TSTP Solution File: KLE011+1 by Enigma---0.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Enigma---0.5.1
% Problem  : KLE011+1 : TPTP v7.5.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : enigmatic-eprover.py %s %d 1

% Computer : n020.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
% DateTime : Tue Mar 30 16:58:57 EDT 2021

% Result   : Theorem 18.81s
% Output   : CNFRefutation 18.81s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   77 (  63 unt;   0 def)
%            Number of atoms       :  112 (  69 equ)
%            Maximal formula atoms :   10 (   1 avg)
%            Number of connectives :   59 (  24   ~;  18   |;  11   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   2 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   86 (   1 sgn  44   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(test_3,axiom,
    ! [X4,X5] :
      ( test(X4)
     => ( c(X4) = X5
      <=> complement(X4,X5) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_3) ).

fof(goals,conjecture,
    ! [X4,X5] :
      ( ( test(X5)
        & test(X4) )
     => one = addition(addition(multiplication(addition(X5,c(X5)),X4),multiplication(addition(X4,c(X4)),X5)),multiplication(c(X4),c(X5))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

fof(test_1,axiom,
    ! [X4] :
      ( test(X4)
    <=> ? [X5] : complement(X5,X4) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_1) ).

fof(test_2,axiom,
    ! [X4,X5] :
      ( complement(X5,X4)
    <=> ( multiplication(X4,X5) = zero
        & multiplication(X5,X4) = zero
        & addition(X4,X5) = one ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_2) ).

fof(additive_commutativity,axiom,
    ! [X1,X2] : addition(X1,X2) = addition(X2,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).

fof(additive_associativity,axiom,
    ! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).

fof(additive_idempotence,axiom,
    ! [X1] : addition(X1,X1) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).

fof(right_distributivity,axiom,
    ! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).

fof(multiplicative_right_identity,axiom,
    ! [X1] : multiplication(X1,one) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).

fof(left_distributivity,axiom,
    ! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).

fof(multiplicative_left_identity,axiom,
    ! [X1] : multiplication(one,X1) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).

fof(c_0_11,plain,
    ! [X34,X35] :
      ( ( c(X34) != X35
        | complement(X34,X35)
        | ~ test(X34) )
      & ( ~ complement(X34,X35)
        | c(X34) = X35
        | ~ test(X34) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])]) ).

fof(c_0_12,negated_conjecture,
    ~ ! [X4,X5] :
        ( ( test(X5)
          & test(X4) )
       => one = addition(addition(multiplication(addition(X5,c(X5)),X4),multiplication(addition(X4,c(X4)),X5)),multiplication(c(X4),c(X5))) ),
    inference(assume_negation,[status(cth)],[goals]) ).

cnf(c_0_13,plain,
    ( complement(X1,X2)
    | c(X1) != X2
    | ~ test(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_14,negated_conjecture,
    ( test(esk3_0)
    & test(esk2_0)
    & one != addition(addition(multiplication(addition(esk3_0,c(esk3_0)),esk2_0),multiplication(addition(esk2_0,c(esk2_0)),esk3_0)),multiplication(c(esk2_0),c(esk3_0))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).

fof(c_0_15,plain,
    ! [X28,X30,X31] :
      ( ( ~ test(X28)
        | complement(esk1_1(X28),X28) )
      & ( ~ complement(X31,X30)
        | test(X30) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[test_1])])])])]) ).

cnf(c_0_16,plain,
    ( complement(X1,c(X1))
    | ~ test(X1) ),
    inference(er,[status(thm)],[c_0_13]) ).

cnf(c_0_17,negated_conjecture,
    test(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_18,plain,
    ( test(X2)
    | ~ complement(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_19,negated_conjecture,
    complement(esk2_0,c(esk2_0)),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

fof(c_0_20,plain,
    ! [X32,X33] :
      ( ( multiplication(X32,X33) = zero
        | ~ complement(X33,X32) )
      & ( multiplication(X33,X32) = zero
        | ~ complement(X33,X32) )
      & ( addition(X32,X33) = one
        | ~ complement(X33,X32) )
      & ( multiplication(X32,X33) != zero
        | multiplication(X33,X32) != zero
        | addition(X32,X33) != one
        | complement(X33,X32) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])]) ).

cnf(c_0_21,negated_conjecture,
    test(esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

fof(c_0_22,plain,
    ! [X6,X7] : addition(X6,X7) = addition(X7,X6),
    inference(variable_rename,[status(thm)],[additive_commutativity]) ).

fof(c_0_23,plain,
    ! [X8,X9,X10] : addition(X10,addition(X9,X8)) = addition(addition(X10,X9),X8),
    inference(variable_rename,[status(thm)],[additive_associativity]) ).

fof(c_0_24,plain,
    ! [X12] : addition(X12,X12) = X12,
    inference(variable_rename,[status(thm)],[additive_idempotence]) ).

cnf(c_0_25,plain,
    ( complement(esk1_1(X1),X1)
    | ~ test(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_26,negated_conjecture,
    test(c(esk2_0)),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

fof(c_0_27,plain,
    ! [X18,X19,X20] : multiplication(X18,addition(X19,X20)) = addition(multiplication(X18,X19),multiplication(X18,X20)),
    inference(variable_rename,[status(thm)],[right_distributivity]) ).

cnf(c_0_28,plain,
    ( addition(X1,X2) = one
    | ~ complement(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_29,negated_conjecture,
    complement(esk3_0,c(esk3_0)),
    inference(spm,[status(thm)],[c_0_16,c_0_21]) ).

cnf(c_0_30,plain,
    addition(X1,X2) = addition(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

fof(c_0_31,plain,
    ! [X16] : multiplication(X16,one) = X16,
    inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).

cnf(c_0_32,plain,
    addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_33,plain,
    addition(X1,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_34,negated_conjecture,
    complement(esk1_1(esk2_0),esk2_0),
    inference(spm,[status(thm)],[c_0_25,c_0_17]) ).

cnf(c_0_35,negated_conjecture,
    complement(esk1_1(c(esk2_0)),c(esk2_0)),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_36,negated_conjecture,
    complement(esk1_1(esk3_0),esk3_0),
    inference(spm,[status(thm)],[c_0_25,c_0_21]) ).

cnf(c_0_37,negated_conjecture,
    one != addition(addition(multiplication(addition(esk3_0,c(esk3_0)),esk2_0),multiplication(addition(esk2_0,c(esk2_0)),esk3_0)),multiplication(c(esk2_0),c(esk3_0))),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

fof(c_0_38,plain,
    ! [X21,X22,X23] : multiplication(addition(X21,X22),X23) = addition(multiplication(X21,X23),multiplication(X22,X23)),
    inference(variable_rename,[status(thm)],[left_distributivity]) ).

fof(c_0_39,plain,
    ! [X17] : multiplication(one,X17) = X17,
    inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).

cnf(c_0_40,plain,
    multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_41,negated_conjecture,
    addition(esk3_0,c(esk3_0)) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).

cnf(c_0_42,plain,
    multiplication(X1,one) = X1,
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_43,plain,
    addition(X1,addition(X1,X2)) = addition(X1,X2),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_44,negated_conjecture,
    addition(esk2_0,esk1_1(esk2_0)) = one,
    inference(spm,[status(thm)],[c_0_28,c_0_34]) ).

cnf(c_0_45,negated_conjecture,
    addition(c(esk2_0),esk1_1(c(esk2_0))) = one,
    inference(spm,[status(thm)],[c_0_28,c_0_35]) ).

cnf(c_0_46,negated_conjecture,
    test(c(esk3_0)),
    inference(spm,[status(thm)],[c_0_18,c_0_29]) ).

cnf(c_0_47,negated_conjecture,
    addition(esk3_0,esk1_1(esk3_0)) = one,
    inference(spm,[status(thm)],[c_0_28,c_0_36]) ).

cnf(c_0_48,negated_conjecture,
    addition(multiplication(c(esk2_0),c(esk3_0)),addition(multiplication(addition(esk2_0,c(esk2_0)),esk3_0),multiplication(addition(esk3_0,c(esk3_0)),esk2_0))) != one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_30]),c_0_30]) ).

cnf(c_0_49,plain,
    multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_50,plain,
    multiplication(one,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_51,negated_conjecture,
    addition(multiplication(X1,esk3_0),multiplication(X1,c(esk3_0))) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).

cnf(c_0_52,negated_conjecture,
    addition(esk2_0,c(esk2_0)) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_19]),c_0_30]) ).

cnf(c_0_53,plain,
    addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_30]),c_0_32]) ).

cnf(c_0_54,negated_conjecture,
    addition(one,esk2_0) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_30]) ).

cnf(c_0_55,negated_conjecture,
    addition(one,c(esk2_0)) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_45]),c_0_30]) ).

cnf(c_0_56,negated_conjecture,
    complement(esk1_1(c(esk3_0)),c(esk3_0)),
    inference(spm,[status(thm)],[c_0_25,c_0_46]) ).

cnf(c_0_57,negated_conjecture,
    addition(one,esk3_0) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_47]),c_0_30]) ).

cnf(c_0_58,negated_conjecture,
    addition(multiplication(c(esk2_0),c(esk3_0)),addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk3_0,esk2_0),multiplication(c(esk3_0),esk2_0))))) != one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49]),c_0_49]),c_0_32]) ).

cnf(c_0_59,negated_conjecture,
    addition(multiplication(esk3_0,X1),multiplication(c(esk3_0),X1)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_41]),c_0_50]) ).

cnf(c_0_60,negated_conjecture,
    addition(multiplication(X1,esk3_0),addition(multiplication(X1,c(esk3_0)),X2)) = addition(X1,X2),
    inference(spm,[status(thm)],[c_0_32,c_0_51]) ).

cnf(c_0_61,negated_conjecture,
    addition(multiplication(esk2_0,X1),multiplication(c(esk2_0),X1)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_52]),c_0_50]) ).

cnf(c_0_62,negated_conjecture,
    addition(multiplication(X1,esk3_0),addition(X2,multiplication(X1,c(esk3_0)))) = addition(X2,X1),
    inference(spm,[status(thm)],[c_0_53,c_0_51]) ).

cnf(c_0_63,negated_conjecture,
    addition(X1,multiplication(esk2_0,X1)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_54]),c_0_50]),c_0_50]) ).

cnf(c_0_64,negated_conjecture,
    addition(X1,multiplication(c(esk2_0),X1)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_55]),c_0_50]),c_0_50]) ).

cnf(c_0_65,negated_conjecture,
    addition(c(esk3_0),esk1_1(c(esk3_0))) = one,
    inference(spm,[status(thm)],[c_0_28,c_0_56]) ).

cnf(c_0_66,negated_conjecture,
    addition(one,addition(esk2_0,X1)) = addition(one,X1),
    inference(spm,[status(thm)],[c_0_32,c_0_54]) ).

cnf(c_0_67,negated_conjecture,
    addition(X1,multiplication(X1,esk3_0)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_57]),c_0_42]),c_0_42]) ).

cnf(c_0_68,negated_conjecture,
    addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk3_0,esk2_0),addition(multiplication(c(esk2_0),c(esk3_0)),multiplication(c(esk3_0),esk2_0))))) != one,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_53]),c_0_53]),c_0_53]) ).

cnf(c_0_69,negated_conjecture,
    addition(multiplication(esk3_0,X1),addition(X2,multiplication(c(esk3_0),X1))) = addition(X2,X1),
    inference(spm,[status(thm)],[c_0_53,c_0_59]) ).

cnf(c_0_70,negated_conjecture,
    addition(esk2_0,multiplication(c(esk2_0),c(esk3_0))) = addition(multiplication(esk2_0,esk3_0),c(esk3_0)),
    inference(spm,[status(thm)],[c_0_60,c_0_61]) ).

cnf(c_0_71,negated_conjecture,
    addition(multiplication(esk2_0,esk3_0),c(esk3_0)) = addition(esk2_0,c(esk3_0)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_30]) ).

cnf(c_0_72,negated_conjecture,
    addition(multiplication(c(esk2_0),esk3_0),c(esk3_0)) = addition(c(esk2_0),c(esk3_0)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_64]),c_0_30]) ).

cnf(c_0_73,negated_conjecture,
    addition(esk2_0,addition(c(esk2_0),X1)) = addition(one,X1),
    inference(spm,[status(thm)],[c_0_32,c_0_52]) ).

cnf(c_0_74,negated_conjecture,
    addition(one,c(esk3_0)) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_65]),c_0_30]) ).

cnf(c_0_75,negated_conjecture,
    addition(one,multiplication(esk2_0,esk3_0)) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_54]) ).

cnf(c_0_76,negated_conjecture,
    $false,
    inference(cn,[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)],[c_0_68,c_0_69]),c_0_30]),c_0_70]),c_0_71]),c_0_53]),c_0_72]),c_0_73]),c_0_74]),c_0_30]),c_0_75])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09  % Problem  : KLE011+1 : TPTP v7.5.0. Released v4.0.0.
% 0.04/0.10  % Command  : enigmatic-eprover.py %s %d 1
% 0.09/0.30  % Computer : n020.cluster.edu
% 0.09/0.30  % Model    : x86_64 x86_64
% 0.09/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30  % Memory   : 8042.1875MB
% 0.09/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit : 300
% 0.09/0.30  % WCLimit  : 600
% 0.09/0.30  % DateTime : Tue Mar 23 12:52:03 EDT 2021
% 0.09/0.30  % CPUTime  : 
% 0.14/0.41  # ENIGMATIC: Selected SinE mode:
% 0.14/0.41  # Parsing /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.41  # Filter: axfilter_auto   0 goes into file theBenchmark_axfilter_auto   0.p
% 0.14/0.41  # Filter: axfilter_auto   1 goes into file theBenchmark_axfilter_auto   1.p
% 0.14/0.41  # Filter: axfilter_auto   2 goes into file theBenchmark_axfilter_auto   2.p
% 18.81/4.18  # ENIGMATIC: Solved by autoschedule:
% 18.81/4.18  # No SInE strategy applied
% 18.81/4.18  # Trying AutoSched0 for 302 seconds
% 18.81/4.18  # AutoSched0-Mode selected heuristic G_E___208_B00_00_F1_SE_CS_SP_PS_S064A
% 18.81/4.18  # and selection function SelectComplexG.
% 18.81/4.18  #
% 18.81/4.18  # Preprocessing time     : 0.022 s
% 18.81/4.18  # Presaturation interreduction done
% 18.81/4.18  
% 18.81/4.18  # Proof found!
% 18.81/4.18  # SZS status Theorem
% 18.81/4.18  # SZS output start CNFRefutation
% See solution above
% 18.81/4.18  # SZS output end CNFRefutation
% 18.81/4.18  # Training examples: 0 positive, 5 negative
% 18.81/4.18  
% 18.81/4.18  # -------------------------------------------------
% 18.81/4.18  # User time              : 0.497 s
% 18.81/4.18  # System time            : 0.017 s
% 18.81/4.18  # Total time             : 0.514 s
% 18.81/4.18  # Maximum resident set size: 7124 pages
% 18.81/4.18  
%------------------------------------------------------------------------------