TSTP Solution File: REL018+1 by Enigma---0.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Enigma---0.5.1
% Problem  : REL018+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : enigmatic-eprover.py %s %d 1

% Computer : n016.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  : 600s
% DateTime : Mon Jul 18 19:13:10 EDT 2022

% Result   : Theorem 7.39s 2.38s
% Output   : CNFRefutation 7.39s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   74 (  71 unt;   0 def)
%            Number of atoms       :   77 (  76 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    6 (   3   ~;   0   |;   1   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    5 (   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   :   98 (   4 sgn  46   !;   0   ?)

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

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

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

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

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

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

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

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

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

fof(c_0_13,plain,
    ! [X23,X24] : converse(composition(X23,X24)) = composition(converse(X24),converse(X23)),
    inference(variable_rename,[status(thm)],[converse_multiplicativity]) ).

fof(c_0_14,plain,
    ! [X20] : converse(converse(X20)) = X20,
    inference(variable_rename,[status(thm)],[converse_idempotence]) ).

cnf(c_0_15,plain,
    converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

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

fof(c_0_17,plain,
    ! [X16] : composition(X16,one) = X16,
    inference(variable_rename,[status(thm)],[composition_identity]) ).

cnf(c_0_18,plain,
    converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

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

fof(c_0_20,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_21,plain,
    ! [X4,X5] : join(X4,X5) = join(X5,X4),
    inference(variable_rename,[status(thm)],[maddux1_join_commutativity]) ).

cnf(c_0_22,plain,
    composition(converse(one),X1) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_16]) ).

fof(c_0_23,plain,
    ! [X28] : zero = meet(X28,complement(X28)),
    inference(variable_rename,[status(thm)],[def_zero]) ).

fof(c_0_24,plain,
    ! [X11,X12] : meet(X11,X12) = complement(join(complement(X11),complement(X12))),
    inference(variable_rename,[status(thm)],[maddux4_definiton_of_meet]) ).

cnf(c_0_25,plain,
    join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

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

cnf(c_0_27,plain,
    converse(one) = one,
    inference(spm,[status(thm)],[c_0_19,c_0_22]) ).

cnf(c_0_28,plain,
    zero = meet(X1,complement(X1)),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_29,plain,
    meet(X1,X2) = complement(join(complement(X1),complement(X2))),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

fof(c_0_30,plain,
    ! [X27] : top = join(X27,complement(X27)),
    inference(variable_rename,[status(thm)],[def_top]) ).

cnf(c_0_31,plain,
    join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
    inference(rw,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_32,plain,
    composition(one,X1) = X1,
    inference(rw,[status(thm)],[c_0_22,c_0_27]) ).

cnf(c_0_33,plain,
    zero = complement(join(complement(X1),complement(complement(X1)))),
    inference(rw,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_34,plain,
    top = join(X1,complement(X1)),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

fof(c_0_35,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_36,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_37,plain,
    join(complement(X1),complement(X1)) = complement(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_27]),c_0_32]) ).

cnf(c_0_38,plain,
    complement(top) = zero,
    inference(rw,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_39,plain,
    X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_40,plain,
    join(X1,join(X2,X3)) = join(join(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_41,plain,
    join(zero,zero) = zero,
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_42,plain,
    join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
    inference(rw,[status(thm)],[c_0_39,c_0_26]) ).

fof(c_0_43,plain,
    ! [X21,X22] : converse(join(X21,X22)) = join(converse(X21),converse(X22)),
    inference(variable_rename,[status(thm)],[converse_additivity]) ).

cnf(c_0_44,plain,
    join(X1,join(complement(X1),X2)) = join(top,X2),
    inference(spm,[status(thm)],[c_0_40,c_0_34]) ).

fof(c_0_45,negated_conjecture,
    ~ ! [X1] :
        ( composition(X1,top) = X1
       => composition(complement(X1),top) = complement(X1) ),
    inference(assume_negation,[status(cth)],[goals]) ).

cnf(c_0_46,plain,
    join(zero,join(zero,X1)) = join(zero,X1),
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_47,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_42,c_0_34]),c_0_37]),c_0_38]),c_0_26]) ).

cnf(c_0_48,plain,
    converse(join(X1,X2)) = join(converse(X1),converse(X2)),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

cnf(c_0_49,plain,
    join(top,complement(X1)) = top,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_37]),c_0_34]) ).

fof(c_0_50,negated_conjecture,
    ( composition(esk1_0,top) = esk1_0
    & composition(complement(esk1_0),top) != complement(esk1_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])]) ).

cnf(c_0_51,plain,
    join(zero,X1) = X1,
    inference(spm,[status(thm)],[c_0_46,c_0_47]) ).

cnf(c_0_52,plain,
    converse(join(X1,converse(X2))) = join(converse(X1),X2),
    inference(spm,[status(thm)],[c_0_48,c_0_16]) ).

fof(c_0_53,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_54,plain,
    join(X1,top) = top,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_34]),c_0_49]) ).

cnf(c_0_55,plain,
    converse(join(converse(X1),X2)) = join(X1,converse(X2)),
    inference(spm,[status(thm)],[c_0_48,c_0_16]) ).

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

cnf(c_0_57,plain,
    join(X1,zero) = X1,
    inference(spm,[status(thm)],[c_0_26,c_0_51]) ).

cnf(c_0_58,plain,
    join(converse(zero),X1) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_51]),c_0_16]) ).

cnf(c_0_59,plain,
    composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_53]) ).

cnf(c_0_60,plain,
    join(top,X1) = top,
    inference(spm,[status(thm)],[c_0_26,c_0_54]) ).

cnf(c_0_61,plain,
    join(X1,converse(top)) = converse(top),
    inference(spm,[status(thm)],[c_0_55,c_0_54]) ).

cnf(c_0_62,negated_conjecture,
    composition(converse(esk1_0),complement(esk1_0)) = zero,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_56]),c_0_38]),c_0_38]),c_0_51]) ).

cnf(c_0_63,plain,
    converse(zero) = zero,
    inference(spm,[status(thm)],[c_0_57,c_0_58]) ).

cnf(c_0_64,plain,
    join(X1,composition(X2,X1)) = composition(join(one,X2),X1),
    inference(spm,[status(thm)],[c_0_59,c_0_32]) ).

cnf(c_0_65,plain,
    converse(top) = top,
    inference(spm,[status(thm)],[c_0_60,c_0_61]) ).

cnf(c_0_66,negated_conjecture,
    composition(converse(complement(esk1_0)),esk1_0) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_62]),c_0_63]) ).

cnf(c_0_67,plain,
    complement(zero) = top,
    inference(spm,[status(thm)],[c_0_34,c_0_51]) ).

cnf(c_0_68,plain,
    join(X1,composition(top,X1)) = composition(top,X1),
    inference(spm,[status(thm)],[c_0_64,c_0_54]) ).

cnf(c_0_69,plain,
    composition(top,converse(X1)) = converse(composition(X1,top)),
    inference(spm,[status(thm)],[c_0_15,c_0_65]) ).

cnf(c_0_70,negated_conjecture,
    join(complement(esk1_0),composition(complement(esk1_0),top)) = complement(esk1_0),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_66]),c_0_16]),c_0_67]) ).

cnf(c_0_71,plain,
    join(X1,composition(X1,top)) = composition(X1,top),
    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_68]),c_0_69]),c_0_16]),c_0_69]),c_0_16]) ).

cnf(c_0_72,negated_conjecture,
    composition(complement(esk1_0),top) != complement(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

cnf(c_0_73,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_71]),c_0_72]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : REL018+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13  % Command  : enigmatic-eprover.py %s %d 1
% 0.13/0.34  % Computer : n016.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Fri Jul  8 09:54:40 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.45  # ENIGMATIC: Selected SinE mode:
% 0.19/0.46  # Parsing /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46  # Filter: axfilter_auto   0 goes into file theBenchmark_axfilter_auto   0.p
% 0.19/0.46  # Filter: axfilter_auto   1 goes into file theBenchmark_axfilter_auto   1.p
% 0.19/0.46  # Filter: axfilter_auto   2 goes into file theBenchmark_axfilter_auto   2.p
% 7.39/2.38  # ENIGMATIC: Solved by autoschedule:
% 7.39/2.38  # No SInE strategy applied
% 7.39/2.38  # Trying AutoSched0 for 150 seconds
% 7.39/2.38  # AutoSched0-Mode selected heuristic H_____047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S
% 7.39/2.38  # and selection function SelectNewComplexAHP.
% 7.39/2.38  #
% 7.39/2.38  # Preprocessing time       : 0.024 s
% 7.39/2.38  # Presaturation interreduction done
% 7.39/2.38  
% 7.39/2.38  # Proof found!
% 7.39/2.38  # SZS status Theorem
% 7.39/2.38  # SZS output start CNFRefutation
% See solution above
% 7.39/2.38  # Training examples: 0 positive, 0 negative
% 7.39/2.38  
% 7.39/2.38  # -------------------------------------------------
% 7.39/2.38  # User time                : 0.061 s
% 7.39/2.38  # System time              : 0.011 s
% 7.39/2.38  # Total time               : 0.071 s
% 7.39/2.38  # Maximum resident set size: 7120 pages
% 7.39/2.38  
%------------------------------------------------------------------------------