TSTP Solution File: HEN003-5 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : HEN003-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n028.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 : Sat Jul 16 12:58:32 EDT 2022

% Result   : Unsatisfiable 0.47s 0.67s
% Output   : CNFRefutation 0.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   15
% Syntax   : Number of clauses     :   47 (  21 unt;   0 nHn;  25 RR)
%            Number of literals    :   86 (  85 equ;  41 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   55 (   7 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(quotient_smaller_than_numerator,axiom,
    divide(divide(X,Y),X) = zero ).

cnf(quotient_property,axiom,
    divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero ).

cnf(zero_is_smallest,axiom,
    divide(zero,X) = zero ).

cnf(divide_and_equal,axiom,
    ( divide(X,Y) != zero
    | divide(Y,X) != zero
    | X = Y ) ).

cnf(prove_x_divide_x_is_zero,negated_conjecture,
    divide(a,a) != zero ).

cnf(refute_0_0,plain,
    ( divide(divide(X_79,X_79),zero) != zero
    | divide(zero,divide(X_79,X_79)) != zero
    | divide(X_79,X_79) = zero ),
    inference(subst,[],[divide_and_equal:[bind(X,$fot(divide(X_79,X_79))),bind(Y,$fot(zero))]]) ).

cnf(refute_0_1,plain,
    ( divide(divide(divide(X_10,X_10),zero),zero) != zero
    | divide(zero,divide(divide(X_10,X_10),zero)) != zero
    | zero = divide(divide(X_10,X_10),zero) ),
    inference(subst,[],[divide_and_equal:[bind(X,$fot(zero)),bind(Y,$fot(divide(divide(X_10,X_10),zero)))]]) ).

cnf(refute_0_2,plain,
    divide(divide(divide(X_6,X_6),divide(X_5,X_6)),divide(divide(X_6,X_5),X_6)) = zero,
    inference(subst,[],[quotient_property:[bind(X,$fot(X_6)),bind(Y,$fot(X_5)),bind(Z,$fot(X_6))]]) ).

cnf(refute_0_3,plain,
    divide(divide(X_6,X_5),X_6) = zero,
    inference(subst,[],[quotient_smaller_than_numerator:[bind(X,$fot(X_6)),bind(Y,$fot(X_5))]]) ).

cnf(refute_0_4,plain,
    ( divide(divide(X_6,X_5),X_6) != zero
    | divide(divide(divide(X_6,X_6),divide(X_5,X_6)),divide(divide(X_6,X_5),X_6)) != zero
    | divide(divide(divide(X_6,X_6),divide(X_5,X_6)),zero) = zero ),
    introduced(tautology,[equality,[$cnf( $equal(divide(divide(divide(X_6,X_6),divide(X_5,X_6)),divide(divide(X_6,X_5),X_6)),zero) ),[0,1],$fot(zero)]]) ).

cnf(refute_0_5,plain,
    ( divide(divide(divide(X_6,X_6),divide(X_5,X_6)),divide(divide(X_6,X_5),X_6)) != zero
    | divide(divide(divide(X_6,X_6),divide(X_5,X_6)),zero) = zero ),
    inference(resolve,[$cnf( $equal(divide(divide(X_6,X_5),X_6),zero) )],[refute_0_3,refute_0_4]) ).

cnf(refute_0_6,plain,
    divide(divide(divide(X_6,X_6),divide(X_5,X_6)),zero) = zero,
    inference(resolve,[$cnf( $equal(divide(divide(divide(X_6,X_6),divide(X_5,X_6)),divide(divide(X_6,X_5),X_6)),zero) )],[refute_0_2,refute_0_5]) ).

cnf(refute_0_7,plain,
    divide(divide(divide(X_10,X_10),divide(divide(X_10,Y),X_10)),zero) = zero,
    inference(subst,[],[refute_0_6:[bind(X_5,$fot(divide(X_10,Y))),bind(X_6,$fot(X_10))]]) ).

cnf(refute_0_8,plain,
    divide(divide(X_10,Y),X_10) = zero,
    inference(subst,[],[quotient_smaller_than_numerator:[bind(X,$fot(X_10))]]) ).

cnf(refute_0_9,plain,
    ( divide(divide(X_10,Y),X_10) != zero
    | divide(divide(divide(X_10,X_10),divide(divide(X_10,Y),X_10)),zero) != zero
    | divide(divide(divide(X_10,X_10),zero),zero) = zero ),
    introduced(tautology,[equality,[$cnf( $equal(divide(divide(divide(X_10,X_10),divide(divide(X_10,Y),X_10)),zero),zero) ),[0,0,1],$fot(zero)]]) ).

cnf(refute_0_10,plain,
    ( divide(divide(divide(X_10,X_10),divide(divide(X_10,Y),X_10)),zero) != zero
    | divide(divide(divide(X_10,X_10),zero),zero) = zero ),
    inference(resolve,[$cnf( $equal(divide(divide(X_10,Y),X_10),zero) )],[refute_0_8,refute_0_9]) ).

cnf(refute_0_11,plain,
    divide(divide(divide(X_10,X_10),zero),zero) = zero,
    inference(resolve,[$cnf( $equal(divide(divide(divide(X_10,X_10),divide(divide(X_10,Y),X_10)),zero),zero) )],[refute_0_7,refute_0_10]) ).

cnf(refute_0_12,plain,
    ( divide(divide(divide(X_10,X_10),zero),zero) != zero
    | zero != zero
    | divide(divide(divide(X_10,X_10),zero),zero) = zero ),
    introduced(tautology,[equality,[$cnf( ~ $equal(divide(divide(divide(X_10,X_10),zero),zero),zero) ),[0],$fot(zero)]]) ).

cnf(refute_0_13,plain,
    ( zero != zero
    | divide(divide(divide(X_10,X_10),zero),zero) = zero ),
    inference(resolve,[$cnf( $equal(divide(divide(divide(X_10,X_10),zero),zero),zero) )],[refute_0_11,refute_0_12]) ).

cnf(refute_0_14,plain,
    ( divide(zero,divide(divide(X_10,X_10),zero)) != zero
    | zero != zero
    | zero = divide(divide(X_10,X_10),zero) ),
    inference(resolve,[$cnf( $equal(divide(divide(divide(X_10,X_10),zero),zero),zero) )],[refute_0_13,refute_0_1]) ).

cnf(refute_0_15,plain,
    zero = zero,
    introduced(tautology,[refl,[$fot(zero)]]) ).

cnf(refute_0_16,plain,
    ( divide(zero,divide(divide(X_10,X_10),zero)) != zero
    | zero = divide(divide(X_10,X_10),zero) ),
    inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_15,refute_0_14]) ).

cnf(refute_0_17,plain,
    divide(zero,divide(divide(X_10,X_10),zero)) = zero,
    inference(subst,[],[zero_is_smallest:[bind(X,$fot(divide(divide(X_10,X_10),zero)))]]) ).

cnf(refute_0_18,plain,
    ( divide(zero,divide(divide(X_10,X_10),zero)) != zero
    | zero != zero
    | divide(zero,divide(divide(X_10,X_10),zero)) = zero ),
    introduced(tautology,[equality,[$cnf( ~ $equal(divide(zero,divide(divide(X_10,X_10),zero)),zero) ),[0],$fot(zero)]]) ).

cnf(refute_0_19,plain,
    ( zero != zero
    | divide(zero,divide(divide(X_10,X_10),zero)) = zero ),
    inference(resolve,[$cnf( $equal(divide(zero,divide(divide(X_10,X_10),zero)),zero) )],[refute_0_17,refute_0_18]) ).

cnf(refute_0_20,plain,
    ( zero != zero
    | zero = divide(divide(X_10,X_10),zero) ),
    inference(resolve,[$cnf( $equal(divide(zero,divide(divide(X_10,X_10),zero)),zero) )],[refute_0_19,refute_0_16]) ).

cnf(refute_0_21,plain,
    zero = divide(divide(X_10,X_10),zero),
    inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_15,refute_0_20]) ).

cnf(refute_0_22,plain,
    zero = divide(divide(X_79,X_79),zero),
    inference(subst,[],[refute_0_21:[bind(X_10,$fot(X_79))]]) ).

cnf(refute_0_23,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_24,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_25,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_23,refute_0_24]) ).

cnf(refute_0_26,plain,
    ( zero != divide(divide(X_79,X_79),zero)
    | divide(divide(X_79,X_79),zero) = zero ),
    inference(subst,[],[refute_0_25:[bind(X0,$fot(zero)),bind(Y0,$fot(divide(divide(X_79,X_79),zero)))]]) ).

cnf(refute_0_27,plain,
    divide(divide(X_79,X_79),zero) = zero,
    inference(resolve,[$cnf( $equal(zero,divide(divide(X_79,X_79),zero)) )],[refute_0_22,refute_0_26]) ).

cnf(refute_0_28,plain,
    ( divide(divide(X_79,X_79),zero) != zero
    | zero != zero
    | divide(divide(X_79,X_79),zero) = zero ),
    introduced(tautology,[equality,[$cnf( ~ $equal(divide(divide(X_79,X_79),zero),zero) ),[0],$fot(zero)]]) ).

cnf(refute_0_29,plain,
    ( zero != zero
    | divide(divide(X_79,X_79),zero) = zero ),
    inference(resolve,[$cnf( $equal(divide(divide(X_79,X_79),zero),zero) )],[refute_0_27,refute_0_28]) ).

cnf(refute_0_30,plain,
    ( divide(zero,divide(X_79,X_79)) != zero
    | zero != zero
    | divide(X_79,X_79) = zero ),
    inference(resolve,[$cnf( $equal(divide(divide(X_79,X_79),zero),zero) )],[refute_0_29,refute_0_0]) ).

cnf(refute_0_31,plain,
    ( divide(zero,divide(X_79,X_79)) != zero
    | divide(X_79,X_79) = zero ),
    inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_15,refute_0_30]) ).

cnf(refute_0_32,plain,
    divide(zero,divide(X_79,X_79)) = zero,
    inference(subst,[],[zero_is_smallest:[bind(X,$fot(divide(X_79,X_79)))]]) ).

cnf(refute_0_33,plain,
    ( divide(zero,divide(X_79,X_79)) != zero
    | zero != zero
    | divide(zero,divide(X_79,X_79)) = zero ),
    introduced(tautology,[equality,[$cnf( ~ $equal(divide(zero,divide(X_79,X_79)),zero) ),[0],$fot(zero)]]) ).

cnf(refute_0_34,plain,
    ( zero != zero
    | divide(zero,divide(X_79,X_79)) = zero ),
    inference(resolve,[$cnf( $equal(divide(zero,divide(X_79,X_79)),zero) )],[refute_0_32,refute_0_33]) ).

cnf(refute_0_35,plain,
    ( zero != zero
    | divide(X_79,X_79) = zero ),
    inference(resolve,[$cnf( $equal(divide(zero,divide(X_79,X_79)),zero) )],[refute_0_34,refute_0_31]) ).

cnf(refute_0_36,plain,
    divide(X_79,X_79) = zero,
    inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_15,refute_0_35]) ).

cnf(refute_0_37,plain,
    divide(a,a) = zero,
    inference(subst,[],[refute_0_36:[bind(X_79,$fot(a))]]) ).

cnf(refute_0_38,plain,
    ( divide(a,a) != zero
    | zero != zero
    | divide(a,a) = zero ),
    introduced(tautology,[equality,[$cnf( ~ $equal(divide(a,a),zero) ),[0],$fot(zero)]]) ).

cnf(refute_0_39,plain,
    ( zero != zero
    | divide(a,a) = zero ),
    inference(resolve,[$cnf( $equal(divide(a,a),zero) )],[refute_0_37,refute_0_38]) ).

cnf(refute_0_40,plain,
    zero != zero,
    inference(resolve,[$cnf( $equal(divide(a,a),zero) )],[refute_0_39,prove_x_divide_x_is_zero]) ).

cnf(refute_0_41,plain,
    $false,
    inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_15,refute_0_40]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : HEN003-5 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n028.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 : Fri Jul  1 14:46:31 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.47/0.67  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.47/0.67  
% 0.47/0.67  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.47/0.67  
%------------------------------------------------------------------------------