TSTP Solution File: HEN010-4 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : HEN010-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 12:58:45 EDT 2022
% Result : Unsatisfiable 0.59s 0.85s
% Output : CNFRefutation 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 30
% Syntax : Number of clauses : 97 ( 50 unt; 0 nHn; 64 RR)
% Number of literals : 165 ( 118 equ; 70 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 86 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(quotient_less_equal2,axiom,
( divide(X,Y) != zero
| less_equal(X,Y) ) ).
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(identity_is_largest,axiom,
less_equal(X,identity) ).
cnf(everything_divide_id_is_zero,axiom,
divide(X,identity) = zero ).
cnf(zero_divide_anything_is_zero,axiom,
divide(zero,X) = zero ).
cnf(x_divide_x_is_zero,axiom,
divide(X,X) = zero ).
cnf(x_divide_zero_is_x,axiom,
divide(a,zero) = a ).
cnf(property_of_divide2,axiom,
( ~ less_equal(X,Y)
| less_equal(divide(Z,Y),divide(Z,X)) ) ).
cnf(one_inversion_equals_three,axiom,
divide(identity,divide(identity,divide(identity,X))) = divide(identity,X) ).
cnf(prove_property_of_inversion,negated_conjecture,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))) ).
cnf(refute_0_0,plain,
less_equal(divide(divide(X_15,zero),divide(a,zero)),divide(divide(X_15,a),zero)),
inference(subst,[],[quotient_property:[bind(X,$fot(X_15)),bind(Y,$fot(a)),bind(Z,$fot(zero))]]) ).
cnf(refute_0_1,plain,
( ~ less_equal(divide(divide(X_15,zero),divide(a,zero)),divide(divide(X_15,a),zero))
| divide(a,zero) != a
| less_equal(divide(divide(X_15,zero),a),divide(divide(X_15,a),zero)) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(X_15,zero),divide(a,zero)),divide(divide(X_15,a),zero)) ),[0,1],$fot(a)]]) ).
cnf(refute_0_2,plain,
( ~ less_equal(divide(divide(X_15,zero),divide(a,zero)),divide(divide(X_15,a),zero))
| less_equal(divide(divide(X_15,zero),a),divide(divide(X_15,a),zero)) ),
inference(resolve,[$cnf( $equal(divide(a,zero),a) )],[x_divide_zero_is_x,refute_0_1]) ).
cnf(refute_0_3,plain,
less_equal(divide(divide(X_15,zero),a),divide(divide(X_15,a),zero)),
inference(resolve,[$cnf( less_equal(divide(divide(X_15,zero),divide(a,zero)),divide(divide(X_15,a),zero)) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ less_equal(divide(divide(X_15,a),zero),divide(divide(X_15,zero),a))
| ~ less_equal(divide(divide(X_15,zero),a),divide(divide(X_15,a),zero))
| divide(divide(X_15,zero),a) = divide(divide(X_15,a),zero) ),
inference(subst,[],[less_equal_and_equal:[bind(X,$fot(divide(divide(X_15,zero),a))),bind(Y,$fot(divide(divide(X_15,a),zero)))]]) ).
cnf(refute_0_5,plain,
( ~ less_equal(divide(divide(X_15,a),zero),divide(divide(X_15,zero),a))
| divide(divide(X_15,zero),a) = divide(divide(X_15,a),zero) ),
inference(resolve,[$cnf( less_equal(divide(divide(X_15,zero),a),divide(divide(X_15,a),zero)) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
less_equal(divide(divide(X_15,X_17),divide(zero,X_17)),divide(divide(X_15,zero),X_17)),
inference(subst,[],[quotient_property:[bind(X,$fot(X_15)),bind(Y,$fot(zero)),bind(Z,$fot(X_17))]]) ).
cnf(refute_0_7,plain,
divide(zero,X_17) = zero,
inference(subst,[],[zero_divide_anything_is_zero:[bind(X,$fot(X_17))]]) ).
cnf(refute_0_8,plain,
( ~ less_equal(divide(divide(X_15,X_17),divide(zero,X_17)),divide(divide(X_15,zero),X_17))
| divide(zero,X_17) != zero
| less_equal(divide(divide(X_15,X_17),zero),divide(divide(X_15,zero),X_17)) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(X_15,X_17),divide(zero,X_17)),divide(divide(X_15,zero),X_17)) ),[0,1],$fot(zero)]]) ).
cnf(refute_0_9,plain,
( ~ less_equal(divide(divide(X_15,X_17),divide(zero,X_17)),divide(divide(X_15,zero),X_17))
| less_equal(divide(divide(X_15,X_17),zero),divide(divide(X_15,zero),X_17)) ),
inference(resolve,[$cnf( $equal(divide(zero,X_17),zero) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
less_equal(divide(divide(X_15,X_17),zero),divide(divide(X_15,zero),X_17)),
inference(resolve,[$cnf( less_equal(divide(divide(X_15,X_17),divide(zero,X_17)),divide(divide(X_15,zero),X_17)) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
less_equal(divide(divide(X_15,a),zero),divide(divide(X_15,zero),a)),
inference(subst,[],[refute_0_10:[bind(X_17,$fot(a))]]) ).
cnf(refute_0_12,plain,
divide(divide(X_15,zero),a) = divide(divide(X_15,a),zero),
inference(resolve,[$cnf( less_equal(divide(divide(X_15,a),zero),divide(divide(X_15,zero),a)) )],[refute_0_11,refute_0_5]) ).
cnf(refute_0_13,plain,
less_equal(divide(divide(X_15,X_17),divide(X_17,X_17)),divide(divide(X_15,X_17),X_17)),
inference(subst,[],[quotient_property:[bind(X,$fot(X_15)),bind(Y,$fot(X_17)),bind(Z,$fot(X_17))]]) ).
cnf(refute_0_14,plain,
divide(X_17,X_17) = zero,
inference(subst,[],[x_divide_x_is_zero:[bind(X,$fot(X_17))]]) ).
cnf(refute_0_15,plain,
( ~ less_equal(divide(divide(X_15,X_17),divide(X_17,X_17)),divide(divide(X_15,X_17),X_17))
| divide(X_17,X_17) != zero
| less_equal(divide(divide(X_15,X_17),zero),divide(divide(X_15,X_17),X_17)) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(X_15,X_17),divide(X_17,X_17)),divide(divide(X_15,X_17),X_17)) ),[0,1],$fot(zero)]]) ).
cnf(refute_0_16,plain,
( ~ less_equal(divide(divide(X_15,X_17),divide(X_17,X_17)),divide(divide(X_15,X_17),X_17))
| less_equal(divide(divide(X_15,X_17),zero),divide(divide(X_15,X_17),X_17)) ),
inference(resolve,[$cnf( $equal(divide(X_17,X_17),zero) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
less_equal(divide(divide(X_15,X_17),zero),divide(divide(X_15,X_17),X_17)),
inference(resolve,[$cnf( less_equal(divide(divide(X_15,X_17),divide(X_17,X_17)),divide(divide(X_15,X_17),X_17)) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ less_equal(divide(divide(X_15,X_17),X_17),divide(divide(X_15,X_17),zero))
| ~ less_equal(divide(divide(X_15,X_17),zero),divide(divide(X_15,X_17),X_17))
| divide(divide(X_15,X_17),zero) = divide(divide(X_15,X_17),X_17) ),
inference(subst,[],[less_equal_and_equal:[bind(X,$fot(divide(divide(X_15,X_17),zero))),bind(Y,$fot(divide(divide(X_15,X_17),X_17)))]]) ).
cnf(refute_0_19,plain,
( ~ less_equal(divide(divide(X_15,X_17),X_17),divide(divide(X_15,X_17),zero))
| divide(divide(X_15,X_17),zero) = divide(divide(X_15,X_17),X_17) ),
inference(resolve,[$cnf( less_equal(divide(divide(X_15,X_17),zero),divide(divide(X_15,X_17),X_17)) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
less_equal(zero,X_101),
inference(subst,[],[zero_is_smallest:[bind(X,$fot(X_101))]]) ).
cnf(refute_0_21,plain,
( ~ less_equal(zero,X_101)
| less_equal(divide(X_102,X_101),divide(X_102,zero)) ),
inference(subst,[],[property_of_divide2:[bind(X,$fot(zero)),bind(Y,$fot(X_101)),bind(Z,$fot(X_102))]]) ).
cnf(refute_0_22,plain,
less_equal(divide(X_102,X_101),divide(X_102,zero)),
inference(resolve,[$cnf( less_equal(zero,X_101) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
less_equal(divide(divide(X_15,X_17),X_17),divide(divide(X_15,X_17),zero)),
inference(subst,[],[refute_0_22:[bind(X_101,$fot(X_17)),bind(X_102,$fot(divide(X_15,X_17)))]]) ).
cnf(refute_0_24,plain,
divide(divide(X_15,X_17),zero) = divide(divide(X_15,X_17),X_17),
inference(resolve,[$cnf( less_equal(divide(divide(X_15,X_17),X_17),divide(divide(X_15,X_17),zero)) )],[refute_0_23,refute_0_19]) ).
cnf(refute_0_25,plain,
divide(divide(X_15,a),zero) = divide(divide(X_15,a),a),
inference(subst,[],[refute_0_24:[bind(X_17,$fot(a))]]) ).
cnf(refute_0_26,plain,
( divide(divide(X_15,a),zero) != divide(divide(X_15,a),a)
| divide(divide(X_15,zero),a) != divide(divide(X_15,a),zero)
| divide(divide(X_15,zero),a) = divide(divide(X_15,a),a) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(X_15,zero),a),divide(divide(X_15,a),zero)) ),[1],$fot(divide(divide(X_15,a),a))]]) ).
cnf(refute_0_27,plain,
( divide(divide(X_15,zero),a) != divide(divide(X_15,a),zero)
| divide(divide(X_15,zero),a) = divide(divide(X_15,a),a) ),
inference(resolve,[$cnf( $equal(divide(divide(X_15,a),zero),divide(divide(X_15,a),a)) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
divide(divide(X_15,zero),a) = divide(divide(X_15,a),a),
inference(resolve,[$cnf( $equal(divide(divide(X_15,zero),a),divide(divide(X_15,a),zero)) )],[refute_0_12,refute_0_27]) ).
cnf(refute_0_29,plain,
divide(divide(identity,zero),a) = divide(divide(identity,a),a),
inference(subst,[],[refute_0_28:[bind(X_15,$fot(identity))]]) ).
cnf(refute_0_30,plain,
( divide(identity,divide(identity,zero)) != zero
| less_equal(identity,divide(identity,zero)) ),
inference(subst,[],[quotient_less_equal2:[bind(X,$fot(identity)),bind(Y,$fot(divide(identity,zero)))]]) ).
cnf(refute_0_31,plain,
divide(identity,divide(identity,divide(identity,identity))) = divide(identity,identity),
inference(subst,[],[one_inversion_equals_three:[bind(X,$fot(identity))]]) ).
cnf(refute_0_32,plain,
divide(identity,identity) = zero,
inference(subst,[],[everything_divide_id_is_zero:[bind(X,$fot(identity))]]) ).
cnf(refute_0_33,plain,
( divide(identity,divide(identity,divide(identity,identity))) != divide(identity,identity)
| divide(identity,identity) != zero
| divide(identity,divide(identity,zero)) = divide(identity,identity) ),
introduced(tautology,[equality,[$cnf( $equal(divide(identity,divide(identity,divide(identity,identity))),divide(identity,identity)) ),[0,1,1],$fot(zero)]]) ).
cnf(refute_0_34,plain,
( divide(identity,divide(identity,divide(identity,identity))) != divide(identity,identity)
| divide(identity,divide(identity,zero)) = divide(identity,identity) ),
inference(resolve,[$cnf( $equal(divide(identity,identity),zero) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
divide(identity,divide(identity,zero)) = divide(identity,identity),
inference(resolve,[$cnf( $equal(divide(identity,divide(identity,divide(identity,identity))),divide(identity,identity)) )],[refute_0_31,refute_0_34]) ).
cnf(refute_0_36,plain,
( divide(identity,divide(identity,zero)) != divide(identity,identity)
| divide(identity,identity) != zero
| divide(identity,divide(identity,zero)) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(identity,divide(identity,zero)),zero) ),[0],$fot(divide(identity,identity))]]) ).
cnf(refute_0_37,plain,
( divide(identity,divide(identity,zero)) != divide(identity,identity)
| divide(identity,divide(identity,zero)) = zero ),
inference(resolve,[$cnf( $equal(divide(identity,identity),zero) )],[refute_0_32,refute_0_36]) ).
cnf(refute_0_38,plain,
divide(identity,divide(identity,zero)) = zero,
inference(resolve,[$cnf( $equal(divide(identity,divide(identity,zero)),divide(identity,identity)) )],[refute_0_35,refute_0_37]) ).
cnf(refute_0_39,plain,
( divide(identity,divide(identity,zero)) != zero
| zero != zero
| divide(identity,divide(identity,zero)) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(identity,divide(identity,zero)),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_40,plain,
( zero != zero
| divide(identity,divide(identity,zero)) = zero ),
inference(resolve,[$cnf( $equal(divide(identity,divide(identity,zero)),zero) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( zero != zero
| less_equal(identity,divide(identity,zero)) ),
inference(resolve,[$cnf( $equal(divide(identity,divide(identity,zero)),zero) )],[refute_0_40,refute_0_30]) ).
cnf(refute_0_42,plain,
zero = zero,
introduced(tautology,[refl,[$fot(zero)]]) ).
cnf(refute_0_43,plain,
less_equal(identity,divide(identity,zero)),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_42,refute_0_41]) ).
cnf(refute_0_44,plain,
less_equal(X_170,identity),
inference(subst,[],[identity_is_largest:[bind(X,$fot(X_170))]]) ).
cnf(refute_0_45,plain,
( ~ less_equal(X_170,identity)
| ~ less_equal(identity,X_170)
| X_170 = identity ),
inference(subst,[],[less_equal_and_equal:[bind(X,$fot(X_170)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_46,plain,
( ~ less_equal(identity,X_170)
| X_170 = identity ),
inference(resolve,[$cnf( less_equal(X_170,identity) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
( ~ less_equal(identity,divide(identity,zero))
| divide(identity,zero) = identity ),
inference(subst,[],[refute_0_46:[bind(X_170,$fot(divide(identity,zero)))]]) ).
cnf(refute_0_48,plain,
divide(identity,zero) = identity,
inference(resolve,[$cnf( less_equal(identity,divide(identity,zero)) )],[refute_0_43,refute_0_47]) ).
cnf(refute_0_49,plain,
( divide(divide(identity,zero),a) != divide(divide(identity,a),a)
| divide(identity,zero) != identity
| divide(identity,a) = divide(divide(identity,a),a) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(identity,zero),a),divide(divide(identity,a),a)) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_50,plain,
( divide(divide(identity,zero),a) != divide(divide(identity,a),a)
| divide(identity,a) = divide(divide(identity,a),a) ),
inference(resolve,[$cnf( $equal(divide(identity,zero),identity) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
divide(identity,a) = divide(divide(identity,a),a),
inference(resolve,[$cnf( $equal(divide(divide(identity,zero),a),divide(divide(identity,a),a)) )],[refute_0_29,refute_0_50]) ).
cnf(refute_0_52,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_53,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_54,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
( divide(identity,a) != divide(divide(identity,a),a)
| divide(divide(identity,a),a) = divide(identity,a) ),
inference(subst,[],[refute_0_54:[bind(X0,$fot(divide(identity,a))),bind(Y0,$fot(divide(divide(identity,a),a)))]]) ).
cnf(refute_0_56,plain,
divide(divide(identity,a),a) = divide(identity,a),
inference(resolve,[$cnf( $equal(divide(identity,a),divide(divide(identity,a),a)) )],[refute_0_51,refute_0_55]) ).
cnf(refute_0_57,plain,
divide(divide(identity,a),zero) = divide(divide(identity,a),a),
inference(subst,[],[refute_0_24:[bind(X_15,$fot(identity)),bind(X_17,$fot(a))]]) ).
cnf(refute_0_58,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_59,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_54,refute_0_58]) ).
cnf(refute_0_60,plain,
( divide(divide(identity,a),a) != divide(identity,a)
| divide(divide(identity,a),zero) != divide(divide(identity,a),a)
| divide(divide(identity,a),zero) = divide(identity,a) ),
inference(subst,[],[refute_0_59:[bind(X0,$fot(divide(divide(identity,a),zero))),bind(Y0,$fot(divide(divide(identity,a),a))),bind(Z0,$fot(divide(identity,a)))]]) ).
cnf(refute_0_61,plain,
( divide(divide(identity,a),a) != divide(identity,a)
| divide(divide(identity,a),zero) = divide(identity,a) ),
inference(resolve,[$cnf( $equal(divide(divide(identity,a),zero),divide(divide(identity,a),a)) )],[refute_0_57,refute_0_60]) ).
cnf(refute_0_62,plain,
divide(divide(identity,a),zero) = divide(identity,a),
inference(resolve,[$cnf( $equal(divide(divide(identity,a),a),divide(identity,a)) )],[refute_0_56,refute_0_61]) ).
cnf(refute_0_63,plain,
divide(divide(identity,divide(identity,divide(identity,X))),zero) = divide(divide(identity,divide(identity,divide(identity,X))),divide(identity,divide(identity,X))),
inference(subst,[],[refute_0_24:[bind(X_15,$fot(identity)),bind(X_17,$fot(divide(identity,divide(identity,X))))]]) ).
cnf(refute_0_64,plain,
( divide(divide(identity,divide(identity,divide(identity,X))),zero) != divide(divide(identity,divide(identity,divide(identity,X))),divide(identity,divide(identity,X)))
| divide(identity,divide(identity,divide(identity,X))) != divide(identity,X)
| divide(divide(identity,divide(identity,divide(identity,X))),zero) = divide(divide(identity,X),divide(identity,divide(identity,X))) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(identity,divide(identity,divide(identity,X))),zero),divide(divide(identity,divide(identity,divide(identity,X))),divide(identity,divide(identity,X)))) ),[1,0],$fot(divide(identity,X))]]) ).
cnf(refute_0_65,plain,
( divide(divide(identity,divide(identity,divide(identity,X))),zero) != divide(divide(identity,divide(identity,divide(identity,X))),divide(identity,divide(identity,X)))
| divide(divide(identity,divide(identity,divide(identity,X))),zero) = divide(divide(identity,X),divide(identity,divide(identity,X))) ),
inference(resolve,[$cnf( $equal(divide(identity,divide(identity,divide(identity,X))),divide(identity,X)) )],[one_inversion_equals_three,refute_0_64]) ).
cnf(refute_0_66,plain,
divide(divide(identity,divide(identity,divide(identity,X))),zero) = divide(divide(identity,X),divide(identity,divide(identity,X))),
inference(resolve,[$cnf( $equal(divide(divide(identity,divide(identity,divide(identity,X))),zero),divide(divide(identity,divide(identity,divide(identity,X))),divide(identity,divide(identity,X)))) )],[refute_0_63,refute_0_65]) ).
cnf(refute_0_67,plain,
divide(divide(identity,divide(identity,divide(identity,X))),zero) = divide(divide(identity,divide(identity,divide(identity,X))),zero),
introduced(tautology,[refl,[$fot(divide(divide(identity,divide(identity,divide(identity,X))),zero))]]) ).
cnf(refute_0_68,plain,
( divide(divide(identity,divide(identity,divide(identity,X))),zero) != divide(divide(identity,divide(identity,divide(identity,X))),zero)
| divide(identity,divide(identity,divide(identity,X))) != divide(identity,X)
| divide(divide(identity,divide(identity,divide(identity,X))),zero) = divide(divide(identity,X),zero) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(identity,divide(identity,divide(identity,X))),zero),divide(divide(identity,divide(identity,divide(identity,X))),zero)) ),[1,0],$fot(divide(identity,X))]]) ).
cnf(refute_0_69,plain,
( divide(identity,divide(identity,divide(identity,X))) != divide(identity,X)
| divide(divide(identity,divide(identity,divide(identity,X))),zero) = divide(divide(identity,X),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(identity,divide(identity,divide(identity,X))),zero),divide(divide(identity,divide(identity,divide(identity,X))),zero)) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
divide(divide(identity,divide(identity,divide(identity,X))),zero) = divide(divide(identity,X),zero),
inference(resolve,[$cnf( $equal(divide(identity,divide(identity,divide(identity,X))),divide(identity,X)) )],[one_inversion_equals_three,refute_0_69]) ).
cnf(refute_0_71,plain,
( divide(divide(identity,divide(identity,divide(identity,X))),zero) != divide(divide(identity,X),divide(identity,divide(identity,X)))
| divide(divide(identity,divide(identity,divide(identity,X))),zero) != divide(divide(identity,X),zero)
| divide(divide(identity,X),zero) = divide(divide(identity,X),divide(identity,divide(identity,X))) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(identity,divide(identity,divide(identity,X))),zero),divide(divide(identity,X),divide(identity,divide(identity,X)))) ),[0],$fot(divide(divide(identity,X),zero))]]) ).
cnf(refute_0_72,plain,
( divide(divide(identity,divide(identity,divide(identity,X))),zero) != divide(divide(identity,X),divide(identity,divide(identity,X)))
| divide(divide(identity,X),zero) = divide(divide(identity,X),divide(identity,divide(identity,X))) ),
inference(resolve,[$cnf( $equal(divide(divide(identity,divide(identity,divide(identity,X))),zero),divide(divide(identity,X),zero)) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
divide(divide(identity,X),zero) = divide(divide(identity,X),divide(identity,divide(identity,X))),
inference(resolve,[$cnf( $equal(divide(divide(identity,divide(identity,divide(identity,X))),zero),divide(divide(identity,X),divide(identity,divide(identity,X)))) )],[refute_0_66,refute_0_72]) ).
cnf(refute_0_74,plain,
( divide(divide(identity,X),zero) != divide(divide(identity,X),divide(identity,divide(identity,X)))
| divide(divide(identity,X),divide(identity,divide(identity,X))) = divide(divide(identity,X),zero) ),
inference(subst,[],[refute_0_54:[bind(X0,$fot(divide(divide(identity,X),zero))),bind(Y0,$fot(divide(divide(identity,X),divide(identity,divide(identity,X)))))]]) ).
cnf(refute_0_75,plain,
divide(divide(identity,X),divide(identity,divide(identity,X))) = divide(divide(identity,X),zero),
inference(resolve,[$cnf( $equal(divide(divide(identity,X),zero),divide(divide(identity,X),divide(identity,divide(identity,X)))) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
divide(divide(identity,a),divide(identity,divide(identity,a))) = divide(divide(identity,a),zero),
inference(subst,[],[refute_0_75:[bind(X,$fot(a))]]) ).
cnf(refute_0_77,plain,
( divide(divide(identity,a),divide(identity,divide(identity,a))) != divide(divide(identity,a),zero)
| divide(divide(identity,a),zero) != divide(identity,a)
| divide(divide(identity,a),divide(identity,divide(identity,a))) = divide(identity,a) ),
inference(subst,[],[refute_0_59:[bind(X0,$fot(divide(divide(identity,a),divide(identity,divide(identity,a))))),bind(Y0,$fot(divide(divide(identity,a),zero))),bind(Z0,$fot(divide(identity,a)))]]) ).
cnf(refute_0_78,plain,
( divide(divide(identity,a),zero) != divide(identity,a)
| divide(divide(identity,a),divide(identity,divide(identity,a))) = divide(identity,a) ),
inference(resolve,[$cnf( $equal(divide(divide(identity,a),divide(identity,divide(identity,a))),divide(divide(identity,a),zero)) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
divide(divide(identity,a),divide(identity,divide(identity,a))) = divide(identity,a),
inference(resolve,[$cnf( $equal(divide(divide(identity,a),zero),divide(identity,a)) )],[refute_0_62,refute_0_78]) ).
cnf(refute_0_80,plain,
( divide(divide(identity,a),divide(identity,divide(identity,a))) != divide(identity,a)
| divide(identity,a) != divide(identity,a)
| divide(identity,a) = divide(divide(identity,a),divide(identity,divide(identity,a))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) ),[1],$fot(divide(identity,a))]]) ).
cnf(refute_0_81,plain,
( divide(identity,a) != divide(identity,a)
| divide(identity,a) = divide(divide(identity,a),divide(identity,divide(identity,a))) ),
inference(resolve,[$cnf( $equal(divide(divide(identity,a),divide(identity,divide(identity,a))),divide(identity,a)) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
divide(identity,a) != divide(identity,a),
inference(resolve,[$cnf( $equal(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) )],[refute_0_81,prove_property_of_inversion]) ).
cnf(refute_0_83,plain,
divide(identity,a) = divide(identity,a),
introduced(tautology,[refl,[$fot(divide(identity,a))]]) ).
cnf(refute_0_84,plain,
$false,
inference(resolve,[$cnf( $equal(divide(identity,a),divide(identity,a)) )],[refute_0_83,refute_0_82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HEN010-4 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n008.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 : Fri Jul 1 14:35:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.59/0.85 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.59/0.85
% 0.59/0.85 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.69/0.87
%------------------------------------------------------------------------------