TSTP Solution File: KLE117+1 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : KLE117+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n012.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 01:56:03 EDT 2022
% Result : Theorem 1.73s 224.88s
% Output : CNFRefutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 18
% Syntax : Number of formulae : 209 ( 206 unt; 0 def)
% Number of atoms : 212 ( 211 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 8 ~; 0 |; 1 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 429 ( 55 sgn 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_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(domain1,axiom,
! [X4] : multiplication(antidomain(X4),X4) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain1) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
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(codomain1,axiom,
! [X4] : multiplication(X4,coantidomain(X4)) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',codomain1) ).
fof(codomain3,axiom,
! [X4] : addition(coantidomain(coantidomain(X4)),coantidomain(X4)) = one,
file('/export/starexec/sandbox2/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/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(domain3,axiom,
! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain3) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
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(goals,conjecture,
! [X4,X5] :
( addition(X4,X5) = X5
=> ! [X6] : addition(forward_diamond(X4,domain(X6)),forward_diamond(X5,domain(X6))) = forward_diamond(X5,domain(X6)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',goals) ).
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(domain4,axiom,
! [X4] : domain(X4) = antidomain(antidomain(X4)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain4) ).
fof(c_0_18,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_19,plain,
! [X4,X5,X6] : multiplication(X4,multiplication(X5,X6)) = multiplication(multiplication(X4,X5),X6),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_20,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_21,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_22,plain,
! [X5] : multiplication(antidomain(X5),X5) = zero,
inference(variable_rename,[status(thm)],[domain1]) ).
fof(c_0_23,plain,
! [X2] : multiplication(X2,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
fof(c_0_24,plain,
! [X2] : addition(X2,zero) = X2,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_25,plain,
addition(multiplication(X1,X2),multiplication(X3,multiplication(X4,X2))) = multiplication(addition(X1,multiplication(X3,X4)),X2),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
multiplication(antidomain(X1),X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_29,plain,
! [X2] : multiplication(one,X2) = X2,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_30,plain,
multiplication(addition(X1,multiplication(X2,antidomain(X3))),X3) = multiplication(X1,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28]) ).
cnf(c_0_31,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_32,plain,
! [X3,X4] : addition(X3,X4) = addition(X4,X3),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
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,plain,
! [X5] : multiplication(X5,coantidomain(X5)) = zero,
inference(variable_rename,[status(thm)],[codomain1]) ).
cnf(c_0_35,plain,
multiplication(addition(X1,antidomain(X2)),X2) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_37,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,plain,
multiplication(X1,coantidomain(X1)) = zero,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_39,plain,
! [X5] : addition(coantidomain(coantidomain(X5)),coantidomain(X5)) = one,
inference(variable_rename,[status(thm)],[codomain3]) ).
fof(c_0_40,plain,
! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_41,plain,
! [X2] : addition(X2,X2) = X2,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_42,plain,
! [X5] : addition(antidomain(antidomain(X5)),antidomain(X5)) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
cnf(c_0_43,plain,
multiplication(addition(antidomain(X1),X2),X1) = multiplication(X2,X1),
inference(pm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_44,plain,
multiplication(addition(X1,antidomain(X2)),multiplication(X2,X3)) = multiplication(X1,multiplication(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_35]),c_0_21]) ).
cnf(c_0_45,plain,
multiplication(X1,addition(X2,coantidomain(X1))) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_28]) ).
cnf(c_0_46,plain,
addition(coantidomain(coantidomain(X1)),coantidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_47,plain,
! [X2] : multiplication(X2,one) = X2,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_48,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_49,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_50,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_51,plain,
multiplication(antidomain(X1),multiplication(X1,X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_26]) ).
cnf(c_0_52,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_36,c_0_28]) ).
cnf(c_0_53,plain,
multiplication(X1,addition(coantidomain(X1),X2)) = multiplication(X1,X2),
inference(pm,[status(thm)],[c_0_45,c_0_36]) ).
cnf(c_0_54,plain,
addition(coantidomain(X1),coantidomain(coantidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_46,c_0_36]) ).
cnf(c_0_55,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_56,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_57,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_50,c_0_36]) ).
cnf(c_0_58,plain,
multiplication(antidomain(X1),addition(multiplication(X1,X2),X3)) = multiplication(antidomain(X1),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_51]),c_0_52]) ).
cnf(c_0_59,plain,
multiplication(X1,coantidomain(coantidomain(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]) ).
cnf(c_0_60,plain,
addition(multiplication(addition(X1,X2),X3),X4) = addition(multiplication(X1,X3),addition(multiplication(X2,X3),X4)),
inference(spm,[status(thm)],[c_0_48,c_0_20]) ).
cnf(c_0_61,plain,
addition(one,antidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_36]) ).
cnf(c_0_62,plain,
multiplication(antidomain(X1),addition(X1,X2)) = multiplication(antidomain(X1),X2),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_63,plain,
addition(X1,addition(X2,X1)) = addition(X1,X2),
inference(pm,[status(thm)],[c_0_56,c_0_36]) ).
cnf(c_0_64,plain,
addition(X1,addition(multiplication(antidomain(X2),X1),X3)) = addition(X1,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_31]),c_0_31]) ).
cnf(c_0_65,plain,
multiplication(antidomain(X1),addition(X2,X1)) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_62]) ).
cnf(c_0_66,plain,
addition(X1,addition(X2,multiplication(antidomain(X3),X1))) = addition(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_63]),c_0_64]) ).
cnf(c_0_67,plain,
multiplication(antidomain(addition(X1,X2)),X1) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_56]),c_0_26]) ).
cnf(c_0_68,plain,
addition(X1,addition(X2,addition(X1,X3))) = addition(X1,addition(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_63]),c_0_48]),c_0_48]) ).
cnf(c_0_69,plain,
addition(X1,multiplication(addition(X2,antidomain(X3)),X1)) = addition(X1,multiplication(X2,X1)),
inference(spm,[status(thm)],[c_0_66,c_0_20]) ).
cnf(c_0_70,plain,
multiplication(addition(antidomain(addition(X1,X2)),X3),X1) = multiplication(X3,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_67]),c_0_52]) ).
cnf(c_0_71,plain,
addition(X1,addition(X2,multiplication(addition(X3,antidomain(X4)),X1))) = addition(X1,addition(X2,multiplication(X3,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_68]) ).
cnf(c_0_72,plain,
addition(multiplication(X1,X2),multiplication(addition(X1,antidomain(X2)),X3)) = multiplication(addition(X1,antidomain(X2)),addition(X2,X3)),
inference(spm,[status(thm)],[c_0_37,c_0_35]) ).
fof(c_0_73,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_74,plain,
antidomain(one) = zero,
inference(spm,[status(thm)],[c_0_26,c_0_55]) ).
cnf(c_0_75,plain,
multiplication(antidomain(antidomain(addition(X1,X2))),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_57]),c_0_31]) ).
cnf(c_0_76,plain,
addition(X1,multiplication(addition(X2,antidomain(X3)),addition(X3,X1))) = addition(X1,multiplication(X2,addition(X3,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_37]) ).
cnf(c_0_77,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_73]) ).
cnf(c_0_78,plain,
addition(X1,multiplication(antidomain(X2),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_49]) ).
cnf(c_0_79,plain,
addition(X1,multiplication(antidomain(X2),addition(X3,X1))) = addition(X1,multiplication(antidomain(X2),X3)),
inference(spm,[status(thm)],[c_0_66,c_0_37]) ).
cnf(c_0_80,plain,
addition(zero,antidomain(zero)) = one,
inference(spm,[status(thm)],[c_0_57,c_0_74]) ).
cnf(c_0_81,plain,
multiplication(antidomain(antidomain(addition(X1,X2))),X2) = X2,
inference(pm,[status(thm)],[c_0_75,c_0_36]) ).
cnf(c_0_82,plain,
multiplication(antidomain(antidomain(X1)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_57]),c_0_31]) ).
cnf(c_0_83,plain,
addition(X1,multiplication(antidomain(X2),addition(X1,X3))) = addition(X1,multiplication(antidomain(X2),X3)),
inference(spm,[status(thm)],[c_0_64,c_0_37]) ).
cnf(c_0_84,plain,
addition(X1,multiplication(antidomain(multiplication(X2,X3)),multiplication(X2,antidomain(antidomain(X3))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_62]),c_0_78]),c_0_79]) ).
cnf(c_0_85,plain,
antidomain(zero) = one,
inference(rw,[status(thm)],[c_0_80,c_0_52]) ).
cnf(c_0_86,plain,
multiplication(antidomain(antidomain(X1)),multiplication(antidomain(X2),X1)) = multiplication(antidomain(X2),X1),
inference(spm,[status(thm)],[c_0_81,c_0_78]) ).
cnf(c_0_87,plain,
antidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_57]),c_0_55]),c_0_82]) ).
cnf(c_0_88,plain,
addition(antidomain(X1),multiplication(antidomain(X2),antidomain(antidomain(X1)))) = addition(antidomain(X1),antidomain(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_57]),c_0_55]) ).
cnf(c_0_89,plain,
addition(X1,multiplication(antidomain(X2),antidomain(antidomain(multiplication(X2,X3))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_51]),c_0_85]),c_0_31]) ).
cnf(c_0_90,plain,
multiplication(antidomain(X1),multiplication(antidomain(X2),addition(X3,X1))) = multiplication(antidomain(X1),multiplication(antidomain(X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_79]),c_0_62]) ).
cnf(c_0_91,plain,
multiplication(antidomain(X1),multiplication(antidomain(X2),antidomain(X1))) = multiplication(antidomain(X2),antidomain(X1)),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_92,plain,
addition(antidomain(X1),antidomain(multiplication(X1,X2))) = antidomain(multiplication(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_36]) ).
cnf(c_0_93,plain,
multiplication(antidomain(X1),antidomain(X2)) = multiplication(antidomain(X2),antidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_57]),c_0_87]),c_0_55]),c_0_87]),c_0_91]) ).
cnf(c_0_94,plain,
multiplication(antidomain(antidomain(addition(X1,X2))),multiplication(X1,X3)) = multiplication(X1,X3),
inference(spm,[status(thm)],[c_0_21,c_0_75]) ).
cnf(c_0_95,plain,
multiplication(antidomain(X1),antidomain(multiplication(X1,X2))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_92]),c_0_87]),c_0_93]) ).
cnf(c_0_96,plain,
antidomain(addition(one,X1)) = zero,
inference(spm,[status(thm)],[c_0_55,c_0_67]) ).
cnf(c_0_97,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_55]),c_0_36]) ).
cnf(c_0_98,plain,
multiplication(antidomain(addition(X1,X2)),addition(multiplication(X1,X3),X4)) = multiplication(antidomain(addition(X1,X2)),X4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_94]),c_0_87]),c_0_87]) ).
cnf(c_0_99,plain,
multiplication(antidomain(addition(X1,X2)),X2) = zero,
inference(pm,[status(thm)],[c_0_67,c_0_36]) ).
cnf(c_0_100,plain,
multiplication(antidomain(addition(X1,X2)),antidomain(multiplication(X1,X3))) = antidomain(addition(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_94]),c_0_87]),c_0_87]) ).
cnf(c_0_101,plain,
antidomain(addition(X1,one)) = zero,
inference(rw,[status(thm)],[inference(pm,[status(thm)],[c_0_96,c_0_97]),c_0_31]) ).
cnf(c_0_102,plain,
addition(multiplication(X1,addition(X2,X3)),X4) = addition(multiplication(X1,X2),addition(multiplication(X1,X3),X4)),
inference(spm,[status(thm)],[c_0_48,c_0_37]) ).
cnf(c_0_103,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(pm,[status(thm)],[c_0_48,c_0_36]),c_0_48]) ).
cnf(c_0_104,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_36,c_0_48]) ).
cnf(c_0_105,plain,
addition(X1,multiplication(antidomain(addition(X2,X3)),multiplication(X2,X4))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_98]),c_0_78]) ).
cnf(c_0_106,plain,
antidomain(addition(X1,antidomain(multiplication(X1,X2)))) = zero,
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_107,plain,
addition(X1,multiplication(X1,addition(X2,X3))) = multiplication(X1,addition(X2,addition(one,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_101]),c_0_28]),c_0_102]),c_0_55]),c_0_28]),c_0_48]),c_0_103]),c_0_37]) ).
cnf(c_0_108,plain,
antidomain(addition(X1,addition(one,X2))) = zero,
inference(pm,[status(thm)],[c_0_96,c_0_104]) ).
cnf(c_0_109,plain,
addition(multiplication(antidomain(addition(X1,X2)),multiplication(X1,X3)),X4) = X4,
inference(spm,[status(thm)],[c_0_36,c_0_105]) ).
cnf(c_0_110,plain,
antidomain(addition(X1,antidomain(X1))) = zero,
inference(spm,[status(thm)],[c_0_106,c_0_59]) ).
cnf(c_0_111,plain,
addition(X1,multiplication(antidomain(antidomain(X1)),X2)) = multiplication(antidomain(antidomain(X1)),addition(X1,X2)),
inference(spm,[status(thm)],[c_0_37,c_0_82]) ).
cnf(c_0_112,plain,
multiplication(antidomain(antidomain(X1)),multiplication(X1,X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_21,c_0_82]) ).
cnf(c_0_113,plain,
addition(antidomain(X1),antidomain(addition(X1,multiplication(X1,addition(X2,X3))))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(pm,[status(thm)],[c_0_77,c_0_107]),c_0_108]),c_0_85]),c_0_55]),c_0_108]),c_0_85]),c_0_55]),c_0_36]) ).
cnf(c_0_114,plain,
addition(multiplication(antidomain(X1),antidomain(addition(antidomain(X1),X2))),X3) = X3,
inference(spm,[status(thm)],[c_0_109,c_0_91]) ).
cnf(c_0_115,plain,
antidomain(multiplication(X1,addition(X2,antidomain(X2)))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_110]),c_0_85]),c_0_55]),c_0_85]),c_0_55]),c_0_36]),c_0_92]) ).
cnf(c_0_116,plain,
multiplication(addition(antidomain(antidomain(X1)),X2),X1) = addition(X1,multiplication(X2,X1)),
inference(spm,[status(thm)],[c_0_20,c_0_82]) ).
cnf(c_0_117,plain,
addition(X1,multiplication(antidomain(antidomain(addition(X1,X2))),X3)) = multiplication(antidomain(antidomain(addition(X1,X2))),addition(X1,X3)),
inference(spm,[status(thm)],[c_0_37,c_0_75]) ).
cnf(c_0_118,plain,
multiplication(antidomain(antidomain(X1)),addition(X1,multiplication(X1,X2))) = addition(X1,multiplication(X1,X2)),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_119,plain,
addition(antidomain(X1),antidomain(addition(X1,multiplication(X1,X2)))) = antidomain(X1),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_120,plain,
addition(X1,addition(multiplication(X1,antidomain(X2)),X3)) = addition(X1,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_61]),c_0_55]),c_0_55]) ).
cnf(c_0_121,plain,
antidomain(multiplication(X1,addition(X2,addition(X3,antidomain(addition(X2,X3)))))) = antidomain(X1),
inference(spm,[status(thm)],[c_0_115,c_0_48]) ).
cnf(c_0_122,plain,
multiplication(antidomain(multiplication(antidomain(X1),X2)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_92]),c_0_78]) ).
cnf(c_0_123,plain,
multiplication(antidomain(antidomain(addition(X1,X2))),addition(X1,multiplication(X1,X3))) = addition(X1,multiplication(X1,X3)),
inference(spm,[status(thm)],[c_0_117,c_0_94]) ).
cnf(c_0_124,plain,
antidomain(addition(X1,multiplication(X1,X2))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_118]),c_0_87]),c_0_119]) ).
cnf(c_0_125,plain,
addition(X1,multiplication(addition(X1,X2),antidomain(X3))) = addition(X1,multiplication(X2,antidomain(X3))),
inference(spm,[status(thm)],[c_0_120,c_0_20]) ).
cnf(c_0_126,plain,
multiplication(antidomain(antidomain(multiplication(antidomain(antidomain(X1)),addition(X1,X2)))),X1) = X1,
inference(spm,[status(thm)],[c_0_75,c_0_111]) ).
cnf(c_0_127,plain,
antidomain(multiplication(antidomain(X1),addition(X2,antidomain(addition(X1,X2))))) = antidomain(antidomain(X1)),
inference(spm,[status(thm)],[c_0_121,c_0_62]) ).
cnf(c_0_128,plain,
multiplication(antidomain(X1),addition(antidomain(addition(antidomain(X1),X2)),X3)) = multiplication(antidomain(X1),X3),
inference(spm,[status(thm)],[c_0_37,c_0_114]) ).
cnf(c_0_129,plain,
multiplication(antidomain(X1),antidomain(addition(X1,X2))) = antidomain(addition(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_124]) ).
cnf(c_0_130,plain,
multiplication(addition(X1,multiplication(X1,X2)),X3) = multiplication(X1,addition(X3,multiplication(X2,X3))),
inference(spm,[status(thm)],[c_0_37,c_0_25]) ).
cnf(c_0_131,plain,
multiplication(addition(X1,multiplication(antidomain(antidomain(multiplication(X2,X3))),X2)),X3) = multiplication(addition(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_82]),c_0_20]) ).
cnf(c_0_132,plain,
addition(antidomain(X1),multiplication(antidomain(antidomain(X1)),antidomain(X2))) = addition(antidomain(X1),antidomain(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_57]),c_0_31]) ).
cnf(c_0_133,plain,
antidomain(multiplication(antidomain(antidomain(X1)),addition(X1,X2))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_126]),c_0_87]),c_0_122]),c_0_87]) ).
cnf(c_0_134,plain,
antidomain(antidomain(addition(X1,antidomain(addition(antidomain(X1),X2))))) = antidomain(antidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_129]) ).
cnf(c_0_135,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,antidomain(antidomain(X1))),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_82]),c_0_36]) ).
cnf(c_0_136,plain,
multiplication(addition(X1,antidomain(antidomain(multiplication(X1,X2)))),X2) = multiplication(antidomain(antidomain(multiplication(X1,X2))),addition(X2,multiplication(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_36]) ).
cnf(c_0_137,plain,
addition(antidomain(X1),antidomain(antidomain(multiplication(antidomain(X1),X2)))) = antidomain(X1),
inference(spm,[status(thm)],[c_0_132,c_0_89]) ).
cnf(c_0_138,plain,
antidomain(addition(X1,antidomain(addition(antidomain(X1),X2)))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_48]),c_0_133]) ).
cnf(c_0_139,plain,
addition(X1,multiplication(X2,addition(X1,antidomain(X1)))) = multiplication(addition(X2,antidomain(antidomain(X1))),addition(X1,antidomain(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(pm,[status(thm)],[c_0_72,c_0_135]),c_0_36]),c_0_103]),c_0_37]),c_0_36]) ).
cnf(c_0_140,plain,
addition(multiplication(X1,multiplication(X2,X3)),multiplication(X4,X3)) = multiplication(addition(multiplication(X1,X2),X4),X3),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_141,plain,
multiplication(antidomain(X1),antidomain(X1)) = antidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_57]),c_0_31]) ).
cnf(c_0_142,plain,
multiplication(addition(antidomain(antidomain(addition(X1,X2))),X3),X1) = addition(X1,multiplication(X3,X1)),
inference(spm,[status(thm)],[c_0_20,c_0_75]) ).
cnf(c_0_143,plain,
addition(X1,multiplication(antidomain(addition(X2,X3)),multiplication(X3,X4))) = X1,
inference(pm,[status(thm)],[c_0_105,c_0_36]) ).
cnf(c_0_144,plain,
multiplication(antidomain(antidomain(multiplication(antidomain(X1),X2))),X2) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_78]) ).
cnf(c_0_145,plain,
antidomain(addition(X1,antidomain(addition(X2,antidomain(X1))))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(pm,[status(thm)],[c_0_138,c_0_139]),c_0_87]),c_0_57]),c_0_55]) ).
cnf(c_0_146,plain,
addition(antidomain(X1),antidomain(addition(X1,X2))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_75]),c_0_87]),c_0_36]) ).
cnf(c_0_147,plain,
addition(X1,multiplication(X2,multiplication(X3,X1))) = multiplication(addition(multiplication(X2,X3),antidomain(antidomain(X1))),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_82]),c_0_36]) ).
cnf(c_0_148,plain,
multiplication(antidomain(X1),multiplication(antidomain(X1),X2)) = multiplication(antidomain(X1),X2),
inference(spm,[status(thm)],[c_0_21,c_0_141]) ).
cnf(c_0_149,plain,
addition(antidomain(X1),antidomain(multiplication(antidomain(X2),X1))) = antidomain(multiplication(antidomain(X2),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_86]),c_0_87]) ).
cnf(c_0_150,plain,
multiplication(antidomain(X1),addition(X2,addition(X1,X3))) = multiplication(antidomain(X1),addition(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_62]),c_0_37]) ).
cnf(c_0_151,plain,
multiplication(addition(antidomain(antidomain(addition(X1,X2))),antidomain(X3)),addition(X3,X1)) = multiplication(antidomain(antidomain(addition(X1,X2))),addition(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_142]),c_0_78]),c_0_36]),c_0_117]) ).
cnf(c_0_152,plain,
addition(X1,multiplication(antidomain(addition(X2,antidomain(antidomain(X3)))),X3)) = X1,
inference(spm,[status(thm)],[c_0_143,c_0_82]) ).
cnf(c_0_153,plain,
multiplication(addition(antidomain(antidomain(multiplication(antidomain(X1),X2))),X3),X2) = multiplication(addition(antidomain(X1),X3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_144]),c_0_20]) ).
cnf(c_0_154,plain,
addition(X1,addition(X2,multiplication(X1,antidomain(X3)))) = addition(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_63]),c_0_120]) ).
cnf(c_0_155,plain,
addition(multiplication(X1,X2),multiplication(addition(antidomain(X2),X1),X3)) = multiplication(addition(antidomain(X2),X1),addition(X2,X3)),
inference(spm,[status(thm)],[c_0_37,c_0_43]) ).
cnf(c_0_156,plain,
antidomain(addition(X1,addition(X2,antidomain(antidomain(X1))))) = antidomain(addition(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_48]) ).
cnf(c_0_157,plain,
multiplication(addition(antidomain(X1),antidomain(antidomain(X2))),X2) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_141]),c_0_148]),c_0_78]) ).
cnf(c_0_158,plain,
antidomain(addition(X1,antidomain(antidomain(multiplication(antidomain(X2),X1))))) = antidomain(X1),
inference(spm,[status(thm)],[c_0_138,c_0_149]) ).
cnf(c_0_159,plain,
antidomain(multiplication(antidomain(X1),addition(X2,antidomain(addition(X2,X1))))) = antidomain(antidomain(X1)),
inference(spm,[status(thm)],[c_0_121,c_0_150]) ).
cnf(c_0_160,plain,
addition(antidomain(X1),antidomain(addition(X2,X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_81]),c_0_87]),c_0_36]) ).
cnf(c_0_161,plain,
multiplication(antidomain(antidomain(addition(X1,X2))),addition(X1,antidomain(antidomain(addition(X1,X2))))) = addition(X1,antidomain(antidomain(addition(X1,X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_57]),c_0_31]),c_0_36]) ).
cnf(c_0_162,plain,
addition(antidomain(X1),antidomain(addition(X2,antidomain(antidomain(X1))))) = antidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_88]),c_0_87]) ).
cnf(c_0_163,plain,
multiplication(antidomain(multiplication(X1,X2)),multiplication(addition(X3,X1),X2)) = multiplication(antidomain(multiplication(X1,X2)),multiplication(X3,X2)),
inference(spm,[status(thm)],[c_0_65,c_0_20]) ).
cnf(c_0_164,plain,
multiplication(addition(antidomain(X1),antidomain(multiplication(antidomain(X1),X2))),X2) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_57]),c_0_31]),c_0_87]) ).
cnf(c_0_165,plain,
antidomain(multiplication(X1,multiplication(X2,addition(X3,antidomain(X3))))) = antidomain(multiplication(X1,X2)),
inference(spm,[status(thm)],[c_0_115,c_0_21]) ).
cnf(c_0_166,plain,
addition(X1,multiplication(addition(X2,X1),antidomain(X3))) = addition(X1,multiplication(X2,antidomain(X3))),
inference(spm,[status(thm)],[c_0_154,c_0_20]) ).
cnf(c_0_167,plain,
multiplication(addition(antidomain(antidomain(X1)),X2),addition(X1,antidomain(X1))) = addition(X1,multiplication(X2,addition(X1,antidomain(X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_116]),c_0_36]),c_0_103]),c_0_37]),c_0_36]) ).
cnf(c_0_168,plain,
antidomain(addition(X1,addition(antidomain(antidomain(X1)),X2))) = antidomain(addition(X1,X2)),
inference(pm,[status(thm)],[c_0_156,c_0_36]) ).
cnf(c_0_169,plain,
addition(X1,multiplication(antidomain(X2),antidomain(X1))) = multiplication(addition(antidomain(X2),antidomain(antidomain(X1))),addition(X1,antidomain(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_157]),c_0_36]),c_0_36]) ).
cnf(c_0_170,plain,
antidomain(addition(X1,antidomain(addition(X1,X2)))) = antidomain(addition(X1,antidomain(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_159]),c_0_87]),c_0_48]),c_0_36]),c_0_160]) ).
cnf(c_0_171,plain,
antidomain(addition(X1,antidomain(antidomain(addition(X1,X2))))) = antidomain(addition(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_161]),c_0_87]),c_0_162]) ).
fof(c_0_172,negated_conjecture,
~ ! [X4,X5] :
( addition(X4,X5) = X5
=> ! [X6] : addition(forward_diamond(X4,domain(X6)),forward_diamond(X5,domain(X6))) = forward_diamond(X5,domain(X6)) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_173,plain,
! [X6,X7] : forward_diamond(X6,X7) = domain(multiplication(X6,domain(X7))),
inference(variable_rename,[status(thm)],[forward_diamond]) ).
fof(c_0_174,plain,
! [X5] : domain(X5) = antidomain(antidomain(X5)),
inference(variable_rename,[status(thm)],[domain4]) ).
cnf(c_0_175,plain,
multiplication(antidomain(multiplication(antidomain(multiplication(antidomain(X1),X2)),X2)),X2) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_164]),c_0_122]) ).
cnf(c_0_176,plain,
antidomain(multiplication(X1,antidomain(antidomain(X2)))) = antidomain(multiplication(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_65]),c_0_82]) ).
cnf(c_0_177,plain,
addition(X1,addition(X2,addition(X3,X1))) = addition(X1,addition(X2,X3)),
inference(spm,[status(thm)],[c_0_63,c_0_48]) ).
cnf(c_0_178,plain,
addition(antidomain(antidomain(X1)),multiplication(antidomain(X1),antidomain(X2))) = addition(antidomain(antidomain(X1)),antidomain(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_57]),c_0_31]) ).
cnf(c_0_179,plain,
antidomain(addition(antidomain(antidomain(X1)),X2)) = antidomain(addition(X1,multiplication(X2,addition(X1,antidomain(X1))))),
inference(spm,[status(thm)],[c_0_115,c_0_167]) ).
cnf(c_0_180,plain,
antidomain(addition(X1,multiplication(antidomain(X2),antidomain(X1)))) = antidomain(addition(X1,antidomain(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(pm,[status(thm)],[c_0_168,c_0_169]),c_0_87]),c_0_87]),c_0_36]),c_0_57]),c_0_55]),c_0_156]),c_0_87]) ).
cnf(c_0_181,plain,
multiplication(antidomain(addition(X1,X2)),addition(X1,X3)) = multiplication(antidomain(addition(X1,X2)),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_67]),c_0_52]) ).
cnf(c_0_182,plain,
antidomain(addition(X1,antidomain(antidomain(X2)))) = antidomain(addition(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_170]),c_0_170]),c_0_171]) ).
fof(c_0_183,negated_conjecture,
( addition(esk1_0,esk2_0) = esk2_0
& addition(forward_diamond(esk1_0,domain(esk3_0)),forward_diamond(esk2_0,domain(esk3_0))) != forward_diamond(esk2_0,domain(esk3_0)) ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_172])])])])]) ).
cnf(c_0_184,plain,
forward_diamond(X1,X2) = domain(multiplication(X1,domain(X2))),
inference(split_conjunct,[status(thm)],[c_0_173]) ).
cnf(c_0_185,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_174]) ).
cnf(c_0_186,plain,
addition(antidomain(X1),antidomain(X2)) = antidomain(multiplication(antidomain(multiplication(antidomain(X2),X1)),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_175]),c_0_88]),c_0_176]),c_0_176]),c_0_149]) ).
cnf(c_0_187,plain,
multiplication(antidomain(X1),addition(X2,addition(X3,X1))) = multiplication(antidomain(X1),addition(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_177]),c_0_62]) ).
cnf(c_0_188,plain,
antidomain(addition(X1,X2)) = antidomain(antidomain(multiplication(antidomain(X1),antidomain(X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_178]),c_0_179]),c_0_83]),c_0_180]),c_0_179]),c_0_181]),c_0_180]),c_0_170]),c_0_92]),c_0_182]) ).
cnf(c_0_189,negated_conjecture,
addition(forward_diamond(esk1_0,domain(esk3_0)),forward_diamond(esk2_0,domain(esk3_0))) != forward_diamond(esk2_0,domain(esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_183]) ).
cnf(c_0_190,plain,
forward_diamond(X1,X2) = antidomain(antidomain(multiplication(X1,antidomain(antidomain(X2))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_184,c_0_185]),c_0_185]) ).
cnf(c_0_191,plain,
multiplication(antidomain(multiplication(antidomain(multiplication(antidomain(X1),X2)),X2)),X1) = multiplication(antidomain(X2),X1),
inference(spm,[status(thm)],[c_0_35,c_0_186]) ).
cnf(c_0_192,plain,
multiplication(antidomain(X1),addition(X2,antidomain(X1))) = multiplication(antidomain(X1),addition(X2,one)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_57]),c_0_87]),c_0_87]) ).
cnf(c_0_193,plain,
antidomain(multiplication(X1,addition(X2,X3))) = antidomain(multiplication(X1,antidomain(multiplication(antidomain(X2),antidomain(X3))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_188]),c_0_87]) ).
cnf(c_0_194,negated_conjecture,
addition(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(esk3_0))))))),antidomain(antidomain(multiplication(esk2_0,antidomain(antidomain(antidomain(antidomain(esk3_0)))))))) != antidomain(antidomain(multiplication(esk2_0,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)],[inference(rw,[status(thm)],[c_0_189,c_0_185]),c_0_185]),c_0_185]),c_0_190]),c_0_190]),c_0_190]) ).
cnf(c_0_195,plain,
multiplication(antidomain(multiplication(antidomain(antidomain(X1)),X2)),X1) = multiplication(antidomain(X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_191,c_0_192]),c_0_193]),c_0_74]),c_0_27]),c_0_85]),c_0_55]),c_0_65]),c_0_188]),c_0_176]),c_0_144]) ).
cnf(c_0_196,negated_conjecture,
addition(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk3_0))))),antidomain(antidomain(multiplication(esk2_0,antidomain(antidomain(esk3_0)))))) != antidomain(antidomain(multiplication(esk2_0,antidomain(antidomain(esk3_0))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_194,c_0_87]),c_0_87]),c_0_87]) ).
cnf(c_0_197,plain,
multiplication(antidomain(multiplication(antidomain(X1),X2)),X2) = multiplication(antidomain(antidomain(X1)),X2),
inference(rw,[status(thm)],[inference(pm,[status(thm)],[c_0_195,c_0_93]),c_0_176]) ).
cnf(c_0_198,negated_conjecture,
addition(antidomain(antidomain(multiplication(esk1_0,esk3_0))),antidomain(antidomain(multiplication(esk2_0,esk3_0)))) != antidomain(antidomain(multiplication(esk2_0,esk3_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_196,c_0_176]),c_0_176]),c_0_176]) ).
cnf(c_0_199,plain,
multiplication(antidomain(X1),addition(X2,antidomain(antidomain(X1)))) = multiplication(antidomain(X1),X2),
inference(spm,[status(thm)],[c_0_65,c_0_87]) ).
cnf(c_0_200,plain,
addition(antidomain(X1),antidomain(X2)) = antidomain(multiplication(antidomain(antidomain(X2)),X1)),
inference(rw,[status(thm)],[c_0_186,c_0_197]) ).
cnf(c_0_201,plain,
multiplication(antidomain(antidomain(multiplication(addition(X1,X2),X3))),multiplication(X1,X3)) = multiplication(X1,X3),
inference(spm,[status(thm)],[c_0_75,c_0_20]) ).
cnf(c_0_202,negated_conjecture,
addition(esk1_0,esk2_0) = esk2_0,
inference(split_conjunct,[status(thm)],[c_0_183]) ).
cnf(c_0_203,negated_conjecture,
antidomain(multiplication(antidomain(multiplication(esk1_0,esk3_0)),antidomain(multiplication(antidomain(multiplication(esk1_0,esk3_0)),multiplication(esk2_0,esk3_0))))) != antidomain(antidomain(multiplication(esk2_0,esk3_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_198,c_0_186]),c_0_93]),c_0_176]),c_0_93]) ).
cnf(c_0_204,plain,
multiplication(antidomain(X1),antidomain(multiplication(antidomain(X1),X2))) = multiplication(antidomain(X1),antidomain(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_200]),c_0_87]) ).
cnf(c_0_205,negated_conjecture,
multiplication(antidomain(antidomain(multiplication(esk2_0,X1))),multiplication(esk1_0,X1)) = multiplication(esk1_0,X1),
inference(spm,[status(thm)],[c_0_201,c_0_202]) ).
cnf(c_0_206,negated_conjecture,
antidomain(multiplication(antidomain(multiplication(esk1_0,esk3_0)),antidomain(multiplication(esk2_0,esk3_0)))) != antidomain(antidomain(multiplication(esk2_0,esk3_0))),
inference(rw,[status(thm)],[c_0_203,c_0_204]) ).
cnf(c_0_207,negated_conjecture,
multiplication(antidomain(multiplication(esk1_0,X1)),antidomain(multiplication(esk2_0,X1))) = antidomain(multiplication(esk2_0,X1)),
inference(spm,[status(thm)],[c_0_122,c_0_205]) ).
cnf(c_0_208,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_206,c_0_207])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE117+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_ET %s %d
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 16 15:39:54 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.38/23.40 eprover: CPU time limit exceeded, terminating
% 0.38/23.40 eprover: CPU time limit exceeded, terminating
% 0.38/23.41 eprover: CPU time limit exceeded, terminating
% 0.38/23.41 eprover: CPU time limit exceeded, terminating
% 0.53/46.41 eprover: CPU time limit exceeded, terminating
% 0.53/46.42 eprover: CPU time limit exceeded, terminating
% 0.53/46.43 eprover: CPU time limit exceeded, terminating
% 0.53/46.43 eprover: CPU time limit exceeded, terminating
% 0.69/69.43 eprover: CPU time limit exceeded, terminating
% 0.69/69.44 eprover: CPU time limit exceeded, terminating
% 0.69/69.44 eprover: CPU time limit exceeded, terminating
% 0.69/69.45 eprover: CPU time limit exceeded, terminating
% 0.84/92.45 eprover: CPU time limit exceeded, terminating
% 0.84/92.45 eprover: CPU time limit exceeded, terminating
% 0.84/92.46 eprover: CPU time limit exceeded, terminating
% 0.84/92.46 eprover: CPU time limit exceeded, terminating
% 0.98/115.46 eprover: CPU time limit exceeded, terminating
% 0.98/115.47 eprover: CPU time limit exceeded, terminating
% 0.98/115.47 eprover: CPU time limit exceeded, terminating
% 0.98/115.48 eprover: CPU time limit exceeded, terminating
% 1.15/138.47 eprover: CPU time limit exceeded, terminating
% 1.15/138.48 eprover: CPU time limit exceeded, terminating
% 1.15/138.49 eprover: CPU time limit exceeded, terminating
% 1.15/138.49 eprover: CPU time limit exceeded, terminating
% 1.31/161.49 eprover: CPU time limit exceeded, terminating
% 1.31/161.49 eprover: CPU time limit exceeded, terminating
% 1.31/161.50 eprover: CPU time limit exceeded, terminating
% 1.31/161.50 eprover: CPU time limit exceeded, terminating
% 1.44/184.50 eprover: CPU time limit exceeded, terminating
% 1.44/184.51 eprover: CPU time limit exceeded, terminating
% 1.44/184.52 eprover: CPU time limit exceeded, terminating
% 1.44/184.54 eprover: CPU time limit exceeded, terminating
% 1.61/207.51 eprover: CPU time limit exceeded, terminating
% 1.61/207.53 eprover: CPU time limit exceeded, terminating
% 1.61/207.53 eprover: CPU time limit exceeded, terminating
% 1.61/207.55 eprover: CPU time limit exceeded, terminating
% 1.73/224.88 # Running protocol protocol_eprover_29fa5c60d0ee03ec4f64b055553dc135fbe4ee3a for 23 seconds:
% 1.73/224.88
% 1.73/224.88 # Failure: Resource limit exceeded (time)
% 1.73/224.88 # OLD status Res
% 1.73/224.88 # Preprocessing time : 0.015 s
% 1.73/224.88 # Running protocol protocol_eprover_773c90a94152ea2e8c9d3df9c4b1eb6152c40c03 for 23 seconds:
% 1.73/224.88
% 1.73/224.88 # Failure: Resource limit exceeded (time)
% 1.73/224.88 # OLD status Res
% 1.73/224.88 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,,100,1.0)
% 1.73/224.88 # Preprocessing time : 0.017 s
% 1.73/224.88 # Running protocol protocol_eprover_75515770aeb32f68e33e9fbd9dff93f5a2e34f2e for 23 seconds:
% 1.73/224.88
% 1.73/224.88 # Failure: Resource limit exceeded (time)
% 1.73/224.88 # OLD status Res
% 1.73/224.88 # Preprocessing time : 0.018 s
% 1.73/224.88 # Running protocol protocol_eprover_6c565d2524e660970ec2a72c26d577f665a55420 for 23 seconds:
% 1.73/224.88
% 1.73/224.88 # Failure: Resource limit exceeded (time)
% 1.73/224.88 # OLD status Res
% 1.73/224.88 # Preprocessing time : 0.008 s
% 1.73/224.88 # Running protocol protocol_eprover_750456fc664a9e0b97096ad0f5110b1ead7d782b for 23 seconds:
% 1.73/224.88
% 1.73/224.88 # Failure: Resource limit exceeded (time)
% 1.73/224.88 # OLD status Res
% 1.73/224.88 # Preprocessing time : 0.009 s
% 1.73/224.88 # Running protocol protocol_eprover_a9abcacdf80c460fdc9fe242616d68da2308faf5 for 23 seconds:
% 1.73/224.88
% 1.73/224.88 # Failure: Resource limit exceeded (time)
% 1.73/224.88 # OLD status Res
% 1.73/224.88 # SinE strategy is GSinE(CountFormulas,hypos,1.1,,02,500,1.0)
% 1.73/224.88 # Preprocessing time : 0.008 s
% 1.73/224.88 # Running protocol protocol_eprover_e60008599937a0dc787316fd87bf9ff4d65ffb48 for 23 seconds:
% 1.73/224.88
% 1.73/224.88 # Failure: Resource limit exceeded (time)
% 1.73/224.88 # OLD status Res
% 1.73/224.88 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,02,20000,1.0)
% 1.73/224.88 # Preprocessing time : 0.015 s
% 1.73/224.88 # Running protocol protocol_eprover_03d534503f753dd3be02bb3c547fa7a3e34e825e for 23 seconds:
% 1.73/224.88
% 1.73/224.88 # Failure: Resource limit exceeded (time)
% 1.73/224.88 # OLD status Res
% 1.73/224.88 # Preprocessing time : 0.015 s
% 1.73/224.88 # Running protocol protocol_eprover_f8481b8ca6e1cbe7ac35251a2832c4c110836158 for 23 seconds:
% 1.73/224.88
% 1.73/224.88 # Failure: Resource limit exceeded (time)
% 1.73/224.88 # OLD status Res
% 1.73/224.88 # SinE strategy is GSinE(CountFormulas,,1.2,,02,60,1.0)
% 1.73/224.88 # Preprocessing time : 0.010 s
% 1.73/224.88 # Running protocol protocol_eprover_4692c23f3ccd5aecc2adbd7957ddb4b4144a02c8 for 23 seconds:
% 1.73/224.88 # Preprocessing time : 0.016 s
% 1.73/224.88
% 1.73/224.88 # Proof found!
% 1.73/224.88 # SZS status Theorem
% 1.73/224.88 # SZS output start CNFRefutation
% See solution above
% 1.73/224.88 # Proof object total steps : 209
% 1.73/224.88 # Proof object clause steps : 172
% 1.73/224.88 # Proof object formula steps : 37
% 1.73/224.88 # Proof object conjectures : 13
% 1.73/224.88 # Proof object clause conjectures : 10
% 1.73/224.88 # Proof object formula conjectures : 3
% 1.73/224.88 # Proof object initial clauses used : 19
% 1.73/224.88 # Proof object initial formulas used : 18
% 1.73/224.88 # Proof object generating inferences : 142
% 1.73/224.88 # Proof object simplifying inferences : 188
% 1.73/224.88 # Training examples: 0 positive, 0 negative
% 1.73/224.88 # Parsed axioms : 27
% 1.73/224.88 # Removed by relevancy pruning/SinE : 0
% 1.73/224.88 # Initial clauses : 29
% 1.73/224.88 # Removed in clause preprocessing : 8
% 1.73/224.88 # Initial clauses in saturation : 21
% 1.73/224.88 # Processed clauses : 20687
% 1.73/224.88 # ...of these trivial : 12209
% 1.73/224.88 # ...subsumed : 6439
% 1.73/224.88 # ...remaining for further processing : 2039
% 1.73/224.88 # Other redundant clauses eliminated : 0
% 1.73/224.88 # Clauses deleted for lack of memory : 478079
% 1.73/224.88 # Backward-subsumed : 2
% 1.73/224.88 # Backward-rewritten : 942
% 1.73/224.88 # Generated clauses : 1289812
% 1.73/224.88 # ...of the previous two non-trivial : 718961
% 1.73/224.88 # Contextual simplify-reflections : 0
% 1.73/224.88 # Paramodulations : 1289812
% 1.73/224.88 # Factorizations : 0
% 1.73/224.88 # Equation resolutions : 0
% 1.73/224.88 # Current number of processed clauses : 1095
% 1.73/224.88 # Positive orientable unit clauses : 1052
% 1.73/224.88 # Positive unorientable unit clauses: 41
% 1.73/224.88 # Negative unit clauses : 0
% 1.73/224.88 # Non-unit-clauses : 2
% 1.73/224.88 # Current number of unprocessed clauses: 56200
% 1.73/224.88 # ...number of literals in the above : 56200
% 1.73/224.88 # Current number of archived formulas : 0
% 1.73/224.88 # Current number of archived clauses : 952
% 1.73/224.88 # Clause-clause subsumption calls (NU) : 0
% 1.73/224.88 # Rec. Clause-clause subsumption calls : 0
% 1.73/224.88 # Non-unit clause-clause subsumptions : 0
% 1.73/224.88 # Unit Clause-clause subsumption calls : 664
% 1.73/224.88 # Rewrite failures with RHS unbound : 166
% 1.73/224.88 # BW rewrite match attempts : 24420
% 1.73/224.88 # BW rewrite match successes : 1574
% 1.73/224.88 # Condensation attempts : 0
% 1.73/224.88 # Condensation successes : 0
% 1.73/224.88 # Termbank termtop insertions : 21677675
% 1.73/224.88
% 1.73/224.88 # -------------------------------------------------
% 1.73/224.88 # User time : 17.092 s
% 1.73/224.88 # System time : 0.159 s
% 1.73/224.88 # Total time : 17.251 s
% 1.73/224.88 # Maximum resident set size: 169400 pages
% 1.73/230.54 eprover: CPU time limit exceeded, terminating
% 1.73/230.55 eprover: CPU time limit exceeded, terminating
% 1.73/230.55 eprover: CPU time limit exceeded, terminating
% 1.73/230.56 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.73/230.56 eprover: No such file or directory
% 1.73/230.56 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 1.73/230.56 eprover: No such file or directory
% 1.73/230.57 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 1.73/230.57 eprover: No such file or directory
% 1.73/230.57 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.73/230.57 eprover: No such file or directory
% 1.73/230.57 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 1.73/230.57 eprover: No such file or directory
% 1.73/230.57 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 1.73/230.57 eprover: No such file or directory
%------------------------------------------------------------------------------