TSTP Solution File: KLE023+1 by Enigma---0.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Enigma---0.5.1
% Problem  : KLE023+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : enigmatic-eprover.py %s %d 1

% Computer : n010.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 : Sun Jul 17 01:49:39 EDT 2022

% Result   : Theorem 9.07s 2.40s
% Output   : CNFRefutation 9.07s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   69 (  53 unt;   0 def)
%            Number of atoms       :  109 (  73 equ)
%            Maximal formula atoms :   10 (   1 avg)
%            Number of connectives :   64 (  24   ~;  20   |;  12   &)
%                                         (   3 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   2 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   99 (   3 sgn  56   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(goals,conjecture,
    ! [X4,X5,X6] :
      ( ( test(X5)
        & test(X6) )
     => ( addition(multiplication(X5,X4),multiplication(X4,X6)) = multiplication(X4,X6)
       => addition(multiplication(X4,c(X6)),multiplication(c(X5),X4)) = multiplication(c(X5),X4) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

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(test_3,axiom,
    ! [X4,X5] :
      ( test(X4)
     => ( c(X4) = X5
      <=> complement(X4,X5) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_3) ).

fof(order,axiom,
    ! [X1,X2] :
      ( leq(X1,X2)
    <=> addition(X1,X2) = X2 ),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',order) ).

fof(additive_commutativity,axiom,
    ! [X1,X2] : addition(X1,X2) = addition(X2,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).

fof(test_2,axiom,
    ! [X4,X5] :
      ( complement(X5,X4)
    <=> ( multiplication(X4,X5) = zero
        & multiplication(X5,X4) = zero
        & addition(X4,X5) = one ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_2) ).

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(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(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(multiplicative_right_identity,axiom,
    ! [X1] : multiplication(X1,one) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).

fof(multiplicative_left_identity,axiom,
    ! [X1] : multiplication(one,X1) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).

fof(right_annihilation,axiom,
    ! [X1] : multiplication(X1,zero) = zero,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).

fof(additive_identity,axiom,
    ! [X1] : addition(X1,zero) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).

fof(c_0_14,negated_conjecture,
    ~ ! [X4,X5,X6] :
        ( ( test(X5)
          & test(X6) )
       => ( addition(multiplication(X5,X4),multiplication(X4,X6)) = multiplication(X4,X6)
         => addition(multiplication(X4,c(X6)),multiplication(c(X5),X4)) = multiplication(c(X5),X4) ) ),
    inference(assume_negation,[status(cth)],[goals]) ).

fof(c_0_15,plain,
    ! [X9,X10,X11] : addition(X11,addition(X10,X9)) = addition(addition(X11,X10),X9),
    inference(variable_rename,[status(thm)],[additive_associativity]) ).

fof(c_0_16,plain,
    ! [X13] : addition(X13,X13) = X13,
    inference(variable_rename,[status(thm)],[additive_idempotence]) ).

fof(c_0_17,plain,
    ! [X35,X36] :
      ( ( c(X35) != X36
        | complement(X35,X36)
        | ~ test(X35) )
      & ( ~ complement(X35,X36)
        | c(X35) = X36
        | ~ test(X35) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])]) ).

fof(c_0_18,negated_conjecture,
    ( test(esk3_0)
    & test(esk4_0)
    & addition(multiplication(esk3_0,esk2_0),multiplication(esk2_0,esk4_0)) = multiplication(esk2_0,esk4_0)
    & addition(multiplication(esk2_0,c(esk4_0)),multiplication(c(esk3_0),esk2_0)) != multiplication(c(esk3_0),esk2_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).

fof(c_0_19,plain,
    ! [X27,X28] :
      ( ( ~ leq(X27,X28)
        | addition(X27,X28) = X28 )
      & ( addition(X27,X28) != X28
        | leq(X27,X28) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).

cnf(c_0_20,plain,
    addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_21,plain,
    addition(X1,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_22,plain,
    ( complement(X1,X2)
    | c(X1) != X2
    | ~ test(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_23,negated_conjecture,
    test(esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_24,plain,
    ( leq(X1,X2)
    | addition(X1,X2) != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_25,plain,
    addition(X1,addition(X1,X2)) = addition(X1,X2),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

fof(c_0_26,plain,
    ! [X7,X8] : addition(X7,X8) = addition(X8,X7),
    inference(variable_rename,[status(thm)],[additive_commutativity]) ).

fof(c_0_27,plain,
    ! [X33,X34] :
      ( ( multiplication(X33,X34) = zero
        | ~ complement(X34,X33) )
      & ( multiplication(X34,X33) = zero
        | ~ complement(X34,X33) )
      & ( addition(X33,X34) = one
        | ~ complement(X34,X33) )
      & ( multiplication(X33,X34) != zero
        | multiplication(X34,X33) != zero
        | addition(X33,X34) != one
        | complement(X34,X33) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])]) ).

cnf(c_0_28,negated_conjecture,
    ( complement(esk4_0,X1)
    | c(esk4_0) != X1 ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_29,plain,
    leq(X1,addition(X1,X2)),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_30,plain,
    addition(X1,X2) = addition(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_31,plain,
    ( addition(X1,X2) = one
    | ~ complement(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_32,negated_conjecture,
    complement(esk4_0,c(esk4_0)),
    inference(er,[status(thm)],[c_0_28]) ).

cnf(c_0_33,negated_conjecture,
    test(esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_34,plain,
    leq(X1,addition(X2,X1)),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_35,negated_conjecture,
    addition(esk4_0,c(esk4_0)) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_30]) ).

cnf(c_0_36,negated_conjecture,
    ( complement(esk3_0,X1)
    | c(esk3_0) != X1 ),
    inference(spm,[status(thm)],[c_0_22,c_0_33]) ).

fof(c_0_37,plain,
    ! [X22,X23,X24] : multiplication(addition(X22,X23),X24) = addition(multiplication(X22,X24),multiplication(X23,X24)),
    inference(variable_rename,[status(thm)],[left_distributivity]) ).

fof(c_0_38,plain,
    ! [X14,X15,X16] : multiplication(X14,multiplication(X15,X16)) = multiplication(multiplication(X14,X15),X16),
    inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).

fof(c_0_39,plain,
    ! [X19,X20,X21] : multiplication(X19,addition(X20,X21)) = addition(multiplication(X19,X20),multiplication(X19,X21)),
    inference(variable_rename,[status(thm)],[right_distributivity]) ).

cnf(c_0_40,plain,
    ( addition(X1,X2) = X2
    | ~ leq(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_41,negated_conjecture,
    leq(c(esk4_0),one),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

fof(c_0_42,plain,
    ! [X17] : multiplication(X17,one) = X17,
    inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).

cnf(c_0_43,negated_conjecture,
    complement(esk3_0,c(esk3_0)),
    inference(er,[status(thm)],[c_0_36]) ).

fof(c_0_44,plain,
    ! [X18] : multiplication(one,X18) = X18,
    inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).

cnf(c_0_45,plain,
    multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_46,negated_conjecture,
    addition(multiplication(esk3_0,esk2_0),multiplication(esk2_0,esk4_0)) = multiplication(esk2_0,esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_47,plain,
    multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_48,plain,
    ( multiplication(X1,X2) = zero
    | ~ complement(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

fof(c_0_49,plain,
    ! [X25] : multiplication(X25,zero) = zero,
    inference(variable_rename,[status(thm)],[right_annihilation]) ).

fof(c_0_50,plain,
    ! [X12] : addition(X12,zero) = X12,
    inference(variable_rename,[status(thm)],[additive_identity]) ).

cnf(c_0_51,plain,
    multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_52,negated_conjecture,
    addition(one,c(esk4_0)) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_30]) ).

cnf(c_0_53,plain,
    multiplication(X1,one) = X1,
    inference(split_conjunct,[status(thm)],[c_0_42]) ).

cnf(c_0_54,negated_conjecture,
    addition(esk3_0,c(esk3_0)) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_43]),c_0_30]) ).

cnf(c_0_55,plain,
    multiplication(one,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_56,negated_conjecture,
    addition(multiplication(esk3_0,multiplication(esk2_0,X1)),multiplication(esk2_0,multiplication(esk4_0,X1))) = multiplication(esk2_0,multiplication(esk4_0,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]),c_0_47]),c_0_47]) ).

cnf(c_0_57,negated_conjecture,
    multiplication(esk4_0,c(esk4_0)) = zero,
    inference(spm,[status(thm)],[c_0_48,c_0_32]) ).

cnf(c_0_58,plain,
    multiplication(X1,zero) = zero,
    inference(split_conjunct,[status(thm)],[c_0_49]) ).

cnf(c_0_59,plain,
    addition(X1,zero) = X1,
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

cnf(c_0_60,negated_conjecture,
    addition(X1,multiplication(X1,c(esk4_0))) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]),c_0_53]) ).

cnf(c_0_61,negated_conjecture,
    addition(multiplication(esk3_0,X1),multiplication(c(esk3_0),X1)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_54]),c_0_55]) ).

cnf(c_0_62,negated_conjecture,
    multiplication(esk3_0,multiplication(esk2_0,c(esk4_0))) = zero,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]),c_0_59]),c_0_58]) ).

cnf(c_0_63,plain,
    addition(zero,X1) = X1,
    inference(spm,[status(thm)],[c_0_59,c_0_30]) ).

cnf(c_0_64,negated_conjecture,
    addition(multiplication(esk2_0,c(esk4_0)),multiplication(c(esk3_0),esk2_0)) != multiplication(c(esk3_0),esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_65,negated_conjecture,
    addition(multiplication(X1,X2),multiplication(X1,multiplication(X2,c(esk4_0)))) = multiplication(X1,X2),
    inference(spm,[status(thm)],[c_0_51,c_0_60]) ).

cnf(c_0_66,negated_conjecture,
    multiplication(c(esk3_0),multiplication(esk2_0,c(esk4_0))) = multiplication(esk2_0,c(esk4_0)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]) ).

cnf(c_0_67,negated_conjecture,
    addition(multiplication(c(esk3_0),esk2_0),multiplication(esk2_0,c(esk4_0))) != multiplication(c(esk3_0),esk2_0),
    inference(rw,[status(thm)],[c_0_64,c_0_30]) ).

cnf(c_0_68,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : KLE023+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12  % Command  : enigmatic-eprover.py %s %d 1
% 0.12/0.33  % Computer : n010.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Thu Jun 16 10:30:25 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.44  # ENIGMATIC: Selected SinE mode:
% 0.18/0.45  # Parsing /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45  # Filter: axfilter_auto   0 goes into file theBenchmark_axfilter_auto   0.p
% 0.18/0.45  # Filter: axfilter_auto   1 goes into file theBenchmark_axfilter_auto   1.p
% 0.18/0.45  # Filter: axfilter_auto   2 goes into file theBenchmark_axfilter_auto   2.p
% 9.07/2.40  # ENIGMATIC: Solved by autoschedule:
% 9.07/2.40  # No SInE strategy applied
% 9.07/2.40  # Trying AutoSched0 for 150 seconds
% 9.07/2.40  # AutoSched0-Mode selected heuristic G_E___107_B00_00_F1_PI_AE_Q4_CS_SP_PS_S071I
% 9.07/2.40  # and selection function SelectCQArEqLast.
% 9.07/2.40  #
% 9.07/2.40  # Preprocessing time       : 0.025 s
% 9.07/2.40  # Presaturation interreduction done
% 9.07/2.40  
% 9.07/2.40  # Proof found!
% 9.07/2.40  # SZS status Theorem
% 9.07/2.40  # SZS output start CNFRefutation
% See solution above
% 9.07/2.40  # Training examples: 0 positive, 0 negative
% 9.07/2.40  
% 9.07/2.40  # -------------------------------------------------
% 9.07/2.40  # User time                : 0.189 s
% 9.07/2.40  # System time              : 0.017 s
% 9.07/2.40  # Total time               : 0.206 s
% 9.07/2.40  # Maximum resident set size: 7116 pages
% 9.07/2.40  
%------------------------------------------------------------------------------