%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE103+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/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 12:58:51 PM UTC 2026
% Result : Theorem 151.73s 31.60s
% Output : CNFRefutation 245.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 25
% Syntax : Number of formulae : 242 ( 239 unt; 0 def)
% Number of atoms : 245 ( 244 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 7 ~; 0 |; 1 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 15 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-2 aty)
% Number of variables : 406 ( 72 sgn 84 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(codomain1,axiom,
! [X4] : multiplication(X4,coantidomain(X4)) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain1) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(codomain3,axiom,
! [X4] : addition(coantidomain(coantidomain(X4)),coantidomain(X4)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain3) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(domain1,axiom,
! [X4] : multiplication(antidomain(X4),X4) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain1) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(domain3,axiom,
! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain3) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(domain2,axiom,
! [X4,X5] : addition(antidomain(multiplication(X4,X5)),antidomain(multiplication(X4,antidomain(antidomain(X5))))) = antidomain(multiplication(X4,antidomain(antidomain(X5)))),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain2) ).
fof(codomain2,axiom,
! [X4,X5] : addition(coantidomain(multiplication(X4,X5)),coantidomain(multiplication(coantidomain(coantidomain(X4)),X5))) = coantidomain(multiplication(coantidomain(coantidomain(X4)),X5)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain2) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(complement,axiom,
! [X4] : c(X4) = antidomain(domain(X4)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+6.ax',complement) ).
fof(domain4,axiom,
! [X4] : domain(X4) = antidomain(antidomain(X4)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain4) ).
fof(forward_diamond,axiom,
! [X4,X5] : forward_diamond(X4,X5) = domain(multiplication(X4,domain(X5))),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',goals) ).
fof(forward_box,axiom,
! [X4,X5] : forward_box(X4,X5) = c(forward_diamond(X4,c(X5))),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/KLE001+6.ax',backward_diamond) ).
fof(codomain4,axiom,
! [X4] : codomain(X4) = coantidomain(coantidomain(X4)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain4) ).
fof(c_0_25,plain,
! [X19,X20,X21] : multiplication(X19,addition(X20,X21)) = addition(multiplication(X19,X20),multiplication(X19,X21)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_26,plain,
! [X34] : multiplication(X34,coantidomain(X34)) = zero,
inference(variable_rename,[status(thm)],[codomain1]) ).
fof(c_0_27,plain,
! [X12] : addition(X12,zero) = X12,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_28,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,plain,
multiplication(X1,coantidomain(X1)) = zero,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_30,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_31,plain,
! [X7,X8] : addition(X7,X8) = addition(X8,X7),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_32,plain,
! [X37] : addition(coantidomain(coantidomain(X37)),coantidomain(X37)) = one,
inference(variable_rename,[status(thm)],[codomain3]) ).
fof(c_0_33,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_34,plain,
multiplication(X1,addition(X2,coantidomain(X1))) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_35,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_36,plain,
addition(coantidomain(coantidomain(X1)),coantidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_37,plain,
! [X17] : multiplication(X17,one) = X17,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_38,plain,
! [X29] : multiplication(antidomain(X29),X29) = zero,
inference(variable_rename,[status(thm)],[domain1]) ).
cnf(c_0_39,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_40,plain,
! [X18] : multiplication(one,X18) = X18,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_41,plain,
multiplication(X1,addition(coantidomain(X1),X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_42,plain,
addition(coantidomain(X1),coantidomain(coantidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_36,c_0_35]) ).
cnf(c_0_43,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_37]) ).
fof(c_0_44,plain,
! [X32] : addition(antidomain(antidomain(X32)),antidomain(X32)) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
fof(c_0_45,plain,
! [X9,X10,X11] : addition(X11,addition(X10,X9)) = addition(addition(X11,X10),X9),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_46,plain,
! [X13] : addition(X13,X13) = X13,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_47,plain,
multiplication(antidomain(X1),X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_48,plain,
multiplication(addition(X1,X2),coantidomain(X2)) = multiplication(X1,coantidomain(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_29]),c_0_30]) ).
cnf(c_0_49,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_50,plain,
multiplication(X1,coantidomain(coantidomain(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
cnf(c_0_51,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_52,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_53,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_46]) ).
fof(c_0_54,plain,
! [X14,X15,X16] : multiplication(X14,multiplication(X15,X16)) = multiplication(multiplication(X14,X15),X16),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(c_0_55,plain,
! [X26] : multiplication(zero,X26) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_56,plain,
multiplication(addition(X1,antidomain(X2)),X2) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_47]),c_0_30]) ).
fof(c_0_57,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_58,plain,
coantidomain(coantidomain(coantidomain(X1))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_42]),c_0_49]),c_0_50]) ).
cnf(c_0_59,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_51,c_0_35]) ).
cnf(c_0_60,plain,
antidomain(one) = zero,
inference(spm,[status(thm)],[c_0_43,c_0_47]) ).
cnf(c_0_61,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_30,c_0_35]) ).
cnf(c_0_62,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_63,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_64,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_65,plain,
multiplication(addition(antidomain(X1),X2),X1) = multiplication(X2,X1),
inference(spm,[status(thm)],[c_0_56,c_0_35]) ).
cnf(c_0_66,plain,
addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,antidomain(antidomain(X2))))) = antidomain(multiplication(X1,antidomain(antidomain(X2)))),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_67,plain,
multiplication(coantidomain(coantidomain(X1)),coantidomain(X1)) = zero,
inference(spm,[status(thm)],[c_0_29,c_0_58]) ).
cnf(c_0_68,plain,
antidomain(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]) ).
cnf(c_0_69,plain,
addition(one,antidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_59]),c_0_35]) ).
fof(c_0_70,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_71,plain,
multiplication(antidomain(X1),multiplication(X1,X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_47]),c_0_64]) ).
cnf(c_0_72,plain,
multiplication(antidomain(antidomain(X1)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_59]),c_0_49]) ).
cnf(c_0_73,plain,
coantidomain(one) = zero,
inference(spm,[status(thm)],[c_0_49,c_0_29]) ).
cnf(c_0_74,plain,
antidomain(multiplication(coantidomain(coantidomain(X1)),antidomain(antidomain(coantidomain(X1))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]),c_0_69]) ).
fof(c_0_75,plain,
! [X25] : multiplication(X25,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
cnf(c_0_76,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_70]) ).
cnf(c_0_77,plain,
multiplication(antidomain(antidomain(antidomain(X1))),X1) = zero,
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_78,plain,
coantidomain(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_73]),c_0_61]) ).
cnf(c_0_79,plain,
addition(one,coantidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_42]),c_0_35]) ).
cnf(c_0_80,plain,
multiplication(X1,multiplication(coantidomain(coantidomain(X1)),X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_63,c_0_50]) ).
cnf(c_0_81,plain,
multiplication(coantidomain(coantidomain(X1)),antidomain(antidomain(coantidomain(X1)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_74]),c_0_49]) ).
cnf(c_0_82,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_83,plain,
coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(X1))))),X1)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]),c_0_79]) ).
cnf(c_0_84,plain,
multiplication(antidomain(X1),addition(X2,X1)) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_47]),c_0_30]) ).
cnf(c_0_85,plain,
multiplication(X1,antidomain(antidomain(coantidomain(X1)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]) ).
cnf(c_0_86,plain,
multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(X1))))),X1) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_83]),c_0_43]) ).
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_84,c_0_59]),c_0_43]),c_0_72]) ).
cnf(c_0_88,plain,
multiplication(antidomain(addition(X1,X2)),X1) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_62]),c_0_47]) ).
cnf(c_0_89,plain,
multiplication(X1,addition(antidomain(antidomain(coantidomain(X1))),X2)) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_85]),c_0_61]) ).
cnf(c_0_90,plain,
multiplication(coantidomain(coantidomain(antidomain(X1))),X1) = zero,
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_91,plain,
multiplication(addition(antidomain(addition(X1,X2)),X3),X1) = multiplication(X3,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_88]),c_0_61]) ).
cnf(c_0_92,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_35,c_0_52]) ).
cnf(c_0_93,plain,
multiplication(X1,antidomain(coantidomain(X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_59]),c_0_43]),c_0_87]) ).
cnf(c_0_94,plain,
multiplication(addition(coantidomain(coantidomain(antidomain(X1))),X2),X1) = multiplication(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_90]),c_0_61]) ).
cnf(c_0_95,plain,
multiplication(X1,coantidomain(addition(X1,X2))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_62]),c_0_29]) ).
cnf(c_0_96,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_76,c_0_63]) ).
cnf(c_0_97,plain,
multiplication(antidomain(antidomain(addition(X1,X2))),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_59]),c_0_49]) ).
cnf(c_0_98,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_92,c_0_53]) ).
cnf(c_0_99,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_49]),c_0_35]) ).
cnf(c_0_100,plain,
multiplication(coantidomain(coantidomain(X1)),antidomain(coantidomain(X1))) = coantidomain(coantidomain(X1)),
inference(spm,[status(thm)],[c_0_93,c_0_58]) ).
cnf(c_0_101,plain,
multiplication(antidomain(X1),addition(X1,X2)) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_47]),c_0_61]) ).
cnf(c_0_102,plain,
antidomain(multiplication(antidomain(X1),antidomain(antidomain(multiplication(X1,X2))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_71]),c_0_68]),c_0_69]) ).
cnf(c_0_103,plain,
multiplication(coantidomain(antidomain(X1)),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_42]),c_0_49]),c_0_58]) ).
cnf(c_0_104,plain,
multiplication(X1,addition(coantidomain(addition(X1,X2)),X3)) = multiplication(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_95]),c_0_61]) ).
cnf(c_0_105,plain,
coantidomain(multiplication(coantidomain(coantidomain(multiplication(X1,antidomain(X2)))),X2)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_47]),c_0_82]),c_0_78]),c_0_79]) ).
cnf(c_0_106,plain,
multiplication(antidomain(antidomain(addition(X1,X2))),X2) = X2,
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_107,plain,
addition(antidomain(coantidomain(X1)),coantidomain(coantidomain(X1))) = antidomain(coantidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_35]),c_0_79]),c_0_49]) ).
cnf(c_0_108,plain,
multiplication(antidomain(coantidomain(X1)),coantidomain(coantidomain(X1))) = antidomain(coantidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_42]),c_0_43]) ).
fof(c_0_109,plain,
! [X39] : c(X39) = antidomain(domain(X39)),
inference(variable_rename,[status(thm)],[complement]) ).
fof(c_0_110,plain,
! [X33] : domain(X33) = antidomain(antidomain(X33)),
inference(variable_rename,[status(thm)],[domain4]) ).
fof(c_0_111,plain,
! [X42,X43] : forward_diamond(X42,X43) = domain(multiplication(X42,domain(X43))),
inference(variable_rename,[status(thm)],[forward_diamond]) ).
cnf(c_0_112,plain,
multiplication(X1,multiplication(antidomain(coantidomain(X1)),X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_63,c_0_93]) ).
cnf(c_0_113,plain,
multiplication(antidomain(X1),antidomain(antidomain(multiplication(X1,X2)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_102]),c_0_49]) ).
cnf(c_0_114,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_43]),c_0_35]) ).
cnf(c_0_115,plain,
multiplication(coantidomain(antidomain(X1)),antidomain(antidomain(X1))) = antidomain(antidomain(X1)),
inference(spm,[status(thm)],[c_0_103,c_0_87]) ).
cnf(c_0_116,plain,
multiplication(X1,coantidomain(coantidomain(addition(X1,X2)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_42]),c_0_43]) ).
cnf(c_0_117,plain,
multiplication(X1,coantidomain(addition(X2,X1))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_98]),c_0_29]) ).
cnf(c_0_118,plain,
multiplication(coantidomain(coantidomain(multiplication(X1,antidomain(X2)))),X2) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_105]),c_0_43]) ).
cnf(c_0_119,plain,
coantidomain(coantidomain(X1)) = antidomain(coantidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_87]),c_0_108]) ).
cnf(c_0_120,plain,
multiplication(addition(X1,one),coantidomain(X1)) = coantidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_29]),c_0_30]) ).
fof(c_0_121,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_122,plain,
! [X46,X47] : forward_box(X46,X47) = c(forward_diamond(X46,c(X47))),
inference(variable_rename,[status(thm)],[forward_box]) ).
cnf(c_0_123,plain,
c(X1) = antidomain(domain(X1)),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_124,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_125,plain,
forward_diamond(X1,X2) = domain(multiplication(X1,domain(X2))),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_126,plain,
multiplication(X1,multiplication(X2,coantidomain(multiplication(X1,X2)))) = zero,
inference(spm,[status(thm)],[c_0_29,c_0_63]) ).
cnf(c_0_127,plain,
multiplication(X1,antidomain(antidomain(multiplication(coantidomain(X1),X2)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_82]) ).
cnf(c_0_128,plain,
addition(antidomain(X1),addition(antidomain(antidomain(X1)),X2)) = addition(one,X2),
inference(spm,[status(thm)],[c_0_52,c_0_59]) ).
cnf(c_0_129,plain,
addition(antidomain(antidomain(X1)),coantidomain(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_114,c_0_115]),c_0_35]),c_0_69]),c_0_43]),c_0_35]) ).
cnf(c_0_130,plain,
multiplication(addition(X1,X2),coantidomain(X1)) = multiplication(X2,coantidomain(X1)),
inference(spm,[status(thm)],[c_0_48,c_0_35]) ).
cnf(c_0_131,plain,
multiplication(X1,coantidomain(coantidomain(multiplication(addition(X2,one),X1)))) = X1,
inference(spm,[status(thm)],[c_0_116,c_0_99]) ).
cnf(c_0_132,plain,
multiplication(addition(X1,one),coantidomain(addition(X2,X1))) = coantidomain(addition(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_117]),c_0_30]) ).
cnf(c_0_133,plain,
multiplication(antidomain(coantidomain(multiplication(X1,antidomain(X2)))),X2) = zero,
inference(rw,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_134,plain,
multiplication(X1,coantidomain(coantidomain(addition(X2,X1)))) = X1,
inference(spm,[status(thm)],[c_0_116,c_0_98]) ).
cnf(c_0_135,plain,
multiplication(addition(one,X1),coantidomain(X1)) = coantidomain(X1),
inference(spm,[status(thm)],[c_0_120,c_0_35]) ).
fof(c_0_136,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_121])])])]) ).
cnf(c_0_137,plain,
forward_box(X1,X2) = c(forward_diamond(X1,c(X2))),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_138,plain,
c(X1) = antidomain(antidomain(antidomain(X1))),
inference(rw,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_139,plain,
forward_diamond(X1,X2) = antidomain(antidomain(multiplication(X1,antidomain(antidomain(X2))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_125,c_0_124]),c_0_124]) ).
cnf(c_0_140,plain,
antidomain(multiplication(antidomain(addition(X1,X2)),antidomain(antidomain(X1)))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_88]),c_0_68]),c_0_69]) ).
cnf(c_0_141,plain,
multiplication(X1,addition(one,multiplication(X2,coantidomain(multiplication(X1,X2))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_126]),c_0_30]),c_0_35]) ).
cnf(c_0_142,plain,
multiplication(antidomain(addition(X1,X2)),X2) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_98]),c_0_47]) ).
cnf(c_0_143,plain,
multiplication(X1,addition(antidomain(antidomain(multiplication(coantidomain(X1),X2))),X3)) = multiplication(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_127]),c_0_61]) ).
cnf(c_0_144,plain,
addition(antidomain(X1),coantidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_79]) ).
cnf(c_0_145,plain,
multiplication(antidomain(antidomain(X1)),coantidomain(antidomain(X1))) = coantidomain(antidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_59]),c_0_49]) ).
cnf(c_0_146,plain,
multiplication(X1,coantidomain(coantidomain(multiplication(addition(one,X2),X1)))) = X1,
inference(spm,[status(thm)],[c_0_131,c_0_35]) ).
cnf(c_0_147,plain,
multiplication(addition(one,X1),coantidomain(addition(X2,X1))) = coantidomain(addition(X2,X1)),
inference(spm,[status(thm)],[c_0_132,c_0_35]) ).
cnf(c_0_148,plain,
multiplication(antidomain(coantidomain(multiplication(X1,multiplication(X2,antidomain(X3))))),X3) = zero,
inference(spm,[status(thm)],[c_0_133,c_0_63]) ).
cnf(c_0_149,plain,
multiplication(X1,antidomain(coantidomain(addition(X2,X1)))) = X1,
inference(rw,[status(thm)],[c_0_134,c_0_119]) ).
cnf(c_0_150,plain,
multiplication(antidomain(coantidomain(coantidomain(X1))),coantidomain(X1)) = antidomain(coantidomain(coantidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_42]),c_0_43]) ).
cnf(c_0_151,plain,
coantidomain(addition(one,X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_62]),c_0_29]) ).
cnf(c_0_152,negated_conjecture,
addition(forward_box(esk1_0,domain(esk2_0)),domain(esk3_0)) = one,
inference(split_conjunct,[status(thm)],[c_0_136]) ).
cnf(c_0_153,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_137,c_0_138]),c_0_138]),c_0_139]) ).
cnf(c_0_154,plain,
multiplication(antidomain(addition(X1,X2)),antidomain(antidomain(X1))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_140]),c_0_49]) ).
cnf(c_0_155,plain,
multiplication(antidomain(addition(X1,X2)),addition(one,X2)) = antidomain(addition(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_78]),c_0_43]) ).
cnf(c_0_156,plain,
multiplication(X1,antidomain(multiplication(coantidomain(X1),X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_59]),c_0_43]),c_0_87]) ).
cnf(c_0_157,plain,
coantidomain(antidomain(X1)) = antidomain(antidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_144]),c_0_43]),c_0_145]) ).
cnf(c_0_158,plain,
multiplication(X1,antidomain(coantidomain(multiplication(addition(one,X2),X1)))) = X1,
inference(rw,[status(thm)],[c_0_146,c_0_119]) ).
cnf(c_0_159,plain,
multiplication(antidomain(X1),coantidomain(addition(antidomain(antidomain(X1)),X2))) = coantidomain(addition(antidomain(antidomain(X1)),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_128]),c_0_147]) ).
cnf(c_0_160,plain,
multiplication(antidomain(coantidomain(multiplication(X1,X2))),coantidomain(addition(X3,X2))) = zero,
inference(spm,[status(thm)],[c_0_148,c_0_149]) ).
cnf(c_0_161,plain,
antidomain(antidomain(coantidomain(X1))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_150,c_0_119]),c_0_72]),c_0_119]) ).
cnf(c_0_162,plain,
coantidomain(addition(X1,addition(one,X2))) = zero,
inference(spm,[status(thm)],[c_0_151,c_0_92]) ).
cnf(c_0_163,plain,
multiplication(coantidomain(X1),coantidomain(X1)) = coantidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_42]),c_0_43]) ).
cnf(c_0_164,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_152,c_0_124]),c_0_124]),c_0_153]) ).
cnf(c_0_165,plain,
multiplication(antidomain(addition(X1,X2)),antidomain(antidomain(X2))) = zero,
inference(spm,[status(thm)],[c_0_154,c_0_98]) ).
cnf(c_0_166,plain,
multiplication(antidomain(addition(antidomain(antidomain(X1)),X2)),antidomain(X1)) = antidomain(addition(antidomain(antidomain(X1)),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_128]),c_0_155]) ).
cnf(c_0_167,plain,
multiplication(addition(X1,one),X1) = multiplication(X1,addition(X1,one)),
inference(spm,[status(thm)],[c_0_114,c_0_99]) ).
cnf(c_0_168,plain,
multiplication(antidomain(X1),antidomain(multiplication(antidomain(antidomain(X1)),X2))) = antidomain(X1),
inference(spm,[status(thm)],[c_0_156,c_0_157]) ).
cnf(c_0_169,plain,
multiplication(antidomain(antidomain(X1)),multiplication(X1,X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_63,c_0_72]) ).
cnf(c_0_170,plain,
addition(coantidomain(multiplication(X1,X2)),coantidomain(multiplication(antidomain(coantidomain(addition(X1,antidomain(X2)))),X2))) = coantidomain(multiplication(antidomain(coantidomain(addition(X1,antidomain(X2)))),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_56]),c_0_119]),c_0_119]) ).
cnf(c_0_171,plain,
multiplication(X1,antidomain(coantidomain(multiplication(addition(X2,addition(one,X3)),X1)))) = X1,
inference(spm,[status(thm)],[c_0_158,c_0_92]) ).
cnf(c_0_172,plain,
coantidomain(addition(X1,coantidomain(multiplication(X2,X1)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_160]),c_0_161]),c_0_35]) ).
cnf(c_0_173,plain,
addition(coantidomain(X1),coantidomain(multiplication(addition(X2,addition(one,X3)),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_76,c_0_162]),c_0_78]),c_0_49]),c_0_78]),c_0_49]),c_0_35]) ).
cnf(c_0_174,plain,
multiplication(coantidomain(X1),addition(X2,coantidomain(X1))) = multiplication(coantidomain(X1),addition(X2,one)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_163]),c_0_35]),c_0_114]) ).
cnf(c_0_175,negated_conjecture,
addition(antidomain(antidomain(esk3_0)),antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk2_0)))))))))))))) = one,
inference(rw,[status(thm)],[c_0_164,c_0_35]) ).
cnf(c_0_176,plain,
addition(multiplication(X1,X2),addition(multiplication(X3,X2),X4)) = addition(multiplication(addition(X1,X3),X2),X4),
inference(spm,[status(thm)],[c_0_52,c_0_39]) ).
cnf(c_0_177,plain,
antidomain(addition(X1,antidomain(X1))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_87]),c_0_35]) ).
cnf(c_0_178,plain,
addition(multiplication(X1,X2),multiplication(X2,addition(X2,one))) = multiplication(addition(X1,addition(X2,one)),X2),
inference(spm,[status(thm)],[c_0_39,c_0_167]) ).
cnf(c_0_179,plain,
multiplication(antidomain(X1),antidomain(multiplication(X1,X2))) = antidomain(X1),
inference(spm,[status(thm)],[c_0_168,c_0_169]) ).
cnf(c_0_180,plain,
coantidomain(multiplication(coantidomain(coantidomain(X1)),coantidomain(addition(X1,X2)))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_95]),c_0_78]),c_0_79]) ).
cnf(c_0_181,plain,
coantidomain(multiplication(addition(X1,addition(one,X2)),X3)) = coantidomain(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(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_171]),c_0_161]),c_0_172]),c_0_68]),c_0_49]),c_0_157]),c_0_161]),c_0_173]),c_0_161]),c_0_172]),c_0_68]),c_0_49]),c_0_157]),c_0_161]) ).
cnf(c_0_182,plain,
addition(X1,multiplication(coantidomain(X2),addition(X1,one))) = addition(X1,coantidomain(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_174]),c_0_52]),c_0_114]),c_0_52]),c_0_53]),c_0_35]),c_0_79]),c_0_49]) ).
cnf(c_0_183,negated_conjecture,
addition(antidomain(antidomain(esk3_0)),antidomain(multiplication(esk1_0,antidomain(esk2_0)))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_175,c_0_87]),c_0_87]),c_0_87]),c_0_87]),c_0_87]) ).
fof(c_0_184,plain,
! [X48,X49] : backward_box(X48,X49) = c(backward_diamond(X48,c(X49))),
inference(variable_rename,[status(thm)],[backward_box]) ).
fof(c_0_185,plain,
! [X44,X45] : backward_diamond(X44,X45) = codomain(multiplication(codomain(X45),X44)),
inference(variable_rename,[status(thm)],[backward_diamond]) ).
fof(c_0_186,plain,
! [X38] : codomain(X38) = coantidomain(coantidomain(X38)),
inference(variable_rename,[status(thm)],[codomain4]) ).
cnf(c_0_187,plain,
addition(X1,addition(coantidomain(X2),multiplication(X2,X1))) = multiplication(addition(X2,one),addition(X1,coantidomain(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_34]),c_0_52]) ).
cnf(c_0_188,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X2,X1)),
inference(spm,[status(thm)],[c_0_92,c_0_35]) ).
cnf(c_0_189,plain,
addition(X1,addition(multiplication(X2,X1),X3)) = addition(multiplication(addition(one,X2),X1),X3),
inference(spm,[status(thm)],[c_0_176,c_0_49]) ).
cnf(c_0_190,plain,
multiplication(antidomain(multiplication(addition(X1,X2),X3)),multiplication(X1,X3)) = zero,
inference(spm,[status(thm)],[c_0_88,c_0_39]) ).
cnf(c_0_191,plain,
addition(antidomain(X1),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(spm,[status(thm)],[c_0_66,c_0_177]),c_0_68]),c_0_43]),c_0_68]),c_0_43]),c_0_35]) ).
cnf(c_0_192,plain,
addition(antidomain(X1),antidomain(multiplication(X1,X2))) = antidomain(multiplication(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_179]),c_0_35]),c_0_69]),c_0_43]),c_0_35]),c_0_69]),c_0_35]),c_0_69]),c_0_49]) ).
cnf(c_0_193,plain,
multiplication(coantidomain(coantidomain(X1)),coantidomain(addition(X1,X2))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_180]),c_0_43]) ).
cnf(c_0_194,plain,
coantidomain(multiplication(addition(X1,one),X2)) = coantidomain(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_182]),c_0_79]) ).
cnf(c_0_195,plain,
multiplication(addition(X1,one),antidomain(coantidomain(X1))) = addition(X1,antidomain(coantidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_93]),c_0_35]) ).
cnf(c_0_196,negated_conjecture,
multiplication(antidomain(antidomain(esk3_0)),multiplication(esk1_0,antidomain(esk2_0))) = multiplication(esk1_0,antidomain(esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_183]),c_0_49]) ).
cnf(c_0_197,plain,
backward_box(X1,X2) = c(backward_diamond(X1,c(X2))),
inference(split_conjunct,[status(thm)],[c_0_184]) ).
cnf(c_0_198,plain,
backward_diamond(X1,X2) = codomain(multiplication(codomain(X2),X1)),
inference(split_conjunct,[status(thm)],[c_0_185]) ).
cnf(c_0_199,plain,
codomain(X1) = coantidomain(coantidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_186]) ).
cnf(c_0_200,plain,
addition(antidomain(antidomain(X1)),antidomain(multiplication(X1,X2))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_179]),c_0_157]),c_0_35]),c_0_59]),c_0_35]),c_0_69]),c_0_35]),c_0_69]),c_0_157]),c_0_35]),c_0_49]) ).
cnf(c_0_201,plain,
multiplication(antidomain(antidomain(addition(X1,addition(X2,X3)))),X3) = X3,
inference(spm,[status(thm)],[c_0_97,c_0_188]) ).
cnf(c_0_202,plain,
addition(X1,addition(multiplication(coantidomain(X2),X1),X3)) = addition(X1,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_182]),c_0_53]),c_0_43]),c_0_79]),c_0_49]) ).
cnf(c_0_203,plain,
addition(coantidomain(X1),addition(coantidomain(coantidomain(X1)),X2)) = addition(one,X2),
inference(spm,[status(thm)],[c_0_52,c_0_42]) ).
cnf(c_0_204,plain,
multiplication(antidomain(X1),multiplication(antidomain(X2),X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_59]),c_0_49]) ).
cnf(c_0_205,plain,
antidomain(multiplication(X1,addition(X2,antidomain(X2)))) = antidomain(X1),
inference(rw,[status(thm)],[c_0_191,c_0_192]) ).
cnf(c_0_206,plain,
multiplication(X1,addition(multiplication(X2,coantidomain(multiplication(X1,X2))),X3)) = multiplication(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_126]),c_0_61]) ).
cnf(c_0_207,plain,
multiplication(coantidomain(coantidomain(X1)),coantidomain(addition(X2,X1))) = zero,
inference(spm,[status(thm)],[c_0_193,c_0_98]) ).
cnf(c_0_208,plain,
coantidomain(addition(X1,antidomain(coantidomain(X1)))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_195]),c_0_157]),c_0_161]) ).
cnf(c_0_209,plain,
addition(multiplication(addition(X1,one),X2),X3) = addition(X2,addition(multiplication(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_52,c_0_99]) ).
cnf(c_0_210,negated_conjecture,
multiplication(antidomain(esk3_0),multiplication(esk1_0,antidomain(esk2_0))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_196]),c_0_87]) ).
cnf(c_0_211,negated_conjecture,
addition(domain(esk2_0),backward_box(esk1_0,domain(esk3_0))) != one,
inference(split_conjunct,[status(thm)],[c_0_136]) ).
cnf(c_0_212,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_197,c_0_138]),c_0_138]) ).
cnf(c_0_213,plain,
backward_diamond(X1,X2) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(X2)),X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_198,c_0_199]),c_0_199]) ).
cnf(c_0_214,plain,
addition(antidomain(X1),antidomain(antidomain(addition(X2,addition(X3,X1))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_200,c_0_201]),c_0_87]),c_0_35]) ).
cnf(c_0_215,plain,
addition(X1,addition(X2,multiplication(coantidomain(X3),X1))) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_202,c_0_35]) ).
cnf(c_0_216,plain,
multiplication(coantidomain(X1),coantidomain(addition(antidomain(coantidomain(X1)),X2))) = coantidomain(addition(antidomain(coantidomain(X1)),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_203]),c_0_119]),c_0_147]),c_0_119]) ).
cnf(c_0_217,plain,
multiplication(antidomain(X1),addition(multiplication(antidomain(X2),X1),X3)) = multiplication(antidomain(X1),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_204]),c_0_61]) ).
cnf(c_0_218,plain,
antidomain(multiplication(X1,antidomain(multiplication(X2,coantidomain(multiplication(X1,X2)))))) = antidomain(X1),
inference(spm,[status(thm)],[c_0_205,c_0_206]) ).
cnf(c_0_219,plain,
multiplication(antidomain(coantidomain(X1)),coantidomain(addition(X2,X1))) = zero,
inference(rw,[status(thm)],[c_0_207,c_0_119]) ).
cnf(c_0_220,plain,
coantidomain(addition(X1,addition(multiplication(X2,X1),antidomain(coantidomain(X1))))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_209]),c_0_194]),c_0_194]) ).
cnf(c_0_221,plain,
addition(coantidomain(X1),addition(X2,addition(X3,antidomain(coantidomain(X1))))) = addition(one,addition(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_203,c_0_92]),c_0_119]) ).
cnf(c_0_222,negated_conjecture,
multiplication(antidomain(esk3_0),addition(multiplication(esk1_0,antidomain(esk2_0)),X1)) = multiplication(antidomain(esk3_0),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_210]),c_0_61]) ).
cnf(c_0_223,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_211,c_0_124]),c_0_124]),c_0_212]),c_0_213]) ).
cnf(c_0_224,plain,
addition(antidomain(multiplication(coantidomain(X1),X2)),antidomain(antidomain(addition(X2,X3)))) = one,
inference(spm,[status(thm)],[c_0_214,c_0_215]) ).
cnf(c_0_225,plain,
addition(coantidomain(X1),coantidomain(addition(antidomain(coantidomain(X1)),X2))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_216]),c_0_35]),c_0_79]),c_0_43]) ).
cnf(c_0_226,plain,
antidomain(multiplication(antidomain(X1),antidomain(multiplication(antidomain(X2),X1)))) = antidomain(antidomain(X1)),
inference(spm,[status(thm)],[c_0_205,c_0_217]) ).
cnf(c_0_227,plain,
antidomain(multiplication(antidomain(coantidomain(X1)),antidomain(coantidomain(addition(X2,X1))))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_219]),c_0_78]),c_0_43]),c_0_161]) ).
cnf(c_0_228,plain,
coantidomain(addition(X1,antidomain(coantidomain(addition(X2,X1))))) = coantidomain(addition(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_220,c_0_149]),c_0_157]),c_0_161]),c_0_98]),c_0_157]),c_0_161]) ).
cnf(c_0_229,plain,
addition(X1,multiplication(X2,multiplication(X3,X1))) = multiplication(addition(one,multiplication(X2,X3)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_63]),c_0_35]) ).
cnf(c_0_230,plain,
coantidomain(multiplication(addition(one,X1),X2)) = coantidomain(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_221]),c_0_62]) ).
cnf(c_0_231,negated_conjecture,
multiplication(antidomain(esk3_0),multiplication(esk1_0,addition(antidomain(esk2_0),X1))) = multiplication(antidomain(esk3_0),multiplication(esk1_0,X1)),
inference(spm,[status(thm)],[c_0_222,c_0_28]) ).
cnf(c_0_232,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(esk3_0))),esk1_0))))) != one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_223,c_0_87]),c_0_87]),c_0_87]) ).
cnf(c_0_233,plain,
addition(coantidomain(X1),antidomain(multiplication(coantidomain(X2),coantidomain(X1)))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_224,c_0_225]),c_0_161]),c_0_35]) ).
cnf(c_0_234,plain,
antidomain(multiplication(coantidomain(addition(X1,X2)),coantidomain(X2))) = antidomain(coantidomain(addition(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_226,c_0_227]),c_0_161]),c_0_87]) ).
cnf(c_0_235,plain,
coantidomain(addition(antidomain(coantidomain(X1)),multiplication(X2,multiplication(X3,X1)))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_228,c_0_229]),c_0_230]),c_0_230]),c_0_35]) ).
cnf(c_0_236,negated_conjecture,
multiplication(antidomain(esk3_0),multiplication(esk1_0,antidomain(antidomain(esk2_0)))) = multiplication(antidomain(esk3_0),esk1_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_231,c_0_59]),c_0_43]) ).
cnf(c_0_237,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),antidomain(antidomain(coantidomain(multiplication(antidomain(esk3_0),esk1_0))))) != one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_232,c_0_119]),c_0_157]),c_0_87]),c_0_119]) ).
cnf(c_0_238,plain,
addition(coantidomain(X1),antidomain(coantidomain(addition(X2,X1)))) = one,
inference(spm,[status(thm)],[c_0_233,c_0_234]) ).
cnf(c_0_239,negated_conjecture,
coantidomain(addition(antidomain(antidomain(esk2_0)),multiplication(antidomain(esk3_0),esk1_0))) = antidomain(esk2_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_236]),c_0_157]),c_0_87]),c_0_157]),c_0_87]) ).
cnf(c_0_240,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),coantidomain(multiplication(antidomain(esk3_0),esk1_0))) != one,
inference(rw,[status(thm)],[c_0_237,c_0_161]) ).
cnf(c_0_241,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_238,c_0_239]),c_0_35]),c_0_240]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE103+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 22:45:01 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 151.73/31.60 % Version: 3.5.1
% 151.73/31.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 151.73/31.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 151.73/31.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 151.73/31.60 % Starting new_bool_3 with 300s (1) cores
% 151.73/31.60 % Starting new_bool_1 with 300s (1) cores
% 151.73/31.60 % Starting sh5l with 300s (1) cores
% 151.73/31.60 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2780094 completed with status 0
% 151.73/31.60 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 151.73/31.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 151.73/31.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 151.73/31.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 151.73/31.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 151.73/31.60 % No SInE strategy applied
% 151.73/31.60 % Search class: FHUSM-FFMF21-DFFFFFNN
% 151.73/31.60 % partial match(1): FHUSM-FFMF21-MFFFFFNN
% 151.73/31.60 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 151.73/31.60 % Starting SubtermCWHack with 136s (1) cores
% 151.73/31.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 151.73/31.60 % Starting G-E--_100_C18_F1_PI_AE_Q4_CS_SP_S0Y with 212s (1) cores
% 151.73/31.60 % Starting H----_042_B03_F1_AE_Q4_SP_S2S with 136s (1) cores
% 151.73/31.60 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 151.73/31.60 % G-E--_100_C18_F1_PI_AE_Q4_CS_SP_S0Y with pid 2780101 completed with status 0
% 151.73/31.60 % Result found by G-E--_100_C18_F1_PI_AE_Q4_CS_SP_S0Y
% 151.73/31.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 151.73/31.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 151.73/31.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 151.73/31.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 151.73/31.60 % No SInE strategy applied
% 151.73/31.60 % Search class: FHUSM-FFMF21-DFFFFFNN
% 151.73/31.60 % partial match(1): FHUSM-FFMF21-MFFFFFNN
% 151.73/31.60 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 151.73/31.60 % Starting SubtermCWHack with 136s (1) cores
% 151.73/31.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 151.73/31.60 % Starting G-E--_100_C18_F1_PI_AE_Q4_CS_SP_S0Y with 212s (1) cores
% 151.73/31.60 % Preprocessing time : 0.001 s
% 151.73/31.60
% 151.73/31.60 % Proof found!
% 151.73/31.60 % SZS status Theorem
% 245.24/31.60 % SZS output start CNFRefutation
% See solution above
% 245.24/31.60 % Parsed axioms : 27
% 245.24/31.60 % Removed by relevancy pruning/SinE : 0
% 245.24/31.60 % Initial clauses : 29
% 245.24/31.60 % Removed in clause preprocessing : 8
% 245.24/31.60 % Initial clauses in saturation : 21
% 245.24/31.60 % Processed clauses : 22420
% 245.24/31.60 % ...of these trivial : 13492
% 245.24/31.60 % ...subsumed : 6464
% 245.24/31.60 % ...remaining for further processing : 2464
% 245.24/31.60 % Other redundant clauses eliminated : 0
% 245.24/31.60 % Clauses deleted for lack of memory : 0
% 245.24/31.60 % Backward-subsumed : 0
% 245.24/31.60 % Backward-rewritten : 491
% 245.24/31.60 % Generated clauses : 2075937
% 245.24/31.60 % ...of the previous two non-redundant : 871992
% 245.24/31.60 % ...aggressively subsumed : 0
% 245.24/31.60 % Contextual simplify-reflections : 0
% 245.24/31.60 % Paramodulations : 2075937
% 245.24/31.60 % Factorizations : 0
% 245.24/31.60 % NegExts : 0
% 245.24/31.60 % Equation resolutions : 0
% 245.24/31.60 % Disequality decompositions : 0
% 245.24/31.60 % Total rewrite steps : 4857374
% 245.24/31.60 % ...of those cached : 4347975
% 245.24/31.60 % Propositional unsat checks : 0
% 245.24/31.60 % Propositional check models : 0
% 245.24/31.60 % Propositional check unsatisfiable : 0
% 245.24/31.60 % Propositional clauses : 0
% 245.24/31.60 % Propositional clauses after purity: 0
% 245.24/31.60 % Propositional unsat core size : 0
% 245.24/31.60 % Propositional preprocessing time : 0.000
% 245.24/31.60 % Propositional encoding time : 0.000
% 245.24/31.60 % Propositional solver time : 0.000
% 245.24/31.60 % Success case prop preproc time : 0.000
% 245.24/31.60 % Success case prop encoding time : 0.000
% 245.24/31.60 % Success case prop solver time : 0.000
% 245.24/31.60 % Current number of processed clauses : 1973
% 245.24/31.60 % Positive orientable unit clauses : 1950
% 245.24/31.60 % Positive unorientable unit clauses: 18
% 245.24/31.60 % Negative unit clauses : 3
% 245.24/31.60 % Non-unit-clauses : 2
% 245.24/31.60 % Current number of unprocessed clauses: 846985
% 245.24/31.60 % ...number of literals in the above : 846985
% 245.24/31.60 % Current number of archived formulas : 0
% 245.24/31.60 % Current number of archived clauses : 499
% 245.24/31.60 % Clause-clause subsumption calls (NU) : 0
% 245.24/31.60 % Rec. Clause-clause subsumption calls : 0
% 245.24/31.60 % Non-unit clause-clause subsumptions : 0
% 245.24/31.60 % Unit Clause-clause subsumption calls : 160
% 245.24/31.60 % Rewrite failures with RHS unbound : 0
% 245.24/31.60 % BW rewrite match attempts : 34213
% 245.24/31.60 % BW rewrite match successes : 539
% 245.24/31.60 % Condensation attempts : 0
% 245.24/31.60 % Condensation successes : 0
% 245.24/31.60 % Termbank termtop insertions : 34141819
% 245.24/31.60 % Search garbage collected termcells : 55
% 245.24/31.60
% 245.24/31.60 % -------------------------------------------------
% 245.24/31.60 % User time : 29.602 s
% 245.24/31.60 % System time : 0.930 s
% 245.24/31.60 % Total time : 30.532 s
% 245.24/31.60 % Maximum resident set size: 3660 pages
% 245.24/31.60
% 245.24/31.60 % -------------------------------------------------
% 245.24/31.60 % User time : 146.745 s
% 245.24/31.60 % System time : 4.825 s
% 245.24/31.60 % Total time : 151.570 s
% 245.24/31.60 % Maximum resident set size: 4864 pages
% 245.24/31.60 % E exiting
%------------------------------------------------------------------------------