain(addition(X2,X3))) = zero,
inference(spm,[status(thm)],[c_0_162,c_0_163]) ).
cnf(c_0_171,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_116]),c_0_29]) ).
cnf(c_0_172,plain,
multiplication(antidomain(X1),multiplication(coantidomain(X2),X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_155]),c_0_44]) ).
cnf(c_0_173,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_165,c_0_166]),c_0_114]),c_0_89]),c_0_35]) ).
cnf(c_0_174,plain,
antidomain(addition(X1,antidomain(multiplication(X1,X2)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_117]),c_0_35]) ).
cnf(c_0_175,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_168,c_0_104]),c_0_44]),c_0_114]),c_0_89]) ).
cnf(c_0_176,plain,
addition(antidomain(X1),antidomain(addition(antidomain(antidomain(X1)),X2))) = antidomain(X1),
inference(spm,[status(thm)],[c_0_120,c_0_89]) ).
cnf(c_0_177,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_178,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_169]),c_0_41]) ).
cnf(c_0_179,plain,
coantidomain(addition(X1,coantidomain(multiplication(X2,X1)))) = zero,
inference(spm,[status(thm)],[c_0_170,c_0_145]) ).
cnf(c_0_180,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_181,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_182,plain,
multiplication(antidomain(addition(X1,X2)),addition(one,X1)) = antidomain(addition(X1,X2)),
inference(spm,[status(thm)],[c_0_171,c_0_35]) ).
cnf(c_0_183,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_172]),c_0_56]),c_0_55]) ).
cnf(c_0_184,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_173]),c_0_44]) ).
cnf(c_0_185,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_186,plain,
antidomain(addition(antidomain(antidomain(X1)),antidomain(addition(X1,antidomain(antidomain(X1)))))) = zero,
inference(spm,[status(thm)],[c_0_174,c_0_68]) ).
cnf(c_0_187,plain,
multiplication(antidomain(antidomain(addition(X1,X2))),X2) = X2,
inference(spm,[status(thm)],[c_0_175,c_0_107]) ).
cnf(c_0_188,plain,
addition(antidomain(X1),antidomain(addition(X2,antidomain(antidomain(X1))))) = antidomain(X1),
inference(spm,[status(thm)],[c_0_176,c_0_107]) ).
cnf(c_0_189,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_177,c_0_178]),c_0_105]),c_0_179]),c_0_66]),c_0_44]),c_0_114]),c_0_105]),c_0_161]),c_0_105]),c_0_179]),c_0_66]),c_0_44]),c_0_114]),c_0_105]) ).
cnf(c_0_190,plain,
multiplication(addition(multiplication(antidomain(multiplication(X1,X2)),X1),X3),X2) = multiplication(X3,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_28]),c_0_59]) ).
cnf(c_0_191,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_181,c_0_122]),c_0_66]),c_0_67]),c_0_35]) ).
cnf(c_0_192,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_182]) ).
cnf(c_0_193,plain,
addition(antidomain(coantidomain(X1)),antidomain(addition(coantidomain(X1),X2))) = antidomain(coantidomain(X1)),
inference(spm,[status(thm)],[c_0_120,c_0_105]) ).
cnf(c_0_194,plain,
multiplication(X1,multiplication(coantidomain(coantidomain(X1)),X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_55,c_0_76]) ).
cnf(c_0_195,plain,
multiplication(X1,multiplication(X2,coantidomain(multiplication(X1,X2)))) = zero,
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_196,plain,
multiplication(X1,antidomain(coantidomain(addition(X2,X1)))) = X1,
inference(spm,[status(thm)],[c_0_163,c_0_107]) ).
cnf(c_0_197,plain,
multiplication(antidomain(addition(X1,X2)),multiplication(coantidomain(X3),X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_175]),c_0_89]) ).
cnf(c_0_198,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_181,c_0_184]),c_0_114]),c_0_89]),c_0_174]),c_0_66]),c_0_41]),c_0_89]),c_0_166]),c_0_114]),c_0_89]),c_0_174]),c_0_66]),c_0_41]),c_0_89]) ).
cnf(c_0_199,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_185,c_0_186]),c_0_187]),c_0_89]),c_0_66]),c_0_41]),c_0_89]),c_0_188]),c_0_66]),c_0_41]),c_0_89]) ).
cnf(c_0_200,plain,
coantidomain(multiplication(coantidomain(multiplication(antidomain(multiplication(X1,X2)),X1)),X2)) = coantidomain(X2),
inference(spm,[status(thm)],[c_0_189,c_0_190]) ).
cnf(c_0_201,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_191]),c_0_44]) ).
cnf(c_0_202,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_192,c_0_193]),c_0_105]),c_0_105]) ).
cnf(c_0_203,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_204,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_194,c_0_195]),c_0_132]),c_0_97]) ).
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_196,c_0_188]),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_158,c_0_197]),c_0_66]),c_0_44]) ).
cnf(c_0_207,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_198,c_0_199]),c_0_49]),c_0_35]),c_0_43]) ).
cnf(c_0_208,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_200,c_0_201]),c_0_66]),c_0_44]),c_0_202]),c_0_97]),c_0_114]),c_0_89]) ).
cnf(c_0_209,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_203]),c_0_51]) ).
cnf(c_0_210,plain,
coantidomain(addition(one,X1)) = zero,
inference(spm,[status(thm)],[c_0_44,c_0_122]) ).
cnf(c_0_211,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_195]),c_0_59]) ).
cnf(c_0_212,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_131]),c_0_54]),c_0_55]),c_0_97]) ).
cnf(c_0_213,plain,
multiplication(X1,multiplication(coantidomain(X2),coantidomain(X1))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_172]),c_0_87]),c_0_41]) ).
cnf(c_0_214,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_215,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_203]),c_0_35]),c_0_51]) ).
cnf(c_0_216,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_217,plain,
addition(antidomain(X1),antidomain(antidomain(addition(X1,X2)))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_143]),c_0_89]),c_0_35]) ).
cnf(c_0_218,plain,
antidomain(addition(antidomain(antidomain(X1)),multiplication(X1,addition(X2,one)))) = antidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_207]),c_0_35]) ).
cnf(c_0_219,plain,
addition(X1,addition(multiplication(X1,X2),X3)) = addition(X3,multiplication(X1,addition(X2,one))),
inference(spm,[status(thm)],[c_0_108,c_0_51]) ).
cnf(c_0_220,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_208]),c_0_105]),c_0_209]),c_0_35]),c_0_69]),c_0_41]) ).
cnf(c_0_221,plain,
multiplication(addition(X1,one),X1) = multiplication(X1,addition(X1,one)),
inference(spm,[status(thm)],[c_0_51,c_0_84]) ).
cnf(c_0_222,plain,
coantidomain(addition(X1,addition(X2,one))) = zero,
inference(spm,[status(thm)],[c_0_210,c_0_108]) ).
cnf(c_0_223,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_224,plain,
antidomain(multiplication(X1,antidomain(multiplication(X2,coantidomain(multiplication(X1,X2)))))) = antidomain(X1),
inference(spm,[status(thm)],[c_0_198,c_0_211]) ).
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_212,c_0_213]),c_0_87]),c_0_41]) ).
cnf(c_0_226,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_227,plain,
addition(X1,addition(multiplication(X2,X1),X3)) = addition(multiplication(addition(one,X2),X1),X3),
inference(spm,[status(thm)],[c_0_214,c_0_44]) ).
cnf(c_0_228,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_215]),c_0_49]),c_0_51]),c_0_49]),c_0_50]),c_0_35]),c_0_69]),c_0_44]) ).
cnf(c_0_229,plain,
antidomain(addition(X1,antidomain(multiplication(antidomain(coantidomain(X2)),X1)))) = zero,
inference(spm,[status(thm)],[c_0_216,c_0_97]) ).
cnf(c_0_230,plain,
addition(antidomain(X1),antidomain(antidomain(addition(X2,addition(X3,X1))))) = one,
inference(spm,[status(thm)],[c_0_217,c_0_124]) ).
cnf(c_0_231,plain,
antidomain(addition(X1,addition(antidomain(antidomain(X1)),multiplication(X1,X2)))) = antidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_219]),c_0_35]) ).
cnf(c_0_232,plain,
addition(coantidomain(X1),antidomain(coantidomain(addition(X1,X2)))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_220]),c_0_105]),c_0_35]) ).
cnf(c_0_233,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_221]) ).
cnf(c_0_234,plain,
coantidomain(multiplication(addition(X1,addition(X2,one)),X3)) = coantidomain(X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_222]),c_0_29]) ).
cnf(c_0_235,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_158,c_0_223]),c_0_66]),c_0_44]) ).
cnf(c_0_236,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_237,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_238,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_239,plain,
addition(antidomain(X1),antidomain(antidomain(addition(X2,addition(X1,X3))))) = one,
inference(spm,[status(thm)],[c_0_217,c_0_226]) ).
cnf(c_0_240,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_227,c_0_228]),c_0_50]),c_0_41]),c_0_69]),c_0_44]) ).
cnf(c_0_241,plain,
antidomain(addition(X1,antidomain(multiplication(antidomain(X2),X1)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_229,c_0_114]),c_0_89]) ).
cnf(c_0_242,plain,
multiplication(addition(X1,X2),coantidomain(X1)) = multiplication(X2,coantidomain(X1)),
inference(spm,[status(thm)],[c_0_75,c_0_35]) ).
cnf(c_0_243,plain,
addition(antidomain(antidomain(X1)),antidomain(multiplication(X1,X2))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_230,c_0_231]),c_0_35]) ).
cnf(c_0_244,plain,
addition(antidomain(coantidomain(X1)),coantidomain(multiplication(X2,X1))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_232,c_0_233]),c_0_234]),c_0_35]) ).
cnf(c_0_245,plain,
multiplication(coantidomain(X1),antidomain(coantidomain(multiplication(X1,coantidomain(X2))))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_236]),c_0_105]) ).
cnf(c_0_246,plain,
multiplication(coantidomain(antidomain(antidomain(X1))),X1) = zero,
inference(spm,[status(thm)],[c_0_237,c_0_238]) ).
cnf(c_0_247,plain,
addition(antidomain(multiplication(coantidomain(X1),X2)),antidomain(antidomain(addition(X2,X3)))) = one,
inference(spm,[status(thm)],[c_0_239,c_0_240]) ).
cnf(c_0_248,plain,
addition(coantidomain(X1),coantidomain(multiplication(X1,addition(X2,one)))) = coantidomain(X1),
inference(spm,[status(thm)],[c_0_220,c_0_51]) ).
cnf(c_0_249,plain,
multiplication(addition(multiplication(antidomain(X1),coantidomain(X2)),X3),X1) = multiplication(X3,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_172]),c_0_59]) ).
cnf(c_0_250,plain,
antidomain(multiplication(X1,addition(X2,antidomain(multiplication(antidomain(X3),X2))))) = antidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_198,c_0_241]),c_0_29]) ).
cnf(c_0_251,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_252,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_242,c_0_243]),c_0_44]),c_0_114]),c_0_89]),c_0_114]),c_0_89]) ).
cnf(c_0_253,plain,
multiplication(coantidomain(multiplication(X1,antidomain(X2))),X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_244]),c_0_44]) ).
cnf(c_0_254,plain,
multiplication(coantidomain(X1),antidomain(coantidomain(multiplication(X1,antidomain(coantidomain(X2)))))) = zero,
inference(spm,[status(thm)],[c_0_245,c_0_97]) ).
cnf(c_0_255,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_246]),c_0_59]) ).
cnf(c_0_256,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_247,c_0_248]),c_0_105]),c_0_35]) ).
cnf(c_0_257,plain,
coantidomain(multiplication(coantidomain(multiplication(antidomain(X1),coantidomain(X2))),X1)) = coantidomain(X1),
inference(spm,[status(thm)],[c_0_189,c_0_249]) ).
cnf(c_0_258,plain,
antidomain(multiplication(antidomain(X1),antidomain(multiplication(antidomain(X2),X1)))) = antidomain(antidomain(X1)),
inference(spm,[status(thm)],[c_0_250,c_0_251]) ).
cnf(c_0_259,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_260,plain,
multiplication(antidomain(X1),antidomain(coantidomain(multiplication(X2,antidomain(X1))))) = antidomain(coantidomain(multiplication(X2,antidomain(X1)))),
inference(spm,[status(thm)],[c_0_252,c_0_253]) ).
cnf(c_0_261,plain,
multiplication(X1,multiplication(antidomain(X2),coantidomain(X1))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_223]),c_0_87]),c_0_41]) ).
cnf(c_0_262,plain,
multiplication(coantidomain(X1),antidomain(coantidomain(multiplication(X1,antidomain(X2))))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_254,c_0_114]),c_0_89]) ).
cnf(c_0_263,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_255,c_0_256]),c_0_44]),c_0_114]),c_0_89]) ).
cnf(c_0_264,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_257,c_0_89]),c_0_114]),c_0_89]) ).
cnf(c_0_265,plain,
antidomain(multiplication(antidomain(X1),antidomain(multiplication(coantidomain(X2),X1)))) = antidomain(antidomain(X1)),
inference(spm,[status(thm)],[c_0_258,c_0_105]) ).
cnf(c_0_266,plain,
multiplication(X1,antidomain(coantidomain(multiplication(X1,antidomain(X2))))) = multiplication(X1,antidomain(X2)),
inference(spm,[status(thm)],[c_0_259,c_0_260]) ).
cnf(c_0_267,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_237]),c_0_29]) ).
cnf(c_0_268,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_261]),c_0_59]) ).
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_262]),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_263,c_0_264]) ).
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_258,c_0_265]),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_194,c_0_245]),c_0_132]) ).
cnf(c_0_273,plain,
multiplication(X1,antidomain(coantidomain(multiplication(X1,coantidomain(X2))))) = multiplication(X1,coantidomain(X2)),
inference(spm,[status(thm)],[c_0_266,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_189,c_0_267]),c_0_194]),c_0_97]) ).
cnf(c_0_275,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_251,c_0_244]),c_0_41]),c_0_105]),c_0_105]) ).
cnf(c_0_276,plain,
antidomain(multiplication(X1,antidomain(multiplication(antidomain(X2),coantidomain(X1))))) = antidomain(X1),
inference(spm,[status(thm)],[c_0_198,c_0_268]) ).
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_242,c_0_244]),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_194,c_0_275]),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_276,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_148,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_179,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_196]),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_194,c_0_262]),c_0_132]) ).
cnf(c_0_296,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_297,plain,
multiplication(addition(X1,antidomain(coantidomain(X1))),multiplication(antidomain(X2),coantidomain(X1))) = zero,
inference(spm,[status(thm)],[c_0_261,c_0_294]) ).
cnf(c_0_298,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_299,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_300,plain,
multiplication(antidomain(coantidomain(X1)),antidomain(coantidomain(multiplication(X1,antidomain(X2))))) = multiplication(antidomain(coantidomain(X1)),antidomain(X2)),
inference(spm,[status(thm)],[c_0_266,c_0_274]) ).
cnf(c_0_301,plain,
multiplication(coantidomain(X1),multiplication(coantidomain(X1),X2)) = multiplication(coantidomain(X1),X2),
inference(spm,[status(thm)],[c_0_55,c_0_203]) ).
cnf(c_0_302,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_131,c_0_28]),c_0_87]),c_0_69]),c_0_97]) ).
cnf(c_0_303,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_296,c_0_97]),c_0_284]),c_0_105]) ).
cnf(c_0_304,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_200,c_0_297]),c_0_66]),c_0_44]),c_0_294]) ).
cnf(c_0_305,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_298]) ).
cnf(c_0_306,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_299]),c_0_97]),c_0_274]),c_0_300]),c_0_97]),c_0_274]) ).
cnf(c_0_307,plain,
coantidomain(multiplication(coantidomain(X1),antidomain(X2))) = antidomain(multiplication(antidomain(X2),coantidomain(X1))),
inference(spm,[status(thm)],[c_0_293,c_0_264]) ).
cnf(c_0_308,plain,
addition(coantidomain(X1),antidomain(multiplication(coantidomain(X1),X2))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_243,c_0_301]),c_0_105]) ).
cnf(c_0_309,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_302]),c_0_41]) ).
cnf(c_0_310,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_266,c_0_303]),c_0_55]),c_0_304]),c_0_298]),c_0_305]) ).
cnf(c_0_311,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_306,c_0_97]),c_0_105]),c_0_307]) ).
cnf(c_0_312,plain,
multiplication(X1,antidomain(multiplication(coantidomain(X1),X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_243]),c_0_41]) ).
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_116]),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_255,c_0_308]),c_0_44]),c_0_114]),c_0_89]) ).
cnf(c_0_315,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_309,c_0_310]),c_0_307]),c_0_311]),c_0_55]) ).
cnf(c_0_316,plain,
multiplication(X1,multiplication(antidomain(multiplication(coantidomain(X1),X2)),X3)) = multiplication(X1,X3),
inference(spm,[status(thm)],[c_0_55,c_0_312]) ).
cnf(c_0_317,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_200,c_0_223]),c_0_66]),c_0_44]),c_0_114]) ).
cnf(c_0_318,plain,
antidomain(coantidomain(multiplication(antidomain(X1),antidomain(X2)))) = multiplication(antidomain(X1),antidomain(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_306,c_0_114]),c_0_89]) ).
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_198,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_231,c_0_314]),c_0_89]),c_0_35]),c_0_107]) ).
cnf(c_0_321,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_194,c_0_303]),c_0_97]) ).
cnf(c_0_322,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_200,c_0_315]),c_0_66]),c_0_44]),c_0_97]),c_0_274]),c_0_316]) ).
cnf(c_0_323,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_305,c_0_97]),c_0_306]),c_0_105]) ).
cnf(c_0_324,plain,
coantidomain(multiplication(antidomain(X1),multiplication(antidomain(X2),antidomain(X1)))) = coantidomain(multiplication(antidomain(X2),antidomain(X1))),
inference(spm,[status(thm)],[c_0_317,c_0_89]) ).
cnf(c_0_325,plain,
coantidomain(multiplication(antidomain(X1),antidomain(X2))) = antidomain(multiplication(antidomain(X1),antidomain(X2))),
inference(spm,[status(thm)],[c_0_114,c_0_318]) ).
fof(c_0_326,plain,
! [X38] : c(X38) = antidomain(domain(X38)),
inference(variable_rename,[status(thm)],[complement]) ).
fof(c_0_327,plain,
! [X32] : domain(X32) = antidomain(antidomain(X32)),
inference(variable_rename,[status(thm)],[domain4]) ).
fof(c_0_328,plain,
! [X41,X42] : forward_diamond(X41,X42) = domain(multiplication(X41,domain(X42))),
inference(variable_rename,[status(thm)],[forward_diamond]) ).
cnf(c_0_329,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_330,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_321,c_0_322]),c_0_321]),c_0_114]),c_0_305]),c_0_284]),c_0_105]) ).
cnf(c_0_331,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_266,c_0_323]),c_0_55]),c_0_324]),c_0_325]) ).
fof(c_0_332,negated_conjecture,
~ ! [X4,X5] : addition(backward_diamond(X4,forward_box(X4,domain(X5))),domain(X5)) = domain(X5),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_333,plain,
! [X45,X46] : forward_box(X45,X46) = c(forward_diamond(X45,c(X46))),
inference(variable_rename,[status(thm)],[forward_box]) ).
cnf(c_0_334,plain,
c(X1) = antidomain(domain(X1)),
inference(split_conjunct,[status(thm)],[c_0_326]) ).
cnf(c_0_335,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_327]) ).
cnf(c_0_336,plain,
forward_diamond(X1,X2) = domain(multiplication(X1,domain(X2))),
inference(split_conjunct,[status(thm)],[c_0_328]) ).
fof(c_0_337,plain,
! [X43,X44] : backward_diamond(X43,X44) = codomain(multiplication(codomain(X44),X43)),
inference(variable_rename,[status(thm)],[backward_diamond]) ).
fof(c_0_338,plain,
! [X37] : codomain(X37) = coantidomain(coantidomain(X37)),
inference(variable_rename,[status(thm)],[codomain4]) ).
cnf(c_0_339,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_329,c_0_311]),c_0_55]),c_0_52]) ).
cnf(c_0_340,plain,
multiplication(X1,coantidomain(multiplication(X1,antidomain(coantidomain(X2))))) = multiplication(X1,coantidomain(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_330,c_0_330]),c_0_273]) ).
cnf(c_0_341,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_329,c_0_331]),c_0_55]),c_0_52]) ).
fof(c_0_342,negated_conjecture,
addition(backward_diamond(esk1_0,forward_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_332])])]) ).
cnf(c_0_343,plain,
forward_box(X1,X2) = c(forward_diamond(X1,c(X2))),
inference(split_conjunct,[status(thm)],[c_0_333]) ).
cnf(c_0_344,plain,
c(X1) = antidomain(antidomain(antidomain(X1))),
inference(rw,[status(thm)],[c_0_334,c_0_335]) ).
cnf(c_0_345,plain,
forward_diamond(X1,X2) = antidomain(antidomain(multiplication(X1,antidomain(antidomain(X2))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_336,c_0_335]),c_0_335]) ).
cnf(c_0_346,plain,
backward_diamond(X1,X2) = codomain(multiplication(codomain(X2),X1)),
inference(split_conjunct,[status(thm)],[c_0_337]) ).
cnf(c_0_347,plain,
codomain(X1) = coantidomain(coantidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_338]) ).
cnf(c_0_348,plain,
multiplication(coantidomain(X1),antidomain(antidomain(X2))) = antidomain(antidomain(multiplication(coantidomain(X1),X2))),
inference(spm,[status(thm)],[c_0_311,c_0_339]) ).
cnf(c_0_349,plain,
multiplication(X1,coantidomain(multiplication(X1,antidomain(X2)))) = multiplication(X1,antidomain(antidomain(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_340,c_0_114]),c_0_89]) ).
cnf(c_0_350,plain,
multiplication(antidomain(X1),antidomain(antidomain(X2))) = antidomain(antidomain(multiplication(antidomain(X1),X2))),
inference(spm,[status(thm)],[c_0_331,c_0_341]) ).
cnf(c_0_351,plain,
antidomain(addition(one,X1)) = zero,
inference(spm,[status(thm)],[c_0_41,c_0_116]) ).
cnf(c_0_352,negated_conjecture,
addition(backward_diamond(esk1_0,forward_box(esk1_0,domain(esk2_0))),domain(esk2_0)) != domain(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_342]) ).
cnf(c_0_353,plain,
forward_box(X1,X2) = antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(X1,antidomain(antidomain(antidomain(antidomain(antidomain(X2))))))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_343,c_0_344]),c_0_344]),c_0_345]) ).
cnf(c_0_354,plain,
backward_diamond(X1,X2) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(X2)),X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_346,c_0_347]),c_0_347]) ).
cnf(c_0_355,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_194,c_0_348]),c_0_97]) ).
cnf(c_0_356,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_349,c_0_350]),c_0_114]),c_0_89]),c_0_89]) ).
cnf(c_0_357,plain,
multiplication(antidomain(X1),antidomain(addition(X2,X1))) = antidomain(addition(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_151]),c_0_89]) ).
cnf(c_0_358,plain,
antidomain(multiplication(X1,addition(one,X2))) = antidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_198,c_0_351]),c_0_29]) ).
cnf(c_0_359,negated_conjecture,
addition(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(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)],[c_0_352,c_0_335]),c_0_335]),c_0_335]),c_0_353]),c_0_354]) ).
cnf(c_0_360,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_355,c_0_224]),c_0_89]),c_0_93]),c_0_89]),c_0_274]) ).
cnf(c_0_361,plain,
multiplication(antidomain(X1),antidomain(X2)) = antidomain(addition(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_356,c_0_81]),c_0_356]),c_0_357]) ).
cnf(c_0_362,plain,
antidomain(multiplication(X1,multiplication(X2,addition(one,X3)))) = antidomain(multiplication(X1,X2)),
inference(spm,[status(thm)],[c_0_358,c_0_55]) ).
cnf(c_0_363,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk2_0))))))))))))))),esk1_0)))) != antidomain(antidomain(esk2_0)),
inference(rw,[status(thm)],[c_0_359,c_0_35]) ).
cnf(c_0_364,plain,
addition(coantidomain(X1),antidomain(multiplication(X2,coantidomain(multiplication(X1,X2))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_244,c_0_360]),c_0_114]),c_0_89]),c_0_35]) ).
cnf(c_0_365,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_356,c_0_361]),c_0_35]),c_0_361]) ).
cnf(c_0_366,plain,
antidomain(multiplication(X1,addition(X2,antidomain(antidomain(X2))))) = antidomain(multiplication(X1,antidomain(antidomain(X2)))),
inference(spm,[status(thm)],[c_0_362,c_0_68]) ).
cnf(c_0_367,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(multiplication(esk1_0,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_363,c_0_89]),c_0_89]),c_0_89]),c_0_89]),c_0_89]) ).
cnf(c_0_368,plain,
addition(antidomain(X1),antidomain(addition(X2,addition(X3,X1)))) = antidomain(X1),
inference(spm,[status(thm)],[c_0_143,c_0_124]) ).
cnf(c_0_369,plain,
addition(antidomain(X1),coantidomain(multiplication(antidomain(multiplication(X2,X1)),X2))) = one,
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_364,c_0_309]),c_0_114]),c_0_105]),c_0_87]),c_0_41]),c_0_35]) ).
cnf(c_0_370,plain,
antidomain(multiplication(X1,antidomain(antidomain(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_365,c_0_158]),c_0_29]),c_0_40]),c_0_35]),c_0_366]) ).
cnf(c_0_371,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),antidomain(coantidomain(multiplication(antidomain(coantidomain(antidomain(multiplication(esk1_0,antidomain(esk2_0))))),esk1_0)))) != antidomain(antidomain(esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_367,c_0_97]),c_0_97]) ).
cnf(c_0_372,plain,
addition(antidomain(X1),antidomain(multiplication(X1,X2))) = antidomain(multiplication(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_368,c_0_231]),c_0_35]) ).
cnf(c_0_373,plain,
multiplication(coantidomain(multiplication(antidomain(multiplication(X1,X2)),X1)),X2) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_369]),c_0_44]),c_0_114]),c_0_370]) ).
cnf(c_0_374,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),antidomain(coantidomain(multiplication(antidomain(multiplication(esk1_0,antidomain(esk2_0))),esk1_0)))) != antidomain(antidomain(esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_371,c_0_114]),c_0_89]) ).
cnf(c_0_375,plain,
addition(antidomain(X1),antidomain(coantidomain(multiplication(antidomain(multiplication(X2,X1)),X2)))) = antidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_372,c_0_373]),c_0_35]) ).
cnf(c_0_376,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_374,c_0_375])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE111+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n023.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 11:27:40 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.55 start to proof: theBenchmark
% 24.74/24.78 % Version : CSE_E---1.5
% 24.74/24.78 % Problem : theBenchmark.p
% 24.74/24.78 % Proof found
% 24.74/24.78 % SZS status Theorem for theBenchmark.p
% 24.74/24.78 % SZS output start Proof
% See solution above
% 24.74/24.80 % Total time : 24.219000 s
% 24.74/24.80 % SZS output end Proof
% 24.74/24.80 % Total time : 24.224000 s
%------------------------------------------------------------------------------