%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : KLE103+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:59:20 PM UTC 2026
% Result : Theorem 215.51s 31.74s
% Output : CNFRefutation 215.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 26
% Syntax : Number of formulae : 312 ( 305 unt; 0 def)
% Number of atoms : 321 ( 309 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 22 ( 13 ~; 4 |; 2 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 15 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-2 aty)
% Number of variables : 484 ( 69 sgn 88 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(domain1,axiom,
! [X4] : multiplication(antidomain(X4),X4) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain1) ).
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(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(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
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(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(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(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',order) ).
fof(domain2,axiom,
! [X4,X5] : addition(antidomain(multiplication(X4,X5)),antidomain(multiplication(X4,antidomain(antidomain(X5))))) = antidomain(multiplication(X4,antidomain(antidomain(X5)))),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain2) ).
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(forward_box(X4,domain(X5)),domain(X6)) = one
=> addition(domain(X5),backward_box(X4,domain(X6))) = one ),
file('/export/starexec/sandbox2/benchmark/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(backward_box,axiom,
! [X4,X5] : backward_box(X4,X5) = c(backward_diamond(X4,c(X5))),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax',backward_box) ).
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_26,plain,
! [X32] : addition(antidomain(antidomain(X32)),antidomain(X32)) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
fof(c_0_27,plain,
! [X7,X8] : addition(X7,X8) = addition(X8,X7),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_28,plain,
! [X17] : multiplication(X17,one) = X17,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_29,plain,
! [X29] : multiplication(antidomain(X29),X29) = zero,
inference(variable_rename,[status(thm)],[domain1]) ).
cnf(c_0_30,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_33,plain,
multiplication(antidomain(X1),X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_34,plain,
! [X12] : addition(X12,zero) = X12,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_35,plain,
! [X18] : multiplication(one,X18) = X18,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_36,plain,
! [X34] : multiplication(X34,coantidomain(X34)) = zero,
inference(variable_rename,[status(thm)],[codomain1]) ).
fof(c_0_37,plain,
! [X37] : addition(coantidomain(coantidomain(X37)),coantidomain(X37)) = one,
inference(variable_rename,[status(thm)],[codomain3]) ).
cnf(c_0_38,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_39,plain,
antidomain(one) = zero,
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_40,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_41,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_42,plain,
multiplication(X1,coantidomain(X1)) = zero,
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_43,plain,
addition(coantidomain(coantidomain(X1)),coantidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_44,plain,
one = addition(zero,antidomain(zero)),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_45,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_40,c_0_31]) ).
cnf(c_0_46,plain,
coantidomain(one) = zero,
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,plain,
addition(coantidomain(X1),coantidomain(coantidomain(X1))) = antidomain(zero),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_31]),c_0_44]),c_0_45]) ).
cnf(c_0_48,plain,
coantidomain(antidomain(zero)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_44]),c_0_45]) ).
fof(c_0_49,plain,
! [X9,X10,X11] : addition(X11,addition(X10,X9)) = addition(addition(X11,X10),X9),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_50,plain,
! [X13] : addition(X13,X13) = X13,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_51,plain,
! [X25] : multiplication(X25,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
fof(c_0_52,plain,
! [X26] : multiplication(zero,X26) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
fof(c_0_53,plain,
! [X14,X15,X16] : multiplication(X14,multiplication(X15,X16)) = multiplication(multiplication(X14,X15),X16),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_54,plain,
antidomain(zero) = coantidomain(zero),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_45]) ).
fof(c_0_55,plain,
! [X19,X20,X21] : multiplication(X19,addition(X20,X21)) = addition(multiplication(X19,X20),multiplication(X19,X21)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_56,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_57,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_58,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_59,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_60,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_61,plain,
multiplication(X1,coantidomain(zero)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_44]),c_0_45]),c_0_54]) ).
cnf(c_0_62,plain,
addition(coantidomain(X1),coantidomain(coantidomain(X1))) = coantidomain(zero),
inference(rw,[status(thm)],[c_0_47,c_0_54]) ).
cnf(c_0_63,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
fof(c_0_64,plain,
! [X22,X23,X24] : multiplication(addition(X22,X23),X24) = addition(multiplication(X22,X24),multiplication(X23,X24)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_65,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_66,plain,
multiplication(X1,multiplication(X2,coantidomain(X2))) = multiplication(X2,coantidomain(X2)),
inference(spm,[status(thm)],[c_0_58,c_0_42]) ).
cnf(c_0_67,plain,
multiplication(antidomain(X1),multiplication(X1,X2)) = multiplication(antidomain(X1),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_33]),c_0_60]) ).
fof(c_0_68,plain,
! [X35,X36] : addition(coantidomain(multiplication(X35,X36)),coantidomain(multiplication(coantidomain(coantidomain(X35)),X36))) = coantidomain(multiplication(coantidomain(coantidomain(X35)),X36)),
inference(variable_rename,[status(thm)],[codomain2]) ).
cnf(c_0_69,plain,
addition(multiplication(X1,coantidomain(X1)),X2) = X2,
inference(spm,[status(thm)],[c_0_45,c_0_42]) ).
cnf(c_0_70,plain,
addition(multiplication(X1,coantidomain(X2)),multiplication(X1,coantidomain(coantidomain(X2)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]) ).
cnf(c_0_71,plain,
multiplication(coantidomain(zero),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_44]),c_0_45]),c_0_54]) ).
cnf(c_0_72,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_73,plain,
addition(coantidomain(X1),coantidomain(zero)) = coantidomain(zero),
inference(spm,[status(thm)],[c_0_65,c_0_62]) ).
cnf(c_0_74,plain,
multiplication(antidomain(X1),X1) = multiplication(X1,coantidomain(X1)),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_75,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_68]) ).
cnf(c_0_76,plain,
multiplication(X1,coantidomain(coantidomain(X1))) = X1,
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_77,plain,
addition(multiplication(coantidomain(X1),X2),multiplication(coantidomain(coantidomain(X1)),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_62]),c_0_72]) ).
cnf(c_0_78,plain,
addition(X1,multiplication(X2,coantidomain(X2))) = X1,
inference(spm,[status(thm)],[c_0_40,c_0_42]) ).
cnf(c_0_79,plain,
addition(X1,multiplication(X1,coantidomain(X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_73]),c_0_61]),c_0_61]),c_0_31]) ).
cnf(c_0_80,plain,
multiplication(antidomain(X1),multiplication(X1,X2)) = multiplication(X1,coantidomain(X1)),
inference(rw,[status(thm)],[c_0_67,c_0_74]) ).
cnf(c_0_81,plain,
multiplication(X1,multiplication(X2,multiplication(X3,coantidomain(multiplication(X2,X3))))) = multiplication(X2,multiplication(X3,coantidomain(multiplication(X2,X3)))),
inference(spm,[status(thm)],[c_0_66,c_0_60]) ).
cnf(c_0_82,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_75,c_0_60]) ).
cnf(c_0_83,plain,
addition(coantidomain(zero),coantidomain(X1)) = coantidomain(zero),
inference(spm,[status(thm)],[c_0_31,c_0_73]) ).
cnf(c_0_84,plain,
multiplication(X1,multiplication(coantidomain(coantidomain(X1)),X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_60,c_0_76]) ).
cnf(c_0_85,plain,
coantidomain(coantidomain(coantidomain(X1))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_76]),c_0_78]) ).
cnf(c_0_86,plain,
addition(multiplication(X1,coantidomain(addition(X1,X2))),multiplication(X2,coantidomain(addition(X1,X2)))) = zero,
inference(spm,[status(thm)],[c_0_42,c_0_72]) ).
cnf(c_0_87,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_65,c_0_31]) ).
cnf(c_0_88,plain,
addition(X1,addition(multiplication(X1,coantidomain(X2)),X3)) = addition(X1,X3),
inference(spm,[status(thm)],[c_0_56,c_0_79]) ).
cnf(c_0_89,plain,
multiplication(X1,multiplication(X2,coantidomain(multiplication(X1,X2)))) = multiplication(X1,coantidomain(X1)),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_90,plain,
coantidomain(zero) = coantidomain(multiplication(coantidomain(coantidomain(multiplication(X1,X2))),coantidomain(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_42]),c_0_58]),c_0_83]) ).
cnf(c_0_91,plain,
multiplication(coantidomain(coantidomain(X1)),coantidomain(X1)) = multiplication(X1,coantidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_84]),c_0_85]),c_0_85]) ).
cnf(c_0_92,plain,
multiplication(X1,coantidomain(addition(X1,X2))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_86]),c_0_40]) ).
cnf(c_0_93,plain,
multiplication(X1,coantidomain(addition(X2,X1))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_86]),c_0_40]) ).
cnf(c_0_94,plain,
addition(coantidomain(X1),multiplication(coantidomain(coantidomain(X1)),coantidomain(X2))) = addition(coantidomain(X1),coantidomain(X2)),
inference(spm,[status(thm)],[c_0_88,c_0_77]) ).
cnf(c_0_95,plain,
multiplication(coantidomain(coantidomain(multiplication(X1,X2))),coantidomain(X2)) = multiplication(X1,coantidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_61]),c_0_85]),c_0_91]),c_0_60]),c_0_89]) ).
cnf(c_0_96,plain,
multiplication(X1,coantidomain(addition(X1,X2))) = multiplication(X1,coantidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_92]),c_0_61]) ).
cnf(c_0_97,plain,
multiplication(X1,coantidomain(addition(X2,X1))) = multiplication(X1,coantidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_93]),c_0_61]) ).
cnf(c_0_98,plain,
coantidomain(coantidomain(zero)) = zero,
inference(rw,[status(thm)],[c_0_48,c_0_54]) ).
cnf(c_0_99,plain,
addition(coantidomain(X1),coantidomain(multiplication(X2,X1))) = coantidomain(multiplication(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_78]),c_0_31]) ).
cnf(c_0_100,plain,
multiplication(X1,coantidomain(coantidomain(addition(X1,X2)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_92]),c_0_45]) ).
cnf(c_0_101,plain,
addition(multiplication(antidomain(addition(X1,X2)),multiplication(X1,X3)),multiplication(antidomain(addition(X1,X2)),multiplication(X2,X3))) = multiplication(X1,coantidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_72]),c_0_63]),c_0_72]),c_0_96]),c_0_97]),c_0_78]) ).
cnf(c_0_102,plain,
coantidomain(addition(coantidomain(X1),coantidomain(coantidomain(X1)))) = zero,
inference(spm,[status(thm)],[c_0_98,c_0_62]) ).
fof(c_0_103,plain,
! [X27,X28] :
( ( leq(X27,X28)
| addition(X27,X28) != X28 )
& ( addition(X27,X28) = X28
| ~ leq(X27,X28) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])])]) ).
fof(c_0_104,plain,
! [X30,X31] : addition(antidomain(multiplication(X30,X31)),antidomain(multiplication(X30,antidomain(antidomain(X31))))) = antidomain(multiplication(X30,antidomain(antidomain(X31)))),
inference(variable_rename,[status(thm)],[domain2]) ).
cnf(c_0_105,plain,
coantidomain(multiplication(coantidomain(coantidomain(X1)),X2)) = coantidomain(multiplication(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_84]),c_0_31]),c_0_75]) ).
cnf(c_0_106,plain,
multiplication(coantidomain(X1),coantidomain(addition(X2,coantidomain(coantidomain(X1))))) = coantidomain(addition(X2,coantidomain(coantidomain(X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_97]),c_0_85]),c_0_91]),c_0_78]) ).
cnf(c_0_107,plain,
multiplication(X1,multiplication(coantidomain(X2),coantidomain(coantidomain(X1)))) = multiplication(X1,coantidomain(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_70]),c_0_60]) ).
cnf(c_0_108,plain,
multiplication(coantidomain(multiplication(X1,X2)),coantidomain(X2)) = coantidomain(X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_95]),c_0_85]),c_0_69]) ).
cnf(c_0_109,plain,
multiplication(antidomain(addition(X1,X2)),multiplication(X1,X3)) = multiplication(X1,coantidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_101]),c_0_78]) ).
cnf(c_0_110,plain,
multiplication(X1,coantidomain(coantidomain(addition(coantidomain(X2),coantidomain(coantidomain(X2)))))) = X1,
inference(spm,[status(thm)],[c_0_61,c_0_102]) ).
cnf(c_0_111,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_112,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_104]) ).
cnf(c_0_113,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = coantidomain(zero),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_44]),c_0_45]),c_0_54]) ).
cnf(c_0_114,plain,
coantidomain(multiplication(X1,coantidomain(addition(X2,coantidomain(X1))))) = coantidomain(coantidomain(addition(X2,coantidomain(X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_85]),c_0_85]) ).
cnf(c_0_115,plain,
addition(coantidomain(X1),coantidomain(addition(X1,X2))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_85]),c_0_31]) ).
cnf(c_0_116,plain,
multiplication(X1,coantidomain(multiplication(X2,coantidomain(X1)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_76]) ).
cnf(c_0_117,plain,
multiplication(X1,coantidomain(coantidomain(addition(X2,X1)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_93]),c_0_45]) ).
cnf(c_0_118,plain,
multiplication(antidomain(addition(X1,X2)),X1) = multiplication(X1,coantidomain(X1)),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_119,plain,
addition(coantidomain(multiplication(X1,coantidomain(X1))),coantidomain(X2)) = coantidomain(multiplication(X1,coantidomain(X1))),
inference(spm,[status(thm)],[c_0_83,c_0_42]) ).
cnf(c_0_120,plain,
leq(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,antidomain(antidomain(X2))))),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_121,plain,
addition(antidomain(X1),coantidomain(zero)) = coantidomain(zero),
inference(spm,[status(thm)],[c_0_65,c_0_113]) ).
cnf(c_0_122,plain,
coantidomain(addition(X1,multiplication(X2,coantidomain(coantidomain(X1))))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_72]),c_0_76]),c_0_85]) ).
cnf(c_0_123,plain,
multiplication(coantidomain(addition(X1,X2)),coantidomain(X2)) = coantidomain(addition(X1,X2)),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_124,plain,
coantidomain(addition(coantidomain(zero),X1)) = zero,
inference(spm,[status(thm)],[c_0_71,c_0_92]) ).
cnf(c_0_125,plain,
coantidomain(coantidomain(multiplication(X1,coantidomain(X1)))) = multiplication(X1,coantidomain(X1)),
inference(spm,[status(thm)],[c_0_98,c_0_42]) ).
cnf(c_0_126,plain,
coantidomain(multiplication(coantidomain(coantidomain(antidomain(addition(X1,X2)))),X1)) = coantidomain(multiplication(X1,coantidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_118]),c_0_119]) ).
cnf(c_0_127,plain,
multiplication(X1,coantidomain(multiplication(X2,coantidomain(X2)))) = X1,
inference(spm,[status(thm)],[c_0_61,c_0_42]) ).
cnf(c_0_128,plain,
coantidomain(multiplication(coantidomain(coantidomain(antidomain(X1))),multiplication(X1,X2))) = coantidomain(multiplication(X1,coantidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_80]),c_0_119]) ).
cnf(c_0_129,plain,
antidomain(multiplication(X1,coantidomain(X1))) = coantidomain(multiplication(X1,coantidomain(X1))),
inference(spm,[status(thm)],[c_0_54,c_0_42]) ).
cnf(c_0_130,plain,
antidomain(antidomain(zero)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_44]),c_0_45]) ).
cnf(c_0_131,plain,
( ~ leq(X1,X2)
| addition(X1,X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_132,plain,
leq(coantidomain(zero),antidomain(multiplication(X1,antidomain(antidomain(coantidomain(X1)))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_42]),c_0_54]) ).
cnf(c_0_133,plain,
addition(coantidomain(zero),antidomain(X1)) = coantidomain(zero),
inference(spm,[status(thm)],[c_0_31,c_0_121]) ).
cnf(c_0_134,plain,
coantidomain(addition(X1,coantidomain(addition(X2,coantidomain(X1))))) = coantidomain(X1),
inference(spm,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_135,plain,
coantidomain(addition(X1,multiplication(X2,X1))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_124]),c_0_71]),c_0_72]),c_0_71]) ).
cnf(c_0_136,plain,
multiplication(X1,coantidomain(coantidomain(addition(coantidomain(coantidomain(X1)),X2)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_100]),c_0_76]) ).
cnf(c_0_137,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X3,X1)),
inference(spm,[status(thm)],[c_0_56,c_0_31]) ).
cnf(c_0_138,plain,
multiplication(coantidomain(coantidomain(antidomain(addition(X1,X2)))),X1) = multiplication(X1,coantidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_127]),c_0_126]),c_0_125]),c_0_127]) ).
cnf(c_0_139,plain,
multiplication(coantidomain(coantidomain(antidomain(X1))),multiplication(X1,X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_128]),c_0_127]) ).
cnf(c_0_140,plain,
addition(coantidomain(multiplication(X1,coantidomain(X1))),antidomain(multiplication(antidomain(X1),antidomain(antidomain(X1))))) = antidomain(multiplication(antidomain(X1),antidomain(antidomain(X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_74]),c_0_129]) ).
cnf(c_0_141,plain,
addition(X1,multiplication(antidomain(X2),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_121]),c_0_71]),c_0_71]),c_0_31]) ).
cnf(c_0_142,plain,
antidomain(coantidomain(zero)) = zero,
inference(rw,[status(thm)],[c_0_130,c_0_54]) ).
cnf(c_0_143,plain,
addition(X1,multiplication(X1,antidomain(X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_121]),c_0_61]),c_0_61]),c_0_31]) ).
cnf(c_0_144,plain,
coantidomain(zero) = coantidomain(multiplication(coantidomain(coantidomain(X1)),coantidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_42]),c_0_83]) ).
cnf(c_0_145,plain,
coantidomain(zero) = antidomain(multiplication(X1,antidomain(antidomain(coantidomain(X1))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_133]) ).
cnf(c_0_146,plain,
coantidomain(addition(X1,addition(X2,coantidomain(coantidomain(X1))))) = coantidomain(addition(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_115]),c_0_56]) ).
cnf(c_0_147,plain,
coantidomain(addition(X1,coantidomain(coantidomain(X1)))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_76]),c_0_31]),c_0_85]) ).
cnf(c_0_148,plain,
coantidomain(addition(X1,addition(coantidomain(coantidomain(X1)),X2))) = coantidomain(addition(coantidomain(coantidomain(X1)),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_136]),c_0_56]),c_0_137]) ).
cnf(c_0_149,plain,
multiplication(coantidomain(antidomain(addition(X1,X2))),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_138]),c_0_85]),c_0_69]) ).
cnf(c_0_150,plain,
multiplication(coantidomain(antidomain(X1)),multiplication(X1,X2)) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_139]),c_0_85]),c_0_45]) ).
cnf(c_0_151,plain,
coantidomain(zero) = antidomain(multiplication(antidomain(X1),antidomain(antidomain(X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_42]),c_0_133]) ).
cnf(c_0_152,plain,
addition(multiplication(antidomain(addition(X1,X2)),X1),multiplication(antidomain(addition(X1,X2)),X2)) = addition(multiplication(X1,coantidomain(addition(X1,X2))),multiplication(X2,coantidomain(addition(X1,X2)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_74]),c_0_72]) ).
cnf(c_0_153,plain,
coantidomain(addition(antidomain(X1),addition(antidomain(antidomain(X1)),X2))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_113]),c_0_56]) ).
cnf(c_0_154,plain,
addition(antidomain(X1),coantidomain(coantidomain(antidomain(X1)))) = coantidomain(coantidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_76]),c_0_31]) ).
cnf(c_0_155,plain,
antidomain(addition(antidomain(X1),antidomain(antidomain(X1)))) = zero,
inference(spm,[status(thm)],[c_0_142,c_0_113]) ).
cnf(c_0_156,plain,
coantidomain(addition(antidomain(X1),antidomain(antidomain(X1)))) = zero,
inference(spm,[status(thm)],[c_0_98,c_0_113]) ).
cnf(c_0_157,plain,
multiplication(X1,multiplication(antidomain(X2),coantidomain(coantidomain(X1)))) = multiplication(X1,antidomain(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_143]),c_0_60]) ).
cnf(c_0_158,plain,
multiplication(coantidomain(coantidomain(X1)),coantidomain(X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_144]),c_0_61]) ).
cnf(c_0_159,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_31]),c_0_56]) ).
cnf(c_0_160,plain,
addition(X1,multiplication(coantidomain(X2),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_71]),c_0_71]),c_0_31]) ).
cnf(c_0_161,plain,
multiplication(X1,antidomain(antidomain(coantidomain(X1)))) = multiplication(X1,coantidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_145]),c_0_71]),c_0_60]),c_0_89]) ).
cnf(c_0_162,plain,
coantidomain(addition(coantidomain(coantidomain(X1)),X2)) = coantidomain(addition(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_56]),c_0_87]),c_0_146]),c_0_56]),c_0_148]) ).
cnf(c_0_163,plain,
multiplication(X1,multiplication(coantidomain(X1),X2)) = multiplication(X1,coantidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_42]),c_0_60]) ).
cnf(c_0_164,plain,
multiplication(X1,multiplication(coantidomain(coantidomain(addition(X1,X2))),X3)) = multiplication(X1,X3),
inference(spm,[status(thm)],[c_0_60,c_0_100]) ).
cnf(c_0_165,plain,
multiplication(coantidomain(antidomain(X1)),multiplication(coantidomain(X2),X1)) = multiplication(coantidomain(X2),X1),
inference(spm,[status(thm)],[c_0_149,c_0_77]) ).
cnf(c_0_166,plain,
multiplication(coantidomain(antidomain(X1)),X1) = X1,
inference(spm,[status(thm)],[c_0_150,c_0_110]) ).
cnf(c_0_167,plain,
addition(antidomain(X1),antidomain(antidomain(antidomain(X1)))) = antidomain(antidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_71]),c_0_71]) ).
cnf(c_0_168,plain,
coantidomain(coantidomain(addition(antidomain(X1),antidomain(antidomain(X1))))) = addition(antidomain(X1),antidomain(antidomain(X1))),
inference(spm,[status(thm)],[c_0_85,c_0_113]) ).
cnf(c_0_169,plain,
multiplication(antidomain(X1),antidomain(antidomain(X1))) = multiplication(antidomain(X1),coantidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_151]),c_0_71]),c_0_60]),c_0_89]) ).
cnf(c_0_170,plain,
multiplication(antidomain(X1),multiplication(antidomain(X2),X1)) = multiplication(X1,coantidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_141]),c_0_74]),c_0_69]),c_0_60]),c_0_66]),c_0_57]) ).
cnf(c_0_171,plain,
multiplication(antidomain(coantidomain(X1)),coantidomain(coantidomain(X1))) = antidomain(coantidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_74]),c_0_69]) ).
cnf(c_0_172,plain,
coantidomain(addition(antidomain(X1),coantidomain(coantidomain(antidomain(antidomain(X1)))))) = zero,
inference(spm,[status(thm)],[c_0_153,c_0_154]) ).
cnf(c_0_173,plain,
addition(antidomain(addition(antidomain(X1),antidomain(antidomain(X1)))),X2) = X2,
inference(spm,[status(thm)],[c_0_45,c_0_155]) ).
cnf(c_0_174,plain,
antidomain(antidomain(addition(antidomain(X1),antidomain(antidomain(X1))))) = coantidomain(antidomain(addition(antidomain(X1),antidomain(antidomain(X1))))),
inference(spm,[status(thm)],[c_0_54,c_0_155]) ).
cnf(c_0_175,plain,
antidomain(coantidomain(coantidomain(addition(coantidomain(X1),coantidomain(coantidomain(X1)))))) = coantidomain(addition(coantidomain(X1),coantidomain(coantidomain(X1)))),
inference(spm,[status(thm)],[c_0_142,c_0_102]) ).
cnf(c_0_176,plain,
addition(X1,coantidomain(addition(antidomain(X2),antidomain(antidomain(X2))))) = X1,
inference(spm,[status(thm)],[c_0_40,c_0_156]) ).
cnf(c_0_177,plain,
multiplication(coantidomain(X1),multiplication(antidomain(X2),coantidomain(X1))) = multiplication(coantidomain(X1),antidomain(X2)),
inference(spm,[status(thm)],[c_0_157,c_0_85]) ).
cnf(c_0_178,plain,
multiplication(coantidomain(X1),multiplication(coantidomain(X2),coantidomain(X1))) = multiplication(coantidomain(X1),coantidomain(X2)),
inference(spm,[status(thm)],[c_0_107,c_0_85]) ).
cnf(c_0_179,plain,
multiplication(coantidomain(X1),coantidomain(X1)) = coantidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_158]),c_0_40]) ).
cnf(c_0_180,plain,
addition(X1,addition(X2,multiplication(coantidomain(X3),X1))) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_159,c_0_160]) ).
cnf(c_0_181,plain,
multiplication(coantidomain(X1),antidomain(antidomain(coantidomain(X1)))) = antidomain(antidomain(coantidomain(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_161]),c_0_85]),c_0_85]),c_0_91]),c_0_78]),c_0_85]) ).
cnf(c_0_182,plain,
coantidomain(addition(X1,addition(multiplication(X2,X1),X3))) = coantidomain(addition(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_135]),c_0_162]),c_0_56]) ).
cnf(c_0_183,plain,
addition(coantidomain(multiplication(X1,coantidomain(X1))),antidomain(multiplication(X1,antidomain(antidomain(multiplication(coantidomain(X1),X2)))))) = antidomain(multiplication(X1,antidomain(antidomain(multiplication(coantidomain(X1),X2))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_163]),c_0_129]) ).
cnf(c_0_184,plain,
addition(coantidomain(multiplication(X1,coantidomain(X1))),antidomain(X2)) = coantidomain(multiplication(X1,coantidomain(X1))),
inference(spm,[status(thm)],[c_0_133,c_0_42]) ).
cnf(c_0_185,plain,
multiplication(coantidomain(coantidomain(addition(coantidomain(antidomain(X1)),X2))),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_165]),c_0_166]) ).
cnf(c_0_186,plain,
addition(multiplication(X1,antidomain(X2)),multiplication(X1,antidomain(antidomain(antidomain(X2))))) = multiplication(X1,antidomain(antidomain(antidomain(X2)))),
inference(spm,[status(thm)],[c_0_63,c_0_167]) ).
cnf(c_0_187,plain,
multiplication(antidomain(X1),antidomain(X1)) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_168]),c_0_63]),c_0_169]),c_0_78]) ).
cnf(c_0_188,plain,
multiplication(antidomain(coantidomain(coantidomain(X1))),antidomain(coantidomain(X1))) = multiplication(X1,coantidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_171]),c_0_85]),c_0_91]) ).
cnf(c_0_189,plain,
coantidomain(coantidomain(antidomain(addition(antidomain(X1),antidomain(antidomain(X1)))))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_173]),c_0_85]),c_0_174]) ).
cnf(c_0_190,plain,
antidomain(addition(antidomain(X1),antidomain(antidomain(X1)))) = coantidomain(addition(antidomain(X1),antidomain(antidomain(X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_168]),c_0_56]),c_0_176]),c_0_168]),c_0_56]),c_0_176]) ).
cnf(c_0_191,plain,
multiplication(coantidomain(addition(antidomain(X1),X2)),antidomain(X1)) = multiplication(antidomain(X1),coantidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_96]),c_0_66]) ).
cnf(c_0_192,plain,
multiplication(coantidomain(addition(X1,antidomain(X2))),antidomain(X2)) = multiplication(antidomain(X2),coantidomain(antidomain(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_97]),c_0_66]) ).
cnf(c_0_193,plain,
addition(multiplication(X1,multiplication(coantidomain(X2),X3)),multiplication(X1,multiplication(coantidomain(coantidomain(X2)),X3))) = multiplication(X1,X3),
inference(spm,[status(thm)],[c_0_63,c_0_77]) ).
cnf(c_0_194,plain,
multiplication(coantidomain(X1),coantidomain(multiplication(X2,X1))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_108]),c_0_179]) ).
cnf(c_0_195,plain,
multiplication(coantidomain(addition(X1,X2)),coantidomain(X1)) = coantidomain(addition(X1,X2)),
inference(spm,[status(thm)],[c_0_116,c_0_100]) ).
cnf(c_0_196,plain,
coantidomain(addition(antidomain(X1),addition(X2,antidomain(antidomain(X1))))) = zero,
inference(spm,[status(thm)],[c_0_153,c_0_180]) ).
cnf(c_0_197,plain,
addition(coantidomain(X1),antidomain(antidomain(coantidomain(X1)))) = coantidomain(X1),
inference(spm,[status(thm)],[c_0_143,c_0_181]) ).
cnf(c_0_198,plain,
coantidomain(addition(X1,addition(X2,multiplication(X3,X1)))) = coantidomain(addition(X1,X2)),
inference(spm,[status(thm)],[c_0_182,c_0_31]) ).
cnf(c_0_199,plain,
multiplication(X1,coantidomain(coantidomain(addition(X2,coantidomain(coantidomain(X1)))))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_117]),c_0_76]) ).
cnf(c_0_200,plain,
multiplication(X1,multiplication(antidomain(X2),coantidomain(X1))) = multiplication(X1,coantidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_143]),c_0_74]),c_0_80]),c_0_57]),c_0_60]),c_0_69]) ).
cnf(c_0_201,plain,
leq(X1,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_111,c_0_65]) ).
cnf(c_0_202,plain,
multiplication(coantidomain(X1),coantidomain(addition(X1,X2))) = coantidomain(addition(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_100]),c_0_85]),c_0_85]) ).
cnf(c_0_203,plain,
antidomain(multiplication(X1,antidomain(antidomain(multiplication(coantidomain(X1),X2))))) = coantidomain(multiplication(X1,coantidomain(X1))),
inference(rw,[status(thm)],[c_0_183,c_0_184]) ).
cnf(c_0_204,plain,
multiplication(coantidomain(multiplication(X1,coantidomain(X1))),X2) = X2,
inference(spm,[status(thm)],[c_0_71,c_0_42]) ).
cnf(c_0_205,plain,
multiplication(coantidomain(antidomain(X1)),antidomain(X1)) = multiplication(antidomain(X1),coantidomain(antidomain(X1))),
inference(spm,[status(thm)],[c_0_66,c_0_177]) ).
cnf(c_0_206,plain,
multiplication(coantidomain(multiplication(X1,antidomain(X2))),X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_99]),c_0_85]) ).
cnf(c_0_207,plain,
multiplication(antidomain(X1),antidomain(antidomain(antidomain(X1)))) = antidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_186,c_0_187]),c_0_143]) ).
cnf(c_0_208,plain,
coantidomain(addition(antidomain(X1),antidomain(antidomain(X1)))) = multiplication(antidomain(X1),coantidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_189]),c_0_54]),c_0_190]),c_0_168]),c_0_190]),c_0_71]),c_0_190]),c_0_190]),c_0_168]),c_0_63]),c_0_191]),c_0_192]),c_0_78]) ).
cnf(c_0_209,plain,
multiplication(X1,coantidomain(multiplication(X1,coantidomain(X2)))) = multiplication(X1,coantidomain(coantidomain(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_89]),c_0_194]),c_0_69]) ).
cnf(c_0_210,plain,
multiplication(coantidomain(X1),coantidomain(multiplication(X1,coantidomain(X2)))) = coantidomain(X1),
inference(spm,[status(thm)],[c_0_195,c_0_70]) ).
cnf(c_0_211,plain,
coantidomain(addition(coantidomain(X1),antidomain(coantidomain(X1)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_197]),c_0_31]) ).
cnf(c_0_212,plain,
coantidomain(addition(X1,multiplication(X2,coantidomain(X1)))) = coantidomain(addition(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_198,c_0_70]),c_0_162]),c_0_162]) ).
cnf(c_0_213,plain,
multiplication(coantidomain(coantidomain(X1)),coantidomain(addition(X2,X1))) = multiplication(X1,coantidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_117]),c_0_85]) ).
cnf(c_0_214,plain,
coantidomain(addition(X1,addition(X2,coantidomain(coantidomain(X2))))) = coantidomain(addition(X1,coantidomain(coantidomain(X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_199]),c_0_56]),c_0_31]) ).
cnf(c_0_215,plain,
multiplication(coantidomain(X1),antidomain(coantidomain(X1))) = multiplication(coantidomain(X1),coantidomain(coantidomain(X1))),
inference(spm,[status(thm)],[c_0_200,c_0_171]) ).
cnf(c_0_216,plain,
leq(addition(X1,X2),addition(X1,addition(X2,X3))),
inference(spm,[status(thm)],[c_0_201,c_0_56]) ).
cnf(c_0_217,plain,
coantidomain(addition(X1,coantidomain(X1))) = multiplication(coantidomain(X1),coantidomain(coantidomain(X1))),
inference(spm,[status(thm)],[c_0_97,c_0_202]) ).
cnf(c_0_218,plain,
multiplication(X1,antidomain(antidomain(multiplication(coantidomain(X1),X2)))) = multiplication(X1,coantidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_203]),c_0_204]),c_0_60]),c_0_89]) ).
cnf(c_0_219,plain,
multiplication(coantidomain(coantidomain(antidomain(X1))),antidomain(X1)) = antidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_205]),c_0_69]) ).
cnf(c_0_220,plain,
addition(X1,addition(X2,multiplication(X1,antidomain(X3)))) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_159,c_0_143]) ).
cnf(c_0_221,plain,
multiplication(coantidomain(antidomain(X1)),antidomain(antidomain(X1))) = antidomain(antidomain(X1)),
inference(spm,[status(thm)],[c_0_206,c_0_207]) ).
cnf(c_0_222,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = coantidomain(multiplication(antidomain(X1),coantidomain(antidomain(X1)))),
inference(rw,[status(thm)],[c_0_168,c_0_208]) ).
cnf(c_0_223,plain,
coantidomain(multiplication(X1,coantidomain(X2))) = addition(coantidomain(X1),coantidomain(coantidomain(X2))),
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_209]),c_0_105]),c_0_210]),c_0_94]),c_0_105]) ).
cnf(c_0_224,plain,
addition(coantidomain(addition(coantidomain(X1),antidomain(coantidomain(X1)))),X2) = X2,
inference(spm,[status(thm)],[c_0_45,c_0_211]) ).
cnf(c_0_225,plain,
coantidomain(addition(X1,coantidomain(coantidomain(X2)))) = coantidomain(addition(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_213]),c_0_78]),c_0_56]),c_0_214]) ).
cnf(c_0_226,plain,
multiplication(coantidomain(X1),coantidomain(addition(X2,X1))) = coantidomain(addition(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_117]),c_0_85]),c_0_85]) ).
cnf(c_0_227,plain,
addition(X1,addition(multiplication(X1,antidomain(X2)),X3)) = addition(X1,X3),
inference(spm,[status(thm)],[c_0_56,c_0_143]) ).
cnf(c_0_228,plain,
multiplication(coantidomain(coantidomain(X1)),antidomain(coantidomain(X1))) = antidomain(coantidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_215]),c_0_69]) ).
cnf(c_0_229,plain,
leq(addition(X1,antidomain(X2)),addition(X1,antidomain(antidomain(antidomain(X2))))),
inference(spm,[status(thm)],[c_0_216,c_0_167]) ).
cnf(c_0_230,plain,
addition(antidomain(X1),addition(coantidomain(zero),X2)) = addition(coantidomain(zero),X2),
inference(spm,[status(thm)],[c_0_56,c_0_121]) ).
cnf(c_0_231,plain,
coantidomain(addition(multiplication(X1,X2),multiplication(coantidomain(X1),X2))) = coantidomain(X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_217]),c_0_204]),c_0_72]) ).
cnf(c_0_232,plain,
multiplication(coantidomain(antidomain(X1)),antidomain(antidomain(antidomain(X1)))) = multiplication(coantidomain(antidomain(X1)),coantidomain(coantidomain(antidomain(X1)))),
inference(spm,[status(thm)],[c_0_218,c_0_219]) ).
fof(c_0_233,plain,
! [X39] : c(X39) = antidomain(domain(X39)),
inference(variable_rename,[status(thm)],[complement]) ).
fof(c_0_234,plain,
! [X33] : domain(X33) = antidomain(antidomain(X33)),
inference(variable_rename,[status(thm)],[domain4]) ).
fof(c_0_235,plain,
! [X42,X43] : forward_diamond(X42,X43) = domain(multiplication(X42,domain(X43))),
inference(variable_rename,[status(thm)],[forward_diamond]) ).
cnf(c_0_236,plain,
addition(coantidomain(antidomain(X1)),addition(X2,antidomain(antidomain(X1)))) = addition(X2,coantidomain(antidomain(X1))),
inference(spm,[status(thm)],[c_0_220,c_0_221]) ).
cnf(c_0_237,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = addition(coantidomain(antidomain(X1)),coantidomain(coantidomain(antidomain(X1)))),
inference(rw,[status(thm)],[c_0_222,c_0_223]) ).
cnf(c_0_238,plain,
multiplication(coantidomain(antidomain(X1)),multiplication(antidomain(X1),X2)) = multiplication(antidomain(X1),coantidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_205]),c_0_60]),c_0_163]) ).
cnf(c_0_239,plain,
coantidomain(addition(coantidomain(X1),antidomain(coantidomain(X1)))) = multiplication(coantidomain(X1),coantidomain(coantidomain(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_217,c_0_224]),c_0_85]),c_0_85]),c_0_91]),c_0_72]),c_0_96]),c_0_97]),c_0_78]) ).
cnf(c_0_240,plain,
multiplication(X1,coantidomain(addition(coantidomain(X1),X2))) = multiplication(X1,coantidomain(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_223]),c_0_225]),c_0_60]),c_0_226]) ).
cnf(c_0_241,plain,
addition(coantidomain(X1),multiplication(coantidomain(coantidomain(X1)),antidomain(X2))) = addition(coantidomain(X1),antidomain(X2)),
inference(spm,[status(thm)],[c_0_227,c_0_77]) ).
cnf(c_0_242,plain,
multiplication(coantidomain(X1),antidomain(antidomain(antidomain(coantidomain(X1))))) = multiplication(coantidomain(X1),coantidomain(coantidomain(X1))),
inference(spm,[status(thm)],[c_0_218,c_0_228]) ).
cnf(c_0_243,plain,
leq(coantidomain(zero),addition(antidomain(X1),antidomain(antidomain(antidomain(antidomain(X1)))))),
inference(spm,[status(thm)],[c_0_229,c_0_113]) ).
cnf(c_0_244,plain,
addition(coantidomain(zero),addition(X1,antidomain(X2))) = addition(coantidomain(zero),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_230]),c_0_56]) ).
cnf(c_0_245,plain,
coantidomain(antidomain(antidomain(antidomain(X1)))) = coantidomain(antidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_231,c_0_232]),c_0_69]),c_0_105]),c_0_207]) ).
fof(c_0_246,negated_conjecture,
~ ! [X4,X5,X6] :
( addition(forward_box(X4,domain(X5)),domain(X6)) = one
=> addition(domain(X5),backward_box(X4,domain(X6))) = one ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_247,plain,
! [X46,X47] : forward_box(X46,X47) = c(forward_diamond(X46,c(X47))),
inference(variable_rename,[status(thm)],[forward_box]) ).
cnf(c_0_248,plain,
c(X1) = antidomain(domain(X1)),
inference(split_conjunct,[status(thm)],[c_0_233]) ).
cnf(c_0_249,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_234]) ).
cnf(c_0_250,plain,
forward_diamond(X1,X2) = domain(multiplication(X1,domain(X2))),
inference(split_conjunct,[status(thm)],[c_0_235]) ).
cnf(c_0_251,plain,
multiplication(X1,multiplication(coantidomain(coantidomain(addition(X2,X1))),X3)) = multiplication(X1,X3),
inference(spm,[status(thm)],[c_0_60,c_0_117]) ).
cnf(c_0_252,plain,
addition(coantidomain(antidomain(X1)),coantidomain(coantidomain(antidomain(X1)))) = addition(antidomain(X1),coantidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_236,c_0_237]),c_0_65]) ).
cnf(c_0_253,plain,
multiplication(coantidomain(coantidomain(antidomain(X1))),multiplication(antidomain(X1),X2)) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_238]),c_0_69]) ).
cnf(c_0_254,plain,
multiplication(coantidomain(coantidomain(X1)),multiplication(coantidomain(X1),X2)) = multiplication(X1,coantidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_85]),c_0_91]) ).
cnf(c_0_255,plain,
coantidomain(addition(X1,antidomain(coantidomain(coantidomain(X1))))) = multiplication(X1,coantidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_239,c_0_162]),c_0_85]),c_0_91]) ).
cnf(c_0_256,plain,
coantidomain(addition(X1,X2)) = multiplication(coantidomain(X1),coantidomain(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_240]),c_0_96]),c_0_85]),c_0_91]),c_0_78]),c_0_162]) ).
cnf(c_0_257,plain,
addition(coantidomain(X1),coantidomain(antidomain(coantidomain(X1)))) = coantidomain(antidomain(coantidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_166]),c_0_31]) ).
cnf(c_0_258,plain,
addition(coantidomain(X1),antidomain(antidomain(antidomain(coantidomain(coantidomain(X1)))))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_241,c_0_242]),c_0_78]) ).
cnf(c_0_259,plain,
coantidomain(zero) = addition(antidomain(X1),antidomain(antidomain(antidomain(antidomain(X1))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_243]),c_0_244]),c_0_133]) ).
cnf(c_0_260,plain,
coantidomain(addition(X1,antidomain(antidomain(antidomain(X2))))) = coantidomain(addition(X1,antidomain(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_225,c_0_245]),c_0_225]) ).
cnf(c_0_261,plain,
antidomain(coantidomain(multiplication(X1,coantidomain(X1)))) = multiplication(X1,coantidomain(X1)),
inference(spm,[status(thm)],[c_0_142,c_0_42]) ).
cnf(c_0_262,plain,
addition(antidomain(X1),coantidomain(multiplication(X2,coantidomain(X2)))) = coantidomain(multiplication(X2,coantidomain(X2))),
inference(spm,[status(thm)],[c_0_121,c_0_42]) ).
cnf(c_0_263,plain,
addition(antidomain(X1),coantidomain(antidomain(antidomain(X1)))) = coantidomain(antidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_166]),c_0_31]) ).
fof(c_0_264,negated_conjecture,
( addition(domain(esk2_0),backward_box(esk1_0,domain(esk3_0))) != one
& addition(forward_box(esk1_0,domain(esk2_0)),domain(esk3_0)) = one ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_246])])])]) ).
cnf(c_0_265,plain,
forward_box(X1,X2) = c(forward_diamond(X1,c(X2))),
inference(split_conjunct,[status(thm)],[c_0_247]) ).
cnf(c_0_266,plain,
c(X1) = antidomain(antidomain(antidomain(X1))),
inference(rw,[status(thm)],[c_0_248,c_0_249]) ).
cnf(c_0_267,plain,
forward_diamond(X1,X2) = antidomain(antidomain(multiplication(X1,antidomain(antidomain(X2))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_250,c_0_249]),c_0_249]) ).
cnf(c_0_268,plain,
multiplication(coantidomain(coantidomain(antidomain(X1))),X2) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_251,c_0_252]),c_0_217]),c_0_223]),c_0_85]),c_0_31]),c_0_252]),c_0_72]),c_0_63]),c_0_253]),c_0_254]),c_0_78]) ).
cnf(c_0_269,plain,
multiplication(coantidomain(X1),coantidomain(antidomain(coantidomain(coantidomain(X1))))) = multiplication(X1,coantidomain(X1)),
inference(rw,[status(thm)],[c_0_255,c_0_256]) ).
cnf(c_0_270,plain,
multiplication(coantidomain(X1),coantidomain(antidomain(coantidomain(X1)))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_257]),c_0_85]) ).
cnf(c_0_271,plain,
addition(antidomain(X1),antidomain(antidomain(antidomain(antidomain(X1))))) = coantidomain(multiplication(antidomain(X1),coantidomain(antidomain(X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_258,c_0_259]),c_0_260]),c_0_222]),c_0_125]),c_0_129]),c_0_261]),c_0_129]),c_0_56]),c_0_262]),c_0_262]) ).
cnf(c_0_272,plain,
multiplication(antidomain(X1),coantidomain(antidomain(antidomain(X1)))) = antidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_263]),c_0_85]) ).
fof(c_0_273,plain,
! [X48,X49] : backward_box(X48,X49) = c(backward_diamond(X48,c(X49))),
inference(variable_rename,[status(thm)],[backward_box]) ).
fof(c_0_274,plain,
! [X44,X45] : backward_diamond(X44,X45) = codomain(multiplication(codomain(X45),X44)),
inference(variable_rename,[status(thm)],[backward_diamond]) ).
fof(c_0_275,plain,
! [X38] : codomain(X38) = coantidomain(coantidomain(X38)),
inference(variable_rename,[status(thm)],[codomain4]) ).
cnf(c_0_276,negated_conjecture,
addition(forward_box(esk1_0,domain(esk2_0)),domain(esk3_0)) = one,
inference(split_conjunct,[status(thm)],[c_0_264]) ).
cnf(c_0_277,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_265,c_0_266]),c_0_266]),c_0_267]) ).
cnf(c_0_278,plain,
coantidomain(coantidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_268]),c_0_268]),c_0_70]) ).
cnf(c_0_279,plain,
coantidomain(antidomain(coantidomain(X1))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_269]),c_0_85]),c_0_270]),c_0_79]),c_0_85]) ).
cnf(c_0_280,plain,
addition(antidomain(X1),antidomain(antidomain(antidomain(antidomain(X1))))) = addition(coantidomain(antidomain(X1)),coantidomain(coantidomain(antidomain(X1)))),
inference(rw,[status(thm)],[c_0_271,c_0_223]) ).
cnf(c_0_281,plain,
multiplication(antidomain(antidomain(X1)),coantidomain(antidomain(X1))) = antidomain(antidomain(X1)),
inference(spm,[status(thm)],[c_0_116,c_0_272]) ).
cnf(c_0_282,plain,
backward_box(X1,X2) = c(backward_diamond(X1,c(X2))),
inference(split_conjunct,[status(thm)],[c_0_273]) ).
cnf(c_0_283,plain,
backward_diamond(X1,X2) = codomain(multiplication(codomain(X2),X1)),
inference(split_conjunct,[status(thm)],[c_0_274]) ).
cnf(c_0_284,plain,
codomain(X1) = coantidomain(coantidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_275]) ).
cnf(c_0_285,negated_conjecture,
addition(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk2_0))))))))))))),antidomain(antidomain(esk3_0))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_276,c_0_249]),c_0_249]),c_0_277]) ).
cnf(c_0_286,plain,
antidomain(coantidomain(X1)) = coantidomain(coantidomain(X1)),
inference(spm,[status(thm)],[c_0_278,c_0_279]) ).
cnf(c_0_287,plain,
multiplication(coantidomain(antidomain(X1)),coantidomain(antidomain(antidomain(X1)))) = multiplication(antidomain(X1),coantidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_256,c_0_280]),c_0_217]),c_0_85]),c_0_91]),c_0_245]) ).
cnf(c_0_288,plain,
multiplication(coantidomain(coantidomain(antidomain(X1))),coantidomain(antidomain(antidomain(X1)))) = coantidomain(coantidomain(antidomain(X1))),
inference(spm,[status(thm)],[c_0_194,c_0_281]) ).
cnf(c_0_289,negated_conjecture,
addition(domain(esk2_0),backward_box(esk1_0,domain(esk3_0))) != one,
inference(split_conjunct,[status(thm)],[c_0_264]) ).
cnf(c_0_290,plain,
backward_box(X1,X2) = antidomain(antidomain(antidomain(backward_diamond(X1,antidomain(antidomain(antidomain(X2))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_282,c_0_266]),c_0_266]) ).
cnf(c_0_291,plain,
backward_diamond(X1,X2) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(X2)),X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_283,c_0_284]),c_0_284]) ).
cnf(c_0_292,negated_conjecture,
addition(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk2_0))))))))))))),antidomain(antidomain(esk3_0))) = coantidomain(zero),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_285,c_0_44]),c_0_45]),c_0_54]) ).
cnf(c_0_293,plain,
antidomain(antidomain(X1)) = coantidomain(antidomain(X1)),
inference(spm,[status(thm)],[c_0_286,c_0_278]) ).
cnf(c_0_294,plain,
coantidomain(antidomain(antidomain(X1))) = coantidomain(coantidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_287]),c_0_288]),c_0_69]) ).
cnf(c_0_295,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk3_0))))))),esk1_0))))))) != one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_289,c_0_249]),c_0_249]),c_0_290]),c_0_291]) ).
cnf(c_0_296,negated_conjecture,
addition(antidomain(multiplication(esk1_0,antidomain(esk2_0))),coantidomain(antidomain(esk3_0))) = coantidomain(zero),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_292,c_0_293]),c_0_245]),c_0_294]),c_0_293]),c_0_286]),c_0_278]),c_0_293]),c_0_286]),c_0_278]),c_0_293]),c_0_286]),c_0_278]),c_0_278]),c_0_293]) ).
cnf(c_0_297,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk3_0))))))),esk1_0))))))) != addition(zero,antidomain(zero)),
inference(rw,[status(thm)],[c_0_295,c_0_44]) ).
cnf(c_0_298,negated_conjecture,
multiplication(coantidomain(antidomain(multiplication(esk1_0,antidomain(esk2_0)))),antidomain(esk3_0)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_256,c_0_296]),c_0_98]),c_0_278]) ).
cnf(c_0_299,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk3_0))))))),esk1_0))))))) != antidomain(zero),
inference(rw,[status(thm)],[c_0_297,c_0_45]) ).
cnf(c_0_300,plain,
multiplication(coantidomain(X1),antidomain(X2)) = multiplication(antidomain(X2),coantidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_200]),c_0_78]),c_0_85]),c_0_177]),c_0_85]) ).
cnf(c_0_301,plain,
multiplication(antidomain(X1),multiplication(antidomain(X2),antidomain(X1))) = multiplication(antidomain(X1),antidomain(X2)),
inference(spm,[status(thm)],[c_0_177,c_0_278]) ).
cnf(c_0_302,negated_conjecture,
multiplication(antidomain(multiplication(esk1_0,antidomain(esk2_0))),antidomain(esk3_0)) = antidomain(esk3_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_298]),c_0_278]),c_0_45]) ).
cnf(c_0_303,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk3_0))))))),esk1_0))))))) != coantidomain(zero),
inference(rw,[status(thm)],[c_0_299,c_0_54]) ).
cnf(c_0_304,plain,
coantidomain(multiplication(X1,antidomain(X2))) = addition(coantidomain(antidomain(X2)),coantidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_300]),c_0_223]),c_0_85]) ).
cnf(c_0_305,plain,
multiplication(coantidomain(coantidomain(multiplication(X1,antidomain(X2)))),X2) = multiplication(X1,coantidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_254,c_0_206]),c_0_60]),c_0_89]) ).
cnf(c_0_306,negated_conjecture,
multiplication(antidomain(esk3_0),antidomain(multiplication(esk1_0,antidomain(esk2_0)))) = antidomain(esk3_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_301,c_0_302]),c_0_187]) ).
cnf(c_0_307,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),coantidomain(multiplication(antidomain(esk3_0),esk1_0))) != coantidomain(zero),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_303,c_0_286]),c_0_245]),c_0_245]),c_0_278]),c_0_85]),c_0_286]),c_0_286]),c_0_85]) ).
cnf(c_0_308,plain,
coantidomain(multiplication(X1,multiplication(X2,antidomain(X3)))) = addition(coantidomain(antidomain(X3)),coantidomain(multiplication(X1,X2))),
inference(spm,[status(thm)],[c_0_304,c_0_60]) ).
cnf(c_0_309,negated_conjecture,
multiplication(antidomain(esk3_0),multiplication(esk1_0,antidomain(esk2_0))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_305,c_0_306]),c_0_278]),c_0_42]) ).
cnf(c_0_310,negated_conjecture,
addition(coantidomain(antidomain(esk2_0)),coantidomain(multiplication(antidomain(esk3_0),esk1_0))) != coantidomain(zero),
inference(rw,[status(thm)],[c_0_307,c_0_293]) ).
cnf(c_0_311,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_308,c_0_309]),c_0_310]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE103+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n003.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 22:45:01 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 215.51/31.74 % Version: 3.5.1
% 215.51/31.74 % Preprocessing class: FSMSSMSSSSSNFFN.
% 215.51/31.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 215.51/31.74 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 215.51/31.74 % Starting new_bool_3 with 300s (1) cores
% 215.51/31.74 % Starting new_bool_1 with 300s (1) cores
% 215.51/31.74 % Starting sh5l with 300s (1) cores
% 215.51/31.74 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2780119 completed with status 0
% 215.51/31.74 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 215.51/31.74 % Preprocessing class: FSMSSMSSSSSNFFN.
% 215.51/31.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 215.51/31.74 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 215.51/31.74 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 215.51/31.74 % No SInE strategy applied
% 215.51/31.74 % Search class: FHUSM-FFMF21-DFFFFFNN
% 215.51/31.74 % partial match(1): FHUSM-FFMF21-MFFFFFNN
% 215.51/31.74 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 215.51/31.74 % Starting SubtermCWHack with 136s (1) cores
% 215.51/31.74 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 215.51/31.74 % Starting G-E--_100_C18_F1_PI_AE_Q4_CS_SP_S0Y with 212s (1) cores
% 215.51/31.74 % Starting H----_042_B03_F1_AE_Q4_SP_S2S with 136s (1) cores
% 215.51/31.74 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 215.51/31.74 % H----_042_B03_F1_AE_Q4_SP_S2S with pid 2780129 completed with status 0
% 215.51/31.74 % Result found by H----_042_B03_F1_AE_Q4_SP_S2S
% 215.51/31.74 % Preprocessing class: FSMSSMSSSSSNFFN.
% 215.51/31.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 215.51/31.74 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 215.51/31.74 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 215.51/31.74 % No SInE strategy applied
% 215.51/31.74 % Search class: FHUSM-FFMF21-DFFFFFNN
% 215.51/31.74 % partial match(1): FHUSM-FFMF21-MFFFFFNN
% 215.51/31.74 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 215.51/31.74 % Starting SubtermCWHack with 136s (1) cores
% 215.51/31.74 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 215.51/31.74 % Starting G-E--_100_C18_F1_PI_AE_Q4_CS_SP_S0Y with 212s (1) cores
% 215.51/31.74 % Starting H----_042_B03_F1_AE_Q4_SP_S2S with 136s (1) cores
% 215.51/31.74 % Preprocessing time : 0.002 s
% 215.51/31.74
% 215.51/31.74 % Proof found!
% 215.51/31.74 % SZS status Theorem
% 215.51/31.74 % SZS output start CNFRefutation
% See solution above
% 215.51/31.74 % Parsed axioms : 27
% 215.51/31.74 % Removed by relevancy pruning/SinE : 0
% 215.51/31.74 % Initial clauses : 29
% 215.51/31.74 % Removed in clause preprocessing : 8
% 215.51/31.74 % Initial clauses in saturation : 21
% 215.51/31.74 % Processed clauses : 69891
% 215.51/31.74 % ...of these trivial : 7219
% 215.51/31.74 % ...subsumed : 59309
% 215.51/31.74 % ...remaining for further processing : 3363
% 215.51/31.74 % Other redundant clauses eliminated : 0
% 215.51/31.74 % Clauses deleted for lack of memory : 0
% 215.51/31.74 % Backward-subsumed : 8
% 215.51/31.74 % Backward-rewritten : 1668
% 215.51/31.74 % Generated clauses : 1339727
% 215.51/31.74 % ...of the previous two non-redundant : 718289
% 215.51/31.74 % ...aggressively subsumed : 0
% 215.51/31.74 % Contextual simplify-reflections : 0
% 215.51/31.74 % Paramodulations : 1339679
% 215.51/31.74 % Factorizations : 0
% 215.51/31.74 % NegExts : 0
% 215.51/31.74 % Equation resolutions : 48
% 215.51/31.74 % Disequality decompositions : 0
% 215.51/31.74 % Total rewrite steps : 2533258
% 215.51/31.74 % ...of those cached : 2253921
% 215.51/31.74 % Propositional unsat checks : 0
% 215.51/31.74 % Propositional check models : 0
% 215.51/31.74 % Propositional check unsatisfiable : 0
% 215.51/31.74 % Propositional clauses : 0
% 215.51/31.74 % Propositional clauses after purity: 0
% 215.51/31.74 % Propositional unsat core size : 0
% 215.51/31.74 % Propositional preprocessing time : 0.000
% 215.51/31.74 % Propositional encoding time : 0.000
% 215.51/31.74 % Propositional solver time : 0.000
% 215.51/31.74 % Success case prop preproc time : 0.000
% 215.51/31.74 % Success case prop encoding time : 0.000
% 215.51/31.74 % Success case prop solver time : 0.000
% 215.51/31.74 % Current number of processed clauses : 1687
% 215.51/31.74 % Positive orientable unit clauses : 947
% 215.51/31.74 % Positive unorientable unit clauses: 23
% 215.51/31.74 % Negative unit clauses : 1
% 215.51/31.74 % Non-unit-clauses : 716
% 215.51/31.74 % Current number of unprocessed clauses: 639519
% 215.51/31.74 % ...number of literals in the above : 953010
% 215.51/31.74 % Current number of archived formulas : 0
% 215.51/31.74 % Current number of archived clauses : 1684
% 215.51/31.74 % Clause-clause subsumption calls (NU) : 266251
% 215.51/31.74 % Rec. Clause-clause subsumption calls : 266009
% 215.51/31.74 % Non-unit clause-clause subsumptions : 30452
% 215.51/31.74 % Unit Clause-clause subsumption calls : 8310
% 215.51/31.74 % Rewrite failures with RHS unbound : 2678
% 215.51/31.74 % BW rewrite match attempts : 24155
% 215.51/31.74 % BW rewrite match successes : 2100
% 215.51/31.74 % Condensation attempts : 0
% 215.51/31.74 % Condensation successes : 0
% 215.51/31.74 % Termbank termtop insertions : 20880284
% 215.51/31.74 % Search garbage collected termcells : 55
% 215.51/31.74
% 215.51/31.74 % -------------------------------------------------
% 215.51/31.74 % User time : 30.082 s
% 215.51/31.74 % System time : 0.876 s
% 215.51/31.74 % Total time : 30.958 s
% 215.51/31.74 % Maximum resident set size: 3660 pages
% 215.51/31.74
% 215.51/31.74 % -------------------------------------------------
% 215.51/31.74 % User time : 148.619 s
% 215.51/31.74 % System time : 4.726 s
% 215.51/31.74 % Total time : 153.345 s
% 215.51/31.74 % Maximum resident set size: 4864 pages
% 215.51/31.74 % E exiting
%------------------------------------------------------------------------------