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CSE_E---1.7.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : REL050+2 : 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 05:04:32 PM UTC 2026

% Result   : Theorem 2.34s 2.04s
% Output   : CNFRefutation 2.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :   14
% Syntax   : Number of formulae    :  106 ( 101 unt;   0 def)
%            Number of atoms       :  111 ( 110 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   13 (   8   ~;   3   |;   2   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-2 aty)
%            Number of variables   :  152 (   9 sgn  52   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(converse_multiplicativity,axiom,
    ! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
    file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_multiplicativity) ).

fof(composition_identity,axiom,
    ! [X1] : composition(X1,one) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_identity) ).

fof(converse_idempotence,axiom,
    ! [X1] : converse(converse(X1)) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).

fof(converse_cancellativity,axiom,
    ! [X1,X2] : join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
    file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_cancellativity) ).

fof(maddux1_join_commutativity,axiom,
    ! [X1,X2] : join(X1,X2) = join(X2,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux1_join_commutativity) ).

fof(def_zero,axiom,
    ! [X1] : zero = meet(X1,complement(X1)),
    file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',def_zero) ).

fof(maddux4_definiton_of_meet,axiom,
    ! [X1,X2] : meet(X1,X2) = complement(join(complement(X1),complement(X2))),
    file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux4_definiton_of_meet) ).

fof(def_top,axiom,
    ! [X1] : top = join(X1,complement(X1)),
    file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',def_top) ).

fof(maddux3_a_kind_of_de_Morgan,axiom,
    ! [X1,X2] : X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
    file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux3_a_kind_of_de_Morgan) ).

fof(maddux2_join_associativity,axiom,
    ! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
    file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux2_join_associativity) ).

fof(converse_additivity,axiom,
    ! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
    file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_additivity) ).

fof(composition_distributivity,axiom,
    ! [X1,X2,X3] : composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
    file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_distributivity) ).

fof(composition_associativity,axiom,
    ! [X1,X2,X3] : composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
    file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_associativity) ).

fof(goals,conjecture,
    ! [X1] :
      ( join(complement(composition(X1,top)),composition(complement(composition(X1,top)),top)) = composition(complement(composition(X1,top)),top)
      & join(composition(complement(composition(X1,top)),top),complement(composition(X1,top))) = complement(composition(X1,top)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

fof(c_0_14,plain,
    ! [X49,X50] : converse(composition(X49,X50)) = composition(converse(X50),converse(X49)),
    inference(variable_rename,[status(thm)],[converse_multiplicativity]) ).

fof(c_0_15,plain,
    ! [X42] : composition(X42,one) = X42,
    inference(variable_rename,[status(thm)],[composition_identity]) ).

cnf(c_0_16,plain,
    converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_17,plain,
    composition(X1,one) = X1,
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

fof(c_0_18,plain,
    ! [X46] : converse(converse(X46)) = X46,
    inference(variable_rename,[status(thm)],[converse_idempotence]) ).

cnf(c_0_19,plain,
    composition(converse(one),converse(X1)) = converse(X1),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_20,plain,
    converse(converse(X1)) = X1,
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

fof(c_0_21,plain,
    ! [X51,X52] : join(composition(converse(X51),complement(composition(X51,X52))),complement(X52)) = complement(X52),
    inference(variable_rename,[status(thm)],[converse_cancellativity]) ).

fof(c_0_22,plain,
    ! [X30,X31] : join(X30,X31) = join(X31,X30),
    inference(variable_rename,[status(thm)],[maddux1_join_commutativity]) ).

cnf(c_0_23,plain,
    composition(converse(one),X1) = X1,
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

fof(c_0_24,plain,
    ! [X54] : zero = meet(X54,complement(X54)),
    inference(variable_rename,[status(thm)],[def_zero]) ).

fof(c_0_25,plain,
    ! [X37,X38] : meet(X37,X38) = complement(join(complement(X37),complement(X38))),
    inference(variable_rename,[status(thm)],[maddux4_definiton_of_meet]) ).

cnf(c_0_26,plain,
    join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_27,plain,
    join(X1,X2) = join(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_28,plain,
    converse(one) = one,
    inference(spm,[status(thm)],[c_0_17,c_0_23]) ).

cnf(c_0_29,plain,
    zero = meet(X1,complement(X1)),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_30,plain,
    meet(X1,X2) = complement(join(complement(X1),complement(X2))),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

fof(c_0_31,plain,
    ! [X53] : top = join(X53,complement(X53)),
    inference(variable_rename,[status(thm)],[def_top]) ).

cnf(c_0_32,plain,
    join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
    inference(rw,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_33,plain,
    composition(one,X1) = X1,
    inference(rw,[status(thm)],[c_0_23,c_0_28]) ).

cnf(c_0_34,plain,
    zero = complement(join(complement(X1),complement(complement(X1)))),
    inference(rw,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_35,plain,
    top = join(X1,complement(X1)),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

fof(c_0_36,plain,
    ! [X35,X36] : X35 = join(complement(join(complement(X35),complement(X36))),complement(join(complement(X35),X36))),
    inference(variable_rename,[status(thm)],[maddux3_a_kind_of_de_Morgan]) ).

fof(c_0_37,plain,
    ! [X32,X33,X34] : join(X32,join(X33,X34)) = join(join(X32,X33),X34),
    inference(variable_rename,[status(thm)],[maddux2_join_associativity]) ).

cnf(c_0_38,plain,
    join(complement(X1),complement(X1)) = complement(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_28]),c_0_33]) ).

cnf(c_0_39,plain,
    complement(top) = zero,
    inference(rw,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_40,plain,
    X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_41,plain,
    join(X1,join(X2,X3)) = join(join(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_42,plain,
    join(zero,zero) = zero,
    inference(spm,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_43,plain,
    join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
    inference(rw,[status(thm)],[c_0_40,c_0_27]) ).

cnf(c_0_44,plain,
    join(zero,join(zero,X1)) = join(zero,X1),
    inference(spm,[status(thm)],[c_0_41,c_0_42]) ).

cnf(c_0_45,plain,
    join(zero,complement(complement(X1))) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_38]),c_0_35]),c_0_39]),c_0_27]) ).

cnf(c_0_46,plain,
    join(zero,X1) = X1,
    inference(spm,[status(thm)],[c_0_44,c_0_45]) ).

cnf(c_0_47,plain,
    complement(complement(X1)) = X1,
    inference(rw,[status(thm)],[c_0_45,c_0_46]) ).

cnf(c_0_48,plain,
    join(X1,join(complement(X1),X2)) = join(top,X2),
    inference(spm,[status(thm)],[c_0_41,c_0_35]) ).

cnf(c_0_49,plain,
    join(X1,X1) = X1,
    inference(spm,[status(thm)],[c_0_38,c_0_47]) ).

fof(c_0_50,plain,
    ! [X47,X48] : converse(join(X47,X48)) = join(converse(X47),converse(X48)),
    inference(variable_rename,[status(thm)],[converse_additivity]) ).

cnf(c_0_51,plain,
    join(top,complement(X1)) = top,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_38]),c_0_35]) ).

cnf(c_0_52,plain,
    join(X1,join(X1,X2)) = join(X1,X2),
    inference(spm,[status(thm)],[c_0_41,c_0_49]) ).

cnf(c_0_53,plain,
    join(complement(join(complement(X1),X2)),join(complement(join(complement(X1),complement(X2))),X3)) = join(X1,X3),
    inference(spm,[status(thm)],[c_0_41,c_0_43]) ).

cnf(c_0_54,plain,
    join(complement(join(X1,complement(X2))),complement(join(complement(X2),complement(X1)))) = X2,
    inference(spm,[status(thm)],[c_0_43,c_0_27]) ).

cnf(c_0_55,plain,
    converse(join(X1,X2)) = join(converse(X1),converse(X2)),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

cnf(c_0_56,plain,
    join(top,X1) = top,
    inference(spm,[status(thm)],[c_0_51,c_0_47]) ).

cnf(c_0_57,plain,
    join(X1,complement(join(complement(X1),X2))) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_43]),c_0_27]) ).

cnf(c_0_58,plain,
    join(X1,join(X2,X1)) = join(X2,X1),
    inference(spm,[status(thm)],[c_0_52,c_0_27]) ).

cnf(c_0_59,plain,
    join(X1,complement(join(complement(X2),X1))) = join(X2,complement(join(complement(X1),X2))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_47]),c_0_27]) ).

cnf(c_0_60,plain,
    join(converse(top),converse(X1)) = converse(top),
    inference(spm,[status(thm)],[c_0_55,c_0_56]) ).

fof(c_0_61,plain,
    ! [X43,X44,X45] : composition(join(X43,X44),X45) = join(composition(X43,X45),composition(X44,X45)),
    inference(variable_rename,[status(thm)],[composition_distributivity]) ).

cnf(c_0_62,plain,
    join(X1,complement(join(X2,complement(X1)))) = X1,
    inference(spm,[status(thm)],[c_0_57,c_0_58]) ).

cnf(c_0_63,plain,
    join(X1,complement(join(complement(X2),X1))) = join(X2,complement(join(X2,complement(X1)))),
    inference(spm,[status(thm)],[c_0_59,c_0_27]) ).

cnf(c_0_64,plain,
    join(X1,top) = top,
    inference(spm,[status(thm)],[c_0_27,c_0_56]) ).

cnf(c_0_65,plain,
    join(converse(top),X1) = converse(top),
    inference(spm,[status(thm)],[c_0_60,c_0_20]) ).

cnf(c_0_66,plain,
    composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_61]) ).

cnf(c_0_67,plain,
    join(complement(X1),complement(join(X2,X1))) = complement(X1),
    inference(spm,[status(thm)],[c_0_62,c_0_47]) ).

cnf(c_0_68,plain,
    join(X1,complement(join(X2,complement(join(X2,X1))))) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_63]),c_0_47]) ).

cnf(c_0_69,plain,
    join(converse(X1),converse(complement(X1))) = converse(top),
    inference(spm,[status(thm)],[c_0_55,c_0_35]) ).

cnf(c_0_70,plain,
    converse(top) = top,
    inference(spm,[status(thm)],[c_0_64,c_0_65]) ).

cnf(c_0_71,plain,
    join(X1,composition(X2,X1)) = composition(join(X2,one),X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_33]),c_0_27]) ).

cnf(c_0_72,plain,
    join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_47]),c_0_41]),c_0_27]),c_0_67]),c_0_47]) ).

cnf(c_0_73,plain,
    join(converse(X1),converse(complement(X1))) = top,
    inference(rw,[status(thm)],[c_0_69,c_0_70]) ).

cnf(c_0_74,plain,
    join(X1,zero) = X1,
    inference(spm,[status(thm)],[c_0_27,c_0_46]) ).

cnf(c_0_75,plain,
    join(X1,join(X2,join(X1,X3))) = join(X2,join(X1,X3)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_58]),c_0_41]),c_0_41]) ).

cnf(c_0_76,plain,
    join(X1,composition(top,X1)) = composition(top,X1),
    inference(spm,[status(thm)],[c_0_71,c_0_56]) ).

cnf(c_0_77,plain,
    join(converse(X1),complement(converse(complement(X1)))) = converse(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_39]),c_0_74]) ).

cnf(c_0_78,plain,
    join(X1,join(X2,composition(top,X1))) = join(X2,composition(top,X1)),
    inference(spm,[status(thm)],[c_0_75,c_0_76]) ).

cnf(c_0_79,plain,
    join(converse(X1),join(converse(complement(X1)),X2)) = top,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_73]),c_0_56]) ).

fof(c_0_80,plain,
    ! [X39,X40,X41] : composition(X39,composition(X40,X41)) = composition(composition(X39,X40),X41),
    inference(variable_rename,[status(thm)],[composition_associativity]) ).

cnf(c_0_81,plain,
    join(X1,converse(complement(converse(complement(X1))))) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_77]),c_0_20]),c_0_20]) ).

cnf(c_0_82,plain,
    join(X1,converse(complement(converse(X1)))) = top,
    inference(spm,[status(thm)],[c_0_73,c_0_20]) ).

cnf(c_0_83,plain,
    join(composition(top,converse(X1)),converse(complement(X1))) = top,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_27]) ).

cnf(c_0_84,plain,
    composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[c_0_80]) ).

cnf(c_0_85,plain,
    composition(top,top) = top,
    inference(spm,[status(thm)],[c_0_56,c_0_76]) ).

cnf(c_0_86,plain,
    join(complement(X1),converse(complement(converse(X1)))) = complement(X1),
    inference(spm,[status(thm)],[c_0_81,c_0_47]) ).

cnf(c_0_87,plain,
    join(X1,complement(converse(complement(converse(X1))))) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_82]),c_0_39]),c_0_74]) ).

fof(c_0_88,negated_conjecture,
    ~ ! [X1] :
        ( join(complement(composition(X1,top)),composition(complement(composition(X1,top)),top)) = composition(complement(composition(X1,top)),top)
        & join(composition(complement(composition(X1,top)),top),complement(composition(X1,top))) = complement(composition(X1,top)) ),
    inference(assume_negation,[status(cth)],[goals]) ).

cnf(c_0_89,plain,
    join(composition(X1,top),complement(X1)) = top,
    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_55,c_0_83]),c_0_70]),c_0_16]),c_0_20]),c_0_70]),c_0_20]) ).

cnf(c_0_90,plain,
    composition(top,composition(top,X1)) = composition(top,X1),
    inference(spm,[status(thm)],[c_0_84,c_0_85]) ).

cnf(c_0_91,plain,
    complement(converse(complement(converse(X1)))) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_86]),c_0_47]),c_0_27]),c_0_87]) ).

fof(c_0_92,negated_conjecture,
    ( join(complement(composition(esk1_0,top)),composition(complement(composition(esk1_0,top)),top)) != composition(complement(composition(esk1_0,top)),top)
    | join(composition(complement(composition(esk1_0,top)),top),complement(composition(esk1_0,top))) != complement(composition(esk1_0,top)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_88])])]) ).

cnf(c_0_93,plain,
    join(X1,composition(complement(X1),top)) = top,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_47]),c_0_27]) ).

cnf(c_0_94,plain,
    composition(top,complement(composition(top,X1))) = complement(composition(top,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_90]),c_0_70]),c_0_76]) ).

cnf(c_0_95,plain,
    converse(complement(converse(X1))) = complement(X1),
    inference(spm,[status(thm)],[c_0_47,c_0_91]) ).

cnf(c_0_96,negated_conjecture,
    ( join(complement(composition(esk1_0,top)),composition(complement(composition(esk1_0,top)),top)) != composition(complement(composition(esk1_0,top)),top)
    | join(composition(complement(composition(esk1_0,top)),top),complement(composition(esk1_0,top))) != complement(composition(esk1_0,top)) ),
    inference(split_conjunct,[status(thm)],[c_0_92]) ).

cnf(c_0_97,plain,
    complement(join(complement(X1),complement(composition(X1,top)))) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_93]),c_0_39]),c_0_47]),c_0_46]) ).

cnf(c_0_98,plain,
    composition(converse(complement(composition(top,X1))),top) = converse(complement(composition(top,X1))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_94]),c_0_70]) ).

cnf(c_0_99,plain,
    converse(complement(X1)) = complement(converse(X1)),
    inference(spm,[status(thm)],[c_0_20,c_0_95]) ).

cnf(c_0_100,negated_conjecture,
    ( join(complement(composition(esk1_0,top)),composition(complement(composition(esk1_0,top)),top)) != composition(complement(composition(esk1_0,top)),top)
    | join(complement(composition(esk1_0,top)),composition(complement(composition(esk1_0,top)),top)) != complement(composition(esk1_0,top)) ),
    inference(rw,[status(thm)],[c_0_96,c_0_27]) ).

cnf(c_0_101,plain,
    join(X1,composition(X1,top)) = composition(X1,top),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_97]),c_0_47]),c_0_27]),c_0_47]) ).

cnf(c_0_102,plain,
    composition(complement(composition(converse(X1),top)),top) = complement(composition(converse(X1),top)),
    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_98,c_0_99]),c_0_16]),c_0_70]),c_0_99]),c_0_16]),c_0_70]) ).

cnf(c_0_103,negated_conjecture,
    composition(complement(composition(esk1_0,top)),top) != complement(composition(esk1_0,top)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_101]),c_0_101])]) ).

cnf(c_0_104,plain,
    composition(complement(composition(X1,top)),top) = complement(composition(X1,top)),
    inference(spm,[status(thm)],[c_0_102,c_0_20]) ).

cnf(c_0_105,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_104])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : REL050+2 : 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   : Tue May  5 01:47:39 EDT 2026
% 0.15/0.33  % CPUTime    : 
% 0.15/0.34  % start to proof: theBenchmark
% 2.34/2.04  % Version  : CSE_E---1.7
% 2.34/2.04  % Problem  : theBenchmark.p
% 2.34/2.04  % SZS status Theorem for theBenchmark.p
% 2.34/2.04  % SZS output start CNFRefutation
% See solution above
% 2.34/2.05  % Total time : 1.368s
%------------------------------------------------------------------------------