%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE101+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 : n004.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 04:35:43 PM UTC 2026
% Result : Theorem 57.49s 34.17s
% Output : CNFRefutation 57.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 22
% Syntax : Number of formulae : 173 ( 170 unt; 0 def)
% Number of atoms : 176 ( 175 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 6 ~; 0 |; 1 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 265 ( 38 sgn 74 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(domain1,axiom,
! [X4] : multiplication(antidomain(X4),X4) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain1) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(domain3,axiom,
! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain3) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(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(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(codomain1,axiom,
! [X4] : multiplication(X4,coantidomain(X4)) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',codomain1) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(codomain3,axiom,
! [X4] : addition(coantidomain(coantidomain(X4)),coantidomain(X4)) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',codomain3) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(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(codomain2,axiom,
! [X4,X5] : addition(coantidomain(multiplication(X4,X5)),coantidomain(multiplication(coantidomain(coantidomain(X4)),X5))) = coantidomain(multiplication(coantidomain(coantidomain(X4)),X5)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',codomain2) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(goals,conjecture,
! [X4,X5,X6] :
( multiplication(forward_diamond(X4,domain(X5)),domain(X6)) = zero
=> multiplication(domain(X5),backward_diamond(X4,domain(X6))) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(forward_diamond,axiom,
! [X4,X5] : forward_diamond(X4,X5) = domain(multiplication(X4,domain(X5))),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax',forward_diamond) ).
fof(domain4,axiom,
! [X4] : domain(X4) = antidomain(antidomain(X4)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain4) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(backward_diamond,axiom,
! [X4,X5] : backward_diamond(X4,X5) = codomain(multiplication(codomain(X5),X4)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax',backward_diamond) ).
fof(codomain4,axiom,
! [X4] : codomain(X4) = coantidomain(coantidomain(X4)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',codomain4) ).
fof(c_0_22,plain,
! [X68,X69,X70] : multiplication(addition(X68,X69),X70) = addition(multiplication(X68,X70),multiplication(X69,X70)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_23,plain,
! [X75] : multiplication(antidomain(X75),X75) = zero,
inference(variable_rename,[status(thm)],[domain1]) ).
fof(c_0_24,plain,
! [X58] : addition(X58,zero) = X58,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_25,plain,
! [X78] : addition(antidomain(antidomain(X78)),antidomain(X78)) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
fof(c_0_26,plain,
! [X53,X54] : addition(X53,X54) = addition(X54,X53),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_27,plain,
! [X63] : multiplication(X63,one) = X63,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_28,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
multiplication(antidomain(X1),X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_31,plain,
! [X76,X77] : addition(antidomain(multiplication(X76,X77)),antidomain(multiplication(X76,antidomain(antidomain(X77))))) = antidomain(multiplication(X76,antidomain(antidomain(X77)))),
inference(variable_rename,[status(thm)],[domain2]) ).
cnf(c_0_32,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_33,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_34,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_35,plain,
! [X65,X66,X67] : multiplication(X65,addition(X66,X67)) = addition(multiplication(X65,X66),multiplication(X65,X67)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_36,plain,
! [X80] : multiplication(X80,coantidomain(X80)) = zero,
inference(variable_rename,[status(thm)],[codomain1]) ).
cnf(c_0_37,plain,
multiplication(addition(X1,antidomain(X2)),X2) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_38,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_31]) ).
cnf(c_0_39,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_40,plain,
antidomain(one) = zero,
inference(spm,[status(thm)],[c_0_29,c_0_34]) ).
cnf(c_0_41,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_30,c_0_33]) ).
fof(c_0_42,plain,
! [X64] : multiplication(one,X64) = X64,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_43,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_44,plain,
multiplication(X1,coantidomain(X1)) = zero,
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_45,plain,
! [X83] : addition(coantidomain(coantidomain(X83)),coantidomain(X83)) = one,
inference(variable_rename,[status(thm)],[codomain3]) ).
cnf(c_0_46,plain,
multiplication(antidomain(multiplication(X1,X2)),multiplication(X1,antidomain(antidomain(X2)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_29]) ).
cnf(c_0_47,plain,
antidomain(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_48,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_49,plain,
multiplication(addition(antidomain(X1),X2),X1) = multiplication(X2,X1),
inference(spm,[status(thm)],[c_0_37,c_0_33]) ).
cnf(c_0_50,plain,
multiplication(X1,addition(X2,coantidomain(X1))) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_30]) ).
cnf(c_0_51,plain,
addition(coantidomain(coantidomain(X1)),coantidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_52,plain,
multiplication(X1,antidomain(antidomain(coantidomain(X1)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_44]),c_0_47]),c_0_48]) ).
cnf(c_0_53,plain,
multiplication(antidomain(X1),addition(X2,X1)) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_29]),c_0_30]) ).
cnf(c_0_54,plain,
multiplication(antidomain(antidomain(X1)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_39]),c_0_48]) ).
cnf(c_0_55,plain,
multiplication(X1,addition(coantidomain(X1),X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_50,c_0_33]) ).
cnf(c_0_56,plain,
addition(coantidomain(X1),coantidomain(coantidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_51,c_0_33]) ).
fof(c_0_57,plain,
! [X55,X56,X57] : addition(X57,addition(X56,X55)) = addition(addition(X57,X56),X55),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_58,plain,
! [X59] : addition(X59,X59) = X59,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_59,plain,
! [X60,X61,X62] : multiplication(X60,multiplication(X61,X62)) = multiplication(multiplication(X60,X61),X62),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_60,plain,
multiplication(X1,addition(antidomain(antidomain(coantidomain(X1))),X2)) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_52]),c_0_41]) ).
cnf(c_0_61,plain,
antidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_39]),c_0_34]),c_0_54]) ).
cnf(c_0_62,plain,
multiplication(addition(X1,X2),coantidomain(X2)) = multiplication(X1,coantidomain(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_44]),c_0_30]) ).
cnf(c_0_63,plain,
multiplication(X1,coantidomain(coantidomain(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_34]) ).
cnf(c_0_64,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_65,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_58]) ).
fof(c_0_66,plain,
! [X81,X82] : addition(coantidomain(multiplication(X81,X82)),coantidomain(multiplication(coantidomain(coantidomain(X81)),X82))) = coantidomain(multiplication(coantidomain(coantidomain(X81)),X82)),
inference(variable_rename,[status(thm)],[codomain2]) ).
cnf(c_0_67,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_68,plain,
multiplication(X1,antidomain(coantidomain(X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_39]),c_0_34]),c_0_61]) ).
cnf(c_0_69,plain,
coantidomain(coantidomain(coantidomain(X1))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_56]),c_0_48]),c_0_63]) ).
cnf(c_0_70,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_71,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_66]) ).
cnf(c_0_72,plain,
multiplication(X1,multiplication(X2,coantidomain(multiplication(X1,X2)))) = zero,
inference(spm,[status(thm)],[c_0_44,c_0_67]) ).
cnf(c_0_73,plain,
coantidomain(one) = zero,
inference(spm,[status(thm)],[c_0_44,c_0_48]) ).
cnf(c_0_74,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_48]),c_0_33]) ).
cnf(c_0_75,plain,
multiplication(coantidomain(coantidomain(X1)),antidomain(coantidomain(X1))) = coantidomain(coantidomain(X1)),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_76,plain,
addition(one,coantidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_56]),c_0_33]) ).
cnf(c_0_77,plain,
multiplication(coantidomain(coantidomain(X1)),multiplication(X2,coantidomain(multiplication(X1,X2)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_71]),c_0_67]),c_0_72]),c_0_67]) ).
cnf(c_0_78,plain,
coantidomain(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_73]),c_0_41]) ).
cnf(c_0_79,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_74,c_0_75]),c_0_33]),c_0_76]),c_0_48]) ).
cnf(c_0_80,plain,
multiplication(coantidomain(coantidomain(antidomain(X1))),X1) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_29]),c_0_78]),c_0_34]) ).
cnf(c_0_81,plain,
addition(coantidomain(X1),addition(coantidomain(coantidomain(X1)),X2)) = addition(one,X2),
inference(spm,[status(thm)],[c_0_64,c_0_56]) ).
cnf(c_0_82,plain,
addition(coantidomain(X1),antidomain(coantidomain(coantidomain(X1)))) = antidomain(coantidomain(coantidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_69]),c_0_33]) ).
cnf(c_0_83,plain,
addition(one,antidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_39]),c_0_33]) ).
cnf(c_0_84,plain,
multiplication(antidomain(X1),addition(X1,X2)) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_29]),c_0_41]) ).
cnf(c_0_85,plain,
multiplication(antidomain(addition(X1,X2)),X1) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_70]),c_0_29]) ).
cnf(c_0_86,plain,
multiplication(addition(coantidomain(coantidomain(antidomain(X1))),X2),X1) = multiplication(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_80]),c_0_41]) ).
cnf(c_0_87,plain,
multiplication(addition(X1,X2),coantidomain(X1)) = multiplication(X2,coantidomain(X1)),
inference(spm,[status(thm)],[c_0_62,c_0_33]) ).
cnf(c_0_88,plain,
addition(coantidomain(X1),antidomain(coantidomain(X1))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_69]),c_0_69]),c_0_83]) ).
cnf(c_0_89,plain,
multiplication(antidomain(coantidomain(X1)),coantidomain(coantidomain(X1))) = antidomain(coantidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_56]),c_0_34]) ).
cnf(c_0_90,plain,
multiplication(antidomain(multiplication(addition(X1,X2),X3)),multiplication(X1,X3)) = zero,
inference(spm,[status(thm)],[c_0_85,c_0_28]) ).
fof(c_0_91,plain,
! [X71] : multiplication(X71,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
cnf(c_0_92,plain,
multiplication(coantidomain(antidomain(X1)),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_56]),c_0_48]),c_0_69]) ).
cnf(c_0_93,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_71,c_0_67]) ).
cnf(c_0_94,plain,
coantidomain(coantidomain(X1)) = antidomain(coantidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_48]),c_0_89]) ).
cnf(c_0_95,plain,
multiplication(X1,multiplication(antidomain(coantidomain(X1)),X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_96,plain,
multiplication(antidomain(X1),multiplication(coantidomain(X2),X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_88]),c_0_48]) ).
cnf(c_0_97,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_98,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_34]),c_0_33]) ).
cnf(c_0_99,plain,
multiplication(coantidomain(antidomain(X1)),antidomain(antidomain(X1))) = antidomain(antidomain(X1)),
inference(spm,[status(thm)],[c_0_92,c_0_61]) ).
fof(c_0_100,negated_conjecture,
~ ! [X4,X5,X6] :
( multiplication(forward_diamond(X4,domain(X5)),domain(X6)) = zero
=> multiplication(domain(X5),backward_diamond(X4,domain(X6))) = zero ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_101,plain,
! [X88,X89] : forward_diamond(X88,X89) = domain(multiplication(X88,domain(X89))),
inference(variable_rename,[status(thm)],[forward_diamond]) ).
fof(c_0_102,plain,
! [X79] : domain(X79) = antidomain(antidomain(X79)),
inference(variable_rename,[status(thm)],[domain4]) ).
cnf(c_0_103,plain,
addition(coantidomain(multiplication(X1,multiplication(X2,X3))),coantidomain(multiplication(antidomain(coantidomain(multiplication(X1,X2))),X3))) = coantidomain(multiplication(antidomain(coantidomain(multiplication(X1,X2))),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_94]),c_0_94]) ).
cnf(c_0_104,plain,
multiplication(X1,multiplication(coantidomain(X2),coantidomain(X1))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97]) ).
cnf(c_0_105,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_98,c_0_99]),c_0_33]),c_0_83]),c_0_34]),c_0_33]) ).
fof(c_0_106,negated_conjecture,
( multiplication(forward_diamond(esk1_0,domain(esk2_0)),domain(esk3_0)) = zero
& multiplication(domain(esk2_0),backward_diamond(esk1_0,domain(esk3_0))) != zero ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_100])])]) ).
cnf(c_0_107,plain,
forward_diamond(X1,X2) = domain(multiplication(X1,domain(X2))),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_108,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_109,plain,
multiplication(X1,antidomain(antidomain(multiplication(X2,coantidomain(multiplication(X1,X2)))))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_72]),c_0_47]),c_0_48]) ).
cnf(c_0_110,plain,
coantidomain(multiplication(antidomain(coantidomain(multiplication(X1,coantidomain(X2)))),coantidomain(X1))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_78]),c_0_76]) ).
cnf(c_0_111,plain,
addition(antidomain(X1),addition(antidomain(antidomain(X1)),X2)) = addition(one,X2),
inference(spm,[status(thm)],[c_0_64,c_0_39]) ).
cnf(c_0_112,plain,
addition(antidomain(X1),coantidomain(antidomain(antidomain(X1)))) = coantidomain(antidomain(antidomain(X1))),
inference(spm,[status(thm)],[c_0_105,c_0_61]) ).
cnf(c_0_113,plain,
multiplication(antidomain(X1),coantidomain(antidomain(antidomain(X1)))) = coantidomain(antidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_39]),c_0_48]) ).
cnf(c_0_114,negated_conjecture,
multiplication(forward_diamond(esk1_0,domain(esk2_0)),domain(esk3_0)) = zero,
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_115,plain,
forward_diamond(X1,X2) = antidomain(antidomain(multiplication(X1,antidomain(antidomain(X2))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_108]),c_0_108]) ).
cnf(c_0_116,plain,
multiplication(X1,addition(antidomain(antidomain(multiplication(X2,coantidomain(multiplication(X1,X2))))),X3)) = multiplication(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_109]),c_0_41]) ).
cnf(c_0_117,plain,
multiplication(antidomain(coantidomain(multiplication(X1,coantidomain(X2)))),coantidomain(X1)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_110]),c_0_67]),c_0_34]) ).
cnf(c_0_118,plain,
addition(antidomain(X1),coantidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_61]),c_0_61]),c_0_76]) ).
cnf(c_0_119,plain,
multiplication(antidomain(antidomain(X1)),coantidomain(antidomain(X1))) = coantidomain(antidomain(X1)),
inference(spm,[status(thm)],[c_0_113,c_0_61]) ).
fof(c_0_120,plain,
! [X72] : multiplication(zero,X72) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_121,negated_conjecture,
multiplication(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(esk2_0))))))),antidomain(antidomain(esk3_0))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_108]),c_0_108]),c_0_115]) ).
cnf(c_0_122,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_93,c_0_29]),c_0_97]),c_0_78]),c_0_76]) ).
cnf(c_0_123,plain,
multiplication(X1,antidomain(multiplication(X2,coantidomain(multiplication(X1,X2))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_39]),c_0_34]),c_0_61]) ).
cnf(c_0_124,plain,
multiplication(antidomain(coantidomain(multiplication(X1,antidomain(coantidomain(X2))))),coantidomain(X1)) = zero,
inference(spm,[status(thm)],[c_0_117,c_0_94]) ).
cnf(c_0_125,plain,
coantidomain(antidomain(X1)) = antidomain(antidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_118]),c_0_34]),c_0_119]) ).
cnf(c_0_126,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_127,negated_conjecture,
multiplication(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0))))),antidomain(antidomain(esk3_0))) = zero,
inference(rw,[status(thm)],[c_0_121,c_0_61]) ).
cnf(c_0_128,plain,
multiplication(coantidomain(coantidomain(multiplication(X1,antidomain(X2)))),X2) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_122]),c_0_67]),c_0_34]) ).
cnf(c_0_129,plain,
multiplication(X1,antidomain(multiplication(X2,coantidomain(multiplication(antidomain(coantidomain(X1)),X2))))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_123]),c_0_68]) ).
cnf(c_0_130,plain,
multiplication(antidomain(coantidomain(multiplication(X1,antidomain(X2)))),coantidomain(X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_61]) ).
cnf(c_0_131,plain,
multiplication(antidomain(X1),multiplication(X1,X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_29]),c_0_126]) ).
cnf(c_0_132,plain,
multiplication(antidomain(X1),multiplication(antidomain(X2),X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_39]),c_0_48]) ).
cnf(c_0_133,negated_conjecture,
multiplication(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0))))),addition(antidomain(antidomain(esk3_0)),X1)) = multiplication(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0))))),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_127]),c_0_41]) ).
cnf(c_0_134,plain,
multiplication(coantidomain(coantidomain(multiplication(X1,multiplication(X2,antidomain(X3))))),X3) = zero,
inference(spm,[status(thm)],[c_0_128,c_0_67]) ).
cnf(c_0_135,plain,
multiplication(X1,multiplication(antidomain(X2),antidomain(coantidomain(X1)))) = multiplication(X1,antidomain(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_78]),c_0_34]),c_0_67]) ).
cnf(c_0_136,plain,
multiplication(antidomain(coantidomain(multiplication(X1,antidomain(X2)))),X2) = zero,
inference(rw,[status(thm)],[c_0_128,c_0_94]) ).
cnf(c_0_137,plain,
antidomain(antidomain(coantidomain(X1))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_88]),c_0_34]),c_0_54]) ).
cnf(c_0_138,plain,
multiplication(antidomain(multiplication(X1,X2)),multiplication(X1,multiplication(X2,X3))) = zero,
inference(spm,[status(thm)],[c_0_131,c_0_67]) ).
cnf(c_0_139,plain,
multiplication(antidomain(antidomain(X1)),multiplication(X1,X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_67,c_0_54]) ).
cnf(c_0_140,plain,
multiplication(antidomain(X1),antidomain(antidomain(multiplication(antidomain(X2),X1)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_132]),c_0_47]),c_0_48]) ).
cnf(c_0_141,negated_conjecture,
multiplication(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0))))),antidomain(esk3_0)) = antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_39]),c_0_34]),c_0_61]) ).
cnf(c_0_142,plain,
multiplication(antidomain(coantidomain(multiplication(X1,multiplication(X2,antidomain(X3))))),X3) = zero,
inference(rw,[status(thm)],[c_0_134,c_0_94]) ).
cnf(c_0_143,plain,
multiplication(X1,antidomain(coantidomain(multiplication(X2,coantidomain(X1))))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_97]),c_0_137]) ).
cnf(c_0_144,plain,
multiplication(antidomain(multiplication(X1,antidomain(antidomain(X2)))),multiplication(X1,multiplication(X2,X3))) = zero,
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_145,negated_conjecture,
multiplication(antidomain(antidomain(esk3_0)),antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0)))))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_61]) ).
cnf(c_0_146,plain,
multiplication(coantidomain(X1),coantidomain(X1)) = coantidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_56]),c_0_34]) ).
cnf(c_0_147,plain,
multiplication(X1,antidomain(coantidomain(multiplication(X2,multiplication(X3,coantidomain(X1)))))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_142]),c_0_97]),c_0_137]) ).
cnf(c_0_148,plain,
multiplication(X1,coantidomain(multiplication(X2,coantidomain(X1)))) = 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_129,c_0_143]),c_0_125]),c_0_137]),c_0_78]),c_0_34]),c_0_137]) ).
cnf(c_0_149,negated_conjecture,
multiplication(antidomain(antidomain(esk3_0)),multiplication(esk1_0,multiplication(antidomain(antidomain(esk2_0)),X1))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_47]),c_0_67]),c_0_48]) ).
fof(c_0_150,plain,
! [X90,X91] : backward_diamond(X90,X91) = codomain(multiplication(codomain(X91),X90)),
inference(variable_rename,[status(thm)],[backward_diamond]) ).
fof(c_0_151,plain,
! [X84] : codomain(X84) = coantidomain(coantidomain(X84)),
inference(variable_rename,[status(thm)],[codomain4]) ).
cnf(c_0_152,plain,
multiplication(coantidomain(X1),multiplication(coantidomain(X1),X2)) = multiplication(coantidomain(X1),X2),
inference(spm,[status(thm)],[c_0_67,c_0_146]) ).
cnf(c_0_153,plain,
multiplication(X1,multiplication(coantidomain(X2),antidomain(coantidomain(multiplication(X3,X2))))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_67]) ).
cnf(c_0_154,negated_conjecture,
multiplication(antidomain(antidomain(esk3_0)),multiplication(esk1_0,esk2_0)) = zero,
inference(spm,[status(thm)],[c_0_149,c_0_54]) ).
cnf(c_0_155,plain,
backward_diamond(X1,X2) = codomain(multiplication(codomain(X2),X1)),
inference(split_conjunct,[status(thm)],[c_0_150]) ).
cnf(c_0_156,plain,
codomain(X1) = coantidomain(coantidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_151]) ).
cnf(c_0_157,plain,
multiplication(coantidomain(X1),antidomain(coantidomain(multiplication(X2,X1)))) = zero,
inference(spm,[status(thm)],[c_0_152,c_0_153]) ).
cnf(c_0_158,negated_conjecture,
coantidomain(multiplication(antidomain(coantidomain(multiplication(antidomain(antidomain(esk3_0)),esk1_0))),esk2_0)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_154]),c_0_78]),c_0_76]) ).
cnf(c_0_159,negated_conjecture,
multiplication(domain(esk2_0),backward_diamond(esk1_0,domain(esk3_0))) != zero,
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_160,plain,
backward_diamond(X1,X2) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(X2)),X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_155,c_0_156]),c_0_156]) ).
cnf(c_0_161,plain,
coantidomain(multiplication(coantidomain(coantidomain(multiplication(X1,X2))),coantidomain(X2))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_44]),c_0_97]),c_0_78]),c_0_76]) ).
cnf(c_0_162,plain,
multiplication(coantidomain(X1),coantidomain(multiplication(X2,X1))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_157]),c_0_78]),c_0_34]),c_0_137]) ).
cnf(c_0_163,negated_conjecture,
multiplication(antidomain(coantidomain(multiplication(antidomain(antidomain(esk3_0)),esk1_0))),esk2_0) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_158]),c_0_67]),c_0_34]) ).
cnf(c_0_164,negated_conjecture,
multiplication(antidomain(antidomain(esk2_0)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(esk3_0)))),esk1_0)))) != zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_159,c_0_108]),c_0_108]),c_0_160]) ).
cnf(c_0_165,plain,
multiplication(coantidomain(coantidomain(multiplication(X1,X2))),coantidomain(X2)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_161]),c_0_67]),c_0_34]) ).
cnf(c_0_166,plain,
multiplication(coantidomain(X1),coantidomain(multiplication(X2,multiplication(X3,X1)))) = coantidomain(X1),
inference(spm,[status(thm)],[c_0_162,c_0_67]) ).
cnf(c_0_167,negated_conjecture,
multiplication(antidomain(antidomain(esk3_0)),multiplication(esk1_0,antidomain(esk2_0))) = multiplication(antidomain(antidomain(esk3_0)),esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_163]),c_0_78]),c_0_34]),c_0_67]) ).
cnf(c_0_168,negated_conjecture,
multiplication(antidomain(antidomain(esk2_0)),coantidomain(coantidomain(multiplication(antidomain(antidomain(esk3_0)),esk1_0)))) != zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_164,c_0_125]),c_0_61]),c_0_125]) ).
cnf(c_0_169,plain,
multiplication(antidomain(coantidomain(multiplication(X1,X2))),coantidomain(X2)) = zero,
inference(rw,[status(thm)],[c_0_165,c_0_94]) ).
cnf(c_0_170,negated_conjecture,
multiplication(antidomain(antidomain(esk2_0)),coantidomain(multiplication(antidomain(antidomain(esk3_0)),esk1_0))) = antidomain(antidomain(esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_167]),c_0_125]),c_0_125]) ).
cnf(c_0_171,negated_conjecture,
multiplication(antidomain(antidomain(esk2_0)),antidomain(coantidomain(multiplication(antidomain(antidomain(esk3_0)),esk1_0)))) != zero,
inference(rw,[status(thm)],[c_0_168,c_0_94]) ).
cnf(c_0_172,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_170]),c_0_125]),c_0_61]),c_0_94]),c_0_171]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE101+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 : n004.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 20:29:02 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 57.49/34.17 % Version : CSE_E---1.7
% 57.49/34.17 % Problem : theBenchmark.p
% 57.49/34.17 % SZS status Theorem for theBenchmark.p
% 57.49/34.17 % SZS output start CNFRefutation
% See solution above
% 57.77/34.43 % Total time : 24.415s
%------------------------------------------------------------------------------