TSTP Solution File: KLE121+1 by Enigma---0.5.1
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%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : KLE121+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 01:50:25 EDT 2022
% Result : Theorem 120.59s 16.66s
% Output : CNFRefutation 120.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 22
% Syntax : Number of formulae : 234 ( 227 unt; 0 def)
% Number of atoms : 246 ( 238 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 22 ( 10 ~; 4 |; 5 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 332 ( 47 sgn 78 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(domain3,axiom,
! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain3) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(domain1,axiom,
! [X4] : multiplication(antidomain(X4),X4) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain1) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(codomain1,axiom,
! [X4] : multiplication(X4,coantidomain(X4)) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain1) ).
fof(codomain3,axiom,
! [X4] : addition(coantidomain(coantidomain(X4)),coantidomain(X4)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain3) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).
fof(domain2,axiom,
! [X4,X5] : addition(antidomain(multiplication(X4,X5)),antidomain(multiplication(X4,antidomain(antidomain(X5))))) = antidomain(multiplication(X4,antidomain(antidomain(X5)))),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain2) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(codomain2,axiom,
! [X4,X5] : addition(coantidomain(multiplication(X4,X5)),coantidomain(multiplication(coantidomain(coantidomain(X4)),X5))) = coantidomain(multiplication(coantidomain(coantidomain(X4)),X5)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain2) ).
fof(goals,conjecture,
! [X4,X5,X6,X7,X8] :
( ( addition(backward_diamond(X7,domain(X4)),domain(X5)) = domain(X5)
& addition(backward_diamond(X8,domain(X5)),domain(X6)) = domain(X6) )
=> addition(backward_diamond(multiplication(X7,X8),domain(X4)),domain(X6)) = domain(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(backward_diamond,axiom,
! [X4,X5] : backward_diamond(X4,X5) = codomain(multiplication(codomain(X5),X4)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+6.ax',backward_diamond) ).
fof(codomain4,axiom,
! [X4] : codomain(X4) = coantidomain(coantidomain(X4)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain4) ).
fof(domain4,axiom,
! [X4] : domain(X4) = antidomain(antidomain(X4)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain4) ).
fof(c_0_22,plain,
! [X34] : addition(antidomain(antidomain(X34)),antidomain(X34)) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
fof(c_0_23,plain,
! [X9,X10] : addition(X9,X10) = addition(X10,X9),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_24,plain,
! [X19] : multiplication(X19,one) = X19,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_25,plain,
! [X31] : multiplication(antidomain(X31),X31) = zero,
inference(variable_rename,[status(thm)],[domain1]) ).
cnf(c_0_26,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,plain,
multiplication(antidomain(X1),X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_30,plain,
! [X14] : addition(X14,zero) = X14,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_31,plain,
! [X20] : multiplication(one,X20) = X20,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_32,plain,
! [X36] : multiplication(X36,coantidomain(X36)) = zero,
inference(variable_rename,[status(thm)],[codomain1]) ).
fof(c_0_33,plain,
! [X39] : addition(coantidomain(coantidomain(X39)),coantidomain(X39)) = one,
inference(variable_rename,[status(thm)],[codomain3]) ).
cnf(c_0_34,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_35,plain,
antidomain(one) = zero,
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_37,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_38,plain,
multiplication(X1,coantidomain(X1)) = zero,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_39,plain,
addition(coantidomain(coantidomain(X1)),coantidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,plain,
one = addition(zero,antidomain(zero)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_36,c_0_27]) ).
cnf(c_0_42,plain,
coantidomain(one) = zero,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
fof(c_0_43,plain,
! [X11,X12,X13] : addition(X13,addition(X12,X11)) = addition(addition(X13,X12),X11),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_44,plain,
! [X15] : addition(X15,X15) = X15,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_45,plain,
addition(coantidomain(X1),coantidomain(coantidomain(X1))) = antidomain(zero),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_27]),c_0_40]),c_0_41]) ).
cnf(c_0_46,plain,
coantidomain(antidomain(zero)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_40]),c_0_41]) ).
fof(c_0_47,plain,
! [X27] : multiplication(X27,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
fof(c_0_48,plain,
! [X28] : multiplication(zero,X28) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
fof(c_0_49,plain,
! [X16,X17,X18] : multiplication(X16,multiplication(X17,X18)) = multiplication(multiplication(X16,X17),X18),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_50,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_51,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_52,plain,
antidomain(zero) = coantidomain(zero),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_41]) ).
cnf(c_0_53,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_54,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_55,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
fof(c_0_56,plain,
! [X29,X30] :
( ( ~ leq(X29,X30)
| addition(X29,X30) = X30 )
& ( addition(X29,X30) != X30
| leq(X29,X30) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
fof(c_0_57,plain,
! [X32,X33] : addition(antidomain(multiplication(X32,X33)),antidomain(multiplication(X32,antidomain(antidomain(X33))))) = antidomain(multiplication(X32,antidomain(antidomain(X33)))),
inference(variable_rename,[status(thm)],[domain2]) ).
cnf(c_0_58,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_59,plain,
addition(coantidomain(X1),coantidomain(coantidomain(X1))) = coantidomain(zero),
inference(rw,[status(thm)],[c_0_45,c_0_52]) ).
cnf(c_0_60,plain,
multiplication(X1,multiplication(X2,coantidomain(X2))) = multiplication(X2,coantidomain(X2)),
inference(spm,[status(thm)],[c_0_53,c_0_38]) ).
cnf(c_0_61,plain,
multiplication(antidomain(X1),multiplication(X1,X2)) = multiplication(antidomain(X1),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_29]),c_0_55]) ).
fof(c_0_62,plain,
! [X24,X25,X26] : multiplication(addition(X24,X25),X26) = addition(multiplication(X24,X26),multiplication(X25,X26)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_63,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_64,plain,
addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,antidomain(antidomain(X2))))) = antidomain(multiplication(X1,antidomain(antidomain(X2)))),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_65,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = coantidomain(zero),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_40]),c_0_41]),c_0_52]) ).
fof(c_0_66,plain,
! [X21,X22,X23] : multiplication(X21,addition(X22,X23)) = addition(multiplication(X21,X22),multiplication(X21,X23)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_67,plain,
addition(coantidomain(X1),coantidomain(zero)) = coantidomain(zero),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_68,plain,
multiplication(antidomain(X1),X1) = multiplication(X1,coantidomain(X1)),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_69,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_70,plain,
leq(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,antidomain(antidomain(X2))))),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_71,plain,
addition(antidomain(X1),coantidomain(zero)) = coantidomain(zero),
inference(spm,[status(thm)],[c_0_58,c_0_65]) ).
cnf(c_0_72,plain,
multiplication(X1,coantidomain(zero)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_40]),c_0_41]),c_0_52]) ).
cnf(c_0_73,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_74,plain,
antidomain(antidomain(zero)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_40]),c_0_41]) ).
fof(c_0_75,plain,
! [X37,X38] : addition(coantidomain(multiplication(X37,X38)),coantidomain(multiplication(coantidomain(coantidomain(X37)),X38))) = coantidomain(multiplication(coantidomain(coantidomain(X37)),X38)),
inference(variable_rename,[status(thm)],[codomain2]) ).
cnf(c_0_76,plain,
addition(coantidomain(zero),coantidomain(X1)) = coantidomain(zero),
inference(spm,[status(thm)],[c_0_27,c_0_67]) ).
cnf(c_0_77,plain,
multiplication(antidomain(X1),multiplication(X1,X2)) = multiplication(X1,coantidomain(X1)),
inference(rw,[status(thm)],[c_0_61,c_0_68]) ).
cnf(c_0_78,plain,
multiplication(X1,multiplication(X2,multiplication(X3,coantidomain(multiplication(X2,X3))))) = multiplication(X2,multiplication(X3,coantidomain(multiplication(X2,X3)))),
inference(spm,[status(thm)],[c_0_60,c_0_55]) ).
cnf(c_0_79,plain,
addition(multiplication(X1,coantidomain(addition(X1,X2))),multiplication(X2,coantidomain(addition(X1,X2)))) = zero,
inference(spm,[status(thm)],[c_0_38,c_0_69]) ).
cnf(c_0_80,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_81,plain,
leq(coantidomain(zero),antidomain(multiplication(X1,antidomain(antidomain(coantidomain(X1)))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_38]),c_0_52]) ).
cnf(c_0_82,plain,
addition(coantidomain(zero),antidomain(X1)) = coantidomain(zero),
inference(spm,[status(thm)],[c_0_27,c_0_71]) ).
cnf(c_0_83,plain,
multiplication(coantidomain(zero),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_40]),c_0_41]),c_0_52]) ).
cnf(c_0_84,plain,
addition(multiplication(X1,coantidomain(X1)),X2) = X2,
inference(spm,[status(thm)],[c_0_41,c_0_38]) ).
cnf(c_0_85,plain,
addition(multiplication(X1,coantidomain(X2)),multiplication(X1,coantidomain(coantidomain(X2)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_59]),c_0_73]) ).
cnf(c_0_86,plain,
antidomain(coantidomain(zero)) = zero,
inference(rw,[status(thm)],[c_0_74,c_0_52]) ).
cnf(c_0_87,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_75]) ).
cnf(c_0_88,plain,
addition(coantidomain(multiplication(X1,coantidomain(X1))),coantidomain(X2)) = coantidomain(multiplication(X1,coantidomain(X1))),
inference(spm,[status(thm)],[c_0_76,c_0_38]) ).
cnf(c_0_89,plain,
multiplication(X1,multiplication(X2,coantidomain(multiplication(X1,X2)))) = multiplication(X1,coantidomain(X1)),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_90,plain,
multiplication(X1,coantidomain(addition(X1,X2))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_79]),c_0_36]) ).
cnf(c_0_91,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_27]),c_0_50]) ).
cnf(c_0_92,plain,
addition(X1,multiplication(X1,coantidomain(X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_67]),c_0_72]),c_0_72]),c_0_27]) ).
cnf(c_0_93,plain,
coantidomain(zero) = antidomain(multiplication(X1,antidomain(antidomain(coantidomain(X1))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]) ).
cnf(c_0_94,plain,
addition(multiplication(coantidomain(X1),X2),multiplication(coantidomain(coantidomain(X1)),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_59]),c_0_69]) ).
cnf(c_0_95,plain,
multiplication(X1,coantidomain(coantidomain(X1))) = X1,
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_96,plain,
addition(X1,multiplication(X2,coantidomain(X2))) = X1,
inference(spm,[status(thm)],[c_0_36,c_0_38]) ).
cnf(c_0_97,plain,
antidomain(coantidomain(multiplication(X1,coantidomain(X1)))) = multiplication(X1,coantidomain(X1)),
inference(spm,[status(thm)],[c_0_86,c_0_38]) ).
cnf(c_0_98,plain,
coantidomain(multiplication(coantidomain(coantidomain(X1)),coantidomain(X1))) = coantidomain(multiplication(X1,coantidomain(X1))),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_99,plain,
multiplication(X1,coantidomain(multiplication(X2,coantidomain(X2)))) = X1,
inference(spm,[status(thm)],[c_0_72,c_0_38]) ).
cnf(c_0_100,plain,
multiplication(X1,coantidomain(addition(X1,X2))) = multiplication(X1,coantidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_72]) ).
cnf(c_0_101,plain,
addition(X1,addition(X2,multiplication(X1,coantidomain(X3)))) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_102,plain,
multiplication(X1,antidomain(antidomain(coantidomain(X1)))) = multiplication(X1,coantidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_93]),c_0_83]),c_0_55]),c_0_89]) ).
cnf(c_0_103,plain,
coantidomain(coantidomain(coantidomain(X1))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_96]) ).
cnf(c_0_104,plain,
multiplication(coantidomain(coantidomain(X1)),coantidomain(X1)) = multiplication(X1,coantidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_55]),c_0_99]),c_0_98]),c_0_97]),c_0_55]),c_0_99]) ).
cnf(c_0_105,plain,
coantidomain(coantidomain(zero)) = zero,
inference(rw,[status(thm)],[c_0_46,c_0_52]) ).
cnf(c_0_106,plain,
multiplication(X1,coantidomain(addition(X2,X1))) = multiplication(X1,coantidomain(X1)),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_107,plain,
coantidomain(multiplication(coantidomain(coantidomain(antidomain(X1))),multiplication(X1,X2))) = coantidomain(multiplication(X1,coantidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_77]),c_0_88]) ).
cnf(c_0_108,plain,
multiplication(coantidomain(coantidomain(X1)),antidomain(antidomain(coantidomain(X1)))) = multiplication(X1,coantidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_104]) ).
cnf(c_0_109,plain,
coantidomain(addition(coantidomain(X1),coantidomain(coantidomain(X1)))) = zero,
inference(spm,[status(thm)],[c_0_105,c_0_59]) ).
cnf(c_0_110,plain,
multiplication(X1,coantidomain(coantidomain(addition(X2,X1)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_106]),c_0_84]) ).
cnf(c_0_111,plain,
addition(X1,multiplication(X1,antidomain(X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_71]),c_0_72]),c_0_72]),c_0_27]) ).
cnf(c_0_112,plain,
coantidomain(multiplication(coantidomain(coantidomain(antidomain(X1))),X1)) = coantidomain(multiplication(X1,coantidomain(X1))),
inference(spm,[status(thm)],[c_0_107,c_0_95]) ).
cnf(c_0_113,plain,
multiplication(coantidomain(X1),antidomain(antidomain(coantidomain(X1)))) = antidomain(antidomain(coantidomain(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_108]),c_0_103]),c_0_84]) ).
cnf(c_0_114,plain,
addition(X1,multiplication(antidomain(X2),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_71]),c_0_83]),c_0_83]),c_0_27]) ).
cnf(c_0_115,plain,
multiplication(antidomain(coantidomain(X1)),coantidomain(coantidomain(X1))) = antidomain(coantidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_68]),c_0_84]) ).
cnf(c_0_116,plain,
coantidomain(addition(antidomain(X1),antidomain(antidomain(X1)))) = zero,
inference(spm,[status(thm)],[c_0_105,c_0_65]) ).
cnf(c_0_117,plain,
multiplication(X1,coantidomain(addition(coantidomain(X2),coantidomain(coantidomain(X2))))) = coantidomain(addition(coantidomain(X2),coantidomain(coantidomain(X2)))),
inference(spm,[status(thm)],[c_0_53,c_0_109]) ).
cnf(c_0_118,plain,
multiplication(X1,multiplication(antidomain(X2),coantidomain(coantidomain(X1)))) = multiplication(X1,antidomain(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_55]) ).
cnf(c_0_119,plain,
multiplication(coantidomain(coantidomain(antidomain(X1))),X1) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_112]),c_0_55]),c_0_99]) ).
cnf(c_0_120,plain,
addition(coantidomain(X1),antidomain(antidomain(coantidomain(X1)))) = coantidomain(X1),
inference(spm,[status(thm)],[c_0_111,c_0_113]) ).
cnf(c_0_121,plain,
antidomain(addition(antidomain(X1),antidomain(antidomain(X1)))) = zero,
inference(spm,[status(thm)],[c_0_86,c_0_65]) ).
cnf(c_0_122,plain,
addition(coantidomain(coantidomain(X1)),antidomain(coantidomain(X1))) = coantidomain(coantidomain(X1)),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_123,plain,
coantidomain(coantidomain(addition(antidomain(X1),antidomain(antidomain(X1))))) = addition(antidomain(X1),antidomain(antidomain(X1))),
inference(spm,[status(thm)],[c_0_103,c_0_65]) ).
cnf(c_0_124,plain,
addition(coantidomain(addition(antidomain(X1),antidomain(antidomain(X1)))),X2) = X2,
inference(spm,[status(thm)],[c_0_41,c_0_116]) ).
cnf(c_0_125,plain,
coantidomain(addition(coantidomain(X1),coantidomain(coantidomain(X1)))) = multiplication(X1,coantidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_117]),c_0_69]),c_0_100]),c_0_106]),c_0_103]),c_0_104]),c_0_84]) ).
cnf(c_0_126,plain,
multiplication(coantidomain(X1),multiplication(antidomain(X2),coantidomain(X1))) = multiplication(coantidomain(X1),antidomain(X2)),
inference(spm,[status(thm)],[c_0_118,c_0_103]) ).
cnf(c_0_127,plain,
multiplication(coantidomain(antidomain(X1)),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_119]),c_0_103]),c_0_41]) ).
cnf(c_0_128,plain,
addition(antidomain(X1),addition(antidomain(antidomain(X1)),coantidomain(X2))) = addition(antidomain(X1),antidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_65]),c_0_50]) ).
cnf(c_0_129,plain,
addition(antidomain(X1),coantidomain(coantidomain(antidomain(X1)))) = coantidomain(coantidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_95]),c_0_27]) ).
cnf(c_0_130,plain,
multiplication(antidomain(antidomain(coantidomain(X1))),coantidomain(X1)) = antidomain(antidomain(coantidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_120]),c_0_103]) ).
cnf(c_0_131,plain,
antidomain(antidomain(addition(antidomain(X1),antidomain(antidomain(X1))))) = coantidomain(antidomain(addition(antidomain(X1),antidomain(antidomain(X1))))),
inference(spm,[status(thm)],[c_0_52,c_0_121]) ).
cnf(c_0_132,plain,
antidomain(addition(antidomain(X1),antidomain(antidomain(X1)))) = coantidomain(addition(antidomain(X1),antidomain(antidomain(X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_124]) ).
cnf(c_0_133,plain,
coantidomain(addition(antidomain(X1),antidomain(antidomain(X1)))) = multiplication(antidomain(antidomain(X1)),coantidomain(antidomain(antidomain(X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_124]),c_0_103]),c_0_69]),c_0_100]),c_0_106]),c_0_84]) ).
cnf(c_0_134,plain,
multiplication(coantidomain(antidomain(X1)),antidomain(X1)) = multiplication(antidomain(X1),coantidomain(antidomain(X1))),
inference(spm,[status(thm)],[c_0_60,c_0_126]) ).
cnf(c_0_135,plain,
addition(antidomain(X1),coantidomain(antidomain(antidomain(X1)))) = coantidomain(antidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_127]),c_0_27]) ).
cnf(c_0_136,plain,
multiplication(coantidomain(addition(antidomain(X1),X2)),antidomain(X1)) = multiplication(antidomain(X1),coantidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_100]),c_0_60]) ).
cnf(c_0_137,plain,
addition(antidomain(X1),antidomain(antidomain(antidomain(X1)))) = antidomain(antidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_83]),c_0_83]) ).
cnf(c_0_138,plain,
addition(antidomain(X1),coantidomain(coantidomain(antidomain(antidomain(X1))))) = addition(antidomain(X1),antidomain(antidomain(X1))),
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_139,plain,
coantidomain(multiplication(antidomain(antidomain(X1)),coantidomain(antidomain(antidomain(X1))))) = addition(antidomain(X1),antidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_65]),c_0_131]),c_0_127]),c_0_131]),c_0_132]),c_0_133]) ).
cnf(c_0_140,plain,
multiplication(coantidomain(coantidomain(antidomain(X1))),X1) = multiplication(X1,coantidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_112]),c_0_55]),c_0_99]),c_0_112]),c_0_97]),c_0_55]),c_0_99]) ).
cnf(c_0_141,plain,
multiplication(coantidomain(coantidomain(antidomain(X1))),antidomain(X1)) = antidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_134]),c_0_84]) ).
cnf(c_0_142,plain,
addition(antidomain(X1),coantidomain(antidomain(antidomain(antidomain(X1))))) = addition(antidomain(X1),antidomain(antidomain(X1))),
inference(spm,[status(thm)],[c_0_128,c_0_135]) ).
cnf(c_0_143,plain,
multiplication(coantidomain(antidomain(antidomain(antidomain(X1)))),antidomain(X1)) = multiplication(antidomain(X1),coantidomain(antidomain(X1))),
inference(spm,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_144,plain,
coantidomain(coantidomain(antidomain(antidomain(X1)))) = antidomain(antidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_138]),c_0_133]),c_0_139]),c_0_73]),c_0_140]),c_0_141]),c_0_84]) ).
cnf(c_0_145,plain,
coantidomain(antidomain(antidomain(antidomain(X1)))) = antidomain(antidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_142]),c_0_133]),c_0_139]),c_0_73]),c_0_143]),c_0_127]),c_0_84]) ).
cnf(c_0_146,plain,
antidomain(antidomain(antidomain(X1))) = coantidomain(antidomain(antidomain(X1))),
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_147,plain,
addition(antidomain(antidomain(X1)),coantidomain(antidomain(antidomain(X1)))) = addition(antidomain(X1),antidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_146]),c_0_144]),c_0_134]),c_0_139]) ).
fof(c_0_148,negated_conjecture,
~ ! [X4,X5,X6,X7,X8] :
( ( addition(backward_diamond(X7,domain(X4)),domain(X5)) = domain(X5)
& addition(backward_diamond(X8,domain(X5)),domain(X6)) = domain(X6) )
=> addition(backward_diamond(multiplication(X7,X8),domain(X4)),domain(X6)) = domain(X6) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_149,plain,
! [X46,X47] : backward_diamond(X46,X47) = codomain(multiplication(codomain(X47),X46)),
inference(variable_rename,[status(thm)],[backward_diamond]) ).
fof(c_0_150,plain,
! [X40] : codomain(X40) = coantidomain(coantidomain(X40)),
inference(variable_rename,[status(thm)],[codomain4]) ).
cnf(c_0_151,plain,
addition(coantidomain(multiplication(X1,multiplication(X2,X3))),coantidomain(multiplication(coantidomain(coantidomain(multiplication(X1,X2))),X3))) = coantidomain(multiplication(coantidomain(coantidomain(multiplication(X1,X2))),X3)),
inference(spm,[status(thm)],[c_0_87,c_0_55]) ).
cnf(c_0_152,plain,
coantidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_147]),c_0_133]),c_0_139]),c_0_73]),c_0_127]),c_0_134]),c_0_96]) ).
fof(c_0_153,negated_conjecture,
( addition(backward_diamond(esk4_0,domain(esk1_0)),domain(esk2_0)) = domain(esk2_0)
& addition(backward_diamond(esk5_0,domain(esk2_0)),domain(esk3_0)) = domain(esk3_0)
& addition(backward_diamond(multiplication(esk4_0,esk5_0),domain(esk1_0)),domain(esk3_0)) != domain(esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_148])])]) ).
fof(c_0_154,plain,
! [X35] : domain(X35) = antidomain(antidomain(X35)),
inference(variable_rename,[status(thm)],[domain4]) ).
cnf(c_0_155,plain,
backward_diamond(X1,X2) = codomain(multiplication(codomain(X2),X1)),
inference(split_conjunct,[status(thm)],[c_0_149]) ).
cnf(c_0_156,plain,
codomain(X1) = coantidomain(coantidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_150]) ).
cnf(c_0_157,plain,
coantidomain(coantidomain(multiplication(X1,coantidomain(X1)))) = multiplication(X1,coantidomain(X1)),
inference(spm,[status(thm)],[c_0_105,c_0_38]) ).
cnf(c_0_158,plain,
coantidomain(multiplication(coantidomain(coantidomain(multiplication(X1,antidomain(X2)))),X2)) = coantidomain(multiplication(X2,coantidomain(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_68]),c_0_60]),c_0_88]) ).
cnf(c_0_159,plain,
antidomain(antidomain(X1)) = coantidomain(antidomain(X1)),
inference(rw,[status(thm)],[c_0_144,c_0_152]) ).
cnf(c_0_160,negated_conjecture,
addition(backward_diamond(esk4_0,domain(esk1_0)),domain(esk2_0)) = domain(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_153]) ).
cnf(c_0_161,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_154]) ).
cnf(c_0_162,plain,
backward_diamond(X1,X2) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(X2)),X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_155,c_0_156]),c_0_156]) ).
cnf(c_0_163,plain,
multiplication(X1,coantidomain(coantidomain(addition(X1,X2)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_100]),c_0_84]) ).
cnf(c_0_164,plain,
multiplication(coantidomain(coantidomain(multiplication(X1,antidomain(X2)))),X2) = multiplication(X2,coantidomain(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_55]),c_0_99]),c_0_158]),c_0_157]),c_0_55]),c_0_99]) ).
cnf(c_0_165,plain,
coantidomain(coantidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[c_0_152,c_0_159]) ).
cnf(c_0_166,plain,
coantidomain(antidomain(coantidomain(X1))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_130,c_0_159]),c_0_127]),c_0_159]) ).
cnf(c_0_167,negated_conjecture,
addition(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(esk1_0)))),esk4_0))),antidomain(antidomain(esk2_0))) = antidomain(antidomain(esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_160,c_0_161]),c_0_161]),c_0_161]),c_0_162]) ).
cnf(c_0_168,plain,
addition(X1,multiplication(coantidomain(X2),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_67]),c_0_83]),c_0_83]),c_0_27]) ).
cnf(c_0_169,plain,
multiplication(X1,multiplication(coantidomain(X2),coantidomain(coantidomain(X1)))) = multiplication(X1,coantidomain(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_85]),c_0_55]) ).
cnf(c_0_170,plain,
multiplication(coantidomain(multiplication(X1,antidomain(X2))),X2) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_164]),c_0_103]),c_0_84]) ).
cnf(c_0_171,plain,
antidomain(coantidomain(X1)) = coantidomain(coantidomain(X1)),
inference(spm,[status(thm)],[c_0_165,c_0_166]) ).
cnf(c_0_172,negated_conjecture,
addition(multiplication(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(esk1_0)))),esk4_0))),X1),multiplication(antidomain(antidomain(esk2_0)),X1)) = multiplication(antidomain(antidomain(esk2_0)),X1),
inference(spm,[status(thm)],[c_0_69,c_0_167]) ).
cnf(c_0_173,plain,
addition(multiplication(X1,X2),multiplication(X1,multiplication(coantidomain(X3),X2))) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_73,c_0_168]) ).
cnf(c_0_174,plain,
multiplication(X1,coantidomain(multiplication(X2,coantidomain(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_170]),c_0_95]),c_0_171]),c_0_103]) ).
cnf(c_0_175,negated_conjecture,
addition(backward_diamond(esk5_0,domain(esk2_0)),domain(esk3_0)) = domain(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_153]) ).
cnf(c_0_176,plain,
multiplication(X1,multiplication(coantidomain(coantidomain(X1)),X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_55,c_0_95]) ).
cnf(c_0_177,negated_conjecture,
multiplication(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(esk1_0)))),esk4_0))),antidomain(esk2_0)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_68]),c_0_96]),c_0_38]) ).
cnf(c_0_178,plain,
multiplication(antidomain(X1),multiplication(coantidomain(X2),X1)) = multiplication(X1,coantidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_68]),c_0_84]) ).
cnf(c_0_179,plain,
multiplication(coantidomain(addition(X1,X2)),coantidomain(X1)) = coantidomain(addition(X1,X2)),
inference(spm,[status(thm)],[c_0_174,c_0_163]) ).
cnf(c_0_180,plain,
addition(X1,addition(multiplication(X1,coantidomain(X2)),X3)) = addition(X1,X3),
inference(spm,[status(thm)],[c_0_50,c_0_92]) ).
cnf(c_0_181,negated_conjecture,
addition(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(esk2_0)))),esk5_0))),antidomain(antidomain(esk3_0))) = antidomain(antidomain(esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_175,c_0_161]),c_0_161]),c_0_161]),c_0_162]) ).
cnf(c_0_182,negated_conjecture,
multiplication(coantidomain(coantidomain(antidomain(antidomain(esk1_0)))),multiplication(esk4_0,antidomain(esk2_0))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_177]),c_0_55]),c_0_53]),c_0_53]),c_0_55]) ).
cnf(c_0_183,plain,
multiplication(coantidomain(coantidomain(X1)),coantidomain(addition(X1,X2))) = multiplication(coantidomain(X1),coantidomain(coantidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_179]),c_0_171]) ).
cnf(c_0_184,plain,
addition(coantidomain(X1),multiplication(coantidomain(coantidomain(X1)),coantidomain(X2))) = addition(coantidomain(X1),coantidomain(X2)),
inference(spm,[status(thm)],[c_0_180,c_0_94]) ).
cnf(c_0_185,plain,
multiplication(X1,coantidomain(coantidomain(multiplication(X2,coantidomain(X1))))) = multiplication(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_169,c_0_164]),c_0_103]),c_0_104]),c_0_60]),c_0_171]),c_0_103]) ).
cnf(c_0_186,plain,
multiplication(X1,coantidomain(multiplication(X2,multiplication(X3,coantidomain(X1))))) = X1,
inference(spm,[status(thm)],[c_0_174,c_0_55]) ).
cnf(c_0_187,negated_conjecture,
addition(multiplication(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(esk2_0)))),esk5_0))),X1),multiplication(antidomain(antidomain(esk3_0)),X1)) = multiplication(antidomain(antidomain(esk3_0)),X1),
inference(spm,[status(thm)],[c_0_69,c_0_181]) ).
cnf(c_0_188,negated_conjecture,
multiplication(antidomain(antidomain(esk1_0)),multiplication(esk4_0,antidomain(esk2_0))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_182]),c_0_53]) ).
cnf(c_0_189,plain,
multiplication(coantidomain(X1),coantidomain(addition(X1,X2))) = coantidomain(addition(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_183]),c_0_103]),c_0_84]) ).
cnf(c_0_190,plain,
addition(coantidomain(X1),coantidomain(addition(X1,X2))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_179]),c_0_184]),c_0_27]) ).
cnf(c_0_191,plain,
multiplication(X1,multiplication(X2,coantidomain(coantidomain(multiplication(X1,X2))))) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_55,c_0_95]) ).
cnf(c_0_192,plain,
multiplication(coantidomain(X1),coantidomain(coantidomain(multiplication(X2,coantidomain(X1))))) = coantidomain(coantidomain(multiplication(X2,coantidomain(X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_185]),c_0_103]),c_0_103]),c_0_104]),c_0_96]),c_0_103]) ).
cnf(c_0_193,plain,
multiplication(coantidomain(X1),coantidomain(multiplication(X2,X1))) = coantidomain(X1),
inference(spm,[status(thm)],[c_0_186,c_0_95]) ).
cnf(c_0_194,plain,
addition(multiplication(antidomain(addition(X1,X2)),X1),multiplication(antidomain(addition(X1,X2)),X2)) = multiplication(X2,coantidomain(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_68]),c_0_69]),c_0_100]),c_0_106]),c_0_84]) ).
cnf(c_0_195,negated_conjecture,
multiplication(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(esk2_0)))),esk5_0))),antidomain(esk3_0)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_68]),c_0_96]),c_0_38]) ).
cnf(c_0_196,negated_conjecture,
coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(antidomain(esk1_0)),esk4_0))),antidomain(esk2_0))) = coantidomain(zero),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_188]),c_0_76]) ).
cnf(c_0_197,plain,
multiplication(antidomain(X1),coantidomain(addition(coantidomain(antidomain(X1)),X2))) = coantidomain(addition(coantidomain(antidomain(X1)),X2)),
inference(spm,[status(thm)],[c_0_189,c_0_165]) ).
cnf(c_0_198,plain,
addition(coantidomain(X1),coantidomain(multiplication(X1,coantidomain(X2)))) = coantidomain(multiplication(X1,coantidomain(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_85]),c_0_27]) ).
cnf(c_0_199,plain,
multiplication(X1,coantidomain(coantidomain(multiplication(X1,coantidomain(X2))))) = multiplication(X1,coantidomain(X2)),
inference(spm,[status(thm)],[c_0_191,c_0_192]) ).
cnf(c_0_200,plain,
addition(coantidomain(X1),coantidomain(multiplication(X2,X1))) = coantidomain(multiplication(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_193]),c_0_184]) ).
cnf(c_0_201,plain,
multiplication(antidomain(addition(X1,X2)),X1) = multiplication(X2,coantidomain(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_194]),c_0_96]) ).
cnf(c_0_202,negated_conjecture,
multiplication(coantidomain(coantidomain(antidomain(antidomain(esk2_0)))),multiplication(esk5_0,antidomain(esk3_0))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_195]),c_0_55]),c_0_53]),c_0_53]),c_0_55]) ).
cnf(c_0_203,negated_conjecture,
multiplication(coantidomain(coantidomain(multiplication(antidomain(antidomain(esk1_0)),esk4_0))),antidomain(esk2_0)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_196]),c_0_55]),c_0_72]) ).
cnf(c_0_204,plain,
antidomain(multiplication(X1,coantidomain(X1))) = coantidomain(multiplication(X1,coantidomain(X1))),
inference(spm,[status(thm)],[c_0_52,c_0_38]) ).
cnf(c_0_205,plain,
coantidomain(coantidomain(multiplication(antidomain(X1),coantidomain(X2)))) = multiplication(antidomain(X1),coantidomain(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_197,c_0_198]),c_0_199]) ).
cnf(c_0_206,plain,
coantidomain(multiplication(coantidomain(coantidomain(X1)),X2)) = coantidomain(multiplication(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_200,c_0_176]),c_0_27]),c_0_87]) ).
cnf(c_0_207,plain,
multiplication(antidomain(addition(X1,X2)),X2) = multiplication(X2,coantidomain(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_194,c_0_201]),c_0_84]) ).
cnf(c_0_208,plain,
multiplication(X1,multiplication(coantidomain(X1),X2)) = multiplication(X1,coantidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_38]),c_0_55]) ).
cnf(c_0_209,negated_conjecture,
multiplication(coantidomain(antidomain(antidomain(esk2_0))),multiplication(esk5_0,antidomain(esk3_0))) = multiplication(esk5_0,antidomain(esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_202]),c_0_103]),c_0_41]) ).
cnf(c_0_210,negated_conjecture,
multiplication(coantidomain(multiplication(antidomain(antidomain(esk1_0)),esk4_0)),antidomain(esk2_0)) = antidomain(esk2_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_203]),c_0_103]),c_0_41]) ).
cnf(c_0_211,plain,
addition(coantidomain(multiplication(X1,coantidomain(X1))),antidomain(multiplication(antidomain(X1),antidomain(antidomain(multiplication(X1,X2)))))) = antidomain(multiplication(antidomain(X1),antidomain(antidomain(multiplication(X1,X2))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_77]),c_0_204]) ).
cnf(c_0_212,plain,
addition(coantidomain(multiplication(X1,coantidomain(X1))),antidomain(X2)) = coantidomain(multiplication(X1,coantidomain(X1))),
inference(spm,[status(thm)],[c_0_82,c_0_38]) ).
cnf(c_0_213,plain,
coantidomain(coantidomain(multiplication(X1,coantidomain(X2)))) = multiplication(coantidomain(coantidomain(X1)),coantidomain(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_205,c_0_171]),c_0_206]) ).
cnf(c_0_214,plain,
multiplication(antidomain(addition(X1,X2)),multiplication(X2,X3)) = multiplication(X2,coantidomain(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_207]),c_0_55]),c_0_208]) ).
cnf(c_0_215,negated_conjecture,
multiplication(antidomain(esk2_0),multiplication(esk5_0,antidomain(esk3_0))) = multiplication(esk5_0,antidomain(esk3_0)),
inference(rw,[status(thm)],[c_0_209,c_0_152]) ).
cnf(c_0_216,negated_conjecture,
addition(coantidomain(multiplication(antidomain(antidomain(esk1_0)),esk4_0)),antidomain(esk2_0)) = coantidomain(multiplication(antidomain(antidomain(esk1_0)),esk4_0)),
inference(spm,[status(thm)],[c_0_111,c_0_210]) ).
cnf(c_0_217,plain,
antidomain(multiplication(antidomain(X1),coantidomain(antidomain(multiplication(X1,X2))))) = coantidomain(multiplication(X1,coantidomain(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_211,c_0_212]),c_0_159]) ).
cnf(c_0_218,plain,
multiplication(coantidomain(multiplication(X1,coantidomain(X1))),X2) = X2,
inference(spm,[status(thm)],[c_0_83,c_0_38]) ).
cnf(c_0_219,plain,
coantidomain(coantidomain(multiplication(X1,antidomain(X2)))) = multiplication(coantidomain(coantidomain(X1)),antidomain(X2)),
inference(spm,[status(thm)],[c_0_213,c_0_165]) ).
cnf(c_0_220,negated_conjecture,
multiplication(antidomain(addition(X1,antidomain(esk2_0))),multiplication(esk5_0,antidomain(esk3_0))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_215]),c_0_38]) ).
cnf(c_0_221,negated_conjecture,
addition(coantidomain(multiplication(coantidomain(antidomain(esk1_0)),esk4_0)),antidomain(esk2_0)) = coantidomain(multiplication(coantidomain(antidomain(esk1_0)),esk4_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_216,c_0_159]),c_0_159]) ).
cnf(c_0_222,negated_conjecture,
addition(backward_diamond(multiplication(esk4_0,esk5_0),domain(esk1_0)),domain(esk3_0)) != domain(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_153]) ).
cnf(c_0_223,plain,
multiplication(antidomain(X1),coantidomain(antidomain(multiplication(X1,X2)))) = multiplication(antidomain(X1),coantidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_217]),c_0_218]),c_0_55]),c_0_89]) ).
cnf(c_0_224,plain,
coantidomain(coantidomain(multiplication(X1,multiplication(X2,antidomain(X3))))) = multiplication(coantidomain(coantidomain(multiplication(X1,X2))),antidomain(X3)),
inference(spm,[status(thm)],[c_0_219,c_0_55]) ).
cnf(c_0_225,negated_conjecture,
multiplication(coantidomain(coantidomain(multiplication(coantidomain(antidomain(esk1_0)),esk4_0))),multiplication(esk5_0,antidomain(esk3_0))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_220,c_0_221]),c_0_171]) ).
cnf(c_0_226,negated_conjecture,
addition(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(esk1_0)))),multiplication(esk4_0,esk5_0)))),antidomain(antidomain(esk3_0))) != antidomain(antidomain(esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_222,c_0_161]),c_0_161]),c_0_161]),c_0_162]) ).
cnf(c_0_227,plain,
multiplication(antidomain(X1),antidomain(multiplication(X1,X2))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_223]),c_0_165]),c_0_84]) ).
cnf(c_0_228,negated_conjecture,
multiplication(coantidomain(coantidomain(multiplication(coantidomain(antidomain(esk1_0)),multiplication(esk4_0,esk5_0)))),antidomain(esk3_0)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_224,c_0_225]),c_0_105]),c_0_206]),c_0_55]) ).
cnf(c_0_229,negated_conjecture,
addition(coantidomain(coantidomain(multiplication(antidomain(antidomain(esk1_0)),multiplication(esk4_0,esk5_0)))),antidomain(antidomain(esk3_0))) != antidomain(antidomain(esk3_0)),
inference(rw,[status(thm)],[c_0_226,c_0_144]) ).
cnf(c_0_230,plain,
addition(antidomain(X1),antidomain(multiplication(X1,X2))) = antidomain(multiplication(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_227]),c_0_27]) ).
cnf(c_0_231,negated_conjecture,
multiplication(coantidomain(multiplication(coantidomain(antidomain(esk1_0)),multiplication(esk4_0,esk5_0))),antidomain(esk3_0)) = antidomain(esk3_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_228]),c_0_103]),c_0_41]) ).
cnf(c_0_232,negated_conjecture,
addition(coantidomain(coantidomain(multiplication(coantidomain(antidomain(esk1_0)),multiplication(esk4_0,esk5_0)))),coantidomain(antidomain(esk3_0))) != coantidomain(antidomain(esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_229,c_0_159]),c_0_159]),c_0_159]) ).
cnf(c_0_233,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_230,c_0_231]),c_0_171]),c_0_159]),c_0_159]),c_0_232]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KLE121+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : enigmatic-eprover.py %s %d 1
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Thu Jun 16 08:25:43 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.46 # ENIGMATIC: Selected SinE mode:
% 0.21/0.47 # Parsing /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.47 # Filter: axfilter_auto 0 goes into file theBenchmark_axfilter_auto 0.p
% 0.21/0.47 # Filter: axfilter_auto 1 goes into file theBenchmark_axfilter_auto 1.p
% 0.21/0.47 # Filter: axfilter_auto 2 goes into file theBenchmark_axfilter_auto 2.p
% 120.59/16.66 # ENIGMATIC: Solved by autoschedule:
% 120.59/16.66 # No SInE strategy applied
% 120.59/16.66 # Trying AutoSched0 for 150 seconds
% 120.59/16.66 # AutoSched0-Mode selected heuristic H_____042_B03_F1_AE_Q4_SP_S2S
% 120.59/16.66 # and selection function SelectNewComplexAHP.
% 120.59/16.66 #
% 120.59/16.66 # Preprocessing time : 0.025 s
% 120.59/16.66
% 120.59/16.66 # Proof found!
% 120.59/16.66 # SZS status Theorem
% 120.59/16.66 # SZS output start CNFRefutation
% See solution above
% 120.59/16.66 # Training examples: 0 positive, 29 negative
% 120.59/16.66
% 120.59/16.66 # -------------------------------------------------
% 120.59/16.66 # User time : 13.719 s
% 120.59/16.66 # System time : 0.521 s
% 120.59/16.66 # Total time : 14.240 s
% 120.59/16.66 # Maximum resident set size: 7124 pages
% 120.59/16.66
%------------------------------------------------------------------------------