%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : KLE106+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 : n011.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 12:59:21 PM UTC 2026
% Result : Theorem 29.77s 4.92s
% Output : CNFRefutation 29.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 23
% Syntax : Number of formulae : 133 ( 129 unt; 0 def)
% Number of atoms : 137 ( 136 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 7 ~; 0 |; 1 &)
% ( 0 <=>; 1 =>; 2 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 15 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-2 aty)
% Number of variables : 182 ( 13 sgn 79 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(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(domain1,axiom,
! [X4] : multiplication(antidomain(X4),X4) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain1) ).
fof(domain3,axiom,
! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain3) ).
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(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(additive_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(codomain3,axiom,
! [X4] : addition(coantidomain(coantidomain(X4)),coantidomain(X4)) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',codomain3) ).
fof(goals,conjecture,
! [X4,X5,X6] :
( addition(forward_diamond(X4,domain(X5)),domain(X6)) = domain(X6)
<= addition(domain(X5),backward_box(X4,domain(X6))) = backward_box(X4,domain(X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
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(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(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(codomain1,axiom,
! [X4] : multiplication(X4,coantidomain(X4)) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',codomain1) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(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(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(c_0_23,plain,
! [X12] : addition(X12,zero) = X12,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_24,plain,
! [X7,X8] : addition(X7,X8) = addition(X8,X7),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_25,plain,
! [X22,X23,X24] : multiplication(addition(X22,X23),X24) = addition(multiplication(X22,X24),multiplication(X23,X24)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_26,plain,
! [X29] : multiplication(antidomain(X29),X29) = zero,
inference(variable_rename,[status(thm)],[domain1]) ).
cnf(c_0_27,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_29,plain,
! [X32] : addition(antidomain(antidomain(X32)),antidomain(X32)) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
fof(c_0_30,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_31,plain,
! [X17] : multiplication(X17,one) = X17,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_32,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_33,plain,
multiplication(antidomain(X1),X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_34,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_35,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_36,plain,
! [X18] : multiplication(one,X18) = X18,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_37,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_38,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_39,plain,
multiplication(addition(antidomain(X1),X2),X1) = multiplication(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_40,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_35,c_0_28]) ).
cnf(c_0_41,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_42,plain,
! [X9,X10,X11] : addition(X11,addition(X10,X9)) = addition(addition(X11,X10),X9),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_43,plain,
! [X13] : addition(X13,X13) = X13,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_44,plain,
! [X37] : addition(coantidomain(coantidomain(X37)),coantidomain(X37)) = one,
inference(variable_rename,[status(thm)],[codomain3]) ).
cnf(c_0_45,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_28]) ).
cnf(c_0_46,plain,
multiplication(antidomain(antidomain(X1)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_47,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_48,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_49,plain,
addition(coantidomain(coantidomain(X1)),coantidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_44]) ).
fof(c_0_50,negated_conjecture,
~ ! [X4,X5,X6] :
( addition(forward_diamond(X4,domain(X5)),domain(X6)) = domain(X6)
<= addition(domain(X5),backward_box(X4,domain(X6))) = backward_box(X4,domain(X6)) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_51,plain,
! [X39] : c(X39) = antidomain(domain(X39)),
inference(variable_rename,[status(thm)],[complement]) ).
fof(c_0_52,plain,
! [X33] : domain(X33) = antidomain(antidomain(X33)),
inference(variable_rename,[status(thm)],[domain4]) ).
cnf(c_0_53,plain,
multiplication(antidomain(antidomain(X1)),addition(X1,one)) = addition(X1,antidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_28]) ).
cnf(c_0_54,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_55,plain,
addition(coantidomain(X1),coantidomain(coantidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_49,c_0_28]) ).
fof(c_0_56,negated_conjecture,
~ ! [X4,X5,X6] :
( addition(domain(X5),backward_box(X4,domain(X6))) = backward_box(X4,domain(X6))
=> addition(forward_diamond(X4,domain(X5)),domain(X6)) = domain(X6) ),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_57,plain,
! [X48,X49] : backward_box(X48,X49) = c(backward_diamond(X48,c(X49))),
inference(variable_rename,[status(thm)],[backward_box]) ).
cnf(c_0_58,plain,
c(X1) = antidomain(domain(X1)),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_59,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
fof(c_0_60,plain,
! [X44,X45] : backward_diamond(X44,X45) = codomain(multiplication(codomain(X45),X44)),
inference(variable_rename,[status(thm)],[backward_diamond]) ).
fof(c_0_61,plain,
! [X38] : codomain(X38) = coantidomain(coantidomain(X38)),
inference(variable_rename,[status(thm)],[codomain4]) ).
cnf(c_0_62,plain,
multiplication(antidomain(antidomain(X1)),addition(one,X1)) = addition(X1,antidomain(antidomain(X1))),
inference(spm,[status(thm)],[c_0_53,c_0_28]) ).
cnf(c_0_63,plain,
addition(one,coantidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_28]) ).
fof(c_0_64,negated_conjecture,
( addition(forward_diamond(esk1_0,domain(esk2_0)),domain(esk3_0)) != domain(esk3_0)
& addition(domain(esk2_0),backward_box(esk1_0,domain(esk3_0))) = backward_box(esk1_0,domain(esk3_0)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_56])])])]) ).
cnf(c_0_65,plain,
backward_box(X1,X2) = c(backward_diamond(X1,c(X2))),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_66,plain,
c(X1) = antidomain(antidomain(antidomain(X1))),
inference(rw,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_67,plain,
backward_diamond(X1,X2) = codomain(multiplication(codomain(X2),X1)),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_68,plain,
codomain(X1) = coantidomain(coantidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
fof(c_0_69,plain,
! [X14,X15,X16] : multiplication(X14,multiplication(X15,X16)) = multiplication(multiplication(X14,X15),X16),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(c_0_70,plain,
! [X34] : multiplication(X34,coantidomain(X34)) = zero,
inference(variable_rename,[status(thm)],[codomain1]) ).
fof(c_0_71,plain,
! [X26] : multiplication(zero,X26) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_72,plain,
addition(coantidomain(X1),addition(coantidomain(coantidomain(X1)),X2)) = addition(one,X2),
inference(spm,[status(thm)],[c_0_47,c_0_55]) ).
cnf(c_0_73,plain,
addition(coantidomain(X1),antidomain(antidomain(coantidomain(X1)))) = antidomain(antidomain(coantidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_38]) ).
cnf(c_0_74,plain,
addition(one,antidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_40]),c_0_28]) ).
cnf(c_0_75,negated_conjecture,
addition(domain(esk2_0),backward_box(esk1_0,domain(esk3_0))) = backward_box(esk1_0,domain(esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_76,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_65,c_0_66]),c_0_66]) ).
cnf(c_0_77,plain,
backward_diamond(X1,X2) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(X2)),X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68]),c_0_68]) ).
cnf(c_0_78,plain,
multiplication(antidomain(X1),addition(X2,X1)) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_33]),c_0_27]) ).
cnf(c_0_79,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_80,plain,
multiplication(X1,coantidomain(X1)) = zero,
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_81,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_82,plain,
multiplication(addition(X1,antidomain(X2)),X2) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_27]) ).
cnf(c_0_83,plain,
addition(coantidomain(X1),antidomain(antidomain(coantidomain(coantidomain(X1))))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]) ).
cnf(c_0_84,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(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk3_0))))))),esk1_0)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_59]),c_0_59]),c_0_59]),c_0_76]),c_0_76]),c_0_77]),c_0_77]) ).
cnf(c_0_85,plain,
antidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_40]),c_0_38]),c_0_46]) ).
cnf(c_0_86,plain,
multiplication(X1,multiplication(coantidomain(X1),X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81]) ).
cnf(c_0_87,plain,
multiplication(coantidomain(X1),antidomain(coantidomain(coantidomain(X1)))) = antidomain(coantidomain(coantidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_41]) ).
cnf(c_0_88,plain,
addition(antidomain(X1),addition(antidomain(antidomain(X1)),X2)) = addition(one,X2),
inference(spm,[status(thm)],[c_0_47,c_0_40]) ).
cnf(c_0_89,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(esk3_0))),esk1_0))))) = antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(esk3_0))),esk1_0)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_85]),c_0_85]),c_0_85]),c_0_85]),c_0_85]),c_0_85]) ).
cnf(c_0_90,plain,
multiplication(X1,addition(coantidomain(X1),X2)) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_80]),c_0_34]) ).
cnf(c_0_91,plain,
multiplication(X1,antidomain(coantidomain(coantidomain(X1)))) = zero,
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_92,negated_conjecture,
addition(antidomain(esk2_0),antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(esk3_0))),esk1_0))))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_74]) ).
cnf(c_0_93,plain,
multiplication(X1,coantidomain(coantidomain(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_55]),c_0_38]) ).
cnf(c_0_94,plain,
multiplication(X1,multiplication(antidomain(coantidomain(coantidomain(X1))),X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_91]),c_0_81]) ).
cnf(c_0_95,negated_conjecture,
multiplication(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(esk3_0))),esk1_0)))),esk2_0) = esk2_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_92]),c_0_41]) ).
fof(c_0_96,plain,
! [X25] : multiplication(X25,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
fof(c_0_97,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_98,plain,
multiplication(X1,multiplication(coantidomain(coantidomain(X1)),X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_79,c_0_93]) ).
cnf(c_0_99,negated_conjecture,
multiplication(coantidomain(coantidomain(antidomain(esk3_0))),multiplication(esk1_0,esk2_0)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_79]) ).
cnf(c_0_100,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_101,plain,
antidomain(one) = zero,
inference(spm,[status(thm)],[c_0_38,c_0_33]) ).
cnf(c_0_102,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_97]) ).
cnf(c_0_103,negated_conjecture,
multiplication(antidomain(esk3_0),multiplication(esk1_0,esk2_0)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_100]) ).
cnf(c_0_104,plain,
antidomain(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_101]),c_0_34]) ).
cnf(c_0_105,negated_conjecture,
antidomain(multiplication(antidomain(esk3_0),antidomain(antidomain(multiplication(esk1_0,esk2_0))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_104]),c_0_74]) ).
cnf(c_0_106,plain,
multiplication(antidomain(addition(X1,X2)),X1) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_54]),c_0_33]) ).
cnf(c_0_107,negated_conjecture,
multiplication(antidomain(esk3_0),antidomain(antidomain(multiplication(esk1_0,esk2_0)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_105]),c_0_41]) ).
cnf(c_0_108,plain,
multiplication(addition(antidomain(addition(X1,X2)),X3),X1) = multiplication(X3,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_106]),c_0_34]) ).
cnf(c_0_109,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_54,c_0_28]) ).
cnf(c_0_110,negated_conjecture,
multiplication(antidomain(esk3_0),addition(antidomain(antidomain(multiplication(esk1_0,esk2_0))),X1)) = multiplication(antidomain(esk3_0),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_107]),c_0_34]) ).
cnf(c_0_111,plain,
multiplication(antidomain(antidomain(addition(X1,X2))),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_40]),c_0_41]) ).
cnf(c_0_112,plain,
addition(X1,addition(X2,addition(X1,X3))) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_109]),c_0_47]),c_0_47]) ).
cnf(c_0_113,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_41]),c_0_28]) ).
cnf(c_0_114,negated_conjecture,
multiplication(antidomain(esk3_0),antidomain(multiplication(esk1_0,esk2_0))) = antidomain(esk3_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_40]),c_0_38]),c_0_85]) ).
cnf(c_0_115,plain,
multiplication(antidomain(antidomain(addition(X1,addition(X2,X3)))),X2) = X2,
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_116,negated_conjecture,
addition(antidomain(esk3_0),antidomain(multiplication(esk1_0,esk2_0))) = antidomain(multiplication(esk1_0,esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_28]),c_0_74]),c_0_41]),c_0_28]) ).
fof(c_0_117,plain,
! [X42,X43] : forward_diamond(X42,X43) = domain(multiplication(X42,domain(X43))),
inference(variable_rename,[status(thm)],[forward_diamond]) ).
cnf(c_0_118,negated_conjecture,
multiplication(antidomain(antidomain(addition(X1,antidomain(multiplication(esk1_0,esk2_0))))),antidomain(esk3_0)) = antidomain(esk3_0),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_119,plain,
forward_diamond(X1,X2) = domain(multiplication(X1,domain(X2))),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_120,negated_conjecture,
multiplication(antidomain(antidomain(addition(antidomain(multiplication(esk1_0,esk2_0)),X1))),antidomain(esk3_0)) = antidomain(esk3_0),
inference(spm,[status(thm)],[c_0_118,c_0_28]) ).
cnf(c_0_121,negated_conjecture,
addition(forward_diamond(esk1_0,domain(esk2_0)),domain(esk3_0)) != domain(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_122,plain,
forward_diamond(X1,X2) = antidomain(antidomain(multiplication(X1,antidomain(antidomain(X2))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_119,c_0_59]),c_0_59]) ).
cnf(c_0_123,plain,
addition(X1,addition(antidomain(X2),multiplication(X1,X2))) = multiplication(addition(X1,antidomain(X2)),addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_82]),c_0_47]) ).
cnf(c_0_124,negated_conjecture,
multiplication(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0)))),antidomain(esk3_0)) = antidomain(esk3_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_102]),c_0_85]) ).
cnf(c_0_125,negated_conjecture,
addition(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(esk2_0))))))),antidomain(antidomain(esk3_0))) != antidomain(antidomain(esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_121,c_0_59]),c_0_59]),c_0_59]),c_0_122]) ).
cnf(c_0_126,plain,
multiplication(addition(X1,one),X1) = multiplication(X1,addition(X1,one)),
inference(spm,[status(thm)],[c_0_45,c_0_113]) ).
cnf(c_0_127,negated_conjecture,
addition(antidomain(antidomain(esk3_0)),antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0))))) = 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(spm,[status(thm)],[c_0_123,c_0_124]),c_0_28]),c_0_74]),c_0_38]),c_0_28]),c_0_40]),c_0_28]),c_0_74]),c_0_28]) ).
cnf(c_0_128,negated_conjecture,
addition(antidomain(antidomain(esk3_0)),antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(esk2_0)))))))) != antidomain(antidomain(esk3_0)),
inference(rw,[status(thm)],[c_0_125,c_0_28]) ).
cnf(c_0_129,plain,
addition(multiplication(X1,addition(X1,one)),multiplication(X2,X1)) = multiplication(addition(X1,addition(one,X2)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_126]),c_0_47]) ).
cnf(c_0_130,negated_conjecture,
multiplication(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0))))),antidomain(antidomain(esk3_0))) = antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_127]),c_0_38]) ).
cnf(c_0_131,negated_conjecture,
addition(antidomain(antidomain(esk3_0)),antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0)))))) != antidomain(antidomain(esk3_0)),
inference(spm,[status(thm)],[c_0_128,c_0_85]) ).
cnf(c_0_132,negated_conjecture,
$false,
inference(sr,[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_129,c_0_130]),c_0_28]),c_0_74]),c_0_38]),c_0_74]),c_0_28]),c_0_74]),c_0_41]),c_0_131]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE106+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 % Computer : n011.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sun Sep 20 22:44:27 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.49 Running first-order theorem proving
% 0.14/0.49 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
% 29.77/4.92 % Version: 3.5.1
% 29.77/4.92 % Preprocessing class: FSMSSMSSSSSNFFN.
% 29.77/4.92 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 29.77/4.92 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 29.77/4.92 % Starting new_bool_3 with 300s (1) cores
% 29.77/4.92 % Starting new_bool_1 with 300s (1) cores
% 29.77/4.92 % Starting sh5l with 300s (1) cores
% 29.77/4.92 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 352262 completed with status 0
% 29.77/4.92 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 29.77/4.92 % Preprocessing class: FSMSSMSSSSSNFFN.
% 29.77/4.92 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 29.77/4.92 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 29.77/4.92 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 29.77/4.92 % No SInE strategy applied
% 29.77/4.92 % Search class: FHUSM-FFMF21-DFFFFFNN
% 29.77/4.92 % partial match(1): FHUSM-FFMF21-MFFFFFNN
% 29.77/4.92 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 29.77/4.92 % Starting SubtermCWHack with 136s (1) cores
% 29.77/4.92 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 29.77/4.92 % Starting G-E--_100_C18_F1_PI_AE_Q4_CS_SP_S0Y with 212s (1) cores
% 29.77/4.92 % Starting H----_042_B03_F1_AE_Q4_SP_S2S with 136s (1) cores
% 29.77/4.92 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 29.77/4.92 % G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with pid 352273 completed with status 0
% 29.77/4.92 % Result found by G-E--_300_C18_F1_SE_CS_SP_PS_S0Y
% 29.77/4.92 % Preprocessing class: FSMSSMSSSSSNFFN.
% 29.77/4.92 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 29.77/4.92 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 29.77/4.92 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 29.77/4.92 % No SInE strategy applied
% 29.77/4.92 % Search class: FHUSM-FFMF21-DFFFFFNN
% 29.77/4.92 % partial match(1): FHUSM-FFMF21-MFFFFFNN
% 29.77/4.92 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 29.77/4.92 % Starting SubtermCWHack with 136s (1) cores
% 29.77/4.92 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 29.77/4.92 % Starting G-E--_100_C18_F1_PI_AE_Q4_CS_SP_S0Y with 212s (1) cores
% 29.77/4.92 % Starting H----_042_B03_F1_AE_Q4_SP_S2S with 136s (1) cores
% 29.77/4.92 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 29.77/4.92 % Preprocessing time : 0.002 s
% 29.77/4.92 % Presaturation interreduction done
% 29.77/4.92
% 29.77/4.92 % Proof found!
% 29.77/4.92 % SZS status Theorem
% 29.77/4.92 % SZS output start CNFRefutation
% See solution above
% 29.77/4.92 % Parsed axioms : 27
% 29.77/4.92 % Removed by relevancy pruning/SinE : 0
% 29.77/4.92 % Initial clauses : 29
% 29.77/4.92 % Removed in clause preprocessing : 8
% 29.77/4.92 % Initial clauses in saturation : 21
% 29.77/4.92 % Processed clauses : 5417
% 29.77/4.92 % ...of these trivial : 3061
% 29.77/4.92 % ...subsumed : 1055
% 29.77/4.92 % ...remaining for further processing : 1301
% 29.77/4.92 % Other redundant clauses eliminated : 0
% 29.77/4.92 % Clauses deleted for lack of memory : 0
% 29.77/4.92 % Backward-subsumed : 0
% 29.77/4.92 % Backward-rewritten : 395
% 29.77/4.92 % Generated clauses : 222515
% 29.77/4.92 % ...of the previous two non-redundant : 97214
% 29.77/4.92 % ...aggressively subsumed : 0
% 29.77/4.92 % Contextual simplify-reflections : 0
% 29.77/4.92 % Paramodulations : 222515
% 29.77/4.92 % Factorizations : 0
% 29.77/4.92 % NegExts : 0
% 29.77/4.92 % Equation resolutions : 0
% 29.77/4.92 % Disequality decompositions : 0
% 29.77/4.92 % Total rewrite steps : 474839
% 29.77/4.92 % ...of those cached : 417546
% 29.77/4.92 % Propositional unsat checks : 0
% 29.77/4.92 % Propositional check models : 0
% 29.77/4.92 % Propositional check unsatisfiable : 0
% 29.77/4.92 % Propositional clauses : 0
% 29.77/4.92 % Propositional clauses after purity: 0
% 29.77/4.92 % Propositional unsat core size : 0
% 29.77/4.92 % Propositional preprocessing time : 0.000
% 29.77/4.92 % Propositional encoding time : 0.000
% 29.77/4.92 % Propositional solver time : 0.000
% 29.77/4.92 % Success case prop preproc time : 0.000
% 29.77/4.92 % Success case prop encoding time : 0.000
% 29.77/4.92 % Success case prop solver time : 0.000
% 29.77/4.92 % Current number of processed clauses : 885
% 29.77/4.92 % Positive orientable unit clauses : 871
% 29.77/4.92 % Positive unorientable unit clauses: 10
% 29.77/4.92 % Negative unit clauses : 2
% 29.77/4.92 % Non-unit-clauses : 2
% 29.77/4.92 % Current number of unprocessed clauses: 90370
% 29.77/4.92 % ...number of literals in the above : 90370
% 29.77/4.92 % Current number of archived formulas : 0
% 29.77/4.92 % Current number of archived clauses : 424
% 29.77/4.92 % Clause-clause subsumption calls (NU) : 0
% 29.77/4.92 % Rec. Clause-clause subsumption calls : 0
% 29.77/4.92 % Non-unit clause-clause subsumptions : 0
% 29.77/4.92 % Unit Clause-clause subsumption calls : 113
% 29.77/4.92 % Rewrite failures with RHS unbound : 0
% 29.77/4.92 % BW rewrite match attempts : 5453
% 29.77/4.92 % BW rewrite match successes : 358
% 29.77/4.92 % Condensation attempts : 0
% 29.77/4.92 % Condensation successes : 0
% 29.77/4.92 % Termbank termtop insertions : 3509489
% 29.77/4.92 % Search garbage collected termcells : 55
% 29.77/4.92
% 29.77/4.92 % -------------------------------------------------
% 29.77/4.92 % User time : 4.109 s
% 29.77/4.92 % System time : 0.171 s
% 29.77/4.92 % Total time : 4.279 s
% 29.77/4.92 % Maximum resident set size: 3660 pages
% 29.77/4.92
% 29.77/4.92 % -------------------------------------------------
% 29.77/4.92 % User time : 20.368 s
% 29.77/4.92 % System time : 0.855 s
% 29.77/4.92 % Total time : 21.223 s
% 29.77/4.92 % Maximum resident set size: 4608 pages
% 29.77/4.92 % E exiting
%------------------------------------------------------------------------------