TSTP Solution File: REL028+2 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : REL028+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n015.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 : Sat May  4 09:13:04 EDT 2024

% Result   : Theorem 3.57s 0.86s
% Output   : CNFRefutation 3.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :   15
% Syntax   : Number of formulae    :  129 ( 126 unt;   0 def)
%            Number of atoms       :  135 ( 134 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   10 (   4   ~;   0   |;   4   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-2 aty)
%            Number of variables   :  160 (   6 sgn  60   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(converse_multiplicativity,axiom,
    ! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
    file('/export/starexec/sandbox2/tmp/tmp.FMhjWvl1aB/E---3.1_32737.p',converse_multiplicativity) ).

fof(converse_idempotence,axiom,
    ! [X1] : converse(converse(X1)) = X1,
    file('/export/starexec/sandbox2/tmp/tmp.FMhjWvl1aB/E---3.1_32737.p',converse_idempotence) ).

fof(composition_identity,axiom,
    ! [X1] : composition(X1,one) = X1,
    file('/export/starexec/sandbox2/tmp/tmp.FMhjWvl1aB/E---3.1_32737.p',composition_identity) ).

fof(converse_cancellativity,axiom,
    ! [X1,X2] : join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
    file('/export/starexec/sandbox2/tmp/tmp.FMhjWvl1aB/E---3.1_32737.p',converse_cancellativity) ).

fof(maddux1_join_commutativity,axiom,
    ! [X1,X2] : join(X1,X2) = join(X2,X1),
    file('/export/starexec/sandbox2/tmp/tmp.FMhjWvl1aB/E---3.1_32737.p',maddux1_join_commutativity) ).

fof(def_zero,axiom,
    ! [X1] : zero = meet(X1,complement(X1)),
    file('/export/starexec/sandbox2/tmp/tmp.FMhjWvl1aB/E---3.1_32737.p',def_zero) ).

fof(maddux4_definiton_of_meet,axiom,
    ! [X1,X2] : meet(X1,X2) = complement(join(complement(X1),complement(X2))),
    file('/export/starexec/sandbox2/tmp/tmp.FMhjWvl1aB/E---3.1_32737.p',maddux4_definiton_of_meet) ).

fof(def_top,axiom,
    ! [X1] : top = join(X1,complement(X1)),
    file('/export/starexec/sandbox2/tmp/tmp.FMhjWvl1aB/E---3.1_32737.p',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/tmp/tmp.FMhjWvl1aB/E---3.1_32737.p',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/tmp/tmp.FMhjWvl1aB/E---3.1_32737.p',maddux2_join_associativity) ).

fof(goals,conjecture,
    ! [X1,X2] :
      ( ( join(X1,one) = one
        & join(X2,one) = one )
     => composition(X1,X2) = meet(X1,X2) ),
    file('/export/starexec/sandbox2/tmp/tmp.FMhjWvl1aB/E---3.1_32737.p',goals) ).

fof(converse_additivity,axiom,
    ! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
    file('/export/starexec/sandbox2/tmp/tmp.FMhjWvl1aB/E---3.1_32737.p',converse_additivity) ).

fof(dedekind_law,axiom,
    ! [X1,X2,X3] : join(meet(composition(X1,X2),X3),composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3)))) = composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3))),
    file('/export/starexec/sandbox2/tmp/tmp.FMhjWvl1aB/E---3.1_32737.p',dedekind_law) ).

fof(composition_distributivity,axiom,
    ! [X1,X2,X3] : composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
    file('/export/starexec/sandbox2/tmp/tmp.FMhjWvl1aB/E---3.1_32737.p',composition_distributivity) ).

fof(composition_associativity,axiom,
    ! [X1,X2,X3] : composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
    file('/export/starexec/sandbox2/tmp/tmp.FMhjWvl1aB/E---3.1_32737.p',composition_associativity) ).

fof(c_0_15,plain,
    ! [X23,X24] : converse(composition(X23,X24)) = composition(converse(X24),converse(X23)),
    inference(variable_rename,[status(thm)],[converse_multiplicativity]) ).

fof(c_0_16,plain,
    ! [X20] : converse(converse(X20)) = X20,
    inference(variable_rename,[status(thm)],[converse_idempotence]) ).

cnf(c_0_17,plain,
    converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_18,plain,
    converse(converse(X1)) = X1,
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_19,plain,
    ! [X16] : composition(X16,one) = X16,
    inference(variable_rename,[status(thm)],[composition_identity]) ).

cnf(c_0_20,plain,
    converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_21,plain,
    composition(X1,one) = X1,
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

fof(c_0_22,plain,
    ! [X25,X26] : join(composition(converse(X25),complement(composition(X25,X26))),complement(X26)) = complement(X26),
    inference(variable_rename,[status(thm)],[converse_cancellativity]) ).

fof(c_0_23,plain,
    ! [X4,X5] : join(X4,X5) = join(X5,X4),
    inference(variable_rename,[status(thm)],[maddux1_join_commutativity]) ).

cnf(c_0_24,plain,
    composition(converse(one),X1) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_18]) ).

fof(c_0_25,plain,
    ! [X28] : zero = meet(X28,complement(X28)),
    inference(variable_rename,[status(thm)],[def_zero]) ).

fof(c_0_26,plain,
    ! [X11,X12] : meet(X11,X12) = complement(join(complement(X11),complement(X12))),
    inference(variable_rename,[status(thm)],[maddux4_definiton_of_meet]) ).

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

cnf(c_0_28,plain,
    join(X1,X2) = join(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_29,plain,
    converse(one) = one,
    inference(spm,[status(thm)],[c_0_21,c_0_24]) ).

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

cnf(c_0_31,plain,
    meet(X1,X2) = complement(join(complement(X1),complement(X2))),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

fof(c_0_32,plain,
    ! [X27] : top = join(X27,complement(X27)),
    inference(variable_rename,[status(thm)],[def_top]) ).

cnf(c_0_33,plain,
    join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
    inference(rw,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_34,plain,
    composition(one,X1) = X1,
    inference(rw,[status(thm)],[c_0_24,c_0_29]) ).

cnf(c_0_35,plain,
    zero = complement(join(complement(X1),complement(complement(X1)))),
    inference(rw,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_36,plain,
    top = join(X1,complement(X1)),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

fof(c_0_37,plain,
    ! [X9,X10] : X9 = join(complement(join(complement(X9),complement(X10))),complement(join(complement(X9),X10))),
    inference(variable_rename,[status(thm)],[maddux3_a_kind_of_de_Morgan]) ).

fof(c_0_38,plain,
    ! [X6,X7,X8] : join(X6,join(X7,X8)) = join(join(X6,X7),X8),
    inference(variable_rename,[status(thm)],[maddux2_join_associativity]) ).

cnf(c_0_39,plain,
    join(complement(X1),complement(X1)) = complement(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_29]),c_0_34]) ).

cnf(c_0_40,plain,
    complement(top) = zero,
    inference(rw,[status(thm)],[c_0_35,c_0_36]) ).

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

cnf(c_0_42,plain,
    join(X1,join(X2,X3)) = join(join(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_43,plain,
    join(zero,zero) = zero,
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_44,plain,
    join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
    inference(rw,[status(thm)],[c_0_41,c_0_28]) ).

cnf(c_0_45,plain,
    join(zero,join(zero,X1)) = join(zero,X1),
    inference(spm,[status(thm)],[c_0_42,c_0_43]) ).

cnf(c_0_46,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_44,c_0_39]),c_0_36]),c_0_40]),c_0_28]) ).

cnf(c_0_47,plain,
    join(zero,X1) = X1,
    inference(spm,[status(thm)],[c_0_45,c_0_46]) ).

fof(c_0_48,negated_conjecture,
    ~ ! [X1,X2] :
        ( ( join(X1,one) = one
          & join(X2,one) = one )
       => composition(X1,X2) = meet(X1,X2) ),
    inference(assume_negation,[status(cth)],[goals]) ).

cnf(c_0_49,plain,
    complement(complement(X1)) = X1,
    inference(rw,[status(thm)],[c_0_46,c_0_47]) ).

fof(c_0_50,negated_conjecture,
    ( join(esk1_0,one) = one
    & join(esk2_0,one) = one
    & composition(esk1_0,esk2_0) != meet(esk1_0,esk2_0) ),
    inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_48])])])]) ).

cnf(c_0_51,plain,
    join(X1,X1) = X1,
    inference(spm,[status(thm)],[c_0_39,c_0_49]) ).

cnf(c_0_52,negated_conjecture,
    join(esk2_0,one) = one,
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

cnf(c_0_53,plain,
    join(X1,join(X1,X2)) = join(X1,X2),
    inference(spm,[status(thm)],[c_0_42,c_0_51]) ).

fof(c_0_54,plain,
    ! [X21,X22] : converse(join(X21,X22)) = join(converse(X21),converse(X22)),
    inference(variable_rename,[status(thm)],[converse_additivity]) ).

cnf(c_0_55,negated_conjecture,
    join(one,esk2_0) = one,
    inference(rw,[status(thm)],[c_0_52,c_0_28]) ).

cnf(c_0_56,negated_conjecture,
    join(esk1_0,one) = one,
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

fof(c_0_57,plain,
    ! [X29,X30,X31] : join(meet(composition(X29,X30),X31),composition(meet(X29,composition(X31,converse(X30))),meet(X30,composition(converse(X29),X31)))) = composition(meet(X29,composition(X31,converse(X30))),meet(X30,composition(converse(X29),X31))),
    inference(variable_rename,[status(thm)],[dedekind_law]) ).

cnf(c_0_58,plain,
    join(X1,complement(join(complement(X1),X2))) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_44]),c_0_28]) ).

cnf(c_0_59,plain,
    join(X1,join(X2,X1)) = join(X2,X1),
    inference(spm,[status(thm)],[c_0_53,c_0_28]) ).

cnf(c_0_60,plain,
    converse(join(X1,X2)) = join(converse(X1),converse(X2)),
    inference(split_conjunct,[status(thm)],[c_0_54]) ).

cnf(c_0_61,negated_conjecture,
    join(one,join(esk2_0,X1)) = join(one,X1),
    inference(spm,[status(thm)],[c_0_42,c_0_55]) ).

cnf(c_0_62,negated_conjecture,
    join(one,esk1_0) = one,
    inference(rw,[status(thm)],[c_0_56,c_0_28]) ).

cnf(c_0_63,plain,
    join(meet(composition(X1,X2),X3),composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3)))) = composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3))),
    inference(split_conjunct,[status(thm)],[c_0_57]) ).

cnf(c_0_64,plain,
    join(X1,complement(join(X2,complement(X1)))) = X1,
    inference(spm,[status(thm)],[c_0_58,c_0_59]) ).

cnf(c_0_65,plain,
    converse(join(one,X1)) = join(one,converse(X1)),
    inference(spm,[status(thm)],[c_0_60,c_0_29]) ).

cnf(c_0_66,negated_conjecture,
    join(one,complement(join(complement(esk2_0),X1))) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_58]),c_0_55]) ).

cnf(c_0_67,plain,
    join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
    inference(spm,[status(thm)],[c_0_28,c_0_42]) ).

fof(c_0_68,plain,
    ! [X17,X18,X19] : composition(join(X17,X18),X19) = join(composition(X17,X19),composition(X18,X19)),
    inference(variable_rename,[status(thm)],[composition_distributivity]) ).

cnf(c_0_69,negated_conjecture,
    join(one,join(esk1_0,X1)) = join(one,X1),
    inference(spm,[status(thm)],[c_0_42,c_0_62]) ).

cnf(c_0_70,plain,
    join(complement(join(complement(composition(X1,X2)),complement(X3))),composition(complement(join(complement(X1),complement(composition(X3,converse(X2))))),complement(join(complement(X2),complement(composition(converse(X1),X3)))))) = composition(complement(join(complement(X1),complement(composition(X3,converse(X2))))),complement(join(complement(X2),complement(composition(converse(X1),X3))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_31]),c_0_31]),c_0_31]),c_0_31]),c_0_31]) ).

cnf(c_0_71,plain,
    join(complement(X1),complement(join(X2,X1))) = complement(X1),
    inference(spm,[status(thm)],[c_0_64,c_0_49]) ).

cnf(c_0_72,negated_conjecture,
    join(one,converse(esk2_0)) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_55]),c_0_29]) ).

cnf(c_0_73,negated_conjecture,
    join(complement(one),join(complement(esk2_0),X1)) = join(complement(esk2_0),X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_66]),c_0_42]),c_0_67]) ).

cnf(c_0_74,plain,
    join(X1,zero) = X1,
    inference(spm,[status(thm)],[c_0_28,c_0_47]) ).

cnf(c_0_75,plain,
    composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_68]) ).

cnf(c_0_76,negated_conjecture,
    join(one,complement(join(complement(esk1_0),X1))) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_58]),c_0_62]) ).

cnf(c_0_77,plain,
    join(complement(join(complement(one),complement(composition(X1,X2)))),composition(complement(join(complement(X1),complement(converse(X2)))),complement(join(complement(X2),complement(converse(X1)))))) = composition(complement(join(complement(X1),complement(converse(X2)))),complement(join(complement(X2),complement(converse(X1))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_21]),c_0_28]),c_0_34]),c_0_34]) ).

cnf(c_0_78,negated_conjecture,
    join(complement(one),complement(converse(esk2_0))) = complement(converse(esk2_0)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_28]) ).

cnf(c_0_79,negated_conjecture,
    join(complement(one),complement(esk2_0)) = complement(esk2_0),
    inference(spm,[status(thm)],[c_0_73,c_0_74]) ).

cnf(c_0_80,plain,
    join(X1,composition(X2,X1)) = composition(join(one,X2),X1),
    inference(spm,[status(thm)],[c_0_75,c_0_34]) ).

cnf(c_0_81,negated_conjecture,
    join(one,converse(esk1_0)) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_62]),c_0_29]) ).

cnf(c_0_82,negated_conjecture,
    join(complement(one),join(complement(esk1_0),X1)) = join(complement(esk1_0),X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_76]),c_0_42]),c_0_67]) ).

cnf(c_0_83,negated_conjecture,
    join(esk2_0,composition(converse(esk2_0),esk2_0)) = composition(converse(esk2_0),esk2_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)],[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_77,c_0_78]),c_0_34]),c_0_79]),c_0_49]),c_0_49]),c_0_29]),c_0_28]),c_0_79]),c_0_49]),c_0_49]),c_0_29]),c_0_28]),c_0_79]),c_0_49]) ).

cnf(c_0_84,negated_conjecture,
    join(X1,composition(converse(esk2_0),X1)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_72]),c_0_34]) ).

cnf(c_0_85,negated_conjecture,
    join(complement(one),complement(converse(esk1_0))) = complement(converse(esk1_0)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_81]),c_0_28]) ).

cnf(c_0_86,negated_conjecture,
    join(complement(one),complement(esk1_0)) = complement(esk1_0),
    inference(spm,[status(thm)],[c_0_82,c_0_74]) ).

cnf(c_0_87,negated_conjecture,
    join(X1,composition(esk2_0,X1)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_55]),c_0_34]) ).

cnf(c_0_88,negated_conjecture,
    composition(converse(esk2_0),esk2_0) = esk2_0,
    inference(rw,[status(thm)],[c_0_83,c_0_84]) ).

cnf(c_0_89,negated_conjecture,
    join(esk1_0,composition(converse(esk1_0),esk1_0)) = composition(converse(esk1_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)],[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_77,c_0_85]),c_0_34]),c_0_86]),c_0_49]),c_0_49]),c_0_29]),c_0_28]),c_0_86]),c_0_49]),c_0_49]),c_0_29]),c_0_28]),c_0_86]),c_0_49]) ).

cnf(c_0_90,negated_conjecture,
    join(X1,composition(converse(esk1_0),X1)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_34]) ).

cnf(c_0_91,plain,
    join(complement(join(complement(X1),complement(X2))),composition(complement(join(complement(one),complement(composition(X2,converse(X1))))),complement(join(complement(X1),complement(X2))))) = composition(complement(join(complement(one),complement(composition(X2,converse(X1))))),complement(join(complement(X1),complement(X2)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_29]),c_0_34]),c_0_34]),c_0_34]) ).

cnf(c_0_92,negated_conjecture,
    join(one,composition(esk2_0,esk1_0)) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_87]),c_0_62]) ).

fof(c_0_93,plain,
    ! [X13,X14,X15] : composition(X13,composition(X14,X15)) = composition(composition(X13,X14),X15),
    inference(variable_rename,[status(thm)],[composition_associativity]) ).

cnf(c_0_94,negated_conjecture,
    converse(esk2_0) = esk2_0,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_88]),c_0_88]) ).

cnf(c_0_95,negated_conjecture,
    composition(converse(esk1_0),esk1_0) = esk1_0,
    inference(rw,[status(thm)],[c_0_89,c_0_90]) ).

cnf(c_0_96,plain,
    composition(complement(join(complement(one),complement(composition(X1,converse(X2))))),complement(join(complement(X2),complement(X1)))) = complement(join(complement(X2),complement(X1))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_80]),c_0_58]),c_0_34]) ).

cnf(c_0_97,negated_conjecture,
    join(complement(one),complement(composition(esk2_0,esk1_0))) = complement(composition(esk2_0,esk1_0)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_92]),c_0_28]) ).

cnf(c_0_98,plain,
    composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[c_0_93]) ).

cnf(c_0_99,negated_conjecture,
    converse(join(esk2_0,X1)) = join(esk2_0,converse(X1)),
    inference(spm,[status(thm)],[c_0_60,c_0_94]) ).

cnf(c_0_100,negated_conjecture,
    converse(composition(X1,esk2_0)) = composition(esk2_0,converse(X1)),
    inference(spm,[status(thm)],[c_0_17,c_0_94]) ).

cnf(c_0_101,negated_conjecture,
    converse(esk1_0) = esk1_0,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_95]),c_0_95]) ).

cnf(c_0_102,negated_conjecture,
    composition(esk2_0,composition(esk1_0,composition(esk2_0,esk1_0))) = composition(esk2_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)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_29]),c_0_21]),c_0_97]),c_0_49]),c_0_49]),c_0_98]),c_0_49]) ).

cnf(c_0_103,plain,
    join(composition(X1,composition(X2,X3)),composition(X4,X3)) = composition(join(composition(X1,X2),X4),X3),
    inference(spm,[status(thm)],[c_0_75,c_0_98]) ).

cnf(c_0_104,negated_conjecture,
    join(X1,composition(esk1_0,X1)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_62]),c_0_34]) ).

cnf(c_0_105,negated_conjecture,
    join(esk2_0,composition(esk2_0,esk1_0)) = esk2_0,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_90]),c_0_94]),c_0_100]),c_0_18]) ).

cnf(c_0_106,negated_conjecture,
    converse(composition(esk1_0,X1)) = composition(converse(X1),esk1_0),
    inference(spm,[status(thm)],[c_0_20,c_0_101]) ).

cnf(c_0_107,negated_conjecture,
    composition(esk1_0,composition(esk2_0,esk1_0)) = composition(esk2_0,esk1_0),
    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_80,c_0_102]),c_0_103]),c_0_55]),c_0_34]),c_0_28]),c_0_104]) ).

cnf(c_0_108,negated_conjecture,
    converse(composition(esk2_0,X1)) = composition(converse(X1),esk2_0),
    inference(spm,[status(thm)],[c_0_20,c_0_94]) ).

cnf(c_0_109,plain,
    join(complement(join(complement(X1),complement(X2))),composition(complement(join(complement(X1),complement(X2))),complement(join(complement(one),complement(composition(converse(X1),X2)))))) = composition(complement(join(complement(X1),complement(X2))),complement(join(complement(one),complement(composition(converse(X1),X2))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_21]),c_0_29]),c_0_21]),c_0_29]),c_0_21]) ).

cnf(c_0_110,plain,
    join(X1,join(X2,complement(join(X1,X2)))) = top,
    inference(spm,[status(thm)],[c_0_36,c_0_42]) ).

cnf(c_0_111,negated_conjecture,
    join(complement(esk2_0),complement(composition(esk2_0,esk1_0))) = complement(composition(esk2_0,esk1_0)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_105]),c_0_28]) ).

cnf(c_0_112,negated_conjecture,
    composition(esk2_0,esk1_0) = composition(esk1_0,esk2_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(spm,[status(thm)],[c_0_106,c_0_107]),c_0_108]),c_0_101]),c_0_108]),c_0_101]),c_0_98]),c_0_107]) ).

cnf(c_0_113,negated_conjecture,
    join(esk2_0,composition(esk2_0,esk2_0)) = composition(esk2_0,esk2_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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_79]),c_0_49]),c_0_49]),c_0_29]),c_0_34]),c_0_79]),c_0_49]),c_0_49]),c_0_29]),c_0_34]),c_0_79]),c_0_49]) ).

cnf(c_0_114,negated_conjecture,
    join(X1,join(composition(esk2_0,X1),X2)) = join(X1,X2),
    inference(spm,[status(thm)],[c_0_42,c_0_87]) ).

cnf(c_0_115,plain,
    join(X1,top) = top,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_51]),c_0_36]) ).

cnf(c_0_116,plain,
    join(complement(join(complement(composition(X1,converse(X2))),complement(X3))),composition(complement(join(complement(X1),complement(composition(X3,X2)))),complement(join(complement(converse(X2)),complement(composition(converse(X1),X3)))))) = composition(complement(join(complement(X1),complement(composition(X3,X2)))),complement(join(complement(converse(X2)),complement(composition(converse(X1),X3))))),
    inference(spm,[status(thm)],[c_0_70,c_0_18]) ).

cnf(c_0_117,negated_conjecture,
    join(complement(esk2_0),complement(composition(esk1_0,esk2_0))) = complement(composition(esk1_0,esk2_0)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_111,c_0_112]),c_0_112]) ).

cnf(c_0_118,negated_conjecture,
    composition(esk2_0,esk2_0) = esk2_0,
    inference(rw,[status(thm)],[c_0_113,c_0_87]) ).

cnf(c_0_119,negated_conjecture,
    composition(esk2_0,composition(esk1_0,esk2_0)) = composition(esk1_0,esk2_0),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_102,c_0_107]),c_0_112]),c_0_112]) ).

cnf(c_0_120,negated_conjecture,
    composition(esk1_0,composition(esk1_0,esk2_0)) = composition(esk1_0,esk2_0),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_112]),c_0_112]) ).

cnf(c_0_121,negated_conjecture,
    join(X1,complement(composition(esk2_0,X1))) = top,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_36]),c_0_115]) ).

cnf(c_0_122,negated_conjecture,
    join(composition(esk1_0,esk2_0),complement(join(complement(esk1_0),complement(esk2_0)))) = composition(esk1_0,esk2_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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_94]),c_0_118]),c_0_49]),c_0_94]),c_0_94]),c_0_112]),c_0_117]),c_0_49]),c_0_98]),c_0_119]),c_0_120]),c_0_49]),c_0_94]),c_0_94]),c_0_112]),c_0_117]),c_0_49]),c_0_98]),c_0_119]),c_0_120]),c_0_28]),c_0_28]) ).

cnf(c_0_123,negated_conjecture,
    composition(esk1_0,esk2_0) != meet(esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

cnf(c_0_124,plain,
    join(complement(join(X1,complement(X2))),complement(join(complement(X2),complement(X1)))) = X2,
    inference(spm,[status(thm)],[c_0_44,c_0_28]) ).

cnf(c_0_125,negated_conjecture,
    join(esk1_0,complement(composition(esk1_0,esk2_0))) = top,
    inference(spm,[status(thm)],[c_0_121,c_0_112]) ).

cnf(c_0_126,negated_conjecture,
    join(complement(esk1_0),complement(composition(esk1_0,esk2_0))) = join(complement(esk1_0),complement(esk2_0)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_122]),c_0_49]),c_0_42]),c_0_117]),c_0_49]) ).

cnf(c_0_127,negated_conjecture,
    composition(esk1_0,esk2_0) != complement(join(complement(esk1_0),complement(esk2_0))),
    inference(rw,[status(thm)],[c_0_123,c_0_31]) ).

cnf(c_0_128,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_40]),c_0_28]),c_0_126]),c_0_47]),c_0_127]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10  % Problem    : REL028+2 : TPTP v8.1.2. Released v4.0.0.
% 0.09/0.11  % Command    : run_E %s %d THM
% 0.11/0.31  % Computer : n015.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit   : 300
% 0.11/0.31  % WCLimit    : 300
% 0.11/0.31  % DateTime   : Fri May  3 10:01:36 EDT 2024
% 0.11/0.31  % CPUTime    : 
% 0.16/0.42  Running first-order theorem proving
% 0.16/0.42  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/tmp/tmp.FMhjWvl1aB/E---3.1_32737.p
% 3.57/0.86  # Version: 3.1.0
% 3.57/0.86  # Preprocessing class: FSMSSMSSSSSNFFN.
% 3.57/0.86  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.57/0.86  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.57/0.86  # Starting new_bool_3 with 300s (1) cores
% 3.57/0.86  # Starting new_bool_1 with 300s (1) cores
% 3.57/0.86  # Starting sh5l with 300s (1) cores
% 3.57/0.86  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 347 completed with status 0
% 3.57/0.86  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 3.57/0.86  # Preprocessing class: FSMSSMSSSSSNFFN.
% 3.57/0.86  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.57/0.86  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.57/0.86  # No SInE strategy applied
% 3.57/0.86  # Search class: FUUPM-FFMF21-DFFFFFNN
% 3.57/0.86  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 3.57/0.86  # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 811s (1) cores
% 3.57/0.86  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 3.57/0.86  # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S2S with 136s (1) cores
% 3.57/0.86  # Starting new_bool_3 with 136s (1) cores
% 3.57/0.86  # Starting new_bool_1 with 136s (1) cores
% 3.57/0.86  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 352 completed with status 0
% 3.57/0.86  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 3.57/0.86  # Preprocessing class: FSMSSMSSSSSNFFN.
% 3.57/0.86  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.57/0.86  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.57/0.86  # No SInE strategy applied
% 3.57/0.86  # Search class: FUUPM-FFMF21-DFFFFFNN
% 3.57/0.86  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 3.57/0.86  # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 811s (1) cores
% 3.57/0.86  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 3.57/0.86  # Preprocessing time       : 0.001 s
% 3.57/0.86  # Presaturation interreduction done
% 3.57/0.86  
% 3.57/0.86  # Proof found!
% 3.57/0.86  # SZS status Theorem
% 3.57/0.86  # SZS output start CNFRefutation
% See solution above
% 3.57/0.86  # Parsed axioms                        : 17
% 3.57/0.86  # Removed by relevancy pruning/SinE    : 0
% 3.57/0.86  # Initial clauses                      : 19
% 3.57/0.86  # Removed in clause preprocessing      : 1
% 3.57/0.86  # Initial clauses in saturation        : 18
% 3.57/0.86  # Processed clauses                    : 1530
% 3.57/0.86  # ...of these trivial                  : 899
% 3.57/0.86  # ...subsumed                          : 90
% 3.57/0.86  # ...remaining for further processing  : 541
% 3.57/0.86  # Other redundant clauses eliminated   : 0
% 3.57/0.86  # Clauses deleted for lack of memory   : 0
% 3.57/0.86  # Backward-subsumed                    : 0
% 3.57/0.86  # Backward-rewritten                   : 133
% 3.57/0.86  # Generated clauses                    : 31238
% 3.57/0.86  # ...of the previous two non-redundant : 17711
% 3.57/0.86  # ...aggressively subsumed             : 0
% 3.57/0.86  # Contextual simplify-reflections      : 0
% 3.57/0.86  # Paramodulations                      : 31238
% 3.57/0.86  # Factorizations                       : 0
% 3.57/0.86  # NegExts                              : 0
% 3.57/0.86  # Equation resolutions                 : 0
% 3.57/0.86  # Disequality decompositions           : 0
% 3.57/0.86  # Total rewrite steps                  : 78685
% 3.57/0.86  # ...of those cached                   : 70111
% 3.57/0.86  # Propositional unsat checks           : 0
% 3.57/0.86  #    Propositional check models        : 0
% 3.57/0.86  #    Propositional check unsatisfiable : 0
% 3.57/0.86  #    Propositional clauses             : 0
% 3.57/0.86  #    Propositional clauses after purity: 0
% 3.57/0.86  #    Propositional unsat core size     : 0
% 3.57/0.86  #    Propositional preprocessing time  : 0.000
% 3.57/0.86  #    Propositional encoding time       : 0.000
% 3.57/0.86  #    Propositional solver time         : 0.000
% 3.57/0.86  #    Success case prop preproc time    : 0.000
% 3.57/0.86  #    Success case prop encoding time   : 0.000
% 3.57/0.86  #    Success case prop solver time     : 0.000
% 3.57/0.86  # Current number of processed clauses  : 390
% 3.57/0.86  #    Positive orientable unit clauses  : 384
% 3.57/0.86  #    Positive unorientable unit clauses: 5
% 3.57/0.86  #    Negative unit clauses             : 1
% 3.57/0.86  #    Non-unit-clauses                  : 0
% 3.57/0.86  # Current number of unprocessed clauses: 16054
% 3.57/0.86  # ...number of literals in the above   : 16054
% 3.57/0.86  # Current number of archived formulas  : 0
% 3.57/0.86  # Current number of archived clauses   : 152
% 3.57/0.86  # Clause-clause subsumption calls (NU) : 0
% 3.57/0.86  # Rec. Clause-clause subsumption calls : 0
% 3.57/0.86  # Non-unit clause-clause subsumptions  : 0
% 3.57/0.86  # Unit Clause-clause subsumption calls : 27
% 3.57/0.86  # Rewrite failures with RHS unbound    : 0
% 3.57/0.86  # BW rewrite match attempts            : 2471
% 3.57/0.86  # BW rewrite match successes           : 192
% 3.57/0.86  # Condensation attempts                : 0
% 3.57/0.86  # Condensation successes               : 0
% 3.57/0.86  # Termbank termtop insertions          : 710959
% 3.57/0.86  # Search garbage collected termcells   : 38
% 3.57/0.86  
% 3.57/0.86  # -------------------------------------------------
% 3.57/0.86  # User time                : 0.403 s
% 3.57/0.86  # System time              : 0.020 s
% 3.57/0.86  # Total time               : 0.423 s
% 3.57/0.86  # Maximum resident set size: 1716 pages
% 3.57/0.86  
% 3.57/0.86  # -------------------------------------------------
% 3.57/0.86  # User time                : 2.075 s
% 3.57/0.86  # System time              : 0.053 s
% 3.57/0.86  # Total time               : 2.128 s
% 3.57/0.86  # Maximum resident set size: 1700 pages
% 3.57/0.86  % E---3.1 exiting
% 3.57/0.86  % E exiting
%------------------------------------------------------------------------------