TSTP Solution File: KLE108+1 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : KLE108+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% 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 : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 01:55:55 EDT 2022
% Result : Theorem 0.62s 52.80s
% Output : CNFRefutation 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 24
% Syntax : Number of formulae : 190 ( 187 unt; 0 def)
% Number of atoms : 193 ( 192 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 6 ~; 0 |; 1 &)
% ( 0 <=>; 0 =>; 2 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 17 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-2 aty)
% Number of variables : 181 ( 10 sgn 80 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(complement,axiom,
! [X4] : c(X4) = antidomain(domain(X4)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax',complement) ).
fof(domain4,axiom,
! [X4] : domain(X4) = antidomain(antidomain(X4)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain4) ).
fof(forward_diamond,axiom,
! [X4,X5] : forward_diamond(X4,X5) = domain(multiplication(X4,domain(X5))),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax',forward_diamond) ).
fof(goals,conjecture,
! [X4,X5,X6] :
( addition(backward_diamond(X4,domain(X5)),domain(X6)) = domain(X6)
<= addition(domain(X5),forward_box(X4,domain(X6))) = forward_box(X4,domain(X6)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',goals) ).
fof(forward_box,axiom,
! [X4,X5] : forward_box(X4,X5) = c(forward_diamond(X4,c(X5))),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax',forward_box) ).
fof(domain1,axiom,
! [X4] : multiplication(antidomain(X4),X4) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain1) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(domain3,axiom,
! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain3) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(domain2,axiom,
! [X4,X5] : addition(antidomain(multiplication(X4,X5)),antidomain(multiplication(X4,antidomain(antidomain(X5))))) = antidomain(multiplication(X4,antidomain(antidomain(X5)))),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain2) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(codomain3,axiom,
! [X4] : addition(coantidomain(coantidomain(X4)),coantidomain(X4)) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',codomain3) ).
fof(codomain1,axiom,
! [X4] : multiplication(X4,coantidomain(X4)) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',codomain1) ).
fof(codomain2,axiom,
! [X4,X5] : addition(coantidomain(multiplication(X4,X5)),coantidomain(multiplication(coantidomain(coantidomain(X4)),X5))) = coantidomain(multiplication(coantidomain(coantidomain(X4)),X5)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',codomain2) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(backward_diamond,axiom,
! [X4,X5] : backward_diamond(X4,X5) = codomain(multiplication(codomain(X5),X4)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax',backward_diamond) ).
fof(codomain4,axiom,
! [X4] : codomain(X4) = coantidomain(coantidomain(X4)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',codomain4) ).
fof(c_0_24,plain,
! [X5] : c(X5) = antidomain(domain(X5)),
inference(variable_rename,[status(thm)],[complement]) ).
fof(c_0_25,plain,
! [X5] : domain(X5) = antidomain(antidomain(X5)),
inference(variable_rename,[status(thm)],[domain4]) ).
fof(c_0_26,plain,
! [X6,X7] : forward_diamond(X6,X7) = domain(multiplication(X6,domain(X7))),
inference(variable_rename,[status(thm)],[forward_diamond]) ).
fof(c_0_27,negated_conjecture,
~ ! [X4,X5,X6] :
( addition(backward_diamond(X4,domain(X5)),domain(X6)) = domain(X6)
<= addition(domain(X5),forward_box(X4,domain(X6))) = forward_box(X4,domain(X6)) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_28,plain,
! [X6,X7] : forward_box(X6,X7) = c(forward_diamond(X6,c(X7))),
inference(variable_rename,[status(thm)],[forward_box]) ).
cnf(c_0_29,plain,
c(X1) = antidomain(domain(X1)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
forward_diamond(X1,X2) = domain(multiplication(X1,domain(X2))),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_32,plain,
! [X5] : multiplication(antidomain(X5),X5) = zero,
inference(variable_rename,[status(thm)],[domain1]) ).
fof(c_0_33,plain,
! [X4,X5,X6] : multiplication(X4,addition(X5,X6)) = addition(multiplication(X4,X5),multiplication(X4,X6)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_34,negated_conjecture,
( addition(domain(esk2_0),forward_box(esk1_0,domain(esk3_0))) = forward_box(esk1_0,domain(esk3_0))
& addition(backward_diamond(esk1_0,domain(esk2_0)),domain(esk3_0)) != domain(esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_27])])])]) ).
cnf(c_0_35,plain,
forward_box(X1,X2) = c(forward_diamond(X1,c(X2))),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_36,plain,
c(X1) = antidomain(antidomain(antidomain(X1))),
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_37,plain,
forward_diamond(X1,X2) = antidomain(antidomain(multiplication(X1,antidomain(antidomain(X2))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_30]),c_0_30]) ).
fof(c_0_38,plain,
! [X5] : addition(antidomain(antidomain(X5)),antidomain(X5)) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
fof(c_0_39,plain,
! [X3,X4] : addition(X3,X4) = addition(X4,X3),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_40,plain,
! [X2] : multiplication(X2,one) = X2,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_41,plain,
! [X2] : addition(X2,zero) = X2,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_42,plain,
! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_43,plain,
! [X2] : addition(X2,X2) = X2,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_44,plain,
multiplication(antidomain(X1),X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_45,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_46,negated_conjecture,
addition(domain(esk2_0),forward_box(esk1_0,domain(esk3_0))) = forward_box(esk1_0,domain(esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_47,plain,
forward_box(X1,X2) = antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(X1,antidomain(antidomain(antidomain(antidomain(antidomain(X2))))))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36]),c_0_36]),c_0_37]) ).
cnf(c_0_48,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_49,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_50,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_51,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_52,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_53,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_43]) ).
fof(c_0_54,plain,
! [X6,X7] : addition(antidomain(multiplication(X6,X7)),antidomain(multiplication(X6,antidomain(antidomain(X7))))) = antidomain(multiplication(X6,antidomain(antidomain(X7)))),
inference(variable_rename,[status(thm)],[domain2]) ).
cnf(c_0_55,plain,
addition(multiplication(antidomain(addition(X1,X2)),X1),multiplication(antidomain(addition(X1,X2)),X2)) = zero,
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_56,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk3_0)))))))))))))) = antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk3_0))))))))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_30]),c_0_30]),c_0_30]),c_0_47]),c_0_47]) ).
cnf(c_0_57,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_58,plain,
antidomain(one) = zero,
inference(spm,[status(thm)],[c_0_50,c_0_44]) ).
cnf(c_0_59,plain,
addition(zero,X1) = X1,
inference(pm,[status(thm)],[c_0_51,c_0_49]) ).
cnf(c_0_60,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
fof(c_0_61,plain,
! [X4,X5,X6] : multiplication(addition(X4,X5),X6) = addition(multiplication(X4,X6),multiplication(X5,X6)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_62,plain,
! [X2] : multiplication(one,X2) = X2,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_63,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_54]) ).
cnf(c_0_64,negated_conjecture,
multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk3_0)))))))))))))),antidomain(antidomain(esk2_0))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_44]),c_0_51]) ).
cnf(c_0_65,plain,
antidomain(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]) ).
cnf(c_0_66,plain,
addition(one,antidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_57]),c_0_49]) ).
cnf(c_0_67,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_68,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_69,negated_conjecture,
antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk3_0)))))))))))))),antidomain(antidomain(antidomain(antidomain(esk2_0)))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]),c_0_66]) ).
cnf(c_0_70,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),addition(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk3_0))))))))))))),X1)) = addition(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk3_0))))))))))))),X1),
inference(spm,[status(thm)],[c_0_52,c_0_56]) ).
cnf(c_0_71,plain,
addition(multiplication(antidomain(X1),X2),multiplication(antidomain(antidomain(X1)),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_57]),c_0_68]) ).
cnf(c_0_72,negated_conjecture,
multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk3_0)))))))))))))),antidomain(antidomain(antidomain(antidomain(esk2_0))))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_69]),c_0_68]) ).
fof(c_0_73,plain,
! [X5] : addition(coantidomain(coantidomain(X5)),coantidomain(X5)) = one,
inference(variable_rename,[status(thm)],[codomain3]) ).
fof(c_0_74,plain,
! [X5] : multiplication(X5,coantidomain(X5)) = zero,
inference(variable_rename,[status(thm)],[codomain1]) ).
fof(c_0_75,plain,
! [X6,X7] : addition(coantidomain(multiplication(X6,X7)),coantidomain(multiplication(coantidomain(coantidomain(X6)),X7))) = coantidomain(multiplication(coantidomain(coantidomain(X6)),X7)),
inference(variable_rename,[status(thm)],[codomain2]) ).
fof(c_0_76,plain,
! [X4,X5,X6] : multiplication(X4,multiplication(X5,X6)) = multiplication(multiplication(X4,X5),X6),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_77,negated_conjecture,
addition(multiplication(antidomain(antidomain(esk2_0)),X1),addition(multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk3_0))))))))))))),X1),multiplication(X2,X1))) = addition(multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk3_0))))))))))))),X1),multiplication(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_70]),c_0_67]),c_0_67]) ).
cnf(c_0_78,negated_conjecture,
multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk3_0))))))))))))),antidomain(antidomain(antidomain(antidomain(esk2_0))))) = antidomain(antidomain(antidomain(antidomain(esk2_0)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_51]) ).
cnf(c_0_79,plain,
addition(coantidomain(coantidomain(X1)),coantidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_80,plain,
multiplication(X1,coantidomain(X1)) = zero,
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_81,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_82,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_83,negated_conjecture,
addition(antidomain(antidomain(antidomain(antidomain(esk2_0)))),multiplication(antidomain(antidomain(esk2_0)),antidomain(antidomain(antidomain(antidomain(esk2_0)))))) = antidomain(antidomain(antidomain(antidomain(esk2_0)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_78]),c_0_53]),c_0_78]),c_0_53]),c_0_49]) ).
cnf(c_0_84,plain,
addition(coantidomain(X1),coantidomain(coantidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_79,c_0_49]) ).
cnf(c_0_85,plain,
coantidomain(one) = zero,
inference(spm,[status(thm)],[c_0_68,c_0_80]) ).
cnf(c_0_86,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_81,c_0_82]) ).
cnf(c_0_87,negated_conjecture,
multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(esk2_0))))),multiplication(antidomain(antidomain(esk2_0)),antidomain(antidomain(antidomain(antidomain(esk2_0)))))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_83]),c_0_44]),c_0_59]) ).
cnf(c_0_88,plain,
coantidomain(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_59]) ).
cnf(c_0_89,plain,
addition(one,coantidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_84]),c_0_49]) ).
cnf(c_0_90,negated_conjecture,
coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(esk2_0))))),antidomain(antidomain(esk2_0))))),antidomain(antidomain(antidomain(antidomain(esk2_0)))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_88]),c_0_89]) ).
cnf(c_0_91,plain,
addition(multiplication(coantidomain(X1),X2),multiplication(coantidomain(coantidomain(X1)),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_84]),c_0_68]) ).
cnf(c_0_92,negated_conjecture,
multiplication(coantidomain(coantidomain(multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(esk2_0))))),antidomain(antidomain(esk2_0))))),antidomain(antidomain(antidomain(antidomain(esk2_0))))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_90]),c_0_82]),c_0_50]) ).
cnf(c_0_93,plain,
addition(X1,multiplication(X1,antidomain(X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_66]),c_0_50]),c_0_50]) ).
cnf(c_0_94,negated_conjecture,
multiplication(coantidomain(multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(esk2_0))))),antidomain(antidomain(esk2_0)))),antidomain(antidomain(antidomain(antidomain(esk2_0))))) = antidomain(antidomain(antidomain(antidomain(esk2_0)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_51]) ).
cnf(c_0_95,plain,
addition(antidomain(X1),antidomain(antidomain(antidomain(X1)))) = antidomain(antidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_68]),c_0_68]) ).
cnf(c_0_96,plain,
addition(multiplication(X1,coantidomain(addition(X1,X2))),multiplication(X2,coantidomain(addition(X1,X2)))) = zero,
inference(spm,[status(thm)],[c_0_80,c_0_67]) ).
cnf(c_0_97,negated_conjecture,
addition(antidomain(antidomain(antidomain(antidomain(esk2_0)))),coantidomain(multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(esk2_0))))),antidomain(antidomain(esk2_0))))) = coantidomain(multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(esk2_0))))),antidomain(antidomain(esk2_0)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_49]) ).
cnf(c_0_98,plain,
addition(multiplication(antidomain(X1),X2),multiplication(antidomain(antidomain(antidomain(X1))),X2)) = multiplication(antidomain(antidomain(antidomain(X1))),X2),
inference(spm,[status(thm)],[c_0_67,c_0_95]) ).
cnf(c_0_99,negated_conjecture,
multiplication(antidomain(antidomain(antidomain(antidomain(esk2_0)))),coantidomain(coantidomain(multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(esk2_0))))),antidomain(antidomain(esk2_0)))))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_80]),c_0_51]) ).
cnf(c_0_100,plain,
addition(multiplication(X1,antidomain(X2)),multiplication(X1,antidomain(antidomain(X2)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_57]),c_0_50]) ).
cnf(c_0_101,plain,
addition(multiplication(X1,coantidomain(X2)),multiplication(X1,coantidomain(coantidomain(X2)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_84]),c_0_50]) ).
cnf(c_0_102,negated_conjecture,
multiplication(antidomain(antidomain(esk2_0)),coantidomain(coantidomain(multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(esk2_0))))),antidomain(antidomain(esk2_0)))))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_51]) ).
cnf(c_0_103,plain,
addition(X1,multiplication(coantidomain(X2),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_89]),c_0_68]),c_0_68]) ).
cnf(c_0_104,negated_conjecture,
multiplication(coantidomain(coantidomain(multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(esk2_0))))),antidomain(antidomain(esk2_0))))),antidomain(antidomain(antidomain(esk2_0)))) = coantidomain(coantidomain(multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(esk2_0))))),antidomain(antidomain(esk2_0))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_92]),c_0_51]) ).
cnf(c_0_105,plain,
multiplication(X1,multiplication(X2,coantidomain(multiplication(X1,X2)))) = zero,
inference(spm,[status(thm)],[c_0_80,c_0_82]) ).
cnf(c_0_106,negated_conjecture,
multiplication(antidomain(antidomain(esk2_0)),coantidomain(multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(esk2_0))))),antidomain(antidomain(esk2_0))))) = antidomain(antidomain(esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_51]) ).
cnf(c_0_107,negated_conjecture,
antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(esk2_0))))),antidomain(antidomain(multiplication(antidomain(antidomain(esk2_0)),antidomain(antidomain(antidomain(antidomain(esk2_0))))))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_87]),c_0_65]),c_0_66]) ).
fof(c_0_108,plain,
! [X2] : multiplication(zero,X2) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_109,negated_conjecture,
addition(antidomain(antidomain(antidomain(esk2_0))),coantidomain(coantidomain(multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(esk2_0))))),antidomain(antidomain(esk2_0)))))) = antidomain(antidomain(antidomain(esk2_0))),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_110,negated_conjecture,
multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(esk2_0))))),antidomain(antidomain(esk2_0))) = zero,
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_111,negated_conjecture,
multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(esk2_0))))),antidomain(antidomain(multiplication(antidomain(antidomain(esk2_0)),antidomain(antidomain(antidomain(antidomain(esk2_0)))))))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_107]),c_0_68]) ).
cnf(c_0_112,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_113,negated_conjecture,
multiplication(coantidomain(coantidomain(multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(esk2_0))))),antidomain(antidomain(esk2_0))))),coantidomain(antidomain(antidomain(antidomain(esk2_0))))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_109]),c_0_80]),c_0_59]) ).
cnf(c_0_114,negated_conjecture,
multiplication(antidomain(antidomain(antidomain(antidomain(esk2_0)))),antidomain(antidomain(esk2_0))) = antidomain(antidomain(esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_110]),c_0_51]) ).
cnf(c_0_115,plain,
addition(X1,multiplication(antidomain(X2),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_66]),c_0_68]),c_0_68]) ).
cnf(c_0_116,negated_conjecture,
multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(esk2_0))))),antidomain(multiplication(antidomain(antidomain(esk2_0)),antidomain(antidomain(antidomain(antidomain(esk2_0))))))) = antidomain(antidomain(antidomain(antidomain(antidomain(esk2_0))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_111]),c_0_51]) ).
cnf(c_0_117,plain,
multiplication(X1,multiplication(coantidomain(X1),X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_80]),c_0_112]) ).
cnf(c_0_118,negated_conjecture,
multiplication(coantidomain(multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(esk2_0))))),antidomain(antidomain(esk2_0)))),coantidomain(antidomain(antidomain(antidomain(esk2_0))))) = coantidomain(antidomain(antidomain(antidomain(esk2_0)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_113]),c_0_51]) ).
cnf(c_0_119,negated_conjecture,
antidomain(antidomain(antidomain(antidomain(esk2_0)))) = antidomain(antidomain(esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_114]),c_0_44]),c_0_51]) ).
cnf(c_0_120,plain,
addition(antidomain(X1),addition(antidomain(antidomain(antidomain(X1))),X2)) = addition(antidomain(antidomain(antidomain(X1))),X2),
inference(spm,[status(thm)],[c_0_52,c_0_95]) ).
cnf(c_0_121,negated_conjecture,
addition(antidomain(antidomain(antidomain(antidomain(antidomain(esk2_0))))),antidomain(multiplication(antidomain(antidomain(esk2_0)),antidomain(antidomain(antidomain(antidomain(esk2_0))))))) = antidomain(multiplication(antidomain(antidomain(esk2_0)),antidomain(antidomain(antidomain(antidomain(esk2_0)))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_49]) ).
cnf(c_0_122,negated_conjecture,
multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(esk2_0))))),multiplication(antidomain(antidomain(esk2_0)),coantidomain(antidomain(antidomain(antidomain(esk2_0)))))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_82]) ).
cnf(c_0_123,negated_conjecture,
multiplication(antidomain(antidomain(esk2_0)),antidomain(antidomain(antidomain(esk2_0)))) = zero,
inference(spm,[status(thm)],[c_0_44,c_0_119]) ).
cnf(c_0_124,negated_conjecture,
addition(antidomain(antidomain(antidomain(esk2_0))),antidomain(multiplication(antidomain(antidomain(esk2_0)),antidomain(antidomain(antidomain(antidomain(esk2_0))))))) = antidomain(multiplication(antidomain(antidomain(esk2_0)),antidomain(antidomain(antidomain(antidomain(esk2_0)))))),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_125,negated_conjecture,
antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(esk2_0))))),antidomain(antidomain(multiplication(antidomain(antidomain(esk2_0)),coantidomain(antidomain(antidomain(antidomain(esk2_0))))))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_122]),c_0_65]),c_0_66]) ).
cnf(c_0_126,negated_conjecture,
multiplication(antidomain(esk2_0),antidomain(antidomain(antidomain(esk2_0)))) = antidomain(antidomain(antidomain(esk2_0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_123]),c_0_51]) ).
cnf(c_0_127,negated_conjecture,
addition(antidomain(esk2_0),antidomain(multiplication(antidomain(antidomain(esk2_0)),antidomain(antidomain(antidomain(antidomain(esk2_0))))))) = antidomain(multiplication(antidomain(antidomain(esk2_0)),antidomain(antidomain(antidomain(antidomain(esk2_0)))))),
inference(spm,[status(thm)],[c_0_120,c_0_124]) ).
cnf(c_0_128,negated_conjecture,
multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(esk2_0))))),antidomain(antidomain(multiplication(antidomain(antidomain(esk2_0)),coantidomain(antidomain(antidomain(antidomain(esk2_0)))))))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_125]),c_0_68]) ).
cnf(c_0_129,negated_conjecture,
addition(multiplication(antidomain(antidomain(esk2_0)),X1),multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk3_0))))))))))))),X1)) = multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk3_0))))))))))))),X1),
inference(spm,[status(thm)],[c_0_67,c_0_56]) ).
cnf(c_0_130,plain,
coantidomain(multiplication(coantidomain(coantidomain(antidomain(X1))),X1)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_44]),c_0_88]),c_0_89]) ).
cnf(c_0_131,negated_conjecture,
antidomain(antidomain(antidomain(esk2_0))) = antidomain(esk2_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_126]),c_0_95]) ).
cnf(c_0_132,negated_conjecture,
multiplication(antidomain(esk2_0),coantidomain(antidomain(multiplication(antidomain(antidomain(esk2_0)),antidomain(antidomain(antidomain(antidomain(esk2_0)))))))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_127]),c_0_80]),c_0_51]) ).
cnf(c_0_133,negated_conjecture,
multiplication(antidomain(antidomain(antidomain(antidomain(esk2_0)))),antidomain(antidomain(multiplication(antidomain(antidomain(esk2_0)),coantidomain(antidomain(antidomain(antidomain(esk2_0)))))))) = antidomain(antidomain(multiplication(antidomain(antidomain(esk2_0)),coantidomain(antidomain(antidomain(antidomain(esk2_0))))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_128]),c_0_51]) ).
cnf(c_0_134,negated_conjecture,
multiplication(antidomain(antidomain(esk2_0)),antidomain(antidomain(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk3_0))))))))))))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_44]),c_0_51]) ).
cnf(c_0_135,negated_conjecture,
coantidomain(multiplication(coantidomain(coantidomain(antidomain(esk2_0))),antidomain(antidomain(esk2_0)))) = one,
inference(spm,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_136,plain,
addition(X1,multiplication(X1,coantidomain(X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_89]),c_0_50]),c_0_50]) ).
cnf(c_0_137,negated_conjecture,
multiplication(antidomain(antidomain(esk2_0)),coantidomain(antidomain(multiplication(antidomain(antidomain(esk2_0)),antidomain(antidomain(antidomain(antidomain(esk2_0)))))))) = coantidomain(antidomain(multiplication(antidomain(antidomain(esk2_0)),antidomain(antidomain(antidomain(antidomain(esk2_0))))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_132]),c_0_59]) ).
cnf(c_0_138,negated_conjecture,
addition(antidomain(antidomain(antidomain(antidomain(esk2_0)))),antidomain(antidomain(multiplication(antidomain(antidomain(esk2_0)),coantidomain(antidomain(antidomain(antidomain(esk2_0)))))))) = antidomain(antidomain(antidomain(antidomain(esk2_0)))),
inference(spm,[status(thm)],[c_0_93,c_0_133]) ).
cnf(c_0_139,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(pm,[status(thm)],[c_0_52,c_0_49]),c_0_52]) ).
cnf(c_0_140,negated_conjecture,
multiplication(antidomain(esk2_0),antidomain(antidomain(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk3_0))))))))))))) = antidomain(antidomain(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk3_0)))))))))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_134]),c_0_51]) ).
cnf(c_0_141,negated_conjecture,
multiplication(coantidomain(coantidomain(antidomain(esk2_0))),antidomain(antidomain(esk2_0))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_135]),c_0_82]),c_0_50]) ).
cnf(c_0_142,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),coantidomain(antidomain(multiplication(antidomain(antidomain(esk2_0)),antidomain(antidomain(antidomain(antidomain(esk2_0)))))))) = antidomain(antidomain(esk2_0)),
inference(spm,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_143,negated_conjecture,
multiplication(antidomain(antidomain(esk2_0)),antidomain(antidomain(esk2_0))) = antidomain(antidomain(esk2_0)),
inference(rw,[status(thm)],[c_0_114,c_0_119]) ).
cnf(c_0_144,negated_conjecture,
multiplication(antidomain(antidomain(multiplication(antidomain(antidomain(esk2_0)),coantidomain(antidomain(antidomain(antidomain(esk2_0))))))),coantidomain(antidomain(antidomain(antidomain(antidomain(esk2_0)))))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_138]),c_0_80]),c_0_59]) ).
cnf(c_0_145,plain,
addition(antidomain(X1),addition(X2,antidomain(antidomain(antidomain(X1))))) = addition(X2,antidomain(antidomain(antidomain(X1)))),
inference(spm,[status(thm)],[c_0_139,c_0_95]) ).
cnf(c_0_146,negated_conjecture,
addition(antidomain(esk2_0),antidomain(antidomain(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk3_0))))))))))))) = antidomain(esk2_0),
inference(spm,[status(thm)],[c_0_93,c_0_140]) ).
cnf(c_0_147,negated_conjecture,
multiplication(coantidomain(antidomain(esk2_0)),antidomain(antidomain(esk2_0))) = antidomain(antidomain(esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_141]),c_0_51]) ).
cnf(c_0_148,negated_conjecture,
addition(coantidomain(antidomain(esk2_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_142,c_0_119]),c_0_143]),c_0_131]),c_0_49]) ).
cnf(c_0_149,plain,
addition(multiplication(antidomain(multiplication(X1,X2)),X3),multiplication(antidomain(multiplication(X1,antidomain(antidomain(X2)))),X3)) = multiplication(antidomain(multiplication(X1,antidomain(antidomain(X2)))),X3),
inference(spm,[status(thm)],[c_0_67,c_0_63]) ).
cnf(c_0_150,negated_conjecture,
multiplication(antidomain(multiplication(antidomain(antidomain(esk2_0)),coantidomain(antidomain(antidomain(antidomain(esk2_0)))))),coantidomain(antidomain(antidomain(antidomain(antidomain(esk2_0)))))) = coantidomain(antidomain(antidomain(antidomain(antidomain(esk2_0))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_144]),c_0_51]) ).
cnf(c_0_151,negated_conjecture,
multiplication(antidomain(esk2_0),coantidomain(coantidomain(antidomain(multiplication(antidomain(antidomain(esk2_0)),antidomain(antidomain(antidomain(antidomain(esk2_0))))))))) = antidomain(esk2_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_132]),c_0_59]) ).
fof(c_0_152,plain,
! [X2] : multiplication(X2,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
cnf(c_0_153,negated_conjecture,
addition(antidomain(esk2_0),antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk3_0))))))))))) = antidomain(esk2_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_49]) ).
cnf(c_0_154,negated_conjecture,
antidomain(antidomain(esk2_0)) = coantidomain(antidomain(esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_147]),c_0_148]) ).
cnf(c_0_155,negated_conjecture,
multiplication(antidomain(multiplication(antidomain(antidomain(esk2_0)),antidomain(antidomain(coantidomain(antidomain(antidomain(antidomain(esk2_0)))))))),coantidomain(antidomain(antidomain(antidomain(antidomain(esk2_0)))))) = coantidomain(antidomain(antidomain(antidomain(antidomain(esk2_0))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_115]) ).
cnf(c_0_156,negated_conjecture,
multiplication(antidomain(antidomain(esk2_0)),coantidomain(antidomain(esk2_0))) = coantidomain(antidomain(esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_137,c_0_119]),c_0_119]),c_0_143]),c_0_131]),c_0_143]),c_0_131]) ).
cnf(c_0_157,negated_conjecture,
addition(antidomain(esk2_0),coantidomain(coantidomain(antidomain(multiplication(antidomain(antidomain(esk2_0)),antidomain(antidomain(antidomain(antidomain(esk2_0))))))))) = coantidomain(coantidomain(antidomain(multiplication(antidomain(antidomain(esk2_0)),antidomain(antidomain(antidomain(antidomain(esk2_0)))))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_151]),c_0_49]) ).
cnf(c_0_158,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_152]) ).
cnf(c_0_159,negated_conjecture,
multiplication(coantidomain(antidomain(esk2_0)),antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk3_0))))))))))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_153]),c_0_44]),c_0_59]),c_0_154]) ).
cnf(c_0_160,negated_conjecture,
addition(coantidomain(antidomain(antidomain(antidomain(antidomain(esk2_0))))),antidomain(multiplication(antidomain(antidomain(esk2_0)),antidomain(antidomain(coantidomain(antidomain(antidomain(antidomain(esk2_0))))))))) = antidomain(multiplication(antidomain(antidomain(esk2_0)),antidomain(antidomain(coantidomain(antidomain(antidomain(antidomain(esk2_0)))))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_155]),c_0_49]) ).
cnf(c_0_161,negated_conjecture,
antidomain(coantidomain(antidomain(esk2_0))) = antidomain(esk2_0),
inference(rw,[status(thm)],[c_0_131,c_0_154]) ).
cnf(c_0_162,negated_conjecture,
multiplication(coantidomain(antidomain(esk2_0)),coantidomain(antidomain(esk2_0))) = coantidomain(antidomain(esk2_0)),
inference(rw,[status(thm)],[c_0_156,c_0_154]) ).
cnf(c_0_163,negated_conjecture,
addition(antidomain(esk2_0),coantidomain(coantidomain(antidomain(esk2_0)))) = coantidomain(coantidomain(antidomain(esk2_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_157,c_0_119]),c_0_119]),c_0_143]),c_0_131]),c_0_143]),c_0_131]) ).
cnf(c_0_164,plain,
coantidomain(multiplication(coantidomain(coantidomain(multiplication(X1,antidomain(X2)))),X2)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_44]),c_0_158]),c_0_88]),c_0_89]) ).
cnf(c_0_165,negated_conjecture,
multiplication(coantidomain(antidomain(esk2_0)),antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk3_0)))))))))) = coantidomain(antidomain(esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_159]),c_0_51]) ).
cnf(c_0_166,negated_conjecture,
coantidomain(coantidomain(antidomain(esk2_0))) = antidomain(esk2_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[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)],[c_0_160,c_0_119]),c_0_154]),c_0_154]),c_0_154]),c_0_161]),c_0_161]),c_0_154]),c_0_162]),c_0_161]),c_0_49]),c_0_163]),c_0_154]),c_0_154]),c_0_161]),c_0_161]),c_0_154]),c_0_162]),c_0_161]) ).
cnf(c_0_167,negated_conjecture,
coantidomain(multiplication(coantidomain(antidomain(esk2_0)),multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk3_0)))))))))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_165]),c_0_166]) ).
cnf(c_0_168,plain,
multiplication(antidomain(antidomain(X1)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_44]),c_0_59]) ).
fof(c_0_169,plain,
! [X6,X7] : backward_diamond(X6,X7) = codomain(multiplication(codomain(X7),X6)),
inference(variable_rename,[status(thm)],[backward_diamond]) ).
fof(c_0_170,plain,
! [X5] : codomain(X5) = coantidomain(coantidomain(X5)),
inference(variable_rename,[status(thm)],[codomain4]) ).
cnf(c_0_171,negated_conjecture,
multiplication(coantidomain(antidomain(esk2_0)),multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk3_0))))))))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_167]),c_0_82]),c_0_82]),c_0_50]) ).
cnf(c_0_172,plain,
antidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_44]),c_0_51]),c_0_168]) ).
cnf(c_0_173,plain,
backward_diamond(X1,X2) = codomain(multiplication(codomain(X2),X1)),
inference(split_conjunct,[status(thm)],[c_0_169]) ).
cnf(c_0_174,plain,
codomain(X1) = coantidomain(coantidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_170]) ).
cnf(c_0_175,negated_conjecture,
multiplication(antidomain(esk2_0),coantidomain(coantidomain(coantidomain(antidomain(esk2_0))))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_163]),c_0_80]),c_0_51]) ).
cnf(c_0_176,negated_conjecture,
multiplication(coantidomain(antidomain(esk2_0)),multiplication(esk1_0,antidomain(esk3_0))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_171,c_0_172]),c_0_172]),c_0_172]) ).
cnf(c_0_177,negated_conjecture,
addition(backward_diamond(esk1_0,domain(esk2_0)),domain(esk3_0)) != domain(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_178,plain,
backward_diamond(X1,X2) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(X2)),X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_173,c_0_174]),c_0_174]) ).
cnf(c_0_179,negated_conjecture,
multiplication(antidomain(antidomain(esk2_0)),coantidomain(coantidomain(coantidomain(antidomain(esk2_0))))) = coantidomain(coantidomain(coantidomain(antidomain(esk2_0)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_175]),c_0_59]) ).
cnf(c_0_180,negated_conjecture,
coantidomain(multiplication(coantidomain(coantidomain(multiplication(coantidomain(antidomain(esk2_0)),esk1_0))),antidomain(esk3_0))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_176]),c_0_88]),c_0_89]) ).
cnf(c_0_181,negated_conjecture,
addition(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(esk2_0)))),esk1_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_177,c_0_30]),c_0_30]),c_0_30]),c_0_178]) ).
cnf(c_0_182,negated_conjecture,
addition(coantidomain(coantidomain(coantidomain(antidomain(esk2_0)))),antidomain(antidomain(esk2_0))) = antidomain(antidomain(esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_179]),c_0_49]) ).
cnf(c_0_183,plain,
addition(coantidomain(X1),coantidomain(coantidomain(coantidomain(X1)))) = coantidomain(coantidomain(coantidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_50]),c_0_50]) ).
cnf(c_0_184,negated_conjecture,
multiplication(coantidomain(coantidomain(multiplication(coantidomain(antidomain(esk2_0)),esk1_0))),antidomain(esk3_0)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_180]),c_0_82]),c_0_50]) ).
cnf(c_0_185,negated_conjecture,
addition(antidomain(antidomain(esk3_0)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(esk2_0)))),esk1_0)))) != antidomain(antidomain(esk3_0)),
inference(rw,[status(thm)],[c_0_181,c_0_49]) ).
cnf(c_0_186,negated_conjecture,
coantidomain(coantidomain(coantidomain(antidomain(esk2_0)))) = coantidomain(antidomain(esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_182,c_0_154]),c_0_49]),c_0_183]),c_0_154]) ).
cnf(c_0_187,negated_conjecture,
multiplication(coantidomain(coantidomain(multiplication(coantidomain(antidomain(esk2_0)),esk1_0))),antidomain(antidomain(esk3_0))) = coantidomain(coantidomain(multiplication(coantidomain(antidomain(esk2_0)),esk1_0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_184]),c_0_59]) ).
cnf(c_0_188,negated_conjecture,
addition(antidomain(antidomain(esk3_0)),coantidomain(coantidomain(multiplication(coantidomain(antidomain(esk2_0)),esk1_0)))) != antidomain(antidomain(esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_185,c_0_154]),c_0_186]) ).
cnf(c_0_189,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_187]),c_0_188]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE108+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 13:12:32 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.40/23.40 eprover: CPU time limit exceeded, terminating
% 0.40/23.41 eprover: CPU time limit exceeded, terminating
% 0.40/23.41 eprover: CPU time limit exceeded, terminating
% 0.40/23.42 eprover: CPU time limit exceeded, terminating
% 0.57/46.42 eprover: CPU time limit exceeded, terminating
% 0.57/46.43 eprover: CPU time limit exceeded, terminating
% 0.57/46.43 eprover: CPU time limit exceeded, terminating
% 0.57/46.52 eprover: CPU time limit exceeded, terminating
% 0.62/52.80 # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.62/52.80
% 0.62/52.80 # Failure: Resource limit exceeded (time)
% 0.62/52.80 # OLD status Res
% 0.62/52.80 # Preprocessing time : 0.017 s
% 0.62/52.80 # Running protocol protocol_eprover_f6eb5f7f05126ea361481ae651a4823314e3d740 for 23 seconds:
% 0.62/52.80
% 0.62/52.80 # Failure: Resource limit exceeded (time)
% 0.62/52.80 # OLD status Res
% 0.62/52.80 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,02,20000,1.0)
% 0.62/52.80 # Preprocessing time : 0.008 s
% 0.62/52.80 # Running protocol protocol_eprover_a172c605141d0894bf6fdc293a5220c6c2a32117 for 23 seconds:
% 0.62/52.80 # Preprocessing time : 0.017 s
% 0.62/52.80
% 0.62/52.80 # Proof found!
% 0.62/52.80 # SZS status Theorem
% 0.62/52.80 # SZS output start CNFRefutation
% See solution above
% 0.62/52.80 # Proof object total steps : 190
% 0.62/52.80 # Proof object clause steps : 141
% 0.62/52.80 # Proof object formula steps : 49
% 0.62/52.80 # Proof object conjectures : 83
% 0.62/52.80 # Proof object clause conjectures : 80
% 0.62/52.80 # Proof object formula conjectures : 3
% 0.62/52.80 # Proof object initial clauses used : 25
% 0.62/52.80 # Proof object initial formulas used : 24
% 0.62/52.80 # Proof object generating inferences : 97
% 0.62/52.80 # Proof object simplifying inferences : 173
% 0.62/52.80 # Training examples: 0 positive, 0 negative
% 0.62/52.80 # Parsed axioms : 27
% 0.62/52.80 # Removed by relevancy pruning/SinE : 0
% 0.62/52.80 # Initial clauses : 29
% 0.62/52.80 # Removed in clause preprocessing : 8
% 0.62/52.80 # Initial clauses in saturation : 21
% 0.62/52.80 # Processed clauses : 3570
% 0.62/52.80 # ...of these trivial : 1266
% 0.62/52.80 # ...subsumed : 374
% 0.62/52.80 # ...remaining for further processing : 1930
% 0.62/52.80 # Other redundant clauses eliminated : 0
% 0.62/52.80 # Clauses deleted for lack of memory : 163583
% 0.62/52.80 # Backward-subsumed : 2
% 0.62/52.80 # Backward-rewritten : 1197
% 0.62/52.80 # Generated clauses : 411304
% 0.62/52.80 # ...of the previous two non-trivial : 295848
% 0.62/52.80 # Contextual simplify-reflections : 0
% 0.62/52.80 # Paramodulations : 411303
% 0.62/52.80 # Factorizations : 0
% 0.62/52.80 # Equation resolutions : 1
% 0.62/52.80 # Current number of processed clauses : 731
% 0.62/52.80 # Positive orientable unit clauses : 631
% 0.62/52.80 # Positive unorientable unit clauses: 15
% 0.62/52.80 # Negative unit clauses : 1
% 0.62/52.80 # Non-unit-clauses : 84
% 0.62/52.80 # Current number of unprocessed clauses: 49452
% 0.62/52.80 # ...number of literals in the above : 60084
% 0.62/52.80 # Current number of archived formulas : 0
% 0.62/52.80 # Current number of archived clauses : 1207
% 0.62/52.80 # Clause-clause subsumption calls (NU) : 3128
% 0.62/52.80 # Rec. Clause-clause subsumption calls : 3128
% 0.62/52.80 # Non-unit clause-clause subsumptions : 314
% 0.62/52.80 # Unit Clause-clause subsumption calls : 322
% 0.62/52.80 # Rewrite failures with RHS unbound : 4
% 0.62/52.80 # BW rewrite match attempts : 20268
% 0.62/52.80 # BW rewrite match successes : 385
% 0.62/52.80 # Condensation attempts : 0
% 0.62/52.80 # Condensation successes : 0
% 0.62/52.80 # Termbank termtop insertions : 21396045
% 0.62/52.80
% 0.62/52.80 # -------------------------------------------------
% 0.62/52.80 # User time : 5.693 s
% 0.62/52.80 # System time : 0.126 s
% 0.62/52.80 # Total time : 5.819 s
% 0.62/52.80 # Maximum resident set size: 149424 pages
% 0.62/69.45 eprover: CPU time limit exceeded, terminating
% 0.62/69.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.62/69.46 eprover: No such file or directory
% 0.62/69.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.62/69.47 eprover: No such file or directory
% 0.62/69.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.62/69.47 eprover: No such file or directory
% 0.62/69.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.62/69.48 eprover: No such file or directory
% 0.62/69.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.62/69.49 eprover: No such file or directory
% 0.62/69.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.62/69.49 eprover: No such file or directory
% 0.62/69.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.62/69.50 eprover: No such file or directory
% 0.62/69.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.62/69.50 eprover: No such file or directory
% 0.62/69.51 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.62/69.51 eprover: No such file or directory
% 0.62/69.54 eprover: CPU time limit exceeded, terminating
% 0.62/69.55 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.62/69.55 eprover: No such file or directory
% 0.62/69.56 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.62/69.56 eprover: No such file or directory
% 0.62/69.56 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.62/69.56 eprover: No such file or directory
% 0.62/69.56 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.62/69.56 eprover: No such file or directory
% 0.62/69.57 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.62/69.57 eprover: No such file or directory
% 0.62/69.57 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.62/69.57 eprover: No such file or directory
% 0.62/69.58 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.62/69.58 eprover: No such file or directory
% 0.62/69.58 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.62/69.58 eprover: No such file or directory
% 0.62/69.58 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.62/69.58 eprover: No such file or directory
%------------------------------------------------------------------------------