TSTP Solution File: KLE007+4 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : KLE007+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n009.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 02:14:32 EDT 2022

% Result   : Theorem 1.31s 1.48s
% Output   : CNFRefutation 1.31s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   36
% Syntax   : Number of formulae    :  200 (  94 unt;   0 def)
%            Number of atoms       :  393 ( 239 equ)
%            Maximal formula atoms :   10 (   1 avg)
%            Number of connectives :  373 ( 180   ~; 142   |;  30   &)
%                                         (  15 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    6 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :  191 (   0 sgn  99   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
    ! [A,B] : addition(A,B) = addition(B,A) ).

fof(additive_idempotence,axiom,
    ! [A] : addition(A,A) = A ).

fof(multiplicative_left_identity,axiom,
    ! [A] : multiplication(one,A) = A ).

fof(right_distributivity,axiom,
    ! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ).

fof(order,axiom,
    ! [A,B] :
      ( leq(A,B)
    <=> addition(A,B) = B ) ).

fof(test_2,axiom,
    ! [X0,X1] :
      ( complement(X1,X0)
    <=> ( multiplication(X0,X1) = zero
        & multiplication(X1,X0) = zero
        & addition(X0,X1) = one ) ) ).

fof(test_3,axiom,
    ! [X0,X1] :
      ( test(X0)
     => ( c(X0) = X1
      <=> complement(X0,X1) ) ) ).

fof(goals,conjecture,
    ! [X0,X1] :
      ( ( test(X1)
        & test(X0) )
     => ( leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))))
        & leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one) ) ) ).

fof(subgoal_0,plain,
    ! [X0,X1] :
      ( ( test(X1)
        & test(X0) )
     => leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1)))) ),
    inference(strip,[],[goals]) ).

fof(subgoal_1,plain,
    ! [X0,X1] :
      ( ( test(X1)
        & test(X0)
        & leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1)))) )
     => leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one) ),
    inference(strip,[],[goals]) ).

fof(negate_0_0,plain,
    ~ ! [X0,X1] :
        ( ( test(X1)
          & test(X0) )
       => leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1)))) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [X0,X1] :
      ( ~ leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))))
      & test(X0)
      & test(X1) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ( ~ leq(one,addition(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1_1),multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),c(skolemFOFtoCNF_X1_1))))
    & test(skolemFOFtoCNF_X0)
    & test(skolemFOFtoCNF_X1_1) ),
    inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ~ leq(one,addition(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1_1),multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),c(skolemFOFtoCNF_X1_1)))),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
    inference(canonicalize,[],[right_distributivity]) ).

fof(normalize_0_4,plain,
    ! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
    inference(specialize,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [A] : multiplication(one,A) = A,
    inference(canonicalize,[],[multiplicative_left_identity]) ).

fof(normalize_0_6,plain,
    ! [A] : multiplication(one,A) = A,
    inference(specialize,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    test(skolemFOFtoCNF_X1_1),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_8,plain,
    ! [X0] :
      ( ~ test(X0)
      | ! [X1] :
          ( c(X0) != X1
        <=> ~ complement(X0,X1) ) ),
    inference(canonicalize,[],[test_3]) ).

fof(normalize_0_9,plain,
    ! [X0] :
      ( ~ test(X0)
      | ! [X1] :
          ( c(X0) != X1
        <=> ~ complement(X0,X1) ) ),
    inference(specialize,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ! [X0,X1] :
      ( ( c(X0) != X1
        | ~ test(X0)
        | complement(X0,X1) )
      & ( ~ complement(X0,X1)
        | ~ test(X0)
        | c(X0) = X1 ) ),
    inference(clausify,[],[normalize_0_9]) ).

fof(normalize_0_11,plain,
    ! [X0,X1] :
      ( c(X0) != X1
      | ~ test(X0)
      | complement(X0,X1) ),
    inference(conjunct,[],[normalize_0_10]) ).

fof(normalize_0_12,plain,
    ! [X0,X1] :
      ( ~ complement(X1,X0)
    <=> ( addition(X0,X1) != one
        | multiplication(X0,X1) != zero
        | multiplication(X1,X0) != zero ) ),
    inference(canonicalize,[],[test_2]) ).

fof(normalize_0_13,plain,
    ! [X0,X1] :
      ( ~ complement(X1,X0)
    <=> ( addition(X0,X1) != one
        | multiplication(X0,X1) != zero
        | multiplication(X1,X0) != zero ) ),
    inference(specialize,[],[normalize_0_12]) ).

fof(normalize_0_14,plain,
    ! [X0,X1] :
      ( ( ~ complement(X1,X0)
        | addition(X0,X1) = one )
      & ( ~ complement(X1,X0)
        | multiplication(X0,X1) = zero )
      & ( ~ complement(X1,X0)
        | multiplication(X1,X0) = zero )
      & ( addition(X0,X1) != one
        | multiplication(X0,X1) != zero
        | multiplication(X1,X0) != zero
        | complement(X1,X0) ) ),
    inference(clausify,[],[normalize_0_13]) ).

fof(normalize_0_15,plain,
    ! [X0,X1] :
      ( ~ complement(X1,X0)
      | addition(X0,X1) = one ),
    inference(conjunct,[],[normalize_0_14]) ).

fof(normalize_0_16,plain,
    ! [A,B] : addition(A,B) = addition(B,A),
    inference(canonicalize,[],[additive_commutativity]) ).

fof(normalize_0_17,plain,
    ! [A,B] : addition(A,B) = addition(B,A),
    inference(specialize,[],[normalize_0_16]) ).

fof(normalize_0_18,plain,
    test(skolemFOFtoCNF_X0),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_19,plain,
    ! [A,B] :
      ( addition(A,B) != B
    <=> ~ leq(A,B) ),
    inference(canonicalize,[],[order]) ).

fof(normalize_0_20,plain,
    ! [A,B] :
      ( addition(A,B) != B
    <=> ~ leq(A,B) ),
    inference(specialize,[],[normalize_0_19]) ).

fof(normalize_0_21,plain,
    ! [A,B] :
      ( ( addition(A,B) != B
        | leq(A,B) )
      & ( ~ leq(A,B)
        | addition(A,B) = B ) ),
    inference(clausify,[],[normalize_0_20]) ).

fof(normalize_0_22,plain,
    ! [A,B] :
      ( addition(A,B) != B
      | leq(A,B) ),
    inference(conjunct,[],[normalize_0_21]) ).

fof(normalize_0_23,plain,
    ! [A] : addition(A,A) = A,
    inference(canonicalize,[],[additive_idempotence]) ).

fof(normalize_0_24,plain,
    ! [A] : addition(A,A) = A,
    inference(specialize,[],[normalize_0_23]) ).

cnf(refute_0_0,plain,
    ~ leq(one,addition(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1_1),multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),c(skolemFOFtoCNF_X1_1)))),
    inference(canonicalize,[],[normalize_0_2]) ).

cnf(refute_0_1,plain,
    multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
    inference(canonicalize,[],[normalize_0_4]) ).

cnf(refute_0_2,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_3,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_4,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_2,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( multiplication(A,addition(B,C)) != addition(multiplication(A,B),multiplication(A,C))
    | addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)) ),
    inference(subst,[],[refute_0_4:[bind(X,$fot(multiplication(A,addition(B,C)))),bind(Y,$fot(addition(multiplication(A,B),multiplication(A,C))))]]) ).

cnf(refute_0_6,plain,
    addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
    inference(resolve,[$cnf( $equal(multiplication(A,addition(B,C)),addition(multiplication(A,B),multiplication(A,C))) )],[refute_0_1,refute_0_5]) ).

cnf(refute_0_7,plain,
    addition(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1_1),multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),c(skolemFOFtoCNF_X1_1))) = multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),
    inference(subst,[],[refute_0_6:[bind(A,$fot(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)))),bind(B,$fot(skolemFOFtoCNF_X1_1)),bind(C,$fot(c(skolemFOFtoCNF_X1_1)))]]) ).

cnf(refute_0_8,plain,
    ( addition(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1_1),multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),c(skolemFOFtoCNF_X1_1))) != multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))
    | ~ leq(one,multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))
    | leq(one,addition(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1_1),multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),c(skolemFOFtoCNF_X1_1)))) ),
    introduced(tautology,[equality,[$cnf( ~ leq(one,addition(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1_1),multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),c(skolemFOFtoCNF_X1_1)))) ),[1],$fot(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))]]) ).

cnf(refute_0_9,plain,
    ( ~ leq(one,multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))
    | leq(one,addition(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1_1),multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),c(skolemFOFtoCNF_X1_1)))) ),
    inference(resolve,[$cnf( $equal(addition(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1_1),multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),c(skolemFOFtoCNF_X1_1))),multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) )],[refute_0_7,refute_0_8]) ).

cnf(refute_0_10,plain,
    ~ leq(one,multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))),
    inference(resolve,[$cnf( leq(one,addition(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1_1),multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),c(skolemFOFtoCNF_X1_1)))) )],[refute_0_9,refute_0_0]) ).

cnf(refute_0_11,plain,
    multiplication(one,A) = A,
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_12,plain,
    multiplication(one,one) = one,
    inference(subst,[],[refute_0_11:[bind(A,$fot(one))]]) ).

cnf(refute_0_13,plain,
    test(skolemFOFtoCNF_X1_1),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_14,plain,
    ( c(X0) != X1
    | ~ test(X0)
    | complement(X0,X1) ),
    inference(canonicalize,[],[normalize_0_11]) ).

cnf(refute_0_15,plain,
    ( c(X0) != c(X0)
    | ~ test(X0)
    | complement(X0,c(X0)) ),
    inference(subst,[],[refute_0_14:[bind(X1,$fot(c(X0)))]]) ).

cnf(refute_0_16,plain,
    c(X0) = c(X0),
    introduced(tautology,[refl,[$fot(c(X0))]]) ).

cnf(refute_0_17,plain,
    ( ~ test(X0)
    | complement(X0,c(X0)) ),
    inference(resolve,[$cnf( $equal(c(X0),c(X0)) )],[refute_0_16,refute_0_15]) ).

cnf(refute_0_18,plain,
    ( ~ test(skolemFOFtoCNF_X1_1)
    | complement(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)) ),
    inference(subst,[],[refute_0_17:[bind(X0,$fot(skolemFOFtoCNF_X1_1))]]) ).

cnf(refute_0_19,plain,
    complement(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)),
    inference(resolve,[$cnf( test(skolemFOFtoCNF_X1_1) )],[refute_0_13,refute_0_18]) ).

cnf(refute_0_20,plain,
    ( ~ complement(X1,X0)
    | addition(X0,X1) = one ),
    inference(canonicalize,[],[normalize_0_15]) ).

cnf(refute_0_21,plain,
    ( ~ complement(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))
    | addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1) = one ),
    inference(subst,[],[refute_0_20:[bind(X0,$fot(c(skolemFOFtoCNF_X1_1))),bind(X1,$fot(skolemFOFtoCNF_X1_1))]]) ).

cnf(refute_0_22,plain,
    addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1) = one,
    inference(resolve,[$cnf( complement(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)) )],[refute_0_19,refute_0_21]) ).

cnf(refute_0_23,plain,
    addition(A,B) = addition(B,A),
    inference(canonicalize,[],[normalize_0_17]) ).

cnf(refute_0_24,plain,
    ( addition(A,B) != addition(B,A)
    | addition(B,A) = addition(A,B) ),
    inference(subst,[],[refute_0_4:[bind(X,$fot(addition(A,B))),bind(Y,$fot(addition(B,A)))]]) ).

cnf(refute_0_25,plain,
    addition(B,A) = addition(A,B),
    inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_0_23,refute_0_24]) ).

cnf(refute_0_26,plain,
    addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1) = addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)),
    inference(subst,[],[refute_0_25:[bind(A,$fot(skolemFOFtoCNF_X1_1)),bind(B,$fot(c(skolemFOFtoCNF_X1_1)))]]) ).

cnf(refute_0_27,plain,
    ( addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1) != addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))
    | addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1) != one
    | addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)) = one ),
    introduced(tautology,[equality,[$cnf( $equal(addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1),one) ),[0],$fot(addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))]]) ).

cnf(refute_0_28,plain,
    ( addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1) != one
    | addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)) = one ),
    inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) )],[refute_0_26,refute_0_27]) ).

cnf(refute_0_29,plain,
    addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)) = one,
    inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1),one) )],[refute_0_22,refute_0_28]) ).

cnf(refute_0_30,plain,
    multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),
    introduced(tautology,[refl,[$fot(multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))]]) ).

cnf(refute_0_31,plain,
    ( addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)) != one
    | multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) != multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))
    | multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(one,one) ),
    introduced(tautology,[equality,[$cnf( $equal(multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) ),[1,1],$fot(one)]]) ).

cnf(refute_0_32,plain,
    ( addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)) != one
    | multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(one,one) ),
    inference(resolve,[$cnf( $equal(multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) )],[refute_0_30,refute_0_31]) ).

cnf(refute_0_33,plain,
    multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(one,one),
    inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)),one) )],[refute_0_29,refute_0_32]) ).

cnf(refute_0_34,plain,
    test(skolemFOFtoCNF_X0),
    inference(canonicalize,[],[normalize_0_18]) ).

cnf(refute_0_35,plain,
    ( ~ test(skolemFOFtoCNF_X0)
    | complement(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)) ),
    inference(subst,[],[refute_0_17:[bind(X0,$fot(skolemFOFtoCNF_X0))]]) ).

cnf(refute_0_36,plain,
    complement(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),
    inference(resolve,[$cnf( test(skolemFOFtoCNF_X0) )],[refute_0_34,refute_0_35]) ).

cnf(refute_0_37,plain,
    ( ~ complement(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0))
    | addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) = one ),
    inference(subst,[],[refute_0_20:[bind(X0,$fot(c(skolemFOFtoCNF_X0))),bind(X1,$fot(skolemFOFtoCNF_X0))]]) ).

cnf(refute_0_38,plain,
    addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) = one,
    inference(resolve,[$cnf( complement(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)) )],[refute_0_36,refute_0_37]) ).

cnf(refute_0_39,plain,
    addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) = addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),
    inference(subst,[],[refute_0_25:[bind(A,$fot(skolemFOFtoCNF_X0)),bind(B,$fot(c(skolemFOFtoCNF_X0)))]]) ).

cnf(refute_0_40,plain,
    ( addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) != addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0))
    | addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) != one
    | addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)) = one ),
    introduced(tautology,[equality,[$cnf( $equal(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),one) ),[0],$fot(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)))]]) ).

cnf(refute_0_41,plain,
    ( addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) != one
    | addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)) = one ),
    inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0))) )],[refute_0_39,refute_0_40]) ).

cnf(refute_0_42,plain,
    addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)) = one,
    inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),one) )],[refute_0_38,refute_0_41]) ).

cnf(refute_0_43,plain,
    multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),
    introduced(tautology,[refl,[$fot(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))]]) ).

cnf(refute_0_44,plain,
    ( addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)) != one
    | multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) != multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))
    | multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) ),[1,0],$fot(one)]]) ).

cnf(refute_0_45,plain,
    ( addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)) != one
    | multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) ),
    inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) )],[refute_0_43,refute_0_44]) ).

cnf(refute_0_46,plain,
    multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),
    inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),one) )],[refute_0_42,refute_0_45]) ).

cnf(refute_0_47,plain,
    ( Y != X
    | Y != Z
    | X = Z ),
    introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).

cnf(refute_0_48,plain,
    ( X != Y
    | Y != Z
    | X = Z ),
    inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_4,refute_0_47]) ).

cnf(refute_0_49,plain,
    ( multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) != multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))
    | multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) != multiplication(one,one)
    | multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(one,one) ),
    inference(subst,[],[refute_0_48:[bind(X,$fot(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))),bind(Y,$fot(multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))),bind(Z,$fot(multiplication(one,one)))]]) ).

cnf(refute_0_50,plain,
    ( multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) != multiplication(one,one)
    | multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(one,one) ),
    inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) )],[refute_0_46,refute_0_49]) ).

cnf(refute_0_51,plain,
    multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(one,one),
    inference(resolve,[$cnf( $equal(multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),multiplication(one,one)) )],[refute_0_33,refute_0_50]) ).

cnf(refute_0_52,plain,
    ( multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) != multiplication(one,one)
    | multiplication(one,one) != one
    | multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = one ),
    inference(subst,[],[refute_0_48:[bind(X,$fot(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))),bind(Y,$fot(multiplication(one,one))),bind(Z,$fot(one))]]) ).

cnf(refute_0_53,plain,
    ( multiplication(one,one) != one
    | multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = one ),
    inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),multiplication(one,one)) )],[refute_0_51,refute_0_52]) ).

cnf(refute_0_54,plain,
    multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = one,
    inference(resolve,[$cnf( $equal(multiplication(one,one),one) )],[refute_0_12,refute_0_53]) ).

cnf(refute_0_55,plain,
    ( multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) != one
    | ~ leq(one,one)
    | leq(one,multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) ),
    introduced(tautology,[equality,[$cnf( ~ leq(one,multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) ),[1],$fot(one)]]) ).

cnf(refute_0_56,plain,
    ( ~ leq(one,one)
    | leq(one,multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) ),
    inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),one) )],[refute_0_54,refute_0_55]) ).

cnf(refute_0_57,plain,
    ~ leq(one,one),
    inference(resolve,[$cnf( leq(one,multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) )],[refute_0_56,refute_0_10]) ).

cnf(refute_0_58,plain,
    ( addition(A,B) != B
    | leq(A,B) ),
    inference(canonicalize,[],[normalize_0_22]) ).

cnf(refute_0_59,plain,
    ( addition(X_57,X_57) != X_57
    | leq(X_57,X_57) ),
    inference(subst,[],[refute_0_58:[bind(A,$fot(X_57)),bind(B,$fot(X_57))]]) ).

cnf(refute_0_60,plain,
    addition(A,A) = A,
    inference(canonicalize,[],[normalize_0_24]) ).

cnf(refute_0_61,plain,
    addition(X_57,X_57) = X_57,
    inference(subst,[],[refute_0_60:[bind(A,$fot(X_57))]]) ).

cnf(refute_0_62,plain,
    ( X_57 != X_57
    | addition(X_57,X_57) != X_57
    | addition(X_57,X_57) = X_57 ),
    introduced(tautology,[equality,[$cnf( $equal(addition(X_57,X_57),X_57) ),[0,0],$fot(X_57)]]) ).

cnf(refute_0_63,plain,
    ( X_57 != X_57
    | addition(X_57,X_57) = X_57 ),
    inference(resolve,[$cnf( $equal(addition(X_57,X_57),X_57) )],[refute_0_61,refute_0_62]) ).

cnf(refute_0_64,plain,
    ( X_57 != X_57
    | leq(X_57,X_57) ),
    inference(resolve,[$cnf( $equal(addition(X_57,X_57),X_57) )],[refute_0_63,refute_0_59]) ).

cnf(refute_0_65,plain,
    X_57 = X_57,
    introduced(tautology,[refl,[$fot(X_57)]]) ).

cnf(refute_0_66,plain,
    leq(X_57,X_57),
    inference(resolve,[$cnf( $equal(X_57,X_57) )],[refute_0_65,refute_0_64]) ).

cnf(refute_0_67,plain,
    leq(one,one),
    inference(subst,[],[refute_0_66:[bind(X_57,$fot(one))]]) ).

cnf(refute_0_68,plain,
    $false,
    inference(resolve,[$cnf( leq(one,one) )],[refute_0_67,refute_0_57]) ).

fof(negate_1_0,plain,
    ~ ! [X0,X1] :
        ( ( test(X1)
          & test(X0)
          & leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1)))) )
       => leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one) ),
    inference(negate,[],[subgoal_1]) ).

fof(normalize_1_0,plain,
    ? [X0,X1] :
      ( ~ leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one)
      & leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))))
      & test(X0)
      & test(X1) ),
    inference(canonicalize,[],[negate_1_0]) ).

fof(normalize_1_1,plain,
    ( ~ leq(addition(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),skolemFOFtoCNF_X1_2),multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),c(skolemFOFtoCNF_X1_2))),one)
    & leq(one,addition(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),skolemFOFtoCNF_X1_2),multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),c(skolemFOFtoCNF_X1_2))))
    & test(skolemFOFtoCNF_X0_1)
    & test(skolemFOFtoCNF_X1_2) ),
    inference(skolemize,[],[normalize_1_0]) ).

fof(normalize_1_2,plain,
    ~ leq(addition(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),skolemFOFtoCNF_X1_2),multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),c(skolemFOFtoCNF_X1_2))),one),
    inference(conjunct,[],[normalize_1_1]) ).

fof(normalize_1_3,plain,
    ! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
    inference(canonicalize,[],[right_distributivity]) ).

fof(normalize_1_4,plain,
    ! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
    inference(specialize,[],[normalize_1_3]) ).

fof(normalize_1_5,plain,
    ! [A] : multiplication(one,A) = A,
    inference(canonicalize,[],[multiplicative_left_identity]) ).

fof(normalize_1_6,plain,
    ! [A] : multiplication(one,A) = A,
    inference(specialize,[],[normalize_1_5]) ).

fof(normalize_1_7,plain,
    test(skolemFOFtoCNF_X1_2),
    inference(conjunct,[],[normalize_1_1]) ).

fof(normalize_1_8,plain,
    ! [X0] :
      ( ~ test(X0)
      | ! [X1] :
          ( c(X0) != X1
        <=> ~ complement(X0,X1) ) ),
    inference(canonicalize,[],[test_3]) ).

fof(normalize_1_9,plain,
    ! [X0] :
      ( ~ test(X0)
      | ! [X1] :
          ( c(X0) != X1
        <=> ~ complement(X0,X1) ) ),
    inference(specialize,[],[normalize_1_8]) ).

fof(normalize_1_10,plain,
    ! [X0,X1] :
      ( ( c(X0) != X1
        | ~ test(X0)
        | complement(X0,X1) )
      & ( ~ complement(X0,X1)
        | ~ test(X0)
        | c(X0) = X1 ) ),
    inference(clausify,[],[normalize_1_9]) ).

fof(normalize_1_11,plain,
    ! [X0,X1] :
      ( c(X0) != X1
      | ~ test(X0)
      | complement(X0,X1) ),
    inference(conjunct,[],[normalize_1_10]) ).

fof(normalize_1_12,plain,
    ! [X0,X1] :
      ( ~ complement(X1,X0)
    <=> ( addition(X0,X1) != one
        | multiplication(X0,X1) != zero
        | multiplication(X1,X0) != zero ) ),
    inference(canonicalize,[],[test_2]) ).

fof(normalize_1_13,plain,
    ! [X0,X1] :
      ( ~ complement(X1,X0)
    <=> ( addition(X0,X1) != one
        | multiplication(X0,X1) != zero
        | multiplication(X1,X0) != zero ) ),
    inference(specialize,[],[normalize_1_12]) ).

fof(normalize_1_14,plain,
    ! [X0,X1] :
      ( ( ~ complement(X1,X0)
        | addition(X0,X1) = one )
      & ( ~ complement(X1,X0)
        | multiplication(X0,X1) = zero )
      & ( ~ complement(X1,X0)
        | multiplication(X1,X0) = zero )
      & ( addition(X0,X1) != one
        | multiplication(X0,X1) != zero
        | multiplication(X1,X0) != zero
        | complement(X1,X0) ) ),
    inference(clausify,[],[normalize_1_13]) ).

fof(normalize_1_15,plain,
    ! [X0,X1] :
      ( ~ complement(X1,X0)
      | addition(X0,X1) = one ),
    inference(conjunct,[],[normalize_1_14]) ).

fof(normalize_1_16,plain,
    ! [A,B] : addition(A,B) = addition(B,A),
    inference(canonicalize,[],[additive_commutativity]) ).

fof(normalize_1_17,plain,
    ! [A,B] : addition(A,B) = addition(B,A),
    inference(specialize,[],[normalize_1_16]) ).

fof(normalize_1_18,plain,
    test(skolemFOFtoCNF_X0_1),
    inference(conjunct,[],[normalize_1_1]) ).

fof(normalize_1_19,plain,
    ! [A,B] :
      ( addition(A,B) != B
    <=> ~ leq(A,B) ),
    inference(canonicalize,[],[order]) ).

fof(normalize_1_20,plain,
    ! [A,B] :
      ( addition(A,B) != B
    <=> ~ leq(A,B) ),
    inference(specialize,[],[normalize_1_19]) ).

fof(normalize_1_21,plain,
    ! [A,B] :
      ( ( addition(A,B) != B
        | leq(A,B) )
      & ( ~ leq(A,B)
        | addition(A,B) = B ) ),
    inference(clausify,[],[normalize_1_20]) ).

fof(normalize_1_22,plain,
    ! [A,B] :
      ( addition(A,B) != B
      | leq(A,B) ),
    inference(conjunct,[],[normalize_1_21]) ).

fof(normalize_1_23,plain,
    ! [A] : addition(A,A) = A,
    inference(canonicalize,[],[additive_idempotence]) ).

fof(normalize_1_24,plain,
    ! [A] : addition(A,A) = A,
    inference(specialize,[],[normalize_1_23]) ).

cnf(refute_1_0,plain,
    ~ leq(addition(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),skolemFOFtoCNF_X1_2),multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),c(skolemFOFtoCNF_X1_2))),one),
    inference(canonicalize,[],[normalize_1_2]) ).

cnf(refute_1_1,plain,
    multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
    inference(canonicalize,[],[normalize_1_4]) ).

cnf(refute_1_2,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_1_3,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_1_4,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_1_2,refute_1_3]) ).

cnf(refute_1_5,plain,
    ( multiplication(A,addition(B,C)) != addition(multiplication(A,B),multiplication(A,C))
    | addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)) ),
    inference(subst,[],[refute_1_4:[bind(X,$fot(multiplication(A,addition(B,C)))),bind(Y,$fot(addition(multiplication(A,B),multiplication(A,C))))]]) ).

cnf(refute_1_6,plain,
    addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
    inference(resolve,[$cnf( $equal(multiplication(A,addition(B,C)),addition(multiplication(A,B),multiplication(A,C))) )],[refute_1_1,refute_1_5]) ).

cnf(refute_1_7,plain,
    addition(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),skolemFOFtoCNF_X1_2),multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),c(skolemFOFtoCNF_X1_2))) = multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),
    inference(subst,[],[refute_1_6:[bind(A,$fot(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)))),bind(B,$fot(skolemFOFtoCNF_X1_2)),bind(C,$fot(c(skolemFOFtoCNF_X1_2)))]]) ).

cnf(refute_1_8,plain,
    ( addition(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),skolemFOFtoCNF_X1_2),multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),c(skolemFOFtoCNF_X1_2))) != multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))
    | ~ leq(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),one)
    | leq(addition(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),skolemFOFtoCNF_X1_2),multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),c(skolemFOFtoCNF_X1_2))),one) ),
    introduced(tautology,[equality,[$cnf( ~ leq(addition(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),skolemFOFtoCNF_X1_2),multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),c(skolemFOFtoCNF_X1_2))),one) ),[0],$fot(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))]]) ).

cnf(refute_1_9,plain,
    ( ~ leq(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),one)
    | leq(addition(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),skolemFOFtoCNF_X1_2),multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),c(skolemFOFtoCNF_X1_2))),one) ),
    inference(resolve,[$cnf( $equal(addition(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),skolemFOFtoCNF_X1_2),multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),c(skolemFOFtoCNF_X1_2))),multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))) )],[refute_1_7,refute_1_8]) ).

cnf(refute_1_10,plain,
    ~ leq(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),one),
    inference(resolve,[$cnf( leq(addition(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),skolemFOFtoCNF_X1_2),multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),c(skolemFOFtoCNF_X1_2))),one) )],[refute_1_9,refute_1_0]) ).

cnf(refute_1_11,plain,
    multiplication(one,A) = A,
    inference(canonicalize,[],[normalize_1_6]) ).

cnf(refute_1_12,plain,
    multiplication(one,one) = one,
    inference(subst,[],[refute_1_11:[bind(A,$fot(one))]]) ).

cnf(refute_1_13,plain,
    test(skolemFOFtoCNF_X1_2),
    inference(canonicalize,[],[normalize_1_7]) ).

cnf(refute_1_14,plain,
    ( c(X0) != X1
    | ~ test(X0)
    | complement(X0,X1) ),
    inference(canonicalize,[],[normalize_1_11]) ).

cnf(refute_1_15,plain,
    ( c(X0) != c(X0)
    | ~ test(X0)
    | complement(X0,c(X0)) ),
    inference(subst,[],[refute_1_14:[bind(X1,$fot(c(X0)))]]) ).

cnf(refute_1_16,plain,
    c(X0) = c(X0),
    introduced(tautology,[refl,[$fot(c(X0))]]) ).

cnf(refute_1_17,plain,
    ( ~ test(X0)
    | complement(X0,c(X0)) ),
    inference(resolve,[$cnf( $equal(c(X0),c(X0)) )],[refute_1_16,refute_1_15]) ).

cnf(refute_1_18,plain,
    ( ~ test(skolemFOFtoCNF_X1_2)
    | complement(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)) ),
    inference(subst,[],[refute_1_17:[bind(X0,$fot(skolemFOFtoCNF_X1_2))]]) ).

cnf(refute_1_19,plain,
    complement(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)),
    inference(resolve,[$cnf( test(skolemFOFtoCNF_X1_2) )],[refute_1_13,refute_1_18]) ).

cnf(refute_1_20,plain,
    ( ~ complement(X1,X0)
    | addition(X0,X1) = one ),
    inference(canonicalize,[],[normalize_1_15]) ).

cnf(refute_1_21,plain,
    ( ~ complement(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))
    | addition(c(skolemFOFtoCNF_X1_2),skolemFOFtoCNF_X1_2) = one ),
    inference(subst,[],[refute_1_20:[bind(X0,$fot(c(skolemFOFtoCNF_X1_2))),bind(X1,$fot(skolemFOFtoCNF_X1_2))]]) ).

cnf(refute_1_22,plain,
    addition(c(skolemFOFtoCNF_X1_2),skolemFOFtoCNF_X1_2) = one,
    inference(resolve,[$cnf( complement(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)) )],[refute_1_19,refute_1_21]) ).

cnf(refute_1_23,plain,
    addition(A,B) = addition(B,A),
    inference(canonicalize,[],[normalize_1_17]) ).

cnf(refute_1_24,plain,
    ( addition(A,B) != addition(B,A)
    | addition(B,A) = addition(A,B) ),
    inference(subst,[],[refute_1_4:[bind(X,$fot(addition(A,B))),bind(Y,$fot(addition(B,A)))]]) ).

cnf(refute_1_25,plain,
    addition(B,A) = addition(A,B),
    inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_1_23,refute_1_24]) ).

cnf(refute_1_26,plain,
    addition(c(skolemFOFtoCNF_X1_2),skolemFOFtoCNF_X1_2) = addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)),
    inference(subst,[],[refute_1_25:[bind(A,$fot(skolemFOFtoCNF_X1_2)),bind(B,$fot(c(skolemFOFtoCNF_X1_2)))]]) ).

cnf(refute_1_27,plain,
    ( addition(c(skolemFOFtoCNF_X1_2),skolemFOFtoCNF_X1_2) != addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))
    | addition(c(skolemFOFtoCNF_X1_2),skolemFOFtoCNF_X1_2) != one
    | addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)) = one ),
    introduced(tautology,[equality,[$cnf( $equal(addition(c(skolemFOFtoCNF_X1_2),skolemFOFtoCNF_X1_2),one) ),[0],$fot(addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))]]) ).

cnf(refute_1_28,plain,
    ( addition(c(skolemFOFtoCNF_X1_2),skolemFOFtoCNF_X1_2) != one
    | addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)) = one ),
    inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X1_2),skolemFOFtoCNF_X1_2),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) )],[refute_1_26,refute_1_27]) ).

cnf(refute_1_29,plain,
    addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)) = one,
    inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X1_2),skolemFOFtoCNF_X1_2),one) )],[refute_1_22,refute_1_28]) ).

cnf(refute_1_30,plain,
    multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),
    introduced(tautology,[refl,[$fot(multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))]]) ).

cnf(refute_1_31,plain,
    ( addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)) != one
    | multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) != multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))
    | multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = multiplication(one,one) ),
    introduced(tautology,[equality,[$cnf( $equal(multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))) ),[1,1],$fot(one)]]) ).

cnf(refute_1_32,plain,
    ( addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)) != one
    | multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = multiplication(one,one) ),
    inference(resolve,[$cnf( $equal(multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))) )],[refute_1_30,refute_1_31]) ).

cnf(refute_1_33,plain,
    multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = multiplication(one,one),
    inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)),one) )],[refute_1_29,refute_1_32]) ).

cnf(refute_1_34,plain,
    test(skolemFOFtoCNF_X0_1),
    inference(canonicalize,[],[normalize_1_18]) ).

cnf(refute_1_35,plain,
    ( ~ test(skolemFOFtoCNF_X0_1)
    | complement(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)) ),
    inference(subst,[],[refute_1_17:[bind(X0,$fot(skolemFOFtoCNF_X0_1))]]) ).

cnf(refute_1_36,plain,
    complement(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),
    inference(resolve,[$cnf( test(skolemFOFtoCNF_X0_1) )],[refute_1_34,refute_1_35]) ).

cnf(refute_1_37,plain,
    ( ~ complement(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1))
    | addition(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X0_1) = one ),
    inference(subst,[],[refute_1_20:[bind(X0,$fot(c(skolemFOFtoCNF_X0_1))),bind(X1,$fot(skolemFOFtoCNF_X0_1))]]) ).

cnf(refute_1_38,plain,
    addition(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X0_1) = one,
    inference(resolve,[$cnf( complement(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)) )],[refute_1_36,refute_1_37]) ).

cnf(refute_1_39,plain,
    addition(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X0_1) = addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),
    inference(subst,[],[refute_1_25:[bind(A,$fot(skolemFOFtoCNF_X0_1)),bind(B,$fot(c(skolemFOFtoCNF_X0_1)))]]) ).

cnf(refute_1_40,plain,
    ( addition(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X0_1) != addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1))
    | addition(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X0_1) != one
    | addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)) = one ),
    introduced(tautology,[equality,[$cnf( $equal(addition(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X0_1),one) ),[0],$fot(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)))]]) ).

cnf(refute_1_41,plain,
    ( addition(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X0_1) != one
    | addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)) = one ),
    inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1))) )],[refute_1_39,refute_1_40]) ).

cnf(refute_1_42,plain,
    addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)) = one,
    inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X0_1),one) )],[refute_1_38,refute_1_41]) ).

cnf(refute_1_43,plain,
    multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),
    introduced(tautology,[refl,[$fot(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))]]) ).

cnf(refute_1_44,plain,
    ( addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)) != one
    | multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) != multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))
    | multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))) ),[1,0],$fot(one)]]) ).

cnf(refute_1_45,plain,
    ( addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)) != one
    | multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) ),
    inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))) )],[refute_1_43,refute_1_44]) ).

cnf(refute_1_46,plain,
    multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),
    inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),one) )],[refute_1_42,refute_1_45]) ).

cnf(refute_1_47,plain,
    ( Y != X
    | Y != Z
    | X = Z ),
    introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).

cnf(refute_1_48,plain,
    ( X != Y
    | Y != Z
    | X = Z ),
    inference(resolve,[$cnf( $equal(Y,X) )],[refute_1_4,refute_1_47]) ).

cnf(refute_1_49,plain,
    ( multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) != multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))
    | multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) != multiplication(one,one)
    | multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = multiplication(one,one) ),
    inference(subst,[],[refute_1_48:[bind(X,$fot(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))),bind(Y,$fot(multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))),bind(Z,$fot(multiplication(one,one)))]]) ).

cnf(refute_1_50,plain,
    ( multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) != multiplication(one,one)
    | multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = multiplication(one,one) ),
    inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))) )],[refute_1_46,refute_1_49]) ).

cnf(refute_1_51,plain,
    multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = multiplication(one,one),
    inference(resolve,[$cnf( $equal(multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),multiplication(one,one)) )],[refute_1_33,refute_1_50]) ).

cnf(refute_1_52,plain,
    ( multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) != multiplication(one,one)
    | multiplication(one,one) != one
    | multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = one ),
    inference(subst,[],[refute_1_48:[bind(X,$fot(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))),bind(Y,$fot(multiplication(one,one))),bind(Z,$fot(one))]]) ).

cnf(refute_1_53,plain,
    ( multiplication(one,one) != one
    | multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = one ),
    inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),multiplication(one,one)) )],[refute_1_51,refute_1_52]) ).

cnf(refute_1_54,plain,
    multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = one,
    inference(resolve,[$cnf( $equal(multiplication(one,one),one) )],[refute_1_12,refute_1_53]) ).

cnf(refute_1_55,plain,
    ( multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) != one
    | ~ leq(one,one)
    | leq(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),one) ),
    introduced(tautology,[equality,[$cnf( ~ leq(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),one) ),[0],$fot(one)]]) ).

cnf(refute_1_56,plain,
    ( ~ leq(one,one)
    | leq(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),one) ),
    inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),one) )],[refute_1_54,refute_1_55]) ).

cnf(refute_1_57,plain,
    ~ leq(one,one),
    inference(resolve,[$cnf( leq(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),one) )],[refute_1_56,refute_1_10]) ).

cnf(refute_1_58,plain,
    ( addition(A,B) != B
    | leq(A,B) ),
    inference(canonicalize,[],[normalize_1_22]) ).

cnf(refute_1_59,plain,
    ( addition(X_141,X_141) != X_141
    | leq(X_141,X_141) ),
    inference(subst,[],[refute_1_58:[bind(A,$fot(X_141)),bind(B,$fot(X_141))]]) ).

cnf(refute_1_60,plain,
    addition(A,A) = A,
    inference(canonicalize,[],[normalize_1_24]) ).

cnf(refute_1_61,plain,
    addition(X_141,X_141) = X_141,
    inference(subst,[],[refute_1_60:[bind(A,$fot(X_141))]]) ).

cnf(refute_1_62,plain,
    ( X_141 != X_141
    | addition(X_141,X_141) != X_141
    | addition(X_141,X_141) = X_141 ),
    introduced(tautology,[equality,[$cnf( $equal(addition(X_141,X_141),X_141) ),[0,0],$fot(X_141)]]) ).

cnf(refute_1_63,plain,
    ( X_141 != X_141
    | addition(X_141,X_141) = X_141 ),
    inference(resolve,[$cnf( $equal(addition(X_141,X_141),X_141) )],[refute_1_61,refute_1_62]) ).

cnf(refute_1_64,plain,
    ( X_141 != X_141
    | leq(X_141,X_141) ),
    inference(resolve,[$cnf( $equal(addition(X_141,X_141),X_141) )],[refute_1_63,refute_1_59]) ).

cnf(refute_1_65,plain,
    X_141 = X_141,
    introduced(tautology,[refl,[$fot(X_141)]]) ).

cnf(refute_1_66,plain,
    leq(X_141,X_141),
    inference(resolve,[$cnf( $equal(X_141,X_141) )],[refute_1_65,refute_1_64]) ).

cnf(refute_1_67,plain,
    leq(one,one),
    inference(subst,[],[refute_1_66:[bind(X_141,$fot(one))]]) ).

cnf(refute_1_68,plain,
    $false,
    inference(resolve,[$cnf( leq(one,one) )],[refute_1_67,refute_1_57]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : KLE007+4 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n009.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 13:04:37 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.31/1.48  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.31/1.48  
% 1.31/1.48  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.31/1.49  
%------------------------------------------------------------------------------