TSTP Solution File: KLE124+1 by E-SAT---3.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : KLE124+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n022.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 18:05:02 EDT 2023
% Result : Theorem 843.39s 107.05s
% Output : CNFRefutation 843.39s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)
% Comments :
%------------------------------------------------------------------------------
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/tmp/tmp.kcjnmxyBc8/E---3.1_7033.p',multiplicative_left_identity) ).
fof(codomain1,axiom,
! [X4] : multiplication(X4,coantidomain(X4)) = zero,
file('/export/starexec/sandbox2/tmp/tmp.kcjnmxyBc8/E---3.1_7033.p',codomain1) ).
fof(codomain3,axiom,
! [X4] : addition(coantidomain(coantidomain(X4)),coantidomain(X4)) = one,
file('/export/starexec/sandbox2/tmp/tmp.kcjnmxyBc8/E---3.1_7033.p',codomain3) ).
fof(codomain4,axiom,
! [X4] : codomain(X4) = coantidomain(coantidomain(X4)),
file('/export/starexec/sandbox2/tmp/tmp.kcjnmxyBc8/E---3.1_7033.p',codomain4) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/tmp/tmp.kcjnmxyBc8/E---3.1_7033.p',additive_commutativity) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/tmp/tmp.kcjnmxyBc8/E---3.1_7033.p',additive_identity) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox2/tmp/tmp.kcjnmxyBc8/E---3.1_7033.p',right_distributivity) ).
fof(backward_diamond,axiom,
! [X4,X5] : backward_diamond(X4,X5) = codomain(multiplication(codomain(X5),X4)),
file('/export/starexec/sandbox2/tmp/tmp.kcjnmxyBc8/E---3.1_7033.p',backward_diamond) ).
fof(domain3,axiom,
! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
file('/export/starexec/sandbox2/tmp/tmp.kcjnmxyBc8/E---3.1_7033.p',domain3) ).
fof(domain4,axiom,
! [X4] : domain(X4) = antidomain(antidomain(X4)),
file('/export/starexec/sandbox2/tmp/tmp.kcjnmxyBc8/E---3.1_7033.p',domain4) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/tmp/tmp.kcjnmxyBc8/E---3.1_7033.p',multiplicative_right_identity) ).
fof(domain1,axiom,
! [X4] : multiplication(antidomain(X4),X4) = zero,
file('/export/starexec/sandbox2/tmp/tmp.kcjnmxyBc8/E---3.1_7033.p',domain1) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox2/tmp/tmp.kcjnmxyBc8/E---3.1_7033.p',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/tmp/tmp.kcjnmxyBc8/E---3.1_7033.p',additive_idempotence) ).
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/tmp/tmp.kcjnmxyBc8/E---3.1_7033.p',domain2) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox2/tmp/tmp.kcjnmxyBc8/E---3.1_7033.p',multiplicative_associativity) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox2/tmp/tmp.kcjnmxyBc8/E---3.1_7033.p',left_annihilation) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox2/tmp/tmp.kcjnmxyBc8/E---3.1_7033.p',left_distributivity) ).
fof(backward_box,axiom,
! [X4,X5] : backward_box(X4,X5) = c(backward_diamond(X4,c(X5))),
file('/export/starexec/sandbox2/tmp/tmp.kcjnmxyBc8/E---3.1_7033.p',backward_box) ).
fof(complement,axiom,
! [X4] : c(X4) = antidomain(domain(X4)),
file('/export/starexec/sandbox2/tmp/tmp.kcjnmxyBc8/E---3.1_7033.p',complement) ).
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/tmp/tmp.kcjnmxyBc8/E---3.1_7033.p',codomain2) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox2/tmp/tmp.kcjnmxyBc8/E---3.1_7033.p',right_annihilation) ).
fof(goals,conjecture,
! [X4,X5,X6,X7,X8] :
( ( addition(domain(X6),domain(X5)) = domain(X5)
& addition(backward_diamond(X4,domain(X5)),domain(X7)) = domain(X7)
& addition(domain(X7),domain(X8)) = domain(X8) )
=> addition(backward_diamond(X4,domain(X6)),domain(X8)) = domain(X8) ),
file('/export/starexec/sandbox2/tmp/tmp.kcjnmxyBc8/E---3.1_7033.p',goals) ).
fof(c_0_23,plain,
! [X50] : multiplication(one,X50) = X50,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_24,plain,
! [X53] : multiplication(X53,coantidomain(X53)) = zero,
inference(variable_rename,[status(thm)],[codomain1]) ).
fof(c_0_25,plain,
! [X38] : addition(coantidomain(coantidomain(X38)),coantidomain(X38)) = one,
inference(variable_rename,[status(thm)],[codomain3]) ).
fof(c_0_26,plain,
! [X54] : codomain(X54) = coantidomain(coantidomain(X54)),
inference(variable_rename,[status(thm)],[codomain4]) ).
fof(c_0_27,plain,
! [X20,X21] : addition(X20,X21) = addition(X21,X20),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_28,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
multiplication(X1,coantidomain(X1)) = zero,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_30,plain,
! [X25] : addition(X25,zero) = X25,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_31,plain,
addition(coantidomain(coantidomain(X1)),coantidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
codomain(X1) = coantidomain(coantidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,plain,
coantidomain(one) = zero,
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,plain,
addition(coantidomain(X1),codomain(X1)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
cnf(c_0_37,plain,
codomain(one) = coantidomain(zero),
inference(spm,[status(thm)],[c_0_32,c_0_34]) ).
cnf(c_0_38,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_35,c_0_33]) ).
fof(c_0_39,plain,
! [X27,X28,X29] : multiplication(X27,addition(X28,X29)) = addition(multiplication(X27,X28),multiplication(X27,X29)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_40,plain,
! [X39,X40] : backward_diamond(X39,X40) = codomain(multiplication(codomain(X40),X39)),
inference(variable_rename,[status(thm)],[backward_diamond]) ).
cnf(c_0_41,plain,
coantidomain(zero) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_34]),c_0_38]) ).
fof(c_0_42,plain,
! [X35] : addition(antidomain(antidomain(X35)),antidomain(X35)) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
fof(c_0_43,plain,
! [X14] : domain(X14) = antidomain(antidomain(X14)),
inference(variable_rename,[status(thm)],[domain4]) ).
fof(c_0_44,plain,
! [X49] : multiplication(X49,one) = X49,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_45,plain,
! [X43] : multiplication(antidomain(X43),X43) = zero,
inference(variable_rename,[status(thm)],[domain1]) ).
fof(c_0_46,plain,
! [X22,X23,X24] : addition(X24,addition(X23,X22)) = addition(addition(X24,X23),X22),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_47,plain,
! [X26] : addition(X26,X26) = X26,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_48,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_49,plain,
backward_diamond(X1,X2) = codomain(multiplication(codomain(X2),X1)),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_50,plain,
codomain(one) = one,
inference(rw,[status(thm)],[c_0_37,c_0_41]) ).
cnf(c_0_51,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_52,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_53,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_54,plain,
multiplication(antidomain(X1),X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_55,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_56,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_57,plain,
multiplication(X1,addition(X2,coantidomain(X1))) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_29]),c_0_35]) ).
cnf(c_0_58,plain,
codomain(X1) = backward_diamond(X1,one),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_28]) ).
fof(c_0_59,plain,
! [X33,X34] : addition(antidomain(multiplication(X33,X34)),antidomain(multiplication(X33,antidomain(antidomain(X34))))) = antidomain(multiplication(X33,antidomain(antidomain(X34)))),
inference(variable_rename,[status(thm)],[domain2]) ).
fof(c_0_60,plain,
! [X46,X47,X48] : multiplication(X46,multiplication(X47,X48)) = multiplication(multiplication(X46,X47),X48),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(c_0_61,plain,
! [X52] : multiplication(zero,X52) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_62,plain,
addition(domain(X1),antidomain(X1)) = one,
inference(rw,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_63,plain,
antidomain(one) = zero,
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_64,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_65,plain,
multiplication(X1,addition(coantidomain(X1),X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_57,c_0_33]) ).
cnf(c_0_66,plain,
addition(coantidomain(X1),backward_diamond(X1,one)) = one,
inference(rw,[status(thm)],[c_0_36,c_0_58]) ).
cnf(c_0_67,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_59]) ).
cnf(c_0_68,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_69,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_70,plain,
domain(one) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_35]) ).
cnf(c_0_71,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_64,c_0_33]) ).
cnf(c_0_72,plain,
multiplication(X1,backward_diamond(X1,one)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_53]) ).
cnf(c_0_73,plain,
addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,domain(X2)))) = antidomain(multiplication(X1,domain(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_52]),c_0_52]) ).
cnf(c_0_74,plain,
multiplication(X1,multiplication(coantidomain(X1),X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_29]),c_0_69]) ).
cnf(c_0_75,plain,
antidomain(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_63]),c_0_70]) ).
cnf(c_0_76,plain,
addition(one,antidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_62]),c_0_33]) ).
cnf(c_0_77,plain,
multiplication(X1,multiplication(backward_diamond(X1,one),X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_68,c_0_72]) ).
fof(c_0_78,plain,
! [X30,X31,X32] : multiplication(addition(X30,X31),X32) = addition(multiplication(X30,X32),multiplication(X31,X32)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_79,plain,
antidomain(multiplication(X1,domain(multiplication(coantidomain(X1),X2)))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75]),c_0_76]) ).
cnf(c_0_80,plain,
multiplication(X1,backward_diamond(backward_diamond(X1,one),one)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_72]),c_0_72]) ).
cnf(c_0_81,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_82,plain,
antidomain(multiplication(X1,domain(coantidomain(X1)))) = one,
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
fof(c_0_83,plain,
! [X41,X42] : backward_box(X41,X42) = c(backward_diamond(X41,c(X42))),
inference(variable_rename,[status(thm)],[backward_box]) ).
fof(c_0_84,plain,
! [X15] : c(X15) = antidomain(domain(X15)),
inference(variable_rename,[status(thm)],[complement]) ).
cnf(c_0_85,plain,
multiplication(antidomain(X1),addition(X2,X1)) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_54]),c_0_35]) ).
cnf(c_0_86,plain,
multiplication(addition(X1,antidomain(X2)),X2) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_54]),c_0_35]) ).
cnf(c_0_87,plain,
coantidomain(coantidomain(X1)) = backward_diamond(X1,one),
inference(rw,[status(thm)],[c_0_32,c_0_58]) ).
cnf(c_0_88,plain,
multiplication(X1,domain(coantidomain(X1))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_82]),c_0_28]) ).
cnf(c_0_89,plain,
backward_box(X1,X2) = c(backward_diamond(X1,c(X2))),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_90,plain,
c(X1) = antidomain(domain(X1)),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_91,plain,
multiplication(antidomain(X1),addition(X1,X2)) = multiplication(antidomain(X1),X2),
inference(spm,[status(thm)],[c_0_85,c_0_33]) ).
cnf(c_0_92,plain,
antidomain(domain(X1)) = domain(antidomain(X1)),
inference(spm,[status(thm)],[c_0_52,c_0_52]) ).
cnf(c_0_93,plain,
multiplication(domain(X1),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_62]),c_0_28]) ).
cnf(c_0_94,plain,
backward_diamond(coantidomain(X1),one) = coantidomain(backward_diamond(X1,one)),
inference(spm,[status(thm)],[c_0_87,c_0_87]) ).
cnf(c_0_95,plain,
multiplication(X1,addition(domain(coantidomain(X1)),X2)) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_88]),c_0_38]) ).
cnf(c_0_96,plain,
antidomain(domain(backward_diamond(X1,antidomain(domain(X2))))) = backward_box(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_90]),c_0_90]) ).
cnf(c_0_97,plain,
domain(antidomain(X1)) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_62]),c_0_92]),c_0_53]),c_0_92]),c_0_93]) ).
cnf(c_0_98,plain,
addition(backward_diamond(X1,one),coantidomain(backward_diamond(X1,one))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_87]),c_0_94]) ).
cnf(c_0_99,plain,
backward_diamond(multiplication(backward_diamond(X1,one),X2),one) = backward_diamond(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_58]),c_0_58]) ).
cnf(c_0_100,plain,
multiplication(X1,antidomain(coantidomain(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_62]),c_0_53]) ).
cnf(c_0_101,plain,
antidomain(backward_diamond(X1,antidomain(X2))) = backward_box(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_92]),c_0_92]),c_0_97]),c_0_97]) ).
cnf(c_0_102,plain,
multiplication(addition(X1,X2),coantidomain(X2)) = multiplication(X1,coantidomain(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_29]),c_0_35]) ).
cnf(c_0_103,plain,
addition(backward_diamond(X1,X2),coantidomain(backward_diamond(X1,X2))) = one,
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_104,plain,
multiplication(antidomain(addition(X1,X2)),X1) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_64]),c_0_54]) ).
cnf(c_0_105,plain,
multiplication(coantidomain(X1),antidomain(backward_diamond(X1,one))) = coantidomain(X1),
inference(spm,[status(thm)],[c_0_100,c_0_87]) ).
cnf(c_0_106,plain,
antidomain(backward_diamond(X1,one)) = backward_box(X1,zero),
inference(spm,[status(thm)],[c_0_101,c_0_75]) ).
cnf(c_0_107,plain,
backward_diamond(backward_diamond(X1,one),one) = backward_diamond(one,X1),
inference(spm,[status(thm)],[c_0_99,c_0_53]) ).
cnf(c_0_108,plain,
backward_diamond(backward_diamond(X1,X2),one) = backward_diamond(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_87]),c_0_28]),c_0_87]),c_0_72]) ).
cnf(c_0_109,plain,
multiplication(addition(X1,antidomain(addition(X2,X3))),X2) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_104]),c_0_35]) ).
cnf(c_0_110,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_28]),c_0_33]) ).
cnf(c_0_111,plain,
multiplication(coantidomain(X1),backward_box(X1,zero)) = coantidomain(X1),
inference(rw,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_112,plain,
addition(one,coantidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_66]),c_0_33]) ).
cnf(c_0_113,plain,
backward_diamond(X1,one) = backward_diamond(one,X1),
inference(rw,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_114,plain,
multiplication(domain(addition(X1,X2)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_62]),c_0_28]) ).
cnf(c_0_115,plain,
addition(coantidomain(X1),backward_box(X1,zero)) = backward_box(X1,zero),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_33]),c_0_112]),c_0_28]),c_0_33]) ).
cnf(c_0_116,plain,
domain(backward_box(X1,X2)) = backward_box(X1,X2),
inference(spm,[status(thm)],[c_0_97,c_0_101]) ).
cnf(c_0_117,plain,
multiplication(X1,backward_diamond(one,X1)) = X1,
inference(rw,[status(thm)],[c_0_80,c_0_107]) ).
cnf(c_0_118,plain,
backward_diamond(one,coantidomain(X1)) = coantidomain(backward_diamond(one,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_94]),c_0_94]),c_0_107]) ).
cnf(c_0_119,plain,
addition(coantidomain(X1),backward_diamond(one,X1)) = one,
inference(spm,[status(thm)],[c_0_66,c_0_113]) ).
cnf(c_0_120,plain,
antidomain(backward_diamond(one,X1)) = backward_box(X1,zero),
inference(spm,[status(thm)],[c_0_106,c_0_113]) ).
cnf(c_0_121,plain,
multiplication(backward_box(X1,zero),coantidomain(X1)) = coantidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_116]) ).
cnf(c_0_122,plain,
multiplication(coantidomain(X1),coantidomain(backward_diamond(one,X1))) = coantidomain(X1),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_123,plain,
backward_box(X1,zero) = coantidomain(X1),
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_119]),c_0_53]),c_0_120]),c_0_120]),c_0_121]) ).
cnf(c_0_124,plain,
coantidomain(backward_diamond(one,X1)) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_119]),c_0_28]),c_0_122]) ).
cnf(c_0_125,plain,
antidomain(backward_diamond(one,X1)) = coantidomain(X1),
inference(rw,[status(thm)],[c_0_120,c_0_123]) ).
cnf(c_0_126,plain,
backward_diamond(one,coantidomain(X1)) = coantidomain(X1),
inference(rw,[status(thm)],[c_0_118,c_0_124]) ).
cnf(c_0_127,plain,
backward_diamond(X1,one) = antidomain(coantidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_32]),c_0_58]) ).
fof(c_0_128,plain,
! [X36,X37] : addition(coantidomain(multiplication(X36,X37)),coantidomain(multiplication(coantidomain(coantidomain(X36)),X37))) = coantidomain(multiplication(coantidomain(coantidomain(X36)),X37)),
inference(variable_rename,[status(thm)],[codomain2]) ).
cnf(c_0_129,plain,
backward_diamond(one,X1) = antidomain(coantidomain(X1)),
inference(rw,[status(thm)],[c_0_113,c_0_127]) ).
cnf(c_0_130,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_128]) ).
cnf(c_0_131,plain,
multiplication(antidomain(addition(X1,X2)),multiplication(X1,X3)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_104]),c_0_69]) ).
cnf(c_0_132,plain,
multiplication(domain(X1),multiplication(X1,X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_68,c_0_93]) ).
cnf(c_0_133,plain,
antidomain(coantidomain(multiplication(antidomain(coantidomain(X1)),X2))) = backward_diamond(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_113]),c_0_127]),c_0_129]) ).
cnf(c_0_134,plain,
domain(coantidomain(X1)) = coantidomain(X1),
inference(spm,[status(thm)],[c_0_116,c_0_123]) ).
cnf(c_0_135,plain,
addition(coantidomain(multiplication(X1,X2)),coantidomain(multiplication(codomain(X1),X2))) = coantidomain(multiplication(codomain(X1),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_130,c_0_32]),c_0_32]) ).
cnf(c_0_136,plain,
multiplication(antidomain(addition(domain(X1),X2)),multiplication(X1,X3)) = zero,
inference(spm,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_137,plain,
coantidomain(multiplication(antidomain(coantidomain(X1)),X2)) = antidomain(backward_diamond(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_133]),c_0_134]) ).
cnf(c_0_138,plain,
addition(one,backward_box(X1,X2)) = one,
inference(spm,[status(thm)],[c_0_76,c_0_101]) ).
cnf(c_0_139,plain,
antidomain(domain(X1)) = antidomain(X1),
inference(rw,[status(thm)],[c_0_92,c_0_97]) ).
cnf(c_0_140,plain,
backward_box(multiplication(X1,X2),addition(domain(X1),X3)) = 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_135,c_0_136]),c_0_41]),c_0_58]),c_0_127]),c_0_137]),c_0_101]),c_0_138]),c_0_58]),c_0_127]),c_0_137]),c_0_101]) ).
cnf(c_0_141,plain,
backward_box(X1,domain(X2)) = backward_box(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_139]),c_0_101]) ).
cnf(c_0_142,plain,
backward_box(multiplication(X1,X2),X1) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_35]),c_0_141]) ).
cnf(c_0_143,plain,
backward_diamond(one,backward_diamond(X1,X2)) = backward_diamond(X1,X2),
inference(rw,[status(thm)],[c_0_108,c_0_113]) ).
cnf(c_0_144,plain,
multiplication(backward_box(X1,X2),backward_diamond(X1,antidomain(X2))) = zero,
inference(spm,[status(thm)],[c_0_54,c_0_101]) ).
cnf(c_0_145,plain,
backward_box(X1,addition(X1,X2)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_114]),c_0_141]) ).
cnf(c_0_146,plain,
antidomain(coantidomain(backward_diamond(X1,X2))) = backward_diamond(X1,X2),
inference(rw,[status(thm)],[c_0_143,c_0_129]) ).
cnf(c_0_147,plain,
backward_diamond(X1,antidomain(addition(X1,X2))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_28]) ).
cnf(c_0_148,plain,
domain(backward_diamond(X1,X2)) = backward_diamond(X1,X2),
inference(spm,[status(thm)],[c_0_97,c_0_146]) ).
cnf(c_0_149,plain,
backward_diamond(coantidomain(multiplication(X1,X2)),backward_diamond(X2,X1)) = zero,
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_147,c_0_135]),c_0_58]),c_0_127]),c_0_137]),c_0_52]),c_0_148]) ).
cnf(c_0_150,plain,
multiplication(X1,coantidomain(addition(X1,X2))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_64]),c_0_29]) ).
cnf(c_0_151,plain,
coantidomain(backward_diamond(X1,X2)) = antidomain(backward_diamond(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_146]),c_0_134]) ).
cnf(c_0_152,plain,
backward_diamond(coantidomain(addition(X1,X2)),X1) = zero,
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_149,c_0_150]),c_0_41]),c_0_129]),c_0_151]),c_0_52]),c_0_148]) ).
cnf(c_0_153,plain,
coantidomain(antidomain(coantidomain(X1))) = coantidomain(X1),
inference(rw,[status(thm)],[c_0_124,c_0_129]) ).
cnf(c_0_154,plain,
multiplication(antidomain(multiplication(X1,X2)),multiplication(X1,domain(X2))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_73]),c_0_54]) ).
cnf(c_0_155,plain,
multiplication(X1,multiplication(X2,coantidomain(multiplication(X1,X2)))) = zero,
inference(spm,[status(thm)],[c_0_29,c_0_68]) ).
fof(c_0_156,plain,
! [X51] : multiplication(X51,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
cnf(c_0_157,plain,
backward_diamond(coantidomain(multiplication(addition(X1,X2),X3)),multiplication(X1,X3)) = zero,
inference(spm,[status(thm)],[c_0_152,c_0_81]) ).
cnf(c_0_158,plain,
addition(coantidomain(X1),antidomain(coantidomain(X1))) = one,
inference(spm,[status(thm)],[c_0_62,c_0_134]) ).
cnf(c_0_159,plain,
backward_diamond(X1,antidomain(coantidomain(X2))) = backward_diamond(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_153]),c_0_133]) ).
cnf(c_0_160,plain,
multiplication(X1,multiplication(backward_diamond(one,X1),X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_68,c_0_117]) ).
cnf(c_0_161,plain,
multiplication(X1,domain(multiplication(X2,coantidomain(multiplication(X1,X2))))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_155]),c_0_75]),c_0_28]) ).
cnf(c_0_162,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_156]) ).
cnf(c_0_163,plain,
backward_diamond(coantidomain(X1),multiplication(coantidomain(X2),X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_28]) ).
cnf(c_0_164,plain,
coantidomain(coantidomain(X1)) = antidomain(coantidomain(X1)),
inference(rw,[status(thm)],[c_0_87,c_0_127]) ).
cnf(c_0_165,plain,
backward_diamond(X1,multiplication(antidomain(coantidomain(X2)),X3)) = backward_diamond(X1,backward_diamond(X3,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_137]),c_0_52]),c_0_148]) ).
cnf(c_0_166,plain,
multiplication(X1,domain(multiplication(X2,antidomain(backward_diamond(X2,X1))))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_161]),c_0_162]),c_0_129]),c_0_137]) ).
cnf(c_0_167,plain,
backward_diamond(coantidomain(X1),backward_diamond(X1,X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_164]),c_0_165]) ).
cnf(c_0_168,plain,
multiplication(backward_diamond(X1,X2),coantidomain(X1)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_167]),c_0_75]),c_0_53]),c_0_134]) ).
cnf(c_0_169,plain,
multiplication(addition(backward_diamond(X1,X2),X3),coantidomain(X1)) = multiplication(X3,coantidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_168]),c_0_38]) ).
cnf(c_0_170,plain,
addition(backward_diamond(X1,X2),antidomain(backward_diamond(X1,X2))) = one,
inference(spm,[status(thm)],[c_0_62,c_0_148]) ).
cnf(c_0_171,plain,
multiplication(domain(X1),antidomain(X1)) = zero,
inference(spm,[status(thm)],[c_0_54,c_0_52]) ).
cnf(c_0_172,plain,
backward_box(multiplication(X1,X2),multiplication(addition(X1,X3),X2)) = one,
inference(spm,[status(thm)],[c_0_145,c_0_81]) ).
cnf(c_0_173,plain,
multiplication(X1,addition(coantidomain(addition(X1,X2)),X3)) = multiplication(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_150]),c_0_38]) ).
cnf(c_0_174,plain,
multiplication(antidomain(backward_diamond(X1,X2)),coantidomain(X1)) = coantidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_170]),c_0_28]) ).
cnf(c_0_175,plain,
addition(X1,multiplication(domain(X1),X2)) = multiplication(domain(X1),addition(X1,X2)),
inference(spm,[status(thm)],[c_0_48,c_0_93]) ).
cnf(c_0_176,plain,
multiplication(domain(X1),multiplication(antidomain(X1),X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_171]),c_0_69]) ).
cnf(c_0_177,plain,
backward_box(multiplication(domain(X1),X2),X2) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_62]),c_0_28]) ).
cnf(c_0_178,plain,
backward_box(X1,antidomain(X2)) = antidomain(backward_diamond(X1,domain(X2))),
inference(spm,[status(thm)],[c_0_101,c_0_52]) ).
cnf(c_0_179,plain,
antidomain(backward_diamond(X1,coantidomain(X2))) = coantidomain(multiplication(coantidomain(X2),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_164]),c_0_52]),c_0_134]) ).
cnf(c_0_180,plain,
multiplication(X1,backward_diamond(addition(X1,X2),one)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_66]),c_0_53]) ).
cnf(c_0_181,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_53]),c_0_33]) ).
cnf(c_0_182,plain,
multiplication(backward_box(X1,X2),coantidomain(X1)) = coantidomain(X1),
inference(spm,[status(thm)],[c_0_174,c_0_101]) ).
cnf(c_0_183,plain,
coantidomain(antidomain(backward_diamond(X1,X2))) = backward_diamond(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_151]),c_0_52]),c_0_148]) ).
cnf(c_0_184,plain,
backward_box(multiplication(X1,multiplication(X2,X3)),multiplication(X1,X2)) = one,
inference(spm,[status(thm)],[c_0_142,c_0_68]) ).
cnf(c_0_185,plain,
multiplication(domain(X1),addition(X1,multiplication(antidomain(X1),X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_176]),c_0_35]) ).
cnf(c_0_186,plain,
coantidomain(multiplication(coantidomain(domain(X1)),domain(X1))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_100]),c_0_178]),c_0_134]),c_0_179]) ).
cnf(c_0_187,plain,
multiplication(X1,antidomain(coantidomain(addition(X1,X2)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_180,c_0_113]),c_0_129]) ).
cnf(c_0_188,plain,
addition(coantidomain(X1),backward_box(X1,X2)) = backward_box(X1,X2),
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_182]),c_0_33]),c_0_112]),c_0_53]),c_0_33]) ).
cnf(c_0_189,plain,
coantidomain(backward_box(X1,X2)) = backward_diamond(X1,antidomain(X2)),
inference(spm,[status(thm)],[c_0_183,c_0_101]) ).
cnf(c_0_190,plain,
backward_box(multiplication(X1,X2),multiplication(X1,domain(X2))) = one,
inference(spm,[status(thm)],[c_0_184,c_0_185]) ).
cnf(c_0_191,plain,
multiplication(coantidomain(domain(X1)),domain(X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_186]),c_0_53]) ).
cnf(c_0_192,plain,
antidomain(coantidomain(multiplication(coantidomain(X1),X2))) = backward_diamond(X2,coantidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_179]),c_0_148]) ).
cnf(c_0_193,plain,
multiplication(coantidomain(X1),backward_box(X1,X2)) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_188]),c_0_189]),c_0_101]) ).
cnf(c_0_194,plain,
coantidomain(multiplication(coantidomain(domain(X1)),X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_191]),c_0_123]) ).
cnf(c_0_195,plain,
backward_diamond(backward_box(X1,X2),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(spm,[status(thm)],[c_0_192,c_0_193]),c_0_32]),c_0_58]),c_0_127]),c_0_52]),c_0_134]) ).
cnf(c_0_196,plain,
backward_box(X1,coantidomain(X2)) = antidomain(backward_diamond(X1,X2)),
inference(spm,[status(thm)],[c_0_101,c_0_159]) ).
cnf(c_0_197,plain,
multiplication(coantidomain(domain(X1)),X1) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_194]),c_0_53]) ).
cnf(c_0_198,plain,
backward_diamond(antidomain(backward_diamond(X1,X2)),coantidomain(X1)) = coantidomain(X1),
inference(spm,[status(thm)],[c_0_195,c_0_196]) ).
cnf(c_0_199,plain,
addition(one,backward_diamond(X1,one)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_66]),c_0_33]) ).
cnf(c_0_200,plain,
codomain(X1) = antidomain(coantidomain(X1)),
inference(rw,[status(thm)],[c_0_58,c_0_127]) ).
cnf(c_0_201,plain,
multiplication(addition(coantidomain(domain(X1)),X2),X1) = multiplication(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_197]),c_0_38]) ).
cnf(c_0_202,plain,
multiplication(X1,coantidomain(addition(X2,X1))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_71]),c_0_29]) ).
cnf(c_0_203,plain,
multiplication(antidomain(coantidomain(X1)),backward_diamond(X1,X2)) = backward_diamond(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_198]),c_0_183]),c_0_183]) ).
cnf(c_0_204,plain,
addition(one,backward_diamond(X1,X2)) = one,
inference(spm,[status(thm)],[c_0_199,c_0_99]) ).
cnf(c_0_205,plain,
backward_box(multiplication(X1,domain(X2)),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(spm,[status(thm)],[c_0_135,c_0_154]),c_0_41]),c_0_200]),c_0_137]),c_0_101]),c_0_138]),c_0_200]),c_0_137]),c_0_101]) ).
cnf(c_0_206,plain,
multiplication(antidomain(coantidomain(domain(X1))),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_158]),c_0_28]) ).
cnf(c_0_207,plain,
addition(domain(X1),domain(antidomain(X1))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_52]),c_0_33]) ).
cnf(c_0_208,plain,
multiplication(X1,multiplication(X2,coantidomain(multiplication(addition(X3,X1),X2)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_81]),c_0_68]) ).
cnf(c_0_209,plain,
addition(antidomain(coantidomain(X1)),backward_diamond(X1,X2)) = antidomain(coantidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_203]),c_0_33]),c_0_204]),c_0_53]) ).
cnf(c_0_210,plain,
backward_box(X1,X1) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_205,c_0_100]),c_0_97]),c_0_100]) ).
cnf(c_0_211,plain,
multiplication(antidomain(coantidomain(domain(X1))),multiplication(X1,X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_68,c_0_206]) ).
cnf(c_0_212,plain,
domain(domain(X1)) = domain(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_85,c_0_207]),c_0_92]),c_0_52]),c_0_53]),c_0_92]),c_0_52]),c_0_93]) ).
cnf(c_0_213,plain,
multiplication(backward_diamond(X1,X2),multiplication(X3,antidomain(backward_diamond(X3,X1)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_209]),c_0_137]) ).
cnf(c_0_214,plain,
backward_diamond(X1,antidomain(X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_210]),c_0_28]) ).
cnf(c_0_215,plain,
multiplication(antidomain(coantidomain(domain(addition(X1,X2)))),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_211,c_0_114]),c_0_212]) ).
cnf(c_0_216,plain,
multiplication(backward_diamond(antidomain(X1),X2),X1) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_213,c_0_214]),c_0_75]),c_0_53]) ).
cnf(c_0_217,plain,
antidomain(backward_diamond(X1,domain(addition(X1,X2)))) = coantidomain(X1),
inference(spm,[status(thm)],[c_0_137,c_0_215]) ).
cnf(c_0_218,plain,
multiplication(addition(backward_diamond(antidomain(X1),X2),X3),X1) = multiplication(X3,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_216]),c_0_38]) ).
cnf(c_0_219,plain,
backward_diamond(X1,domain(addition(X1,X2))) = antidomain(coantidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_217]),c_0_148]) ).
cnf(c_0_220,plain,
multiplication(coantidomain(domain(X1)),addition(X1,X2)) = multiplication(coantidomain(domain(X1)),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_197]),c_0_38]) ).
cnf(c_0_221,plain,
multiplication(antidomain(backward_diamond(antidomain(X1),X2)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_170]),c_0_28]) ).
cnf(c_0_222,plain,
backward_diamond(X1,domain(multiplication(X1,addition(X2,one)))) = antidomain(coantidomain(X1)),
inference(spm,[status(thm)],[c_0_219,c_0_181]) ).
cnf(c_0_223,plain,
multiplication(coantidomain(domain(X1)),antidomain(X1)) = coantidomain(domain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_220,c_0_62]),c_0_212]),c_0_53]),c_0_212]) ).
cnf(c_0_224,plain,
multiplication(coantidomain(antidomain(X1)),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_222]),c_0_52]),c_0_134]) ).
cnf(c_0_225,plain,
multiplication(coantidomain(antidomain(X1)),domain(X1)) = coantidomain(antidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_223,c_0_52]),c_0_97]),c_0_97]) ).
cnf(c_0_226,plain,
multiplication(X1,domain(multiplication(coantidomain(X1),X2))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_79]),c_0_28]) ).
cnf(c_0_227,plain,
coantidomain(antidomain(X1)) = domain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_224,c_0_139]),c_0_225]) ).
cnf(c_0_228,plain,
multiplication(X1,addition(domain(multiplication(coantidomain(X1),X2)),X3)) = multiplication(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_226]),c_0_38]) ).
cnf(c_0_229,plain,
backward_diamond(coantidomain(multiplication(X1,addition(X2,X3))),multiplication(X1,X2)) = zero,
inference(spm,[status(thm)],[c_0_152,c_0_48]) ).
cnf(c_0_230,plain,
antidomain(coantidomain(multiplication(domain(X1),X2))) = backward_diamond(X2,domain(X1)),
inference(spm,[status(thm)],[c_0_192,c_0_227]) ).
cnf(c_0_231,plain,
multiplication(X1,antidomain(multiplication(coantidomain(X1),X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_228,c_0_62]),c_0_53]) ).
cnf(c_0_232,plain,
coantidomain(domain(X1)) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_227]),c_0_92]),c_0_97]) ).
cnf(c_0_233,plain,
backward_diamond(coantidomain(X1),multiplication(X1,coantidomain(X2))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_229,c_0_158]),c_0_53]) ).
cnf(c_0_234,plain,
backward_diamond(antidomain(multiplication(antidomain(X1),X2)),domain(X1)) = domain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_230,c_0_231]),c_0_232]),c_0_52]),c_0_232]) ).
cnf(c_0_235,plain,
coantidomain(multiplication(X1,multiplication(X2,antidomain(backward_diamond(X2,X1))))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_166]),c_0_123]) ).
cnf(c_0_236,plain,
backward_diamond(coantidomain(X1),backward_diamond(coantidomain(X2),X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_233]),c_0_153]) ).
cnf(c_0_237,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_33]),c_0_55]) ).
cnf(c_0_238,plain,
backward_diamond(antidomain(X1),antidomain(addition(X1,X2))) = 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_234,c_0_215]),c_0_134]),c_0_232]),c_0_134]),c_0_232]) ).
cnf(c_0_239,plain,
multiplication(X1,multiplication(X2,antidomain(backward_diamond(X2,X1)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_235]),c_0_53]) ).
cnf(c_0_240,plain,
backward_diamond(multiplication(X1,X2),antidomain(multiplication(X1,domain(X2)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_190]),c_0_28]) ).
cnf(c_0_241,plain,
multiplication(backward_diamond(coantidomain(X1),X2),coantidomain(X2)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_236]),c_0_75]),c_0_53]),c_0_134]) ).
cnf(c_0_242,plain,
addition(domain(X1),addition(X2,antidomain(X1))) = addition(X2,one),
inference(spm,[status(thm)],[c_0_237,c_0_62]) ).
cnf(c_0_243,plain,
addition(antidomain(X1),antidomain(addition(X1,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(spm,[status(thm)],[c_0_209,c_0_238]),c_0_227]),c_0_92]),c_0_97]),c_0_227]),c_0_92]),c_0_97]) ).
cnf(c_0_244,plain,
multiplication(antidomain(multiplication(X1,domain(X2))),multiplication(X1,X2)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_239,c_0_240]),c_0_75]),c_0_53]) ).
cnf(c_0_245,plain,
multiplication(backward_diamond(coantidomain(X1),antidomain(X2)),domain(X2)) = zero,
inference(spm,[status(thm)],[c_0_241,c_0_227]) ).
cnf(c_0_246,plain,
multiplication(domain(X1),addition(X1,one)) = addition(X1,domain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_93]),c_0_33]) ).
cnf(c_0_247,plain,
addition(antidomain(X1),domain(addition(X1,X2))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_242,c_0_243]),c_0_33]),c_0_33]),c_0_76]) ).
cnf(c_0_248,plain,
addition(coantidomain(X1),antidomain(backward_diamond(X1,X2))) = antidomain(backward_diamond(X1,X2)),
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_174]),c_0_33]),c_0_112]),c_0_53]),c_0_33]) ).
cnf(c_0_249,plain,
backward_diamond(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(spm,[status(thm)],[c_0_234,c_0_211]),c_0_134]),c_0_232]),c_0_134]),c_0_232]) ).
cnf(c_0_250,plain,
multiplication(backward_diamond(coantidomain(X1),antidomain(X2)),X2) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_244,c_0_245]),c_0_75]),c_0_28]) ).
cnf(c_0_251,plain,
multiplication(X1,multiplication(X2,antidomain(coantidomain(multiplication(X1,X2))))) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_68,c_0_100]) ).
cnf(c_0_252,plain,
multiplication(domain(X1),addition(one,X1)) = addition(X1,domain(X1)),
inference(spm,[status(thm)],[c_0_246,c_0_33]) ).
cnf(c_0_253,plain,
addition(antidomain(X1),domain(addition(X2,X1))) = one,
inference(spm,[status(thm)],[c_0_247,c_0_71]) ).
cnf(c_0_254,plain,
addition(domain(X1),domain(multiplication(X1,X2))) = domain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_248,c_0_249]),c_0_227]),c_0_52]),c_0_52]),c_0_33]) ).
cnf(c_0_255,plain,
multiplication(addition(backward_diamond(coantidomain(X1),antidomain(X2)),X3),X2) = multiplication(X3,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_250]),c_0_38]) ).
cnf(c_0_256,plain,
backward_box(X1,X2) = coantidomain(multiplication(antidomain(X2),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_227]),c_0_92]),c_0_97]),c_0_101]) ).
cnf(c_0_257,plain,
multiplication(X1,multiplication(X2,backward_diamond(X2,X1))) = 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_160,c_0_251]),c_0_160]),c_0_129]),c_0_137]),c_0_52]),c_0_148]) ).
cnf(c_0_258,plain,
multiplication(coantidomain(X1),backward_diamond(coantidomain(X1),X2)) = backward_diamond(coantidomain(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_203,c_0_164]),c_0_52]),c_0_134]) ).
cnf(c_0_259,plain,
multiplication(addition(X1,domain(X2)),antidomain(X2)) = multiplication(X1,antidomain(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_171]),c_0_35]) ).
cnf(c_0_260,plain,
addition(coantidomain(X1),domain(coantidomain(X1))) = domain(coantidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_252,c_0_112]),c_0_53]) ).
cnf(c_0_261,plain,
multiplication(domain(addition(X1,X2)),X2) = X2,
inference(spm,[status(thm)],[c_0_114,c_0_71]) ).
cnf(c_0_262,plain,
addition(domain(X1),antidomain(multiplication(X1,X2))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_253,c_0_254]),c_0_139]),c_0_212]),c_0_33]) ).
cnf(c_0_263,plain,
multiplication(antidomain(multiplication(X1,X2)),antidomain(X1)) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_203,c_0_249]),c_0_227]),c_0_139]) ).
cnf(c_0_264,plain,
multiplication(coantidomain(multiplication(antidomain(X1),coantidomain(X2))),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_255,c_0_170]),c_0_28]),c_0_101]),c_0_256]) ).
cnf(c_0_265,plain,
antidomain(coantidomain(multiplication(antidomain(X1),X2))) = backward_diamond(X2,antidomain(X1)),
inference(spm,[status(thm)],[c_0_192,c_0_232]) ).
cnf(c_0_266,plain,
multiplication(X1,backward_diamond(coantidomain(X2),X1)) = multiplication(X1,coantidomain(X2)),
inference(spm,[status(thm)],[c_0_257,c_0_258]) ).
cnf(c_0_267,plain,
multiplication(coantidomain(X1),antidomain(coantidomain(X1))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_259,c_0_260]),c_0_171]) ).
cnf(c_0_268,plain,
backward_box(X1,addition(X2,X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_261]),c_0_141]) ).
cnf(c_0_269,plain,
addition(backward_diamond(X1,X2),antidomain(multiplication(backward_diamond(X1,X2),X3))) = one,
inference(spm,[status(thm)],[c_0_262,c_0_148]) ).
cnf(c_0_270,plain,
backward_diamond(coantidomain(X1),antidomain(X2)) = multiplication(antidomain(X2),coantidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_263,c_0_264]),c_0_265]),c_0_266]),c_0_265]) ).
cnf(c_0_271,plain,
multiplication(backward_diamond(X1,one),backward_box(X1,zero)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_267,c_0_87]),c_0_106]) ).
cnf(c_0_272,plain,
backward_diamond(X1,antidomain(addition(X2,X1))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_268]),c_0_28]) ).
cnf(c_0_273,plain,
multiplication(antidomain(multiplication(backward_diamond(antidomain(X1),X2),X3)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_269]),c_0_28]) ).
cnf(c_0_274,plain,
backward_diamond(antidomain(X1),antidomain(X2)) = multiplication(antidomain(X2),antidomain(X1)),
inference(spm,[status(thm)],[c_0_270,c_0_232]) ).
cnf(c_0_275,plain,
multiplication(X1,backward_box(X1,zero)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_271]),c_0_162]) ).
cnf(c_0_276,plain,
antidomain(backward_box(X1,X2)) = domain(backward_diamond(X1,antidomain(X2))),
inference(spm,[status(thm)],[c_0_52,c_0_101]) ).
cnf(c_0_277,plain,
addition(domain(X1),addition(antidomain(X1),X2)) = addition(one,X2),
inference(spm,[status(thm)],[c_0_55,c_0_62]) ).
cnf(c_0_278,plain,
antidomain(addition(X1,antidomain(X1))) = zero,
inference(spm,[status(thm)],[c_0_272,c_0_238]) ).
cnf(c_0_279,plain,
multiplication(coantidomain(X1),antidomain(backward_diamond(X1,X2))) = coantidomain(X1),
inference(spm,[status(thm)],[c_0_193,c_0_196]) ).
cnf(c_0_280,plain,
multiplication(antidomain(multiplication(antidomain(X1),multiplication(antidomain(X2),X3))),X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_273,c_0_274]),c_0_68]) ).
cnf(c_0_281,plain,
multiplication(X1,addition(backward_box(X1,zero),X2)) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_275]),c_0_38]) ).
cnf(c_0_282,plain,
addition(backward_box(X1,X2),domain(backward_diamond(X1,antidomain(X2)))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_116]),c_0_276]) ).
cnf(c_0_283,plain,
addition(domain(multiplication(X1,X2)),antidomain(multiplication(X1,domain(X2)))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_277,c_0_73]),c_0_76]) ).
cnf(c_0_284,plain,
domain(addition(X1,antidomain(X1))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_278]),c_0_75]) ).
cnf(c_0_285,plain,
multiplication(domain(multiplication(X1,X2)),domain(X1)) = domain(multiplication(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_279,c_0_249]),c_0_227]),c_0_52]),c_0_227]) ).
cnf(c_0_286,plain,
multiplication(antidomain(coantidomain(X1)),coantidomain(X2)) = backward_diamond(coantidomain(X2),X1),
inference(spm,[status(thm)],[c_0_159,c_0_270]) ).
cnf(c_0_287,plain,
antidomain(backward_diamond(multiplication(X1,X2),domain(X1))) = coantidomain(multiplication(X1,X2)),
inference(spm,[status(thm)],[c_0_137,c_0_211]) ).
cnf(c_0_288,plain,
multiplication(antidomain(multiplication(antidomain(X1),X2)),antidomain(X2)) = antidomain(X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_280,c_0_206]),c_0_232]),c_0_232]) ).
cnf(c_0_289,plain,
multiplication(X1,domain(backward_diamond(X1,one))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_281,c_0_282]),c_0_53]),c_0_75]) ).
cnf(c_0_290,plain,
addition(antidomain(X1),domain(multiplication(X1,addition(X2,antidomain(X2))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_283,c_0_284]),c_0_53]),c_0_33]) ).
cnf(c_0_291,plain,
multiplication(domain(X1),domain(multiplication(X1,X2))) = domain(multiplication(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_249]),c_0_52]),c_0_227]),c_0_227]) ).
cnf(c_0_292,plain,
multiplication(X1,multiplication(X2,multiplication(backward_diamond(X2,X1),X3))) = multiplication(X1,multiplication(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_257]),c_0_68]),c_0_68]) ).
cnf(c_0_293,plain,
multiplication(backward_diamond(coantidomain(X1),X2),antidomain(coantidomain(X2))) = backward_diamond(coantidomain(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_285,c_0_286]),c_0_148]),c_0_97]),c_0_148]) ).
cnf(c_0_294,plain,
backward_diamond(multiplication(X1,X2),domain(X1)) = antidomain(coantidomain(multiplication(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_287]),c_0_148]) ).
cnf(c_0_295,plain,
addition(domain(X1),antidomain(multiplication(antidomain(X2),X1))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_262,c_0_288]),c_0_97]),c_0_52]),c_0_33]) ).
cnf(c_0_296,plain,
backward_diamond(domain(backward_diamond(one,X1)),X1) = backward_diamond(one,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_289]),c_0_107]),c_0_107]) ).
cnf(c_0_297,plain,
multiplication(domain(addition(X1,X2)),multiplication(X2,X3)) = multiplication(X2,X3),
inference(spm,[status(thm)],[c_0_68,c_0_261]) ).
cnf(c_0_298,plain,
domain(multiplication(X1,addition(X2,antidomain(X2)))) = domain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_290]),c_0_52]),c_0_53]),c_0_52]),c_0_291]) ).
cnf(c_0_299,plain,
multiplication(X1,addition(multiplication(X2,coantidomain(multiplication(X1,X2))),X3)) = multiplication(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_155]),c_0_38]) ).
cnf(c_0_300,plain,
backward_diamond(multiplication(antidomain(coantidomain(X1)),X2),X1) = backward_diamond(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_77]),c_0_133]),c_0_113]),c_0_129]),c_0_153]) ).
cnf(c_0_301,plain,
multiplication(X1,multiplication(coantidomain(X2),antidomain(coantidomain(X1)))) = multiplication(X1,coantidomain(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_292,c_0_293]),c_0_258]),c_0_266]) ).
cnf(c_0_302,plain,
multiplication(antidomain(coantidomain(X1)),antidomain(X2)) = backward_diamond(antidomain(X2),X1),
inference(spm,[status(thm)],[c_0_159,c_0_274]) ).
cnf(c_0_303,plain,
backward_diamond(coantidomain(X1),antidomain(backward_diamond(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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_294,c_0_174]),c_0_97]),c_0_32]),c_0_58]),c_0_127]),c_0_52]),c_0_134]) ).
cnf(c_0_304,plain,
addition(domain(X1),antidomain(multiplication(domain(X2),X1))) = one,
inference(spm,[status(thm)],[c_0_295,c_0_52]) ).
cnf(c_0_305,plain,
multiplication(backward_diamond(X1,X2),antidomain(coantidomain(X1))) = backward_diamond(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_279,c_0_198]),c_0_183]),c_0_183]) ).
cnf(c_0_306,plain,
backward_diamond(antidomain(coantidomain(X1)),X1) = antidomain(coantidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_296,c_0_129]),c_0_97]),c_0_129]) ).
cnf(c_0_307,plain,
backward_diamond(multiplication(X1,X2),antidomain(X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_142]),c_0_28]) ).
cnf(c_0_308,plain,
multiplication(domain(addition(X1,domain(addition(X2,X3)))),X2) = X2,
inference(spm,[status(thm)],[c_0_297,c_0_114]) ).
cnf(c_0_309,plain,
backward_diamond(coantidomain(X1),domain(X2)) = multiplication(domain(X2),coantidomain(X1)),
inference(spm,[status(thm)],[c_0_270,c_0_52]) ).
cnf(c_0_310,plain,
domain(multiplication(X1,antidomain(multiplication(X2,coantidomain(multiplication(X1,X2)))))) = domain(X1),
inference(spm,[status(thm)],[c_0_298,c_0_299]) ).
cnf(c_0_311,plain,
multiplication(antidomain(coantidomain(X1)),multiplication(X2,coantidomain(multiplication(X1,X2)))) = zero,
inference(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_57,c_0_135]),c_0_58]),c_0_58]),c_0_29]),c_0_58]),c_0_68]),c_0_127]) ).
cnf(c_0_312,plain,
backward_diamond(multiplication(antidomain(X1),X2),antidomain(X1)) = backward_diamond(X2,antidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_300,c_0_227]),c_0_92]),c_0_97]) ).
cnf(c_0_313,plain,
multiplication(X1,backward_diamond(antidomain(coantidomain(X1)),X2)) = multiplication(X1,antidomain(coantidomain(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_301,c_0_164]),c_0_302]) ).
cnf(c_0_314,plain,
backward_diamond(backward_diamond(X1,X2),X1) = backward_diamond(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_303,c_0_198]),c_0_183]),c_0_159]),c_0_183]) ).
cnf(c_0_315,plain,
addition(domain(X1),antidomain(multiplication(coantidomain(X2),X1))) = one,
inference(spm,[status(thm)],[c_0_304,c_0_134]) ).
cnf(c_0_316,plain,
multiplication(antidomain(X1),antidomain(multiplication(X1,X2))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_305,c_0_249]),c_0_227]),c_0_139]) ).
cnf(c_0_317,plain,
multiplication(X1,addition(multiplication(coantidomain(X1),X2),X3)) = multiplication(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_74]),c_0_38]) ).
cnf(c_0_318,plain,
backward_diamond(antidomain(multiplication(coantidomain(X1),X2)),X1) = antidomain(coantidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_300,c_0_231]),c_0_306]),c_0_227]),c_0_134]) ).
cnf(c_0_319,plain,
backward_diamond(X1,antidomain(addition(X2,domain(addition(X1,X3))))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_307,c_0_308]),c_0_139]) ).
cnf(c_0_320,plain,
backward_diamond(coantidomain(X1),coantidomain(X2)) = multiplication(coantidomain(X2),coantidomain(X1)),
inference(spm,[status(thm)],[c_0_309,c_0_134]) ).
cnf(c_0_321,plain,
backward_diamond(antidomain(multiplication(X1,coantidomain(multiplication(X2,X1)))),X2) = 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_310,c_0_311]),c_0_41]),c_0_53]),c_0_302]),c_0_148]),c_0_97]) ).
cnf(c_0_322,plain,
multiplication(antidomain(X1),antidomain(coantidomain(X2))) = backward_diamond(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_312,c_0_313]),c_0_312]),c_0_274]),c_0_227]),c_0_92]),c_0_97]),c_0_314]) ).
cnf(c_0_323,plain,
multiplication(X1,multiplication(X2,multiplication(coantidomain(multiplication(X1,X2)),X3))) = zero,
inference(spm,[status(thm)],[c_0_68,c_0_74]) ).
cnf(c_0_324,plain,
multiplication(domain(X1),multiplication(coantidomain(X2),X1)) = multiplication(coantidomain(X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_315]),c_0_28]) ).
cnf(c_0_325,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(spm,[status(thm)],[c_0_102,c_0_290]),c_0_232]),c_0_28]),c_0_232]),c_0_316]) ).
cnf(c_0_326,plain,
backward_diamond(addition(multiplication(coantidomain(X1),X2),X3),X1) = backward_diamond(X3,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_300,c_0_317]),c_0_300]),c_0_153]) ).
cnf(c_0_327,plain,
addition(coantidomain(X1),domain(multiplication(coantidomain(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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_248,c_0_318]),c_0_227]),c_0_52]),c_0_134]),c_0_52]),c_0_134]),c_0_33]) ).
cnf(c_0_328,plain,
antidomain(addition(X1,domain(addition(antidomain(X1),X2)))) = zero,
inference(spm,[status(thm)],[c_0_319,c_0_238]) ).
cnf(c_0_329,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_209,c_0_249]),c_0_227]),c_0_139]),c_0_227]),c_0_139]),c_0_33]) ).
cnf(c_0_330,plain,
multiplication(backward_diamond(antidomain(X1),X2),addition(X3,X1)) = multiplication(backward_diamond(antidomain(X1),X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_216]),c_0_35]) ).
cnf(c_0_331,plain,
backward_diamond(X1,antidomain(backward_diamond(antidomain(X1),X2))) = antidomain(coantidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_294,c_0_221]),c_0_97]) ).
cnf(c_0_332,plain,
backward_diamond(antidomain(X1),coantidomain(X2)) = multiplication(coantidomain(X2),antidomain(X1)),
inference(spm,[status(thm)],[c_0_320,c_0_232]) ).
cnf(c_0_333,plain,
multiplication(X1,antidomain(multiplication(X2,coantidomain(multiplication(X1,X2))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_257,c_0_321]),c_0_322]),c_0_321]),c_0_100]) ).
cnf(c_0_334,plain,
multiplication(X1,multiplication(coantidomain(multiplication(X1,domain(X2))),X2)) = zero,
inference(spm,[status(thm)],[c_0_323,c_0_324]) ).
cnf(c_0_335,plain,
backward_diamond(domain(X1),coantidomain(X2)) = multiplication(coantidomain(X2),domain(X1)),
inference(spm,[status(thm)],[c_0_320,c_0_227]) ).
cnf(c_0_336,plain,
antidomain(multiplication(X1,multiplication(X2,addition(X3,antidomain(X3))))) = antidomain(multiplication(X1,X2)),
inference(spm,[status(thm)],[c_0_325,c_0_68]) ).
cnf(c_0_337,plain,
multiplication(domain(X1),addition(X2,antidomain(X1))) = multiplication(domain(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_171]),c_0_35]) ).
cnf(c_0_338,plain,
backward_diamond(multiplication(addition(coantidomain(X1),X2),X3),X1) = backward_diamond(multiplication(X2,X3),X1),
inference(spm,[status(thm)],[c_0_326,c_0_81]) ).
cnf(c_0_339,plain,
addition(coantidomain(X1),antidomain(multiplication(coantidomain(X1),X2))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_253,c_0_327]),c_0_139]),c_0_134]),c_0_33]) ).
cnf(c_0_340,plain,
antidomain(addition(X1,antidomain(multiplication(X1,X2)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_328,c_0_329]),c_0_97]) ).
cnf(c_0_341,plain,
domain(multiplication(backward_diamond(domain(X1),X2),X1)) = backward_diamond(domain(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_298,c_0_330]),c_0_52]),c_0_52]),c_0_148]) ).
cnf(c_0_342,plain,
backward_diamond(domain(X1),domain(X2)) = multiplication(domain(X2),domain(X1)),
inference(spm,[status(thm)],[c_0_309,c_0_227]) ).
cnf(c_0_343,plain,
backward_diamond(X1,antidomain(multiplication(coantidomain(X2),antidomain(X1)))) = antidomain(coantidomain(X1)),
inference(spm,[status(thm)],[c_0_331,c_0_332]) ).
cnf(c_0_344,plain,
multiplication(X1,antidomain(multiplication(coantidomain(multiplication(X1,domain(X2))),X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_333,c_0_334]),c_0_41]),c_0_53]) ).
cnf(c_0_345,plain,
coantidomain(multiplication(coantidomain(X1),domain(X2))) = antidomain(multiplication(coantidomain(X1),domain(X2))),
inference(spm,[status(thm)],[c_0_151,c_0_335]) ).
cnf(c_0_346,plain,
antidomain(multiplication(X1,domain(X2))) = antidomain(multiplication(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_336,c_0_337]),c_0_93]) ).
cnf(c_0_347,plain,
backward_diamond(multiplication(antidomain(multiplication(coantidomain(X1),X2)),X3),X1) = backward_diamond(X3,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_338,c_0_339]),c_0_28]) ).
cnf(c_0_348,plain,
antidomain(multiplication(X1,addition(X2,antidomain(multiplication(X2,X3))))) = antidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_325,c_0_340]),c_0_35]) ).
cnf(c_0_349,plain,
domain(multiplication(domain(X1),X2)) = multiplication(domain(X1),domain(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_341,c_0_342]),c_0_68]),c_0_93]) ).
cnf(c_0_350,plain,
backward_diamond(domain(X1),antidomain(X2)) = multiplication(antidomain(X2),domain(X1)),
inference(spm,[status(thm)],[c_0_270,c_0_227]) ).
cnf(c_0_351,plain,
backward_diamond(X1,antidomain(multiplication(coantidomain(X2),X1))) = backward_diamond(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_343,c_0_344]),c_0_345]),c_0_346]),c_0_159]),c_0_347]),c_0_192]),c_0_345]),c_0_346]) ).
cnf(c_0_352,plain,
antidomain(multiplication(domain(multiplication(X1,X2)),X1)) = antidomain(multiplication(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_348,c_0_337]),c_0_139]) ).
cnf(c_0_353,plain,
antidomain(multiplication(domain(X1),domain(X2))) = antidomain(multiplication(domain(X1),X2)),
inference(spm,[status(thm)],[c_0_139,c_0_349]) ).
cnf(c_0_354,plain,
multiplication(domain(X1),multiplication(domain(X2),X1)) = multiplication(domain(X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_304]),c_0_28]) ).
cnf(c_0_355,plain,
domain(multiplication(antidomain(X1),X2)) = multiplication(antidomain(X1),domain(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_341,c_0_350]),c_0_68]),c_0_93]) ).
cnf(c_0_356,plain,
codomain(zero) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_41]),c_0_34]) ).
cnf(c_0_357,plain,
backward_diamond(X1,antidomain(multiplication(domain(X2),X1))) = backward_diamond(X1,antidomain(X2)),
inference(spm,[status(thm)],[c_0_351,c_0_227]) ).
cnf(c_0_358,plain,
antidomain(multiplication(domain(X1),X2)) = antidomain(multiplication(domain(X2),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_352,c_0_353]),c_0_349]),c_0_68]),c_0_354]) ).
cnf(c_0_359,plain,
multiplication(X1,multiplication(antidomain(coantidomain(X1)),X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_68,c_0_100]) ).
cnf(c_0_360,plain,
multiplication(antidomain(X1),domain(addition(X2,X1))) = multiplication(antidomain(X1),domain(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_355,c_0_85]),c_0_355]) ).
cnf(c_0_361,plain,
addition(domain(X1),domain(addition(antidomain(X1),X2))) = one,
inference(spm,[status(thm)],[c_0_247,c_0_52]) ).
cnf(c_0_362,plain,
backward_diamond(zero,one) = zero,
inference(rw,[status(thm)],[c_0_356,c_0_58]) ).
cnf(c_0_363,plain,
backward_diamond(X1,antidomain(multiplication(domain(X1),X2))) = backward_diamond(X1,antidomain(X2)),
inference(spm,[status(thm)],[c_0_357,c_0_358]) ).
cnf(c_0_364,plain,
multiplication(X1,domain(addition(X2,coantidomain(X1)))) = multiplication(X1,domain(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_359,c_0_360]),c_0_359]) ).
cnf(c_0_365,plain,
multiplication(antidomain(X1),backward_diamond(antidomain(X1),X2)) = backward_diamond(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_203,c_0_227]),c_0_92]),c_0_97]) ).
cnf(c_0_366,plain,
multiplication(X1,domain(addition(antidomain(coantidomain(X1)),X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_361]),c_0_53]) ).
cnf(c_0_367,plain,
backward_diamond(antidomain(X1),domain(X2)) = multiplication(domain(X2),antidomain(X1)),
inference(spm,[status(thm)],[c_0_309,c_0_232]) ).
cnf(c_0_368,plain,
backward_diamond(zero,X1) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_162]),c_0_362]) ).
cnf(c_0_369,plain,
backward_diamond(X1,antidomain(addition(X2,antidomain(X1)))) = backward_diamond(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_363,c_0_364]),c_0_346]),c_0_363]),c_0_232]),c_0_139]) ).
cnf(c_0_370,plain,
multiplication(X1,backward_diamond(antidomain(X2),X1)) = multiplication(X1,antidomain(X2)),
inference(spm,[status(thm)],[c_0_257,c_0_365]) ).
cnf(c_0_371,plain,
backward_diamond(coantidomain(X1),coantidomain(multiplication(coantidomain(X2),X1))) = coantidomain(X1),
inference(spm,[status(thm)],[c_0_303,c_0_179]) ).
cnf(c_0_372,plain,
multiplication(X1,domain(addition(X2,antidomain(coantidomain(X1))))) = X1,
inference(spm,[status(thm)],[c_0_366,c_0_71]) ).
cnf(c_0_373,plain,
multiplication(domain(X1),antidomain(coantidomain(X2))) = backward_diamond(domain(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_230,c_0_313]),c_0_230]),c_0_367]),c_0_232]),c_0_52]),c_0_314]) ).
cnf(c_0_374,plain,
backward_diamond(multiplication(X1,multiplication(antidomain(backward_diamond(X1,X2)),X3)),X2) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_300,c_0_323]),c_0_368]),c_0_137]) ).
cnf(c_0_375,plain,
multiplication(X1,antidomain(addition(X2,coantidomain(X1)))) = multiplication(X1,antidomain(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_313,c_0_369]),c_0_274]),c_0_322]),c_0_370]),c_0_52]),c_0_134]),c_0_227]),c_0_139]) ).
cnf(c_0_376,plain,
backward_diamond(antidomain(addition(X1,coantidomain(X2))),X2) = antidomain(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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_371,c_0_372]),c_0_164]),c_0_52]),c_0_134]),c_0_232]),c_0_164]),c_0_159]),c_0_164]),c_0_52]),c_0_134]),c_0_232]) ).
cnf(c_0_377,plain,
antidomain(multiplication(antidomain(X1),domain(X2))) = antidomain(multiplication(antidomain(X1),X2)),
inference(spm,[status(thm)],[c_0_139,c_0_355]) ).
cnf(c_0_378,plain,
multiplication(domain(X1),antidomain(X2)) = multiplication(antidomain(X2),domain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_373,c_0_227]),c_0_92]),c_0_97]),c_0_350]) ).
cnf(c_0_379,plain,
multiplication(coantidomain(X1),antidomain(coantidomain(X2))) = backward_diamond(coantidomain(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_313]),c_0_192]),c_0_332]),c_0_32]),c_0_58]),c_0_127]),c_0_52]),c_0_134]),c_0_314]) ).
cnf(c_0_380,plain,
backward_diamond(multiplication(coantidomain(X1),X2),multiplication(X1,coantidomain(X3))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_374,c_0_233]),c_0_75]),c_0_28]) ).
cnf(c_0_381,plain,
multiplication(coantidomain(multiplication(coantidomain(X1),X2)),coantidomain(X2)) = coantidomain(X2),
inference(spm,[status(thm)],[c_0_174,c_0_179]) ).
cnf(c_0_382,plain,
multiplication(antidomain(multiplication(coantidomain(X1),antidomain(X2))),X2) = X2,
inference(spm,[status(thm)],[c_0_221,c_0_332]) ).
cnf(c_0_383,plain,
multiplication(antidomain(X1),multiplication(antidomain(multiplication(X1,X2)),X3)) = multiplication(antidomain(X1),X3),
inference(spm,[status(thm)],[c_0_68,c_0_316]) ).
cnf(c_0_384,plain,
antidomain(backward_diamond(X1,domain(X2))) = coantidomain(multiplication(domain(X2),X1)),
inference(spm,[status(thm)],[c_0_179,c_0_227]) ).
cnf(c_0_385,plain,
backward_diamond(antidomain(X1),X2) = antidomain(addition(X1,coantidomain(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_300,c_0_375]),c_0_300]),c_0_227]),c_0_134]),c_0_376]) ).
cnf(c_0_386,plain,
coantidomain(multiplication(domain(X1),antidomain(X2))) = antidomain(multiplication(domain(X1),antidomain(X2))),
inference(spm,[status(thm)],[c_0_151,c_0_367]) ).
cnf(c_0_387,plain,
antidomain(multiplication(domain(X1),antidomain(X2))) = antidomain(multiplication(antidomain(X2),X1)),
inference(spm,[status(thm)],[c_0_377,c_0_378]) ).
cnf(c_0_388,plain,
multiplication(coantidomain(X1),backward_diamond(antidomain(backward_diamond(coantidomain(X1),X2)),X2)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_379]),c_0_151]),c_0_302]) ).
cnf(c_0_389,plain,
backward_diamond(coantidomain(X1),multiplication(coantidomain(X2),multiplication(X1,coantidomain(X3)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_380,c_0_381]),c_0_68]) ).
cnf(c_0_390,plain,
multiplication(antidomain(multiplication(coantidomain(X1),X2)),X2) = multiplication(antidomain(coantidomain(X1)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_382,c_0_344]),c_0_345]),c_0_346]),c_0_383]),c_0_345]),c_0_346]) ).
cnf(c_0_391,plain,
antidomain(multiplication(antidomain(X1),X2)) = domain(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_384,c_0_385]),c_0_232]),c_0_52]),c_0_386]),c_0_387]) ).
cnf(c_0_392,plain,
multiplication(coantidomain(multiplication(domain(X1),X2)),coantidomain(X2)) = coantidomain(X2),
inference(spm,[status(thm)],[c_0_381,c_0_227]) ).
cnf(c_0_393,plain,
multiplication(coantidomain(X1),backward_diamond(multiplication(X1,coantidomain(X2)),coantidomain(X3))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_388,c_0_389]),c_0_75]),c_0_129]),c_0_192]) ).
cnf(c_0_394,plain,
multiplication(domain(addition(X1,antidomain(X2))),X2) = multiplication(domain(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_390,c_0_232]),c_0_391]),c_0_52]) ).
cnf(c_0_395,plain,
antidomain(addition(X1,antidomain(X2))) = multiplication(domain(X2),antidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_367,c_0_385]),c_0_232]) ).
cnf(c_0_396,plain,
addition(antidomain(coantidomain(X1)),coantidomain(multiplication(domain(X2),X1))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_262,c_0_392]),c_0_134]),c_0_33]) ).
cnf(c_0_397,plain,
multiplication(coantidomain(X1),backward_diamond(multiplication(X1,coantidomain(X2)),X3)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_393,c_0_164]),c_0_159]) ).
cnf(c_0_398,plain,
antidomain(backward_diamond(X1,backward_diamond(X2,X3))) = coantidomain(multiplication(backward_diamond(X2,X3),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_151]),c_0_52]),c_0_148]) ).
cnf(c_0_399,plain,
multiplication(domain(addition(antidomain(X1),X2)),X1) = multiplication(domain(X2),X1),
inference(spm,[status(thm)],[c_0_394,c_0_33]) ).
cnf(c_0_400,plain,
domain(addition(X1,addition(X2,antidomain(addition(X1,X2))))) = one,
inference(spm,[status(thm)],[c_0_284,c_0_55]) ).
cnf(c_0_401,plain,
antidomain(addition(antidomain(X1),X2)) = multiplication(domain(X1),antidomain(X2)),
inference(spm,[status(thm)],[c_0_395,c_0_33]) ).
cnf(c_0_402,plain,
backward_diamond(multiplication(X1,coantidomain(multiplication(X2,X1))),X2) = zero,
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_149,c_0_155]),c_0_41]),c_0_129]),c_0_151]),c_0_52]),c_0_148]) ).
cnf(c_0_403,plain,
multiplication(addition(antidomain(X1),X2),X1) = multiplication(X2,X1),
inference(spm,[status(thm)],[c_0_86,c_0_33]) ).
cnf(c_0_404,plain,
multiplication(antidomain(X1),antidomain(X1)) = antidomain(X1),
inference(spm,[status(thm)],[c_0_93,c_0_97]) ).
cnf(c_0_405,plain,
addition(antidomain(X1),antidomain(coantidomain(addition(domain(X1),X2)))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_396,c_0_187]),c_0_153]),c_0_232]),c_0_33]) ).
cnf(c_0_406,plain,
backward_diamond(multiplication(X1,backward_diamond(X1,X2)),X2) = backward_diamond(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_300,c_0_251]),c_0_300]),c_0_137]),c_0_52]),c_0_148]) ).
cnf(c_0_407,plain,
multiplication(coantidomain(X1),antidomain(backward_diamond(multiplication(X1,coantidomain(X2)),X3))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_333,c_0_397]),c_0_41]),c_0_53]) ).
cnf(c_0_408,plain,
backward_diamond(X1,coantidomain(multiplication(backward_diamond(X2,X3),antidomain(X1)))) = antidomain(coantidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_331,c_0_165]),c_0_398]) ).
cnf(c_0_409,plain,
multiplication(domain(addition(X1,multiplication(domain(X2),antidomain(X1)))),X2) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_399,c_0_400]),c_0_28]),c_0_401]) ).
cnf(c_0_410,plain,
backward_diamond(multiplication(X1,coantidomain(multiplication(X2,X1))),addition(antidomain(X1),X2)) = zero,
inference(spm,[status(thm)],[c_0_402,c_0_403]) ).
cnf(c_0_411,plain,
addition(X1,multiplication(X2,antidomain(coantidomain(X1)))) = multiplication(addition(X1,X2),antidomain(coantidomain(X1))),
inference(spm,[status(thm)],[c_0_81,c_0_100]) ).
cnf(c_0_412,plain,
multiplication(addition(antidomain(X1),X2),antidomain(X1)) = multiplication(addition(X2,one),antidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_404]),c_0_110]) ).
cnf(c_0_413,plain,
backward_diamond(domain(multiplication(X1,X2)),domain(X1)) = domain(multiplication(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_303,c_0_249]),c_0_227]),c_0_52]),c_0_227]) ).
cnf(c_0_414,plain,
multiplication(antidomain(coantidomain(addition(domain(X1),X2))),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_403,c_0_405]),c_0_28]) ).
fof(c_0_415,negated_conjecture,
~ ! [X4,X5,X6,X7,X8] :
( ( addition(domain(X6),domain(X5)) = domain(X5)
& addition(backward_diamond(X4,domain(X5)),domain(X7)) = domain(X7)
& addition(domain(X7),domain(X8)) = domain(X8) )
=> addition(backward_diamond(X4,domain(X6)),domain(X8)) = domain(X8) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_416,plain,
backward_diamond(addition(multiplication(X1,antidomain(backward_diamond(X1,X2))),X3),X2) = backward_diamond(X3,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_300,c_0_299]),c_0_300]),c_0_137]) ).
cnf(c_0_417,plain,
backward_diamond(backward_diamond(antidomain(X1),X2),X2) = backward_diamond(antidomain(X1),X2),
inference(spm,[status(thm)],[c_0_406,c_0_365]) ).
cnf(c_0_418,plain,
backward_diamond(backward_diamond(antidomain(coantidomain(X1)),X2),X1) = backward_diamond(antidomain(coantidomain(X1)),X2),
inference(spm,[status(thm)],[c_0_159,c_0_314]) ).
cnf(c_0_419,plain,
multiplication(coantidomain(X1),coantidomain(multiplication(X1,coantidomain(X2)))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_407,c_0_408]),c_0_52]),c_0_134]) ).
cnf(c_0_420,plain,
multiplication(domain(addition(coantidomain(X1),backward_diamond(domain(X2),X1))),X2) = X2,
inference(spm,[status(thm)],[c_0_409,c_0_373]) ).
cnf(c_0_421,plain,
backward_diamond(X1,multiplication(addition(X2,one),antidomain(X1))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(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_410,c_0_411]),c_0_227]),c_0_92]),c_0_97]),c_0_68]),c_0_54]),c_0_162]),c_0_41]),c_0_53]),c_0_227]),c_0_92]),c_0_97]),c_0_412]) ).
cnf(c_0_422,plain,
backward_diamond(domain(X1),addition(domain(X1),X2)) = domain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_413,c_0_414]),c_0_97]),c_0_159]) ).
fof(c_0_423,negated_conjecture,
( addition(domain(esk3_0),domain(esk2_0)) = domain(esk2_0)
& addition(backward_diamond(esk1_0,domain(esk2_0)),domain(esk4_0)) = domain(esk4_0)
& addition(domain(esk4_0),domain(esk5_0)) = domain(esk5_0)
& addition(backward_diamond(esk1_0,domain(esk3_0)),domain(esk5_0)) != domain(esk5_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_415])])]) ).
cnf(c_0_424,plain,
backward_diamond(addition(coantidomain(addition(X1,X2)),X3),X1) = backward_diamond(X3,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_416,c_0_152]),c_0_75]),c_0_53]) ).
cnf(c_0_425,plain,
backward_diamond(antidomain(coantidomain(X1)),X2) = backward_diamond(antidomain(coantidomain(X2)),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_300,c_0_313]),c_0_302]),c_0_417]),c_0_227]),c_0_134]),c_0_418]) ).
cnf(c_0_426,plain,
multiplication(coantidomain(X1),coantidomain(multiplication(X1,antidomain(X2)))) = coantidomain(X1),
inference(spm,[status(thm)],[c_0_419,c_0_232]) ).
cnf(c_0_427,plain,
multiplication(coantidomain(multiplication(addition(X1,one),antidomain(X2))),X2) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_420,c_0_421]),c_0_92]),c_0_97]),c_0_35]),c_0_134]) ).
cnf(c_0_428,plain,
multiplication(antidomain(coantidomain(X1)),domain(X2)) = backward_diamond(domain(X2),X1),
inference(spm,[status(thm)],[c_0_159,c_0_350]) ).
cnf(c_0_429,plain,
backward_diamond(domain(X1),multiplication(addition(X2,one),domain(X1))) = domain(X1),
inference(spm,[status(thm)],[c_0_422,c_0_110]) ).
cnf(c_0_430,plain,
multiplication(antidomain(addition(domain(X1),X2)),X1) = zero,
inference(spm,[status(thm)],[c_0_131,c_0_93]) ).
cnf(c_0_431,negated_conjecture,
addition(domain(esk3_0),domain(esk2_0)) = domain(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_423]) ).
cnf(c_0_432,plain,
multiplication(coantidomain(X1),antidomain(backward_diamond(antidomain(X2),X1))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_316,c_0_302]),c_0_52]),c_0_134]),c_0_52]),c_0_134]) ).
cnf(c_0_433,plain,
backward_diamond(antidomain(coantidomain(X1)),addition(X1,X2)) = antidomain(coantidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_424,c_0_158]),c_0_129]),c_0_425]) ).
cnf(c_0_434,plain,
multiplication(coantidomain(X1),coantidomain(X2)) = multiplication(coantidomain(X2),coantidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_379,c_0_164]),c_0_52]),c_0_134]),c_0_320]) ).
cnf(c_0_435,plain,
antidomain(coantidomain(multiplication(addition(X1,one),domain(X2)))) = domain(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_426,c_0_427]),c_0_52]),c_0_164]),c_0_227]),c_0_428]),c_0_429]),c_0_52]),c_0_164]) ).
cnf(c_0_436,plain,
multiplication(antidomain(addition(X1,domain(X2))),X2) = zero,
inference(spm,[status(thm)],[c_0_430,c_0_71]) ).
cnf(c_0_437,negated_conjecture,
addition(domain(esk2_0),domain(esk3_0)) = domain(esk2_0),
inference(rw,[status(thm)],[c_0_431,c_0_33]) ).
cnf(c_0_438,plain,
multiplication(X1,multiplication(X2,coantidomain(addition(X3,multiplication(X1,X2))))) = zero,
inference(spm,[status(thm)],[c_0_68,c_0_202]) ).
cnf(c_0_439,plain,
multiplication(coantidomain(X1),coantidomain(addition(X1,X2))) = coantidomain(addition(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_432,c_0_433]),c_0_52]),c_0_134]),c_0_434]) ).
cnf(c_0_440,plain,
multiplication(antidomain(multiplication(antidomain(X1),X2)),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_339]),c_0_28]),c_0_232]) ).
cnf(c_0_441,plain,
coantidomain(multiplication(addition(X1,one),domain(X2))) = antidomain(X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_435]),c_0_92]),c_0_97]),c_0_134]) ).
cnf(c_0_442,negated_conjecture,
multiplication(antidomain(esk2_0),esk3_0) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_436,c_0_437]),c_0_92]),c_0_97]) ).
cnf(c_0_443,plain,
backward_diamond(backward_diamond(X1,X2),coantidomain(X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_233,c_0_174]),c_0_183]) ).
cnf(c_0_444,plain,
multiplication(antidomain(multiplication(domain(X1),X2)),multiplication(domain(X2),X1)) = zero,
inference(spm,[status(thm)],[c_0_54,c_0_358]) ).
cnf(c_0_445,plain,
multiplication(X1,coantidomain(addition(X2,multiplication(X1,coantidomain(X2))))) = zero,
inference(spm,[status(thm)],[c_0_438,c_0_439]) ).
cnf(c_0_446,plain,
multiplication(domain(X1),multiplication(antidomain(X2),X1)) = multiplication(antidomain(X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_440,c_0_288]),c_0_52]) ).
cnf(c_0_447,plain,
coantidomain(multiplication(addition(X1,one),antidomain(X2))) = domain(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_441,c_0_97]),c_0_52]) ).
cnf(c_0_448,negated_conjecture,
multiplication(addition(X1,antidomain(esk2_0)),esk3_0) = multiplication(X1,esk3_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_442]),c_0_35]) ).
cnf(c_0_449,plain,
backward_diamond(backward_diamond(coantidomain(X1),X2),X1) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_443,c_0_164]),c_0_159]) ).
cnf(c_0_450,plain,
multiplication(coantidomain(addition(X1,multiplication(domain(X2),coantidomain(X1)))),X2) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_444,c_0_445]),c_0_75]),c_0_134]),c_0_28]) ).
cnf(c_0_451,plain,
backward_diamond(multiplication(antidomain(backward_diamond(domain(X1),X2)),X1),X2) = zero,
inference(spm,[status(thm)],[c_0_374,c_0_446]) ).
cnf(c_0_452,plain,
backward_diamond(domain(X1),multiplication(X2,antidomain(X1))) = zero,
inference(spm,[status(thm)],[c_0_157,c_0_447]) ).
cnf(c_0_453,plain,
addition(coantidomain(X1),backward_diamond(coantidomain(X1),X2)) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_209,c_0_164]),c_0_52]),c_0_134]),c_0_52]),c_0_134]) ).
cnf(c_0_454,negated_conjecture,
multiplication(domain(esk2_0),esk3_0) = esk3_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_448,c_0_62]),c_0_28]) ).
cnf(c_0_455,plain,
multiplication(X1,backward_diamond(coantidomain(X1),X2)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_449]),c_0_75]),c_0_53]),c_0_148]) ).
cnf(c_0_456,negated_conjecture,
addition(domain(esk4_0),domain(esk5_0)) = domain(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_423]) ).
cnf(c_0_457,plain,
multiplication(coantidomain(addition(coantidomain(X1),backward_diamond(domain(X2),X1))),X2) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_450,c_0_164]),c_0_373]) ).
cnf(c_0_458,plain,
backward_diamond(X1,multiplication(X2,antidomain(X1))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_451,c_0_452]),c_0_75]),c_0_28]) ).
cnf(c_0_459,plain,
multiplication(backward_diamond(coantidomain(domain(X1)),X2),X1) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_453]),c_0_197]) ).
cnf(c_0_460,negated_conjecture,
multiplication(antidomain(coantidomain(domain(esk2_0))),esk3_0) = esk3_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_211,c_0_454]),c_0_212]) ).
cnf(c_0_461,plain,
multiplication(X1,multiplication(X2,backward_diamond(coantidomain(multiplication(X1,X2)),X3))) = zero,
inference(spm,[status(thm)],[c_0_68,c_0_455]) ).
cnf(c_0_462,plain,
multiplication(antidomain(coantidomain(domain(addition(X1,X2)))),X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_211,c_0_261]),c_0_212]) ).
cnf(c_0_463,negated_conjecture,
addition(domain(esk5_0),domain(esk4_0)) = domain(esk5_0),
inference(rw,[status(thm)],[c_0_456,c_0_33]) ).
cnf(c_0_464,negated_conjecture,
addition(backward_diamond(esk1_0,domain(esk2_0)),domain(esk4_0)) = domain(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_423]) ).
cnf(c_0_465,plain,
backward_diamond(backward_diamond(coantidomain(X1),X2),X2) = backward_diamond(coantidomain(X1),X2),
inference(spm,[status(thm)],[c_0_406,c_0_258]) ).
cnf(c_0_466,plain,
backward_diamond(X1,addition(coantidomain(X2),backward_diamond(domain(X1),X2))) = antidomain(coantidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_351,c_0_457]),c_0_75]),c_0_127]) ).
cnf(c_0_467,plain,
backward_diamond(X1,multiplication(X2,multiplication(X3,antidomain(X1)))) = zero,
inference(spm,[status(thm)],[c_0_458,c_0_68]) ).
cnf(c_0_468,plain,
multiplication(addition(X1,backward_diamond(coantidomain(X1),X2)),antidomain(coantidomain(X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_411,c_0_459]),c_0_35]),c_0_97]),c_0_227]),c_0_134]) ).
cnf(c_0_469,negated_conjecture,
backward_diamond(antidomain(esk3_0),antidomain(esk2_0)) = 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_234,c_0_460]),c_0_134]),c_0_232]),c_0_134]),c_0_232]) ).
cnf(c_0_470,plain,
multiplication(X1,multiplication(X2,backward_diamond(antidomain(backward_diamond(X2,X1)),X3))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_461]),c_0_162]),c_0_129]),c_0_137]) ).
cnf(c_0_471,plain,
backward_diamond(antidomain(X1),antidomain(addition(X2,X1))) = antidomain(addition(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_234,c_0_462]),c_0_134]),c_0_232]),c_0_134]),c_0_232]) ).
cnf(c_0_472,negated_conjecture,
addition(domain(esk5_0),addition(domain(esk4_0),X1)) = addition(domain(esk5_0),X1),
inference(spm,[status(thm)],[c_0_55,c_0_463]) ).
cnf(c_0_473,negated_conjecture,
addition(domain(esk4_0),backward_diamond(esk1_0,domain(esk2_0))) = domain(esk4_0),
inference(rw,[status(thm)],[c_0_464,c_0_33]) ).
cnf(c_0_474,plain,
backward_diamond(coantidomain(X1),addition(coantidomain(X2),backward_diamond(coantidomain(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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_465,c_0_466]),c_0_32]),c_0_58]),c_0_127]),c_0_52]),c_0_134]),c_0_134]),c_0_32]),c_0_58]),c_0_127]),c_0_52]),c_0_134]) ).
cnf(c_0_475,plain,
backward_diamond(coantidomain(X1),multiplication(X2,X1)) = zero,
inference(spm,[status(thm)],[c_0_467,c_0_468]) ).
cnf(c_0_476,plain,
multiplication(coantidomain(X1),antidomain(X2)) = multiplication(antidomain(X2),coantidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_379,c_0_227]),c_0_92]),c_0_97]),c_0_270]) ).
cnf(c_0_477,plain,
backward_diamond(backward_diamond(X1,X2),coantidomain(multiplication(X2,X1))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_135]),c_0_58]),c_0_127]),c_0_137]),c_0_183]) ).
cnf(c_0_478,negated_conjecture,
multiplication(domain(esk3_0),domain(esk2_0)) = domain(esk3_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_279,c_0_469]),c_0_227]),c_0_52]),c_0_227]) ).
cnf(c_0_479,plain,
multiplication(X1,multiplication(X2,antidomain(addition(X3,backward_diamond(X2,X1))))) = zero,
inference(spm,[status(thm)],[c_0_470,c_0_471]) ).
cnf(c_0_480,negated_conjecture,
addition(domain(esk5_0),backward_diamond(esk1_0,domain(esk2_0))) = domain(esk5_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_472,c_0_473]),c_0_463]) ).
cnf(c_0_481,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_474,c_0_475]),c_0_35]),c_0_320]),c_0_434]) ).
cnf(c_0_482,plain,
multiplication(coantidomain(multiplication(X1,X2)),antidomain(backward_diamond(X2,X1))) = 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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_135]),c_0_58]),c_0_127]),c_0_137]),c_0_97]),c_0_183]),c_0_476]) ).
cnf(c_0_483,plain,
coantidomain(multiplication(coantidomain(multiplication(X1,X2)),backward_diamond(X2,X1))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_477]),c_0_75]) ).
cnf(c_0_484,negated_conjecture,
multiplication(domain(esk3_0),multiplication(domain(esk2_0),X1)) = multiplication(domain(esk3_0),X1),
inference(spm,[status(thm)],[c_0_68,c_0_478]) ).
cnf(c_0_485,negated_conjecture,
multiplication(domain(esk2_0),multiplication(esk1_0,antidomain(esk5_0))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_479,c_0_480]),c_0_92]),c_0_97]) ).
cnf(c_0_486,plain,
antidomain(backward_diamond(X1,X2)) = coantidomain(multiplication(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_481,c_0_77]),c_0_127]),c_0_137]),c_0_476]),c_0_482]),c_0_127]),c_0_137]) ).
cnf(c_0_487,plain,
multiplication(coantidomain(multiplication(X1,X2)),backward_diamond(X2,X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_483]),c_0_53]) ).
cnf(c_0_488,negated_conjecture,
multiplication(domain(esk3_0),multiplication(esk1_0,antidomain(esk5_0))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_484,c_0_485]),c_0_162]) ).
cnf(c_0_489,plain,
antidomain(coantidomain(multiplication(X1,X2))) = backward_diamond(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_486]),c_0_148]) ).
cnf(c_0_490,plain,
multiplication(antidomain(X1),domain(addition(X1,X2))) = multiplication(antidomain(X1),domain(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_355,c_0_91]),c_0_355]) ).
cnf(c_0_491,negated_conjecture,
backward_diamond(multiplication(esk1_0,antidomain(esk5_0)),domain(esk3_0)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_487,c_0_488]),c_0_41]),c_0_28]) ).
cnf(c_0_492,plain,
backward_diamond(multiplication(X1,X2),X3) = backward_diamond(X2,multiplication(X3,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_489,c_0_68]),c_0_489]) ).
cnf(c_0_493,plain,
domain(addition(X1,antidomain(addition(X1,X2)))) = domain(addition(X1,antidomain(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_391,c_0_490]),c_0_346]),c_0_391]),c_0_139]) ).
cnf(c_0_494,negated_conjecture,
antidomain(addition(esk5_0,coantidomain(multiplication(domain(esk3_0),esk1_0)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_491,c_0_492]),c_0_385]) ).
cnf(c_0_495,negated_conjecture,
addition(backward_diamond(esk1_0,domain(esk3_0)),domain(esk5_0)) != domain(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_423]) ).
cnf(c_0_496,plain,
addition(domain(X1),domain(addition(X2,X1))) = domain(addition(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_254,c_0_261]),c_0_212]),c_0_212]),c_0_33]) ).
cnf(c_0_497,negated_conjecture,
domain(addition(esk5_0,backward_diamond(esk1_0,domain(esk3_0)))) = domain(esk5_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_493,c_0_494]),c_0_35]),c_0_489]) ).
cnf(c_0_498,negated_conjecture,
addition(domain(esk5_0),backward_diamond(esk1_0,domain(esk3_0))) != domain(esk5_0),
inference(rw,[status(thm)],[c_0_495,c_0_33]) ).
cnf(c_0_499,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_496,c_0_497]),c_0_148]),c_0_33]),c_0_498]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : KLE124+1 : TPTP v8.1.2. Released v4.0.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n022.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 2400
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue Oct 3 04:50:09 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.17/0.44 Running first-order model finding
% 0.17/0.44 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.kcjnmxyBc8/E---3.1_7033.p
% 843.39/107.05 # Version: 3.1pre001
% 843.39/107.05 # Preprocessing class: FSMSSMSSSSSNFFN.
% 843.39/107.05 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 843.39/107.05 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 843.39/107.05 # Starting new_bool_3 with 300s (1) cores
% 843.39/107.05 # Starting new_bool_1 with 300s (1) cores
% 843.39/107.05 # Starting sh5l with 300s (1) cores
% 843.39/107.05 # sh5l with pid 7113 completed with status 0
% 843.39/107.05 # Result found by sh5l
% 843.39/107.05 # Preprocessing class: FSMSSMSSSSSNFFN.
% 843.39/107.05 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 843.39/107.05 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 843.39/107.05 # Starting new_bool_3 with 300s (1) cores
% 843.39/107.05 # Starting new_bool_1 with 300s (1) cores
% 843.39/107.05 # Starting sh5l with 300s (1) cores
% 843.39/107.05 # SinE strategy is gf500_gu_R04_F100_L20000
% 843.39/107.05 # Search class: FUUPM-FFMS21-MFFFFFNN
% 843.39/107.05 # partial match(1): FUUPM-FFSS21-MFFFFFNN
% 843.39/107.05 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 843.39/107.05 # Starting G-E--_209_C18_F1_AE_CS_SP_PI_S0Y with 163s (1) cores
% 843.39/107.05 # G-E--_209_C18_F1_AE_CS_SP_PI_S0Y with pid 7120 completed with status 0
% 843.39/107.05 # Result found by G-E--_209_C18_F1_AE_CS_SP_PI_S0Y
% 843.39/107.05 # Preprocessing class: FSMSSMSSSSSNFFN.
% 843.39/107.05 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 843.39/107.05 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 843.39/107.05 # Starting new_bool_3 with 300s (1) cores
% 843.39/107.05 # Starting new_bool_1 with 300s (1) cores
% 843.39/107.05 # Starting sh5l with 300s (1) cores
% 843.39/107.05 # SinE strategy is gf500_gu_R04_F100_L20000
% 843.39/107.05 # Search class: FUUPM-FFMS21-MFFFFFNN
% 843.39/107.05 # partial match(1): FUUPM-FFSS21-MFFFFFNN
% 843.39/107.05 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 843.39/107.05 # Starting G-E--_209_C18_F1_AE_CS_SP_PI_S0Y with 163s (1) cores
% 843.39/107.05 # Preprocessing time : 0.001 s
% 843.39/107.05
% 843.39/107.05 # Proof found!
% 843.39/107.05 # SZS status Theorem
% 843.39/107.05 # SZS output start CNFRefutation
% See solution above
% 843.39/107.05 # Parsed axioms : 27
% 843.39/107.05 # Removed by relevancy pruning/SinE : 1
% 843.39/107.05 # Initial clauses : 29
% 843.39/107.05 # Removed in clause preprocessing : 0
% 843.39/107.05 # Initial clauses in saturation : 29
% 843.39/107.05 # Processed clauses : 123347
% 843.39/107.05 # ...of these trivial : 91831
% 843.39/107.05 # ...subsumed : 22168
% 843.39/107.05 # ...remaining for further processing : 9348
% 843.39/107.05 # Other redundant clauses eliminated : 0
% 843.39/107.05 # Clauses deleted for lack of memory : 716925
% 843.39/107.05 # Backward-subsumed : 0
% 843.39/107.05 # Backward-rewritten : 6039
% 843.39/107.05 # Generated clauses : 11480157
% 843.39/107.05 # ...of the previous two non-redundant : 2618718
% 843.39/107.05 # ...aggressively subsumed : 0
% 843.39/107.05 # Contextual simplify-reflections : 0
% 843.39/107.05 # Paramodulations : 11480157
% 843.39/107.05 # Factorizations : 0
% 843.39/107.05 # NegExts : 0
% 843.39/107.05 # Equation resolutions : 0
% 843.39/107.05 # Total rewrite steps : 27367660
% 843.39/107.05 # Propositional unsat checks : 0
% 843.39/107.05 # Propositional check models : 0
% 843.39/107.05 # Propositional check unsatisfiable : 0
% 843.39/107.05 # Propositional clauses : 0
% 843.39/107.05 # Propositional clauses after purity: 0
% 843.39/107.05 # Propositional unsat core size : 0
% 843.39/107.05 # Propositional preprocessing time : 0.000
% 843.39/107.05 # Propositional encoding time : 0.000
% 843.39/107.05 # Propositional solver time : 0.000
% 843.39/107.05 # Success case prop preproc time : 0.000
% 843.39/107.05 # Success case prop encoding time : 0.000
% 843.39/107.05 # Success case prop solver time : 0.000
% 843.39/107.05 # Current number of processed clauses : 3309
% 843.39/107.05 # Positive orientable unit clauses : 3297
% 843.39/107.05 # Positive unorientable unit clauses: 11
% 843.39/107.05 # Negative unit clauses : 1
% 843.39/107.05 # Non-unit-clauses : 0
% 843.39/107.05 # Current number of unprocessed clauses: 1672391
% 843.39/107.05 # ...number of literals in the above : 1672391
% 843.39/107.05 # Current number of archived formulas : 0
% 843.39/107.05 # Current number of archived clauses : 6039
% 843.39/107.05 # Clause-clause subsumption calls (NU) : 0
% 843.39/107.05 # Rec. Clause-clause subsumption calls : 0
% 843.39/107.05 # Non-unit clause-clause subsumptions : 0
% 843.39/107.05 # Unit Clause-clause subsumption calls : 146
% 843.39/107.05 # Rewrite failures with RHS unbound : 0
% 843.39/107.05 # BW rewrite match attempts : 117422
% 843.39/107.05 # BW rewrite match successes : 6028
% 843.39/107.05 # Condensation attempts : 0
% 843.39/107.05 # Condensation successes : 0
% 843.39/107.05 # Termbank termtop insertions : 123228547
% 843.39/107.05
% 843.39/107.05 # -------------------------------------------------
% 843.39/107.05 # User time : 103.868 s
% 843.39/107.05 # System time : 1.811 s
% 843.39/107.05 # Total time : 105.679 s
% 843.39/107.05 # Maximum resident set size: 1952 pages
% 843.39/107.05
% 843.39/107.05 # -------------------------------------------------
% 843.39/107.05 # User time : 103.868 s
% 843.39/107.05 # System time : 1.819 s
% 843.39/107.05 # Total time : 105.687 s
% 843.39/107.05 # Maximum resident set size: 1728 pages
% 843.39/107.05 % E---3.1 exiting
%------------------------------------------------------------------------------