%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE080+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:35:40 PM UTC 2026
% Result : Theorem 2.46s 2.11s
% Output : CNFRefutation 2.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 16
% Syntax : Number of formulae : 113 ( 110 unt; 0 def)
% Number of atoms : 119 ( 118 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 9 ( 3 ~; 0 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 178 ( 23 sgn 55 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4] :
( ! [X5] :
( addition(domain(X5),antidomain(X5)) = one
& multiplication(domain(X5),antidomain(X5)) = zero )
=> antidomain(antidomain(X4)) = domain(X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(domain3,axiom,
! [X4] : addition(domain(X4),one) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax',domain3) ).
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(domain1,axiom,
! [X4] : addition(X4,multiplication(domain(X4),X4)) = multiplication(domain(X4),X4),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax',domain1) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(domain5,axiom,
! [X4,X5] : domain(addition(X4,X5)) = addition(domain(X4),domain(X5)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax',domain5) ).
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(domain2,axiom,
! [X4,X5] : domain(multiplication(X4,X5)) = domain(multiplication(X4,domain(X5))),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax',domain2) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(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(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(domain4,axiom,
domain(zero) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax',domain4) ).
fof(c_0_16,negated_conjecture,
~ ! [X4] :
( ! [X5] :
( addition(domain(X5),antidomain(X5)) = one
& multiplication(domain(X5),antidomain(X5)) = zero )
=> antidomain(antidomain(X4)) = domain(X4) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_17,negated_conjecture,
! [X65] :
( addition(domain(X65),antidomain(X65)) = one
& multiplication(domain(X65),antidomain(X65)) = zero
& antidomain(antidomain(esk1_0)) != domain(esk1_0) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).
fof(c_0_18,plain,
! [X36,X37] : addition(X36,X37) = addition(X37,X36),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_19,plain,
! [X61] : addition(domain(X61),one) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
fof(c_0_20,plain,
! [X38,X39,X40] : addition(X40,addition(X39,X38)) = addition(addition(X40,X39),X38),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
cnf(c_0_21,negated_conjecture,
addition(domain(X1),antidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_23,plain,
! [X42] : addition(X42,X42) = X42,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_24,plain,
! [X58] : addition(X58,multiplication(domain(X58),X58)) = multiplication(domain(X58),X58),
inference(variable_rename,[status(thm)],[domain1]) ).
fof(c_0_25,plain,
! [X46] : multiplication(X46,one) = X46,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_26,plain,
addition(domain(X1),one) = one,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,negated_conjecture,
addition(antidomain(X1),domain(X1)) = one,
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_29,plain,
! [X62,X63] : domain(addition(X62,X63)) = addition(domain(X62),domain(X63)),
inference(variable_rename,[status(thm)],[domain5]) ).
cnf(c_0_30,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,plain,
addition(X1,multiplication(domain(X1),X1)) = multiplication(domain(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_33,plain,
addition(one,domain(X1)) = one,
inference(rw,[status(thm)],[c_0_26,c_0_22]) ).
cnf(c_0_34,negated_conjecture,
addition(antidomain(X1),addition(domain(X1),X2)) = addition(one,X2),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_35,plain,
domain(addition(X1,X2)) = addition(domain(X1),domain(X2)),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_27,c_0_30]) ).
fof(c_0_37,plain,
! [X48,X49,X50] : multiplication(X48,addition(X49,X50)) = addition(multiplication(X48,X49),multiplication(X48,X50)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_38,plain,
! [X59,X60] : domain(multiplication(X59,X60)) = domain(multiplication(X59,domain(X60))),
inference(variable_rename,[status(thm)],[domain2]) ).
cnf(c_0_39,plain,
domain(one) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
fof(c_0_40,plain,
! [X51,X52,X53] : multiplication(addition(X51,X52),X53) = addition(multiplication(X51,X53),multiplication(X52,X53)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_41,plain,
! [X41] : addition(X41,zero) = X41,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_42,negated_conjecture,
addition(antidomain(X1),domain(addition(X1,X2))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_33]) ).
cnf(c_0_43,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_36,c_0_22]) ).
cnf(c_0_44,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_45,plain,
domain(multiplication(X1,X2)) = domain(multiplication(X1,domain(X2))),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_46,plain,
domain(addition(X1,one)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_39]),c_0_22]),c_0_33]) ).
fof(c_0_47,plain,
! [X47] : multiplication(one,X47) = X47,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_48,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_49,negated_conjecture,
multiplication(domain(X1),antidomain(X1)) = zero,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_50,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_51,negated_conjecture,
addition(antidomain(X1),domain(addition(X2,X1))) = one,
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_52,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_32]),c_0_22]) ).
cnf(c_0_53,plain,
domain(multiplication(X1,addition(X2,one))) = domain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_32]) ).
cnf(c_0_54,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_55,negated_conjecture,
multiplication(addition(X1,domain(X2)),antidomain(X2)) = multiplication(X1,antidomain(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).
cnf(c_0_56,negated_conjecture,
addition(antidomain(multiplication(X1,X2)),domain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]) ).
cnf(c_0_57,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_54]),c_0_22]) ).
cnf(c_0_58,plain,
domain(domain(X1)) = domain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_54]),c_0_54]) ).
cnf(c_0_59,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_50,c_0_22]) ).
cnf(c_0_60,negated_conjecture,
multiplication(antidomain(multiplication(X1,X2)),antidomain(X1)) = antidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_54]) ).
cnf(c_0_61,plain,
multiplication(domain(X1),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_57]),c_0_22]),c_0_33]),c_0_54]) ).
cnf(c_0_62,plain,
domain(addition(X1,domain(X2))) = domain(addition(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_58]),c_0_35]) ).
cnf(c_0_63,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(spm,[status(thm)],[c_0_44,c_0_32]) ).
cnf(c_0_64,negated_conjecture,
multiplication(addition(domain(X1),X2),antidomain(X1)) = multiplication(X2,antidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_59]) ).
cnf(c_0_65,negated_conjecture,
addition(domain(X1),antidomain(domain(X1))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_58]),c_0_22]) ).
cnf(c_0_66,negated_conjecture,
multiplication(antidomain(X1),antidomain(domain(X1))) = antidomain(domain(X1)),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_67,negated_conjecture,
addition(one,antidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_28]),c_0_22]) ).
cnf(c_0_68,negated_conjecture,
domain(addition(X1,antidomain(X1))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_28]),c_0_39]),c_0_22]) ).
cnf(c_0_69,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(spm,[status(thm)],[c_0_48,c_0_54]) ).
cnf(c_0_70,plain,
addition(X1,multiplication(X1,domain(X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_33]),c_0_32]) ).
cnf(c_0_71,negated_conjecture,
multiplication(antidomain(domain(X1)),antidomain(X1)) = antidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_54]) ).
cnf(c_0_72,negated_conjecture,
addition(antidomain(X1),antidomain(domain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_66]),c_0_22]),c_0_67]),c_0_32]) ).
cnf(c_0_73,negated_conjecture,
domain(multiplication(X1,addition(X2,antidomain(X2)))) = domain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_68]),c_0_32]) ).
cnf(c_0_74,negated_conjecture,
multiplication(domain(X1),addition(antidomain(X1),X2)) = multiplication(domain(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_49]),c_0_59]) ).
cnf(c_0_75,plain,
addition(X1,multiplication(domain(X2),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_54]),c_0_54]) ).
cnf(c_0_76,negated_conjecture,
antidomain(domain(X1)) = 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_52,c_0_71]),c_0_22]),c_0_72]),c_0_22]),c_0_67]),c_0_32]) ).
cnf(c_0_77,negated_conjecture,
domain(multiplication(domain(X1),antidomain(antidomain(X1)))) = domain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_58]) ).
cnf(c_0_78,negated_conjecture,
addition(domain(X1),antidomain(multiplication(domain(X2),X1))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_75]),c_0_22]) ).
cnf(c_0_79,negated_conjecture,
antidomain(multiplication(domain(X1),antidomain(antidomain(X1)))) = antidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_76]) ).
fof(c_0_80,plain,
! [X55] : multiplication(zero,X55) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_81,negated_conjecture,
addition(antidomain(X1),domain(antidomain(antidomain(X1)))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_22]) ).
fof(c_0_82,plain,
! [X43,X44,X45] : multiplication(X43,multiplication(X44,X45)) = multiplication(multiplication(X43,X44),X45),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_83,plain,
addition(multiplication(X1,domain(X2)),multiplication(domain(multiplication(X1,X2)),multiplication(X1,domain(X2)))) = multiplication(domain(multiplication(X1,X2)),multiplication(X1,domain(X2))),
inference(spm,[status(thm)],[c_0_31,c_0_45]) ).
cnf(c_0_84,plain,
domain(zero) = zero,
inference(split_conjunct,[status(thm)],[domain4]) ).
cnf(c_0_85,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_86,plain,
multiplication(addition(domain(X1),X2),X1) = addition(X1,multiplication(X2,X1)),
inference(spm,[status(thm)],[c_0_48,c_0_61]) ).
cnf(c_0_87,negated_conjecture,
multiplication(domain(X1),domain(antidomain(antidomain(X1)))) = domain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_81]),c_0_32]) ).
cnf(c_0_88,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_89,negated_conjecture,
multiplication(domain(X1),domain(antidomain(X1))) = zero,
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_83,c_0_49]),c_0_84]),c_0_85]),c_0_50]),c_0_84]),c_0_85]) ).
cnf(c_0_90,plain,
multiplication(domain(addition(X1,X2)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_35]),c_0_75]) ).
cnf(c_0_91,negated_conjecture,
domain(addition(X1,antidomain(antidomain(X1)))) = domain(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_57,c_0_87]),c_0_35]),c_0_22]),c_0_22]),c_0_33]),c_0_54]) ).
cnf(c_0_92,negated_conjecture,
multiplication(domain(X1),multiplication(domain(antidomain(X1)),X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_85]) ).
cnf(c_0_93,negated_conjecture,
multiplication(domain(antidomain(antidomain(X1))),X1) = X1,
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_94,negated_conjecture,
multiplication(domain(antidomain(X1)),X1) = zero,
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_95,negated_conjecture,
multiplication(domain(antidomain(X1)),multiplication(X1,X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_94]),c_0_85]) ).
cnf(c_0_96,plain,
multiplication(domain(addition(X1,X2)),X2) = X2,
inference(spm,[status(thm)],[c_0_90,c_0_43]) ).
cnf(c_0_97,negated_conjecture,
addition(X1,multiplication(X1,antidomain(X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_67]),c_0_32]) ).
cnf(c_0_98,negated_conjecture,
multiplication(domain(antidomain(addition(X1,X2))),X2) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_76]) ).
cnf(c_0_99,negated_conjecture,
addition(X1,multiplication(antidomain(X2),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_97]),c_0_54]),c_0_54]) ).
cnf(c_0_100,plain,
multiplication(domain(X1),multiplication(X1,X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_88,c_0_61]) ).
cnf(c_0_101,negated_conjecture,
multiplication(domain(antidomain(X1)),multiplication(antidomain(X2),X1)) = zero,
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_102,negated_conjecture,
multiplication(antidomain(X1),X1) = zero,
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_103,negated_conjecture,
multiplication(addition(domain(antidomain(X1)),X2),X1) = multiplication(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_94]),c_0_59]) ).
cnf(c_0_104,negated_conjecture,
addition(domain(X1),antidomain(multiplication(X1,X2))) = one,
inference(spm,[status(thm)],[c_0_22,c_0_56]) ).
cnf(c_0_105,negated_conjecture,
multiplication(antidomain(X1),addition(X1,X2)) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_102]),c_0_59]) ).
cnf(c_0_106,negated_conjecture,
multiplication(antidomain(multiplication(antidomain(X1),X2)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_54]) ).
cnf(c_0_107,negated_conjecture,
multiplication(antidomain(antidomain(X1)),domain(X1)) = antidomain(antidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_28]),c_0_32]) ).
cnf(c_0_108,negated_conjecture,
multiplication(antidomain(antidomain(X1)),X1) = X1,
inference(spm,[status(thm)],[c_0_106,c_0_32]) ).
cnf(c_0_109,negated_conjecture,
addition(antidomain(antidomain(X1)),domain(X1)) = domain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_107]),c_0_22]),c_0_22]),c_0_67]),c_0_54]) ).
cnf(c_0_110,negated_conjecture,
antidomain(antidomain(esk1_0)) != domain(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_111,negated_conjecture,
domain(X1) = antidomain(antidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_108]),c_0_76]),c_0_109]),c_0_76]) ).
cnf(c_0_112,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_111])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE080+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n031.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 20:30:53 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 2.46/2.11 % Version : CSE_E---1.7
% 2.46/2.11 % Problem : theBenchmark.p
% 2.46/2.11 % SZS status Theorem for theBenchmark.p
% 2.46/2.11 % SZS output start CNFRefutation
% See solution above
% 2.46/2.12 % Total time : 1.370s
%------------------------------------------------------------------------------