TSTP Solution File: KLE148+2 by Enigma---0.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Enigma---0.5.1
% Problem  : KLE148+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : enigmatic-eprover.py %s %d 1

% Computer : n022.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 01:50:35 EDT 2022

% Result   : Theorem 8.50s 2.46s
% Output   : CNFRefutation 8.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   47 (  36 unt;   0 def)
%            Number of atoms       :   64 (  48 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   33 (  16   ~;  10   |;   4   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   66 (   3 sgn  40   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(goals,conjecture,
    ! [X4,X5] :
      ( ( multiplication(X4,X5) = zero
       => leq(multiplication(X4,strong_iteration(X5)),X4) )
      & leq(X4,multiplication(X4,strong_iteration(X5))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

fof(additive_associativity,axiom,
    ! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_associativity) ).

fof(idempotence,axiom,
    ! [X1] : addition(X1,X1) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',idempotence) ).

fof(infty_unfold1,axiom,
    ! [X1] : strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',infty_unfold1) ).

fof(additive_commutativity,axiom,
    ! [X1,X2] : addition(X1,X2) = addition(X2,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).

fof(order,axiom,
    ! [X1,X2] :
      ( leq(X1,X2)
    <=> addition(X1,X2) = X2 ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',order) ).

fof(distributivity1,axiom,
    ! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',distributivity1) ).

fof(multiplicative_right_identity,axiom,
    ! [X1] : multiplication(X1,one) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).

fof(multiplicative_associativity,axiom,
    ! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_associativity) ).

fof(left_annihilation,axiom,
    ! [X1] : multiplication(zero,X1) = zero,
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).

fof(additive_identity,axiom,
    ! [X1] : addition(X1,zero) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_identity) ).

fof(c_0_11,negated_conjecture,
    ~ ! [X4,X5] :
        ( ( multiplication(X4,X5) = zero
         => leq(multiplication(X4,strong_iteration(X5)),X4) )
        & leq(X4,multiplication(X4,strong_iteration(X5))) ),
    inference(assume_negation,[status(cth)],[goals]) ).

fof(c_0_12,plain,
    ! [X8,X9,X10] : addition(X10,addition(X9,X8)) = addition(addition(X10,X9),X8),
    inference(variable_rename,[status(thm)],[additive_associativity]) ).

fof(c_0_13,plain,
    ! [X12] : addition(X12,X12) = X12,
    inference(variable_rename,[status(thm)],[idempotence]) ).

fof(c_0_14,plain,
    ! [X33] : strong_iteration(X33) = addition(multiplication(X33,strong_iteration(X33)),one),
    inference(variable_rename,[status(thm)],[infty_unfold1]) ).

fof(c_0_15,plain,
    ! [X6,X7] : addition(X6,X7) = addition(X7,X6),
    inference(variable_rename,[status(thm)],[additive_commutativity]) ).

fof(c_0_16,negated_conjecture,
    ( ( multiplication(esk1_0,esk2_0) = zero
      | ~ leq(esk1_0,multiplication(esk1_0,strong_iteration(esk2_0))) )
    & ( ~ leq(multiplication(esk1_0,strong_iteration(esk2_0)),esk1_0)
      | ~ leq(esk1_0,multiplication(esk1_0,strong_iteration(esk2_0))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).

fof(c_0_17,plain,
    ! [X38,X39] :
      ( ( ~ leq(X38,X39)
        | addition(X38,X39) = X39 )
      & ( addition(X38,X39) != X39
        | leq(X38,X39) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).

fof(c_0_18,plain,
    ! [X18,X19,X20] : multiplication(X18,addition(X19,X20)) = addition(multiplication(X18,X19),multiplication(X18,X20)),
    inference(variable_rename,[status(thm)],[distributivity1]) ).

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

cnf(c_0_20,plain,
    addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_21,plain,
    addition(X1,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_22,plain,
    strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_23,plain,
    addition(X1,X2) = addition(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_24,negated_conjecture,
    ( multiplication(esk1_0,esk2_0) = zero
    | ~ leq(esk1_0,multiplication(esk1_0,strong_iteration(esk2_0))) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_25,plain,
    ( leq(X1,X2)
    | addition(X1,X2) != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_26,plain,
    multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_27,plain,
    multiplication(X1,one) = X1,
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_28,plain,
    addition(X1,addition(X1,X2)) = addition(X1,X2),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_29,plain,
    addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
    inference(rw,[status(thm)],[c_0_22,c_0_23]) ).

fof(c_0_30,plain,
    ! [X13,X14,X15] : multiplication(X13,multiplication(X14,X15)) = multiplication(multiplication(X13,X14),X15),
    inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).

cnf(c_0_31,negated_conjecture,
    ( multiplication(esk1_0,esk2_0) = zero
    | addition(esk1_0,multiplication(esk1_0,strong_iteration(esk2_0))) != multiplication(esk1_0,strong_iteration(esk2_0)) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_32,plain,
    addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_23]) ).

cnf(c_0_33,plain,
    addition(one,strong_iteration(X1)) = strong_iteration(X1),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

fof(c_0_34,plain,
    ! [X24] : multiplication(zero,X24) = zero,
    inference(variable_rename,[status(thm)],[left_annihilation]) ).

cnf(c_0_35,negated_conjecture,
    ( ~ leq(multiplication(esk1_0,strong_iteration(esk2_0)),esk1_0)
    | ~ leq(esk1_0,multiplication(esk1_0,strong_iteration(esk2_0))) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_36,plain,
    multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_37,negated_conjecture,
    multiplication(esk1_0,esk2_0) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_23]),c_0_33])]) ).

cnf(c_0_38,plain,
    multiplication(zero,X1) = zero,
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

fof(c_0_39,plain,
    ! [X11] : addition(X11,zero) = X11,
    inference(variable_rename,[status(thm)],[additive_identity]) ).

cnf(c_0_40,negated_conjecture,
    ( addition(esk1_0,multiplication(esk1_0,strong_iteration(esk2_0))) != multiplication(esk1_0,strong_iteration(esk2_0))
    | ~ leq(multiplication(esk1_0,strong_iteration(esk2_0)),esk1_0) ),
    inference(spm,[status(thm)],[c_0_35,c_0_25]) ).

cnf(c_0_41,negated_conjecture,
    multiplication(esk1_0,multiplication(esk2_0,X1)) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).

cnf(c_0_42,plain,
    addition(X1,zero) = X1,
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_43,negated_conjecture,
    ( addition(esk1_0,multiplication(esk1_0,strong_iteration(esk2_0))) != multiplication(esk1_0,strong_iteration(esk2_0))
    | addition(esk1_0,multiplication(esk1_0,strong_iteration(esk2_0))) != esk1_0 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_25]),c_0_23]) ).

cnf(c_0_44,negated_conjecture,
    multiplication(esk1_0,addition(one,multiplication(esk2_0,X1))) = esk1_0,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_41]),c_0_42]),c_0_23]) ).

cnf(c_0_45,negated_conjecture,
    multiplication(esk1_0,strong_iteration(esk2_0)) != esk1_0,
    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)],[c_0_43,c_0_32]),c_0_23]),c_0_33]),c_0_32]),c_0_23]),c_0_33])]) ).

cnf(c_0_46,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_29]),c_0_45]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : KLE148+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : enigmatic-eprover.py %s %d 1
% 0.12/0.34  % Computer : n022.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Thu Jun 16 13:41:49 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.45  # ENIGMATIC: Selected SinE mode:
% 0.19/0.45  # Parsing /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45  # Filter: axfilter_auto   0 goes into file theBenchmark_axfilter_auto   0.p
% 0.19/0.45  # Filter: axfilter_auto   1 goes into file theBenchmark_axfilter_auto   1.p
% 0.19/0.45  # Filter: axfilter_auto   2 goes into file theBenchmark_axfilter_auto   2.p
% 8.50/2.46  # ENIGMATIC: Solved by autoschedule:
% 8.50/2.46  # No SInE strategy applied
% 8.50/2.46  # Trying AutoSched0 for 150 seconds
% 8.50/2.46  # AutoSched0-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_S059I
% 8.50/2.46  # and selection function SelectComplexExceptUniqMaxPosHorn.
% 8.50/2.46  #
% 8.50/2.46  # Preprocessing time       : 0.014 s
% 8.50/2.46  # Presaturation interreduction done
% 8.50/2.46  
% 8.50/2.46  # Proof found!
% 8.50/2.46  # SZS status Theorem
% 8.50/2.46  # SZS output start CNFRefutation
% See solution above
% 8.50/2.46  # Training examples: 0 positive, 0 negative
% 8.50/2.46  
% 8.50/2.46  # -------------------------------------------------
% 8.50/2.46  # User time                : 0.099 s
% 8.50/2.46  # System time              : 0.010 s
% 8.50/2.46  # Total time               : 0.110 s
% 8.50/2.46  # Maximum resident set size: 7124 pages
% 8.50/2.46  
%------------------------------------------------------------------------------