TSTP Solution File: HEN004-3 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : HEN004-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n007.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 0.19s 0.49s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   40
%            Number of leaves      :   19
% Syntax   : Number of clauses     :   91 (  48 unt;   0 nHn;  43 RR)
%            Number of literals    :  148 (  80 equ;  59 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :  110 (  14 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(quotient_less_equal1,axiom,
    ( ~ less_equal(X,Y)
    | divide(X,Y) = zero ) ).

cnf(quotient_less_equal2,axiom,
    ( divide(X,Y) != zero
    | less_equal(X,Y) ) ).

cnf(quotient_smaller_than_numerator,axiom,
    less_equal(divide(X,Y),X) ).

cnf(quotient_property,axiom,
    less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) ).

cnf(zero_is_smallest,axiom,
    less_equal(zero,X) ).

cnf(less_equal_and_equal,axiom,
    ( ~ less_equal(X,Y)
    | ~ less_equal(Y,X)
    | X = Y ) ).

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

cnf(refute_0_0,plain,
    ( divide(X,divide(X,zero)) != zero
    | less_equal(X,divide(X,zero)) ),
    inference(subst,[],[quotient_less_equal2:[bind(Y,$fot(divide(X,zero)))]]) ).

cnf(refute_0_1,plain,
    less_equal(zero,X_30),
    inference(subst,[],[zero_is_smallest:[bind(X,$fot(X_30))]]) ).

cnf(refute_0_2,plain,
    ( ~ less_equal(X_30,zero)
    | ~ less_equal(zero,X_30)
    | zero = X_30 ),
    inference(subst,[],[less_equal_and_equal:[bind(X,$fot(zero)),bind(Y,$fot(X_30))]]) ).

cnf(refute_0_3,plain,
    ( ~ less_equal(X_30,zero)
    | zero = X_30 ),
    inference(resolve,[$cnf( less_equal(zero,X_30) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    ( ~ less_equal(divide(X_48,divide(X_48,zero)),zero)
    | zero = divide(X_48,divide(X_48,zero)) ),
    inference(subst,[],[refute_0_3:[bind(X_30,$fot(divide(X_48,divide(X_48,zero))))]]) ).

cnf(refute_0_5,plain,
    ( divide(divide(X_47,divide(X_47,zero)),zero) != zero
    | less_equal(divide(X_47,divide(X_47,zero)),zero) ),
    inference(subst,[],[quotient_less_equal2:[bind(X,$fot(divide(X_47,divide(X_47,zero)))),bind(Y,$fot(zero))]]) ).

cnf(refute_0_6,plain,
    ( ~ less_equal(divide(divide(X_46,divide(X_46,zero)),zero),zero)
    | zero = divide(divide(X_46,divide(X_46,zero)),zero) ),
    inference(subst,[],[refute_0_3:[bind(X_30,$fot(divide(divide(X_46,divide(X_46,zero)),zero)))]]) ).

cnf(refute_0_7,plain,
    less_equal(divide(divide(X_12,X_14),divide(zero,X_14)),divide(divide(X_12,zero),X_14)),
    inference(subst,[],[quotient_property:[bind(X,$fot(X_12)),bind(Y,$fot(zero)),bind(Z,$fot(X_14))]]) ).

cnf(refute_0_8,plain,
    less_equal(zero,X_7),
    inference(subst,[],[zero_is_smallest:[bind(X,$fot(X_7))]]) ).

cnf(refute_0_9,plain,
    ( ~ less_equal(zero,X_7)
    | divide(zero,X_7) = zero ),
    inference(subst,[],[quotient_less_equal1:[bind(X,$fot(zero)),bind(Y,$fot(X_7))]]) ).

cnf(refute_0_10,plain,
    divide(zero,X_7) = zero,
    inference(resolve,[$cnf( less_equal(zero,X_7) )],[refute_0_8,refute_0_9]) ).

cnf(refute_0_11,plain,
    divide(zero,X_14) = zero,
    inference(subst,[],[refute_0_10:[bind(X_7,$fot(X_14))]]) ).

cnf(refute_0_12,plain,
    ( ~ less_equal(divide(divide(X_12,X_14),divide(zero,X_14)),divide(divide(X_12,zero),X_14))
    | divide(zero,X_14) != zero
    | less_equal(divide(divide(X_12,X_14),zero),divide(divide(X_12,zero),X_14)) ),
    introduced(tautology,[equality,[$cnf( less_equal(divide(divide(X_12,X_14),divide(zero,X_14)),divide(divide(X_12,zero),X_14)) ),[0,1],$fot(zero)]]) ).

cnf(refute_0_13,plain,
    ( ~ less_equal(divide(divide(X_12,X_14),divide(zero,X_14)),divide(divide(X_12,zero),X_14))
    | less_equal(divide(divide(X_12,X_14),zero),divide(divide(X_12,zero),X_14)) ),
    inference(resolve,[$cnf( $equal(divide(zero,X_14),zero) )],[refute_0_11,refute_0_12]) ).

cnf(refute_0_14,plain,
    less_equal(divide(divide(X_12,X_14),zero),divide(divide(X_12,zero),X_14)),
    inference(resolve,[$cnf( less_equal(divide(divide(X_12,X_14),divide(zero,X_14)),divide(divide(X_12,zero),X_14)) )],[refute_0_7,refute_0_13]) ).

cnf(refute_0_15,plain,
    less_equal(divide(divide(X_12,divide(X_12,zero)),zero),divide(divide(X_12,zero),divide(X_12,zero))),
    inference(subst,[],[refute_0_14:[bind(X_14,$fot(divide(X_12,zero)))]]) ).

cnf(refute_0_16,plain,
    ( ~ less_equal(divide(X_32,X_32),zero)
    | ~ less_equal(zero,divide(X_32,X_32))
    | zero = divide(X_32,X_32) ),
    inference(subst,[],[less_equal_and_equal:[bind(X,$fot(zero)),bind(Y,$fot(divide(X_32,X_32)))]]) ).

cnf(refute_0_17,plain,
    ( divide(divide(X_31,X_31),zero) != zero
    | less_equal(divide(X_31,X_31),zero) ),
    inference(subst,[],[quotient_less_equal2:[bind(X,$fot(divide(X_31,X_31))),bind(Y,$fot(zero))]]) ).

cnf(refute_0_18,plain,
    less_equal(divide(divide(X_14,X_14),divide(X_13,X_14)),divide(divide(X_14,X_13),X_14)),
    inference(subst,[],[quotient_property:[bind(X,$fot(X_14)),bind(Y,$fot(X_13)),bind(Z,$fot(X_14))]]) ).

cnf(refute_0_19,plain,
    less_equal(divide(X_7,Y),X_7),
    inference(subst,[],[quotient_smaller_than_numerator:[bind(X,$fot(X_7))]]) ).

cnf(refute_0_20,plain,
    ( ~ less_equal(divide(X_7,Y),X_7)
    | divide(divide(X_7,Y),X_7) = zero ),
    inference(subst,[],[quotient_less_equal1:[bind(X,$fot(divide(X_7,Y))),bind(Y,$fot(X_7))]]) ).

cnf(refute_0_21,plain,
    divide(divide(X_7,Y),X_7) = zero,
    inference(resolve,[$cnf( less_equal(divide(X_7,Y),X_7) )],[refute_0_19,refute_0_20]) ).

cnf(refute_0_22,plain,
    divide(divide(X_14,X_13),X_14) = zero,
    inference(subst,[],[refute_0_21:[bind(Y,$fot(X_13)),bind(X_7,$fot(X_14))]]) ).

cnf(refute_0_23,plain,
    ( ~ less_equal(divide(divide(X_14,X_14),divide(X_13,X_14)),divide(divide(X_14,X_13),X_14))
    | divide(divide(X_14,X_13),X_14) != zero
    | less_equal(divide(divide(X_14,X_14),divide(X_13,X_14)),zero) ),
    introduced(tautology,[equality,[$cnf( less_equal(divide(divide(X_14,X_14),divide(X_13,X_14)),divide(divide(X_14,X_13),X_14)) ),[1],$fot(zero)]]) ).

cnf(refute_0_24,plain,
    ( ~ less_equal(divide(divide(X_14,X_14),divide(X_13,X_14)),divide(divide(X_14,X_13),X_14))
    | less_equal(divide(divide(X_14,X_14),divide(X_13,X_14)),zero) ),
    inference(resolve,[$cnf( $equal(divide(divide(X_14,X_13),X_14),zero) )],[refute_0_22,refute_0_23]) ).

cnf(refute_0_25,plain,
    less_equal(divide(divide(X_14,X_14),divide(X_13,X_14)),zero),
    inference(resolve,[$cnf( less_equal(divide(divide(X_14,X_14),divide(X_13,X_14)),divide(divide(X_14,X_13),X_14)) )],[refute_0_18,refute_0_24]) ).

cnf(refute_0_26,plain,
    less_equal(divide(divide(X_18,X_18),divide(divide(X_18,Y),X_18)),zero),
    inference(subst,[],[refute_0_25:[bind(X_13,$fot(divide(X_18,Y))),bind(X_14,$fot(X_18))]]) ).

cnf(refute_0_27,plain,
    divide(divide(X_18,Y),X_18) = zero,
    inference(subst,[],[refute_0_21:[bind(X_7,$fot(X_18))]]) ).

cnf(refute_0_28,plain,
    ( ~ less_equal(divide(divide(X_18,X_18),divide(divide(X_18,Y),X_18)),zero)
    | divide(divide(X_18,Y),X_18) != zero
    | less_equal(divide(divide(X_18,X_18),zero),zero) ),
    introduced(tautology,[equality,[$cnf( less_equal(divide(divide(X_18,X_18),divide(divide(X_18,Y),X_18)),zero) ),[0,1],$fot(zero)]]) ).

cnf(refute_0_29,plain,
    ( ~ less_equal(divide(divide(X_18,X_18),divide(divide(X_18,Y),X_18)),zero)
    | less_equal(divide(divide(X_18,X_18),zero),zero) ),
    inference(resolve,[$cnf( $equal(divide(divide(X_18,Y),X_18),zero) )],[refute_0_27,refute_0_28]) ).

cnf(refute_0_30,plain,
    less_equal(divide(divide(X_18,X_18),zero),zero),
    inference(resolve,[$cnf( less_equal(divide(divide(X_18,X_18),divide(divide(X_18,Y),X_18)),zero) )],[refute_0_26,refute_0_29]) ).

cnf(refute_0_31,plain,
    ( ~ less_equal(divide(divide(X_18,X_18),zero),zero)
    | ~ less_equal(zero,divide(divide(X_18,X_18),zero))
    | divide(divide(X_18,X_18),zero) = zero ),
    inference(subst,[],[less_equal_and_equal:[bind(X,$fot(divide(divide(X_18,X_18),zero))),bind(Y,$fot(zero))]]) ).

cnf(refute_0_32,plain,
    ( ~ less_equal(zero,divide(divide(X_18,X_18),zero))
    | divide(divide(X_18,X_18),zero) = zero ),
    inference(resolve,[$cnf( less_equal(divide(divide(X_18,X_18),zero),zero) )],[refute_0_30,refute_0_31]) ).

cnf(refute_0_33,plain,
    less_equal(zero,divide(divide(X_18,X_18),zero)),
    inference(subst,[],[zero_is_smallest:[bind(X,$fot(divide(divide(X_18,X_18),zero)))]]) ).

cnf(refute_0_34,plain,
    divide(divide(X_18,X_18),zero) = zero,
    inference(resolve,[$cnf( less_equal(zero,divide(divide(X_18,X_18),zero)) )],[refute_0_33,refute_0_32]) ).

cnf(refute_0_35,plain,
    divide(divide(X_31,X_31),zero) = zero,
    inference(subst,[],[refute_0_34:[bind(X_18,$fot(X_31))]]) ).

cnf(refute_0_36,plain,
    ( divide(divide(X_31,X_31),zero) != zero
    | zero != zero
    | divide(divide(X_31,X_31),zero) = zero ),
    introduced(tautology,[equality,[$cnf( ~ $equal(divide(divide(X_31,X_31),zero),zero) ),[0],$fot(zero)]]) ).

cnf(refute_0_37,plain,
    ( zero != zero
    | divide(divide(X_31,X_31),zero) = zero ),
    inference(resolve,[$cnf( $equal(divide(divide(X_31,X_31),zero),zero) )],[refute_0_35,refute_0_36]) ).

cnf(refute_0_38,plain,
    ( zero != zero
    | less_equal(divide(X_31,X_31),zero) ),
    inference(resolve,[$cnf( $equal(divide(divide(X_31,X_31),zero),zero) )],[refute_0_37,refute_0_17]) ).

cnf(refute_0_39,plain,
    zero = zero,
    introduced(tautology,[refl,[$fot(zero)]]) ).

cnf(refute_0_40,plain,
    less_equal(divide(X_31,X_31),zero),
    inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_39,refute_0_38]) ).

cnf(refute_0_41,plain,
    less_equal(divide(X_32,X_32),zero),
    inference(subst,[],[refute_0_40:[bind(X_31,$fot(X_32))]]) ).

cnf(refute_0_42,plain,
    ( ~ less_equal(zero,divide(X_32,X_32))
    | zero = divide(X_32,X_32) ),
    inference(resolve,[$cnf( less_equal(divide(X_32,X_32),zero) )],[refute_0_41,refute_0_16]) ).

cnf(refute_0_43,plain,
    less_equal(zero,divide(X_32,X_32)),
    inference(subst,[],[zero_is_smallest:[bind(X,$fot(divide(X_32,X_32)))]]) ).

cnf(refute_0_44,plain,
    zero = divide(X_32,X_32),
    inference(resolve,[$cnf( less_equal(zero,divide(X_32,X_32)) )],[refute_0_43,refute_0_42]) ).

cnf(refute_0_45,plain,
    zero = divide(divide(X_12,zero),divide(X_12,zero)),
    inference(subst,[],[refute_0_44:[bind(X_32,$fot(divide(X_12,zero)))]]) ).

cnf(refute_0_46,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_47,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_48,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_46,refute_0_47]) ).

cnf(refute_0_49,plain,
    ( zero != divide(divide(X_12,zero),divide(X_12,zero))
    | divide(divide(X_12,zero),divide(X_12,zero)) = zero ),
    inference(subst,[],[refute_0_48:[bind(X0,$fot(zero)),bind(Y0,$fot(divide(divide(X_12,zero),divide(X_12,zero))))]]) ).

cnf(refute_0_50,plain,
    divide(divide(X_12,zero),divide(X_12,zero)) = zero,
    inference(resolve,[$cnf( $equal(zero,divide(divide(X_12,zero),divide(X_12,zero))) )],[refute_0_45,refute_0_49]) ).

cnf(refute_0_51,plain,
    ( ~ less_equal(divide(divide(X_12,divide(X_12,zero)),zero),divide(divide(X_12,zero),divide(X_12,zero)))
    | divide(divide(X_12,zero),divide(X_12,zero)) != zero
    | less_equal(divide(divide(X_12,divide(X_12,zero)),zero),zero) ),
    introduced(tautology,[equality,[$cnf( less_equal(divide(divide(X_12,divide(X_12,zero)),zero),divide(divide(X_12,zero),divide(X_12,zero))) ),[1],$fot(zero)]]) ).

cnf(refute_0_52,plain,
    ( ~ less_equal(divide(divide(X_12,divide(X_12,zero)),zero),divide(divide(X_12,zero),divide(X_12,zero)))
    | less_equal(divide(divide(X_12,divide(X_12,zero)),zero),zero) ),
    inference(resolve,[$cnf( $equal(divide(divide(X_12,zero),divide(X_12,zero)),zero) )],[refute_0_50,refute_0_51]) ).

cnf(refute_0_53,plain,
    less_equal(divide(divide(X_12,divide(X_12,zero)),zero),zero),
    inference(resolve,[$cnf( less_equal(divide(divide(X_12,divide(X_12,zero)),zero),divide(divide(X_12,zero),divide(X_12,zero))) )],[refute_0_15,refute_0_52]) ).

cnf(refute_0_54,plain,
    less_equal(divide(divide(X_46,divide(X_46,zero)),zero),zero),
    inference(subst,[],[refute_0_53:[bind(X_12,$fot(X_46))]]) ).

cnf(refute_0_55,plain,
    zero = divide(divide(X_46,divide(X_46,zero)),zero),
    inference(resolve,[$cnf( less_equal(divide(divide(X_46,divide(X_46,zero)),zero),zero) )],[refute_0_54,refute_0_6]) ).

cnf(refute_0_56,plain,
    zero = divide(divide(X_47,divide(X_47,zero)),zero),
    inference(subst,[],[refute_0_55:[bind(X_46,$fot(X_47))]]) ).

cnf(refute_0_57,plain,
    ( zero != divide(divide(X_47,divide(X_47,zero)),zero)
    | divide(divide(X_47,divide(X_47,zero)),zero) = zero ),
    inference(subst,[],[refute_0_48:[bind(X0,$fot(zero)),bind(Y0,$fot(divide(divide(X_47,divide(X_47,zero)),zero)))]]) ).

cnf(refute_0_58,plain,
    divide(divide(X_47,divide(X_47,zero)),zero) = zero,
    inference(resolve,[$cnf( $equal(zero,divide(divide(X_47,divide(X_47,zero)),zero)) )],[refute_0_56,refute_0_57]) ).

cnf(refute_0_59,plain,
    ( divide(divide(X_47,divide(X_47,zero)),zero) != zero
    | zero != zero
    | divide(divide(X_47,divide(X_47,zero)),zero) = zero ),
    introduced(tautology,[equality,[$cnf( ~ $equal(divide(divide(X_47,divide(X_47,zero)),zero),zero) ),[0],$fot(zero)]]) ).

cnf(refute_0_60,plain,
    ( zero != zero
    | divide(divide(X_47,divide(X_47,zero)),zero) = zero ),
    inference(resolve,[$cnf( $equal(divide(divide(X_47,divide(X_47,zero)),zero),zero) )],[refute_0_58,refute_0_59]) ).

cnf(refute_0_61,plain,
    ( zero != zero
    | less_equal(divide(X_47,divide(X_47,zero)),zero) ),
    inference(resolve,[$cnf( $equal(divide(divide(X_47,divide(X_47,zero)),zero),zero) )],[refute_0_60,refute_0_5]) ).

cnf(refute_0_62,plain,
    less_equal(divide(X_47,divide(X_47,zero)),zero),
    inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_39,refute_0_61]) ).

cnf(refute_0_63,plain,
    less_equal(divide(X_48,divide(X_48,zero)),zero),
    inference(subst,[],[refute_0_62:[bind(X_47,$fot(X_48))]]) ).

cnf(refute_0_64,plain,
    zero = divide(X_48,divide(X_48,zero)),
    inference(resolve,[$cnf( less_equal(divide(X_48,divide(X_48,zero)),zero) )],[refute_0_63,refute_0_4]) ).

cnf(refute_0_65,plain,
    zero = divide(X,divide(X,zero)),
    inference(subst,[],[refute_0_64:[bind(X_48,$fot(X))]]) ).

cnf(refute_0_66,plain,
    ( zero != divide(X,divide(X,zero))
    | divide(X,divide(X,zero)) = zero ),
    inference(subst,[],[refute_0_48:[bind(X0,$fot(zero)),bind(Y0,$fot(divide(X,divide(X,zero))))]]) ).

cnf(refute_0_67,plain,
    divide(X,divide(X,zero)) = zero,
    inference(resolve,[$cnf( $equal(zero,divide(X,divide(X,zero))) )],[refute_0_65,refute_0_66]) ).

cnf(refute_0_68,plain,
    ( divide(X,divide(X,zero)) != zero
    | zero != zero
    | divide(X,divide(X,zero)) = zero ),
    introduced(tautology,[equality,[$cnf( ~ $equal(divide(X,divide(X,zero)),zero) ),[0],$fot(zero)]]) ).

cnf(refute_0_69,plain,
    ( zero != zero
    | divide(X,divide(X,zero)) = zero ),
    inference(resolve,[$cnf( $equal(divide(X,divide(X,zero)),zero) )],[refute_0_67,refute_0_68]) ).

cnf(refute_0_70,plain,
    ( zero != zero
    | less_equal(X,divide(X,zero)) ),
    inference(resolve,[$cnf( $equal(divide(X,divide(X,zero)),zero) )],[refute_0_69,refute_0_0]) ).

cnf(refute_0_71,plain,
    less_equal(X,divide(X,zero)),
    inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_39,refute_0_70]) ).

cnf(refute_0_72,plain,
    less_equal(X_125,divide(X_125,zero)),
    inference(subst,[],[refute_0_71:[bind(X,$fot(X_125))]]) ).

cnf(refute_0_73,plain,
    less_equal(divide(X_30,Y),X_30),
    inference(subst,[],[quotient_smaller_than_numerator:[bind(X,$fot(X_30))]]) ).

cnf(refute_0_74,plain,
    ( ~ less_equal(X_30,divide(X_30,Y))
    | ~ less_equal(divide(X_30,Y),X_30)
    | divide(X_30,Y) = X_30 ),
    inference(subst,[],[less_equal_and_equal:[bind(X,$fot(divide(X_30,Y))),bind(Y,$fot(X_30))]]) ).

cnf(refute_0_75,plain,
    ( ~ less_equal(X_30,divide(X_30,Y))
    | divide(X_30,Y) = X_30 ),
    inference(resolve,[$cnf( less_equal(divide(X_30,Y),X_30) )],[refute_0_73,refute_0_74]) ).

cnf(refute_0_76,plain,
    ( ~ less_equal(X_125,divide(X_125,zero))
    | divide(X_125,zero) = X_125 ),
    inference(subst,[],[refute_0_75:[bind(Y,$fot(zero)),bind(X_30,$fot(X_125))]]) ).

cnf(refute_0_77,plain,
    divide(X_125,zero) = X_125,
    inference(resolve,[$cnf( less_equal(X_125,divide(X_125,zero)) )],[refute_0_72,refute_0_76]) ).

cnf(refute_0_78,plain,
    divide(a,zero) = a,
    inference(subst,[],[refute_0_77:[bind(X_125,$fot(a))]]) ).

cnf(refute_0_79,plain,
    ( divide(a,zero) != a
    | a != a
    | divide(a,zero) = a ),
    introduced(tautology,[equality,[$cnf( ~ $equal(divide(a,zero),a) ),[0],$fot(a)]]) ).

cnf(refute_0_80,plain,
    ( a != a
    | divide(a,zero) = a ),
    inference(resolve,[$cnf( $equal(divide(a,zero),a) )],[refute_0_78,refute_0_79]) ).

cnf(refute_0_81,plain,
    a != a,
    inference(resolve,[$cnf( $equal(divide(a,zero),a) )],[refute_0_80,prove_x_divide_zero_is_x]) ).

cnf(refute_0_82,plain,
    a = a,
    introduced(tautology,[refl,[$fot(a)]]) ).

cnf(refute_0_83,plain,
    $false,
    inference(resolve,[$cnf( $equal(a,a) )],[refute_0_82,refute_0_81]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : HEN004-3 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n007.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 13:01:24 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.49  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.49  
% 0.19/0.49  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.50  
%------------------------------------------------------------------------------