TSTP Solution File: HEN009-3 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : HEN009-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n004.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 12:58:42 EDT 2022
% Result : Unsatisfiable 1.17s 1.34s
% Output : CNFRefutation 1.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 52
% Syntax : Number of clauses : 236 ( 105 unt; 0 nHn; 189 RR)
% Number of literals : 417 ( 208 equ; 183 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 108 ( 27 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(identity_is_largest,axiom,
less_equal(X,identity) ).
cnf(id_divide_a_is_b,hypothesis,
divide(identity,a) = b ).
cnf(id_divide_b_is_c,hypothesis,
divide(identity,b) = c ).
cnf(id_divide_c_is_d,hypothesis,
divide(identity,c) = d ).
cnf(prove_b_equals_d,negated_conjecture,
b != d ).
cnf(refute_0_0,plain,
less_equal(divide(d,a),d),
inference(subst,[],[quotient_smaller_than_numerator:[bind(X,$fot(d)),bind(Y,$fot(a))]]) ).
cnf(refute_0_1,plain,
( divide(b,divide(d,a)) != zero
| less_equal(b,divide(d,a)) ),
inference(subst,[],[quotient_less_equal2:[bind(X,$fot(b)),bind(Y,$fot(divide(d,a)))]]) ).
cnf(refute_0_2,plain,
less_equal(zero,X_66),
inference(subst,[],[zero_is_smallest:[bind(X,$fot(X_66))]]) ).
cnf(refute_0_3,plain,
( ~ less_equal(X_66,zero)
| ~ less_equal(zero,X_66)
| zero = X_66 ),
inference(subst,[],[less_equal_and_equal:[bind(X,$fot(zero)),bind(Y,$fot(X_66))]]) ).
cnf(refute_0_4,plain,
( ~ less_equal(X_66,zero)
| zero = X_66 ),
inference(resolve,[$cnf( less_equal(zero,X_66) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ less_equal(divide(b,divide(d,a)),zero)
| zero = divide(b,divide(d,a)) ),
inference(subst,[],[refute_0_4:[bind(X_66,$fot(divide(b,divide(d,a))))]]) ).
cnf(refute_0_6,plain,
( divide(divide(b,divide(d,a)),divide(divide(c,a),divide(d,a))) != zero
| less_equal(divide(b,divide(d,a)),divide(divide(c,a),divide(d,a))) ),
inference(subst,[],[quotient_less_equal2:[bind(X,$fot(divide(b,divide(d,a)))),bind(Y,$fot(divide(divide(c,a),divide(d,a))))]]) ).
cnf(refute_0_7,plain,
less_equal(divide(divide(b,divide(d,a)),divide(divide(c,a),divide(d,a))),divide(divide(b,divide(c,a)),divide(d,a))),
inference(subst,[],[quotient_property:[bind(X,$fot(b)),bind(Y,$fot(divide(c,a))),bind(Z,$fot(divide(d,a)))]]) ).
cnf(refute_0_8,plain,
( ~ less_equal(divide(b,divide(c,a)),divide(d,a))
| divide(divide(b,divide(c,a)),divide(d,a)) = zero ),
inference(subst,[],[quotient_less_equal1:[bind(X,$fot(divide(b,divide(c,a)))),bind(Y,$fot(divide(d,a)))]]) ).
cnf(refute_0_9,plain,
less_equal(divide(divide(identity,a),divide(X_13,a)),divide(divide(identity,X_13),a)),
inference(subst,[],[quotient_property:[bind(X,$fot(identity)),bind(Y,$fot(X_13)),bind(Z,$fot(a))]]) ).
cnf(refute_0_10,plain,
( ~ less_equal(divide(divide(identity,a),divide(X_13,a)),divide(divide(identity,X_13),a))
| divide(identity,a) != b
| less_equal(divide(b,divide(X_13,a)),divide(divide(identity,X_13),a)) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(identity,a),divide(X_13,a)),divide(divide(identity,X_13),a)) ),[0,0],$fot(b)]]) ).
cnf(refute_0_11,plain,
( ~ less_equal(divide(divide(identity,a),divide(X_13,a)),divide(divide(identity,X_13),a))
| less_equal(divide(b,divide(X_13,a)),divide(divide(identity,X_13),a)) ),
inference(resolve,[$cnf( $equal(divide(identity,a),b) )],[id_divide_a_is_b,refute_0_10]) ).
cnf(refute_0_12,plain,
less_equal(divide(b,divide(X_13,a)),divide(divide(identity,X_13),a)),
inference(resolve,[$cnf( less_equal(divide(divide(identity,a),divide(X_13,a)),divide(divide(identity,X_13),a)) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
less_equal(divide(b,divide(c,a)),divide(divide(identity,c),a)),
inference(subst,[],[refute_0_12:[bind(X_13,$fot(c))]]) ).
cnf(refute_0_14,plain,
( ~ less_equal(divide(b,divide(c,a)),divide(divide(identity,c),a))
| divide(identity,c) != d
| less_equal(divide(b,divide(c,a)),divide(d,a)) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(b,divide(c,a)),divide(divide(identity,c),a)) ),[1,0],$fot(d)]]) ).
cnf(refute_0_15,plain,
( ~ less_equal(divide(b,divide(c,a)),divide(divide(identity,c),a))
| less_equal(divide(b,divide(c,a)),divide(d,a)) ),
inference(resolve,[$cnf( $equal(divide(identity,c),d) )],[id_divide_c_is_d,refute_0_14]) ).
cnf(refute_0_16,plain,
less_equal(divide(b,divide(c,a)),divide(d,a)),
inference(resolve,[$cnf( less_equal(divide(b,divide(c,a)),divide(divide(identity,c),a)) )],[refute_0_13,refute_0_15]) ).
cnf(refute_0_17,plain,
divide(divide(b,divide(c,a)),divide(d,a)) = zero,
inference(resolve,[$cnf( less_equal(divide(b,divide(c,a)),divide(d,a)) )],[refute_0_16,refute_0_8]) ).
cnf(refute_0_18,plain,
( ~ less_equal(divide(divide(b,divide(d,a)),divide(divide(c,a),divide(d,a))),divide(divide(b,divide(c,a)),divide(d,a)))
| divide(divide(b,divide(c,a)),divide(d,a)) != zero
| less_equal(divide(divide(b,divide(d,a)),divide(divide(c,a),divide(d,a))),zero) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(b,divide(d,a)),divide(divide(c,a),divide(d,a))),divide(divide(b,divide(c,a)),divide(d,a))) ),[1],$fot(zero)]]) ).
cnf(refute_0_19,plain,
( ~ less_equal(divide(divide(b,divide(d,a)),divide(divide(c,a),divide(d,a))),divide(divide(b,divide(c,a)),divide(d,a)))
| less_equal(divide(divide(b,divide(d,a)),divide(divide(c,a),divide(d,a))),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(b,divide(c,a)),divide(d,a)),zero) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
less_equal(divide(divide(b,divide(d,a)),divide(divide(c,a),divide(d,a))),zero),
inference(resolve,[$cnf( less_equal(divide(divide(b,divide(d,a)),divide(divide(c,a),divide(d,a))),divide(divide(b,divide(c,a)),divide(d,a))) )],[refute_0_7,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ less_equal(divide(divide(b,divide(d,a)),divide(divide(c,a),divide(d,a))),zero)
| ~ less_equal(zero,divide(divide(b,divide(d,a)),divide(divide(c,a),divide(d,a))))
| divide(divide(b,divide(d,a)),divide(divide(c,a),divide(d,a))) = zero ),
inference(subst,[],[less_equal_and_equal:[bind(X,$fot(divide(divide(b,divide(d,a)),divide(divide(c,a),divide(d,a))))),bind(Y,$fot(zero))]]) ).
cnf(refute_0_22,plain,
( ~ less_equal(zero,divide(divide(b,divide(d,a)),divide(divide(c,a),divide(d,a))))
| divide(divide(b,divide(d,a)),divide(divide(c,a),divide(d,a))) = zero ),
inference(resolve,[$cnf( less_equal(divide(divide(b,divide(d,a)),divide(divide(c,a),divide(d,a))),zero) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
less_equal(zero,divide(divide(b,divide(d,a)),divide(divide(c,a),divide(d,a)))),
inference(subst,[],[zero_is_smallest:[bind(X,$fot(divide(divide(b,divide(d,a)),divide(divide(c,a),divide(d,a)))))]]) ).
cnf(refute_0_24,plain,
divide(divide(b,divide(d,a)),divide(divide(c,a),divide(d,a))) = zero,
inference(resolve,[$cnf( less_equal(zero,divide(divide(b,divide(d,a)),divide(divide(c,a),divide(d,a)))) )],[refute_0_23,refute_0_22]) ).
cnf(refute_0_25,plain,
( divide(divide(b,divide(d,a)),divide(divide(c,a),divide(d,a))) != zero
| zero != zero
| divide(divide(b,divide(d,a)),divide(divide(c,a),divide(d,a))) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(divide(b,divide(d,a)),divide(divide(c,a),divide(d,a))),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_26,plain,
( zero != zero
| divide(divide(b,divide(d,a)),divide(divide(c,a),divide(d,a))) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(b,divide(d,a)),divide(divide(c,a),divide(d,a))),zero) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
( zero != zero
| less_equal(divide(b,divide(d,a)),divide(divide(c,a),divide(d,a))) ),
inference(resolve,[$cnf( $equal(divide(divide(b,divide(d,a)),divide(divide(c,a),divide(d,a))),zero) )],[refute_0_26,refute_0_6]) ).
cnf(refute_0_28,plain,
zero = zero,
introduced(tautology,[refl,[$fot(zero)]]) ).
cnf(refute_0_29,plain,
less_equal(divide(b,divide(d,a)),divide(divide(c,a),divide(d,a))),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_28,refute_0_27]) ).
cnf(refute_0_30,plain,
less_equal(zero,X_5),
inference(subst,[],[zero_is_smallest:[bind(X,$fot(X_5))]]) ).
cnf(refute_0_31,plain,
( ~ less_equal(zero,X_5)
| divide(zero,X_5) = zero ),
inference(subst,[],[quotient_less_equal1:[bind(X,$fot(zero)),bind(Y,$fot(X_5))]]) ).
cnf(refute_0_32,plain,
divide(zero,X_5) = zero,
inference(resolve,[$cnf( less_equal(zero,X_5) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
divide(zero,divide(d,a)) = zero,
inference(subst,[],[refute_0_32:[bind(X_5,$fot(divide(d,a)))]]) ).
cnf(refute_0_34,plain,
( ~ less_equal(divide(c,a),zero)
| zero = divide(c,a) ),
inference(subst,[],[refute_0_4:[bind(X_66,$fot(divide(c,a)))]]) ).
cnf(refute_0_35,plain,
( divide(divide(c,a),zero) != zero
| less_equal(divide(c,a),zero) ),
inference(subst,[],[quotient_less_equal2:[bind(X,$fot(divide(c,a))),bind(Y,$fot(zero))]]) ).
cnf(refute_0_36,plain,
( ~ less_equal(divide(divide(c,a),zero),zero)
| zero = divide(divide(c,a),zero) ),
inference(subst,[],[refute_0_4:[bind(X_66,$fot(divide(divide(c,a),zero)))]]) ).
cnf(refute_0_37,plain,
less_equal(divide(divide(c,Z),divide(divide(a,b),Z)),divide(divide(c,divide(a,b)),Z)),
inference(subst,[],[quotient_property:[bind(X,$fot(c)),bind(Y,$fot(divide(a,b)))]]) ).
cnf(refute_0_38,plain,
less_equal(divide(divide(identity,b),divide(X_13,b)),divide(divide(identity,X_13),b)),
inference(subst,[],[quotient_property:[bind(X,$fot(identity)),bind(Y,$fot(X_13)),bind(Z,$fot(b))]]) ).
cnf(refute_0_39,plain,
( ~ less_equal(divide(divide(identity,b),divide(X_13,b)),divide(divide(identity,X_13),b))
| divide(identity,b) != c
| less_equal(divide(c,divide(X_13,b)),divide(divide(identity,X_13),b)) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(identity,b),divide(X_13,b)),divide(divide(identity,X_13),b)) ),[0,0],$fot(c)]]) ).
cnf(refute_0_40,plain,
( ~ less_equal(divide(divide(identity,b),divide(X_13,b)),divide(divide(identity,X_13),b))
| less_equal(divide(c,divide(X_13,b)),divide(divide(identity,X_13),b)) ),
inference(resolve,[$cnf( $equal(divide(identity,b),c) )],[id_divide_b_is_c,refute_0_39]) ).
cnf(refute_0_41,plain,
less_equal(divide(c,divide(X_13,b)),divide(divide(identity,X_13),b)),
inference(resolve,[$cnf( less_equal(divide(divide(identity,b),divide(X_13,b)),divide(divide(identity,X_13),b)) )],[refute_0_38,refute_0_40]) ).
cnf(refute_0_42,plain,
less_equal(divide(c,divide(a,b)),divide(divide(identity,a),b)),
inference(subst,[],[refute_0_41:[bind(X_13,$fot(a))]]) ).
cnf(refute_0_43,plain,
( ~ less_equal(divide(c,divide(a,b)),divide(divide(identity,a),b))
| divide(identity,a) != b
| less_equal(divide(c,divide(a,b)),divide(b,b)) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(c,divide(a,b)),divide(divide(identity,a),b)) ),[1,0],$fot(b)]]) ).
cnf(refute_0_44,plain,
( ~ less_equal(divide(c,divide(a,b)),divide(divide(identity,a),b))
| less_equal(divide(c,divide(a,b)),divide(b,b)) ),
inference(resolve,[$cnf( $equal(divide(identity,a),b) )],[id_divide_a_is_b,refute_0_43]) ).
cnf(refute_0_45,plain,
less_equal(divide(c,divide(a,b)),divide(b,b)),
inference(resolve,[$cnf( less_equal(divide(c,divide(a,b)),divide(divide(identity,a),b)) )],[refute_0_42,refute_0_44]) ).
cnf(refute_0_46,plain,
( ~ less_equal(divide(b,b),divide(c,divide(a,b)))
| ~ less_equal(divide(c,divide(a,b)),divide(b,b))
| divide(c,divide(a,b)) = divide(b,b) ),
inference(subst,[],[less_equal_and_equal:[bind(X,$fot(divide(c,divide(a,b)))),bind(Y,$fot(divide(b,b)))]]) ).
cnf(refute_0_47,plain,
( ~ less_equal(divide(b,b),divide(c,divide(a,b)))
| divide(c,divide(a,b)) = divide(b,b) ),
inference(resolve,[$cnf( less_equal(divide(c,divide(a,b)),divide(b,b)) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
less_equal(divide(divide(X_12,a),divide(identity,a)),divide(divide(X_12,identity),a)),
inference(subst,[],[quotient_property:[bind(X,$fot(X_12)),bind(Y,$fot(identity)),bind(Z,$fot(a))]]) ).
cnf(refute_0_49,plain,
( ~ less_equal(divide(divide(X_12,a),divide(identity,a)),divide(divide(X_12,identity),a))
| divide(identity,a) != b
| less_equal(divide(divide(X_12,a),b),divide(divide(X_12,identity),a)) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(X_12,a),divide(identity,a)),divide(divide(X_12,identity),a)) ),[0,1],$fot(b)]]) ).
cnf(refute_0_50,plain,
( ~ less_equal(divide(divide(X_12,a),divide(identity,a)),divide(divide(X_12,identity),a))
| less_equal(divide(divide(X_12,a),b),divide(divide(X_12,identity),a)) ),
inference(resolve,[$cnf( $equal(divide(identity,a),b) )],[id_divide_a_is_b,refute_0_49]) ).
cnf(refute_0_51,plain,
less_equal(divide(divide(X_12,a),b),divide(divide(X_12,identity),a)),
inference(resolve,[$cnf( less_equal(divide(divide(X_12,a),divide(identity,a)),divide(divide(X_12,identity),a)) )],[refute_0_48,refute_0_50]) ).
cnf(refute_0_52,plain,
divide(zero,a) = zero,
inference(subst,[],[refute_0_32:[bind(X_5,$fot(a))]]) ).
cnf(refute_0_53,plain,
less_equal(X_4,identity),
inference(subst,[],[identity_is_largest:[bind(X,$fot(X_4))]]) ).
cnf(refute_0_54,plain,
( ~ less_equal(X_4,identity)
| divide(X_4,identity) = zero ),
inference(subst,[],[quotient_less_equal1:[bind(X,$fot(X_4)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_55,plain,
divide(X_4,identity) = zero,
inference(resolve,[$cnf( less_equal(X_4,identity) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
divide(X_12,identity) = zero,
inference(subst,[],[refute_0_55:[bind(X_4,$fot(X_12))]]) ).
cnf(refute_0_57,plain,
divide(divide(X_12,identity),a) = divide(divide(X_12,identity),a),
introduced(tautology,[refl,[$fot(divide(divide(X_12,identity),a))]]) ).
cnf(refute_0_58,plain,
( divide(X_12,identity) != zero
| divide(divide(X_12,identity),a) != divide(divide(X_12,identity),a)
| divide(divide(X_12,identity),a) = divide(zero,a) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(X_12,identity),a),divide(divide(X_12,identity),a)) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_59,plain,
( divide(X_12,identity) != zero
| divide(divide(X_12,identity),a) = divide(zero,a) ),
inference(resolve,[$cnf( $equal(divide(divide(X_12,identity),a),divide(divide(X_12,identity),a)) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
divide(divide(X_12,identity),a) = divide(zero,a),
inference(resolve,[$cnf( $equal(divide(X_12,identity),zero) )],[refute_0_56,refute_0_59]) ).
cnf(refute_0_61,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_62,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_63,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_65,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
( divide(divide(X_12,identity),a) != divide(zero,a)
| divide(zero,a) != zero
| divide(divide(X_12,identity),a) = zero ),
inference(subst,[],[refute_0_65:[bind(X0,$fot(divide(divide(X_12,identity),a))),bind(Y0,$fot(divide(zero,a))),bind(Z0,$fot(zero))]]) ).
cnf(refute_0_67,plain,
( divide(zero,a) != zero
| divide(divide(X_12,identity),a) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(X_12,identity),a),divide(zero,a)) )],[refute_0_60,refute_0_66]) ).
cnf(refute_0_68,plain,
divide(divide(X_12,identity),a) = zero,
inference(resolve,[$cnf( $equal(divide(zero,a),zero) )],[refute_0_52,refute_0_67]) ).
cnf(refute_0_69,plain,
( ~ less_equal(divide(divide(X_12,a),b),divide(divide(X_12,identity),a))
| divide(divide(X_12,identity),a) != zero
| less_equal(divide(divide(X_12,a),b),zero) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(X_12,a),b),divide(divide(X_12,identity),a)) ),[1],$fot(zero)]]) ).
cnf(refute_0_70,plain,
( ~ less_equal(divide(divide(X_12,a),b),divide(divide(X_12,identity),a))
| less_equal(divide(divide(X_12,a),b),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(X_12,identity),a),zero) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
less_equal(divide(divide(X_12,a),b),zero),
inference(resolve,[$cnf( less_equal(divide(divide(X_12,a),b),divide(divide(X_12,identity),a)) )],[refute_0_51,refute_0_70]) ).
cnf(refute_0_72,plain,
less_equal(divide(divide(identity,a),b),zero),
inference(subst,[],[refute_0_71:[bind(X_12,$fot(identity))]]) ).
cnf(refute_0_73,plain,
( ~ less_equal(divide(divide(identity,a),b),zero)
| divide(identity,a) != b
| less_equal(divide(b,b),zero) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(identity,a),b),zero) ),[0,0],$fot(b)]]) ).
cnf(refute_0_74,plain,
( ~ less_equal(divide(divide(identity,a),b),zero)
| less_equal(divide(b,b),zero) ),
inference(resolve,[$cnf( $equal(divide(identity,a),b) )],[id_divide_a_is_b,refute_0_73]) ).
cnf(refute_0_75,plain,
less_equal(divide(b,b),zero),
inference(resolve,[$cnf( less_equal(divide(divide(identity,a),b),zero) )],[refute_0_72,refute_0_74]) ).
cnf(refute_0_76,plain,
( ~ less_equal(divide(b,b),zero)
| ~ less_equal(zero,divide(b,b))
| divide(b,b) = zero ),
inference(subst,[],[less_equal_and_equal:[bind(X,$fot(divide(b,b))),bind(Y,$fot(zero))]]) ).
cnf(refute_0_77,plain,
( ~ less_equal(zero,divide(b,b))
| divide(b,b) = zero ),
inference(resolve,[$cnf( less_equal(divide(b,b),zero) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
less_equal(zero,divide(b,b)),
inference(subst,[],[zero_is_smallest:[bind(X,$fot(divide(b,b)))]]) ).
cnf(refute_0_79,plain,
divide(b,b) = zero,
inference(resolve,[$cnf( less_equal(zero,divide(b,b)) )],[refute_0_78,refute_0_77]) ).
cnf(refute_0_80,plain,
( ~ less_equal(zero,divide(c,divide(a,b)))
| divide(b,b) != zero
| less_equal(divide(b,b),divide(c,divide(a,b))) ),
introduced(tautology,[equality,[$cnf( ~ less_equal(divide(b,b),divide(c,divide(a,b))) ),[0],$fot(zero)]]) ).
cnf(refute_0_81,plain,
( ~ less_equal(zero,divide(c,divide(a,b)))
| less_equal(divide(b,b),divide(c,divide(a,b))) ),
inference(resolve,[$cnf( $equal(divide(b,b),zero) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
( ~ less_equal(zero,divide(c,divide(a,b)))
| divide(c,divide(a,b)) = divide(b,b) ),
inference(resolve,[$cnf( less_equal(divide(b,b),divide(c,divide(a,b))) )],[refute_0_81,refute_0_47]) ).
cnf(refute_0_83,plain,
( divide(b,b) != zero
| divide(c,divide(a,b)) != divide(b,b)
| divide(c,divide(a,b)) = zero ),
introduced(tautology,[equality,[$cnf( $equal(divide(c,divide(a,b)),divide(b,b)) ),[1],$fot(zero)]]) ).
cnf(refute_0_84,plain,
( divide(c,divide(a,b)) != divide(b,b)
| divide(c,divide(a,b)) = zero ),
inference(resolve,[$cnf( $equal(divide(b,b),zero) )],[refute_0_79,refute_0_83]) ).
cnf(refute_0_85,plain,
( ~ less_equal(zero,divide(c,divide(a,b)))
| divide(c,divide(a,b)) = zero ),
inference(resolve,[$cnf( $equal(divide(c,divide(a,b)),divide(b,b)) )],[refute_0_82,refute_0_84]) ).
cnf(refute_0_86,plain,
less_equal(zero,divide(c,divide(a,b))),
inference(subst,[],[zero_is_smallest:[bind(X,$fot(divide(c,divide(a,b))))]]) ).
cnf(refute_0_87,plain,
divide(c,divide(a,b)) = zero,
inference(resolve,[$cnf( less_equal(zero,divide(c,divide(a,b))) )],[refute_0_86,refute_0_85]) ).
cnf(refute_0_88,plain,
( ~ less_equal(divide(divide(c,Z),divide(divide(a,b),Z)),divide(divide(c,divide(a,b)),Z))
| divide(c,divide(a,b)) != zero
| less_equal(divide(divide(c,Z),divide(divide(a,b),Z)),divide(zero,Z)) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(c,Z),divide(divide(a,b),Z)),divide(divide(c,divide(a,b)),Z)) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_89,plain,
( ~ less_equal(divide(divide(c,Z),divide(divide(a,b),Z)),divide(divide(c,divide(a,b)),Z))
| less_equal(divide(divide(c,Z),divide(divide(a,b),Z)),divide(zero,Z)) ),
inference(resolve,[$cnf( $equal(divide(c,divide(a,b)),zero) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
less_equal(divide(divide(c,Z),divide(divide(a,b),Z)),divide(zero,Z)),
inference(resolve,[$cnf( less_equal(divide(divide(c,Z),divide(divide(a,b),Z)),divide(divide(c,divide(a,b)),Z)) )],[refute_0_37,refute_0_89]) ).
cnf(refute_0_91,plain,
divide(zero,Z) = zero,
inference(subst,[],[refute_0_32:[bind(X_5,$fot(Z))]]) ).
cnf(refute_0_92,plain,
( ~ less_equal(divide(divide(c,Z),divide(divide(a,b),Z)),divide(zero,Z))
| divide(zero,Z) != zero
| less_equal(divide(divide(c,Z),divide(divide(a,b),Z)),zero) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(c,Z),divide(divide(a,b),Z)),divide(zero,Z)) ),[1],$fot(zero)]]) ).
cnf(refute_0_93,plain,
( ~ less_equal(divide(divide(c,Z),divide(divide(a,b),Z)),divide(zero,Z))
| less_equal(divide(divide(c,Z),divide(divide(a,b),Z)),zero) ),
inference(resolve,[$cnf( $equal(divide(zero,Z),zero) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
less_equal(divide(divide(c,Z),divide(divide(a,b),Z)),zero),
inference(resolve,[$cnf( less_equal(divide(divide(c,Z),divide(divide(a,b),Z)),divide(zero,Z)) )],[refute_0_90,refute_0_93]) ).
cnf(refute_0_95,plain,
less_equal(divide(divide(c,a),divide(divide(a,b),a)),zero),
inference(subst,[],[refute_0_94:[bind(Z,$fot(a))]]) ).
cnf(refute_0_96,plain,
less_equal(divide(X_5,Y),X_5),
inference(subst,[],[quotient_smaller_than_numerator:[bind(X,$fot(X_5))]]) ).
cnf(refute_0_97,plain,
( ~ less_equal(divide(X_5,Y),X_5)
| divide(divide(X_5,Y),X_5) = zero ),
inference(subst,[],[quotient_less_equal1:[bind(X,$fot(divide(X_5,Y))),bind(Y,$fot(X_5))]]) ).
cnf(refute_0_98,plain,
divide(divide(X_5,Y),X_5) = zero,
inference(resolve,[$cnf( less_equal(divide(X_5,Y),X_5) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
divide(divide(a,b),a) = zero,
inference(subst,[],[refute_0_98:[bind(Y,$fot(b)),bind(X_5,$fot(a))]]) ).
cnf(refute_0_100,plain,
( ~ less_equal(divide(divide(c,a),divide(divide(a,b),a)),zero)
| divide(divide(a,b),a) != zero
| less_equal(divide(divide(c,a),zero),zero) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(c,a),divide(divide(a,b),a)),zero) ),[0,1],$fot(zero)]]) ).
cnf(refute_0_101,plain,
( ~ less_equal(divide(divide(c,a),divide(divide(a,b),a)),zero)
| less_equal(divide(divide(c,a),zero),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(a,b),a),zero) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
less_equal(divide(divide(c,a),zero),zero),
inference(resolve,[$cnf( less_equal(divide(divide(c,a),divide(divide(a,b),a)),zero) )],[refute_0_95,refute_0_101]) ).
cnf(refute_0_103,plain,
zero = divide(divide(c,a),zero),
inference(resolve,[$cnf( less_equal(divide(divide(c,a),zero),zero) )],[refute_0_102,refute_0_36]) ).
cnf(refute_0_104,plain,
( zero != divide(divide(c,a),zero)
| divide(divide(c,a),zero) = zero ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(zero)),bind(Y0,$fot(divide(divide(c,a),zero)))]]) ).
cnf(refute_0_105,plain,
divide(divide(c,a),zero) = zero,
inference(resolve,[$cnf( $equal(zero,divide(divide(c,a),zero)) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
( divide(divide(c,a),zero) != zero
| zero != zero
| divide(divide(c,a),zero) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(divide(c,a),zero),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_107,plain,
( zero != zero
| divide(divide(c,a),zero) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(c,a),zero),zero) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
( zero != zero
| less_equal(divide(c,a),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(c,a),zero),zero) )],[refute_0_107,refute_0_35]) ).
cnf(refute_0_109,plain,
less_equal(divide(c,a),zero),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_28,refute_0_108]) ).
cnf(refute_0_110,plain,
zero = divide(c,a),
inference(resolve,[$cnf( less_equal(divide(c,a),zero) )],[refute_0_109,refute_0_34]) ).
cnf(refute_0_111,plain,
( zero != divide(c,a)
| divide(c,a) = zero ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(zero)),bind(Y0,$fot(divide(c,a)))]]) ).
cnf(refute_0_112,plain,
divide(c,a) = zero,
inference(resolve,[$cnf( $equal(zero,divide(c,a)) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
divide(divide(c,a),divide(d,a)) = divide(divide(c,a),divide(d,a)),
introduced(tautology,[refl,[$fot(divide(divide(c,a),divide(d,a)))]]) ).
cnf(refute_0_114,plain,
( divide(divide(c,a),divide(d,a)) != divide(divide(c,a),divide(d,a))
| divide(c,a) != zero
| divide(divide(c,a),divide(d,a)) = divide(zero,divide(d,a)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(c,a),divide(d,a)),divide(divide(c,a),divide(d,a))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_115,plain,
( divide(c,a) != zero
| divide(divide(c,a),divide(d,a)) = divide(zero,divide(d,a)) ),
inference(resolve,[$cnf( $equal(divide(divide(c,a),divide(d,a)),divide(divide(c,a),divide(d,a))) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
divide(divide(c,a),divide(d,a)) = divide(zero,divide(d,a)),
inference(resolve,[$cnf( $equal(divide(c,a),zero) )],[refute_0_112,refute_0_115]) ).
cnf(refute_0_117,plain,
( divide(divide(c,a),divide(d,a)) != divide(zero,divide(d,a))
| divide(zero,divide(d,a)) != zero
| divide(divide(c,a),divide(d,a)) = zero ),
inference(subst,[],[refute_0_65:[bind(X0,$fot(divide(divide(c,a),divide(d,a)))),bind(Y0,$fot(divide(zero,divide(d,a)))),bind(Z0,$fot(zero))]]) ).
cnf(refute_0_118,plain,
( divide(zero,divide(d,a)) != zero
| divide(divide(c,a),divide(d,a)) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(c,a),divide(d,a)),divide(zero,divide(d,a))) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
divide(divide(c,a),divide(d,a)) = zero,
inference(resolve,[$cnf( $equal(divide(zero,divide(d,a)),zero) )],[refute_0_33,refute_0_118]) ).
cnf(refute_0_120,plain,
( ~ less_equal(divide(b,divide(d,a)),divide(divide(c,a),divide(d,a)))
| divide(divide(c,a),divide(d,a)) != zero
| less_equal(divide(b,divide(d,a)),zero) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(b,divide(d,a)),divide(divide(c,a),divide(d,a))) ),[1],$fot(zero)]]) ).
cnf(refute_0_121,plain,
( ~ less_equal(divide(b,divide(d,a)),divide(divide(c,a),divide(d,a)))
| less_equal(divide(b,divide(d,a)),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(c,a),divide(d,a)),zero) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
less_equal(divide(b,divide(d,a)),zero),
inference(resolve,[$cnf( less_equal(divide(b,divide(d,a)),divide(divide(c,a),divide(d,a))) )],[refute_0_29,refute_0_121]) ).
cnf(refute_0_123,plain,
zero = divide(b,divide(d,a)),
inference(resolve,[$cnf( less_equal(divide(b,divide(d,a)),zero) )],[refute_0_122,refute_0_5]) ).
cnf(refute_0_124,plain,
( zero != divide(b,divide(d,a))
| divide(b,divide(d,a)) = zero ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(zero)),bind(Y0,$fot(divide(b,divide(d,a))))]]) ).
cnf(refute_0_125,plain,
divide(b,divide(d,a)) = zero,
inference(resolve,[$cnf( $equal(zero,divide(b,divide(d,a))) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
( divide(b,divide(d,a)) != zero
| zero != zero
| divide(b,divide(d,a)) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(b,divide(d,a)),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_127,plain,
( zero != zero
| divide(b,divide(d,a)) = zero ),
inference(resolve,[$cnf( $equal(divide(b,divide(d,a)),zero) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
( zero != zero
| less_equal(b,divide(d,a)) ),
inference(resolve,[$cnf( $equal(divide(b,divide(d,a)),zero) )],[refute_0_127,refute_0_1]) ).
cnf(refute_0_129,plain,
less_equal(b,divide(d,a)),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_28,refute_0_128]) ).
cnf(refute_0_130,plain,
( ~ less_equal(divide(X_73,a),b)
| ~ less_equal(b,divide(X_73,a))
| b = divide(X_73,a) ),
inference(subst,[],[less_equal_and_equal:[bind(X,$fot(b)),bind(Y,$fot(divide(X_73,a)))]]) ).
cnf(refute_0_131,plain,
( divide(divide(X_72,a),b) != zero
| less_equal(divide(X_72,a),b) ),
inference(subst,[],[quotient_less_equal2:[bind(X,$fot(divide(X_72,a))),bind(Y,$fot(b))]]) ).
cnf(refute_0_132,plain,
( ~ less_equal(divide(divide(X_12,a),b),zero)
| ~ less_equal(zero,divide(divide(X_12,a),b))
| divide(divide(X_12,a),b) = zero ),
inference(subst,[],[less_equal_and_equal:[bind(X,$fot(divide(divide(X_12,a),b))),bind(Y,$fot(zero))]]) ).
cnf(refute_0_133,plain,
( ~ less_equal(zero,divide(divide(X_12,a),b))
| divide(divide(X_12,a),b) = zero ),
inference(resolve,[$cnf( less_equal(divide(divide(X_12,a),b),zero) )],[refute_0_71,refute_0_132]) ).
cnf(refute_0_134,plain,
less_equal(zero,divide(divide(X_12,a),b)),
inference(subst,[],[zero_is_smallest:[bind(X,$fot(divide(divide(X_12,a),b)))]]) ).
cnf(refute_0_135,plain,
divide(divide(X_12,a),b) = zero,
inference(resolve,[$cnf( less_equal(zero,divide(divide(X_12,a),b)) )],[refute_0_134,refute_0_133]) ).
cnf(refute_0_136,plain,
divide(divide(X_72,a),b) = zero,
inference(subst,[],[refute_0_135:[bind(X_12,$fot(X_72))]]) ).
cnf(refute_0_137,plain,
( divide(divide(X_72,a),b) != zero
| zero != zero
| divide(divide(X_72,a),b) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(divide(X_72,a),b),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_138,plain,
( zero != zero
| divide(divide(X_72,a),b) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(X_72,a),b),zero) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
( zero != zero
| less_equal(divide(X_72,a),b) ),
inference(resolve,[$cnf( $equal(divide(divide(X_72,a),b),zero) )],[refute_0_138,refute_0_131]) ).
cnf(refute_0_140,plain,
less_equal(divide(X_72,a),b),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_28,refute_0_139]) ).
cnf(refute_0_141,plain,
less_equal(divide(X_73,a),b),
inference(subst,[],[refute_0_140:[bind(X_72,$fot(X_73))]]) ).
cnf(refute_0_142,plain,
( ~ less_equal(b,divide(X_73,a))
| b = divide(X_73,a) ),
inference(resolve,[$cnf( less_equal(divide(X_73,a),b) )],[refute_0_141,refute_0_130]) ).
cnf(refute_0_143,plain,
( ~ less_equal(b,divide(d,a))
| b = divide(d,a) ),
inference(subst,[],[refute_0_142:[bind(X_73,$fot(d))]]) ).
cnf(refute_0_144,plain,
b = divide(d,a),
inference(resolve,[$cnf( less_equal(b,divide(d,a)) )],[refute_0_129,refute_0_143]) ).
cnf(refute_0_145,plain,
( b != divide(d,a)
| divide(d,a) = b ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(b)),bind(Y0,$fot(divide(d,a)))]]) ).
cnf(refute_0_146,plain,
divide(d,a) = b,
inference(resolve,[$cnf( $equal(b,divide(d,a)) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
( ~ less_equal(divide(d,a),d)
| divide(d,a) != b
| less_equal(b,d) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(d,a),d) ),[0],$fot(b)]]) ).
cnf(refute_0_148,plain,
( ~ less_equal(divide(d,a),d)
| less_equal(b,d) ),
inference(resolve,[$cnf( $equal(divide(d,a),b) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
less_equal(b,d),
inference(resolve,[$cnf( less_equal(divide(d,a),d) )],[refute_0_0,refute_0_148]) ).
cnf(refute_0_150,plain,
( ~ less_equal(b,d)
| ~ less_equal(d,b)
| b = d ),
inference(subst,[],[less_equal_and_equal:[bind(X,$fot(b)),bind(Y,$fot(d))]]) ).
cnf(refute_0_151,plain,
( divide(d,b) != zero
| less_equal(d,b) ),
inference(subst,[],[quotient_less_equal2:[bind(X,$fot(d)),bind(Y,$fot(b))]]) ).
cnf(refute_0_152,plain,
( ~ less_equal(divide(d,b),zero)
| zero = divide(d,b) ),
inference(subst,[],[refute_0_4:[bind(X_66,$fot(divide(d,b)))]]) ).
cnf(refute_0_153,plain,
( divide(divide(d,b),zero) != zero
| less_equal(divide(d,b),zero) ),
inference(subst,[],[quotient_less_equal2:[bind(X,$fot(divide(d,b))),bind(Y,$fot(zero))]]) ).
cnf(refute_0_154,plain,
( ~ less_equal(divide(divide(d,b),zero),zero)
| zero = divide(divide(d,b),zero) ),
inference(subst,[],[refute_0_4:[bind(X_66,$fot(divide(divide(d,b),zero)))]]) ).
cnf(refute_0_155,plain,
less_equal(divide(divide(d,Z),divide(divide(b,c),Z)),divide(divide(d,divide(b,c)),Z)),
inference(subst,[],[quotient_property:[bind(X,$fot(d)),bind(Y,$fot(divide(b,c)))]]) ).
cnf(refute_0_156,plain,
less_equal(divide(divide(identity,c),divide(X_13,c)),divide(divide(identity,X_13),c)),
inference(subst,[],[quotient_property:[bind(X,$fot(identity)),bind(Y,$fot(X_13)),bind(Z,$fot(c))]]) ).
cnf(refute_0_157,plain,
( ~ less_equal(divide(divide(identity,c),divide(X_13,c)),divide(divide(identity,X_13),c))
| divide(identity,c) != d
| less_equal(divide(d,divide(X_13,c)),divide(divide(identity,X_13),c)) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(identity,c),divide(X_13,c)),divide(divide(identity,X_13),c)) ),[0,0],$fot(d)]]) ).
cnf(refute_0_158,plain,
( ~ less_equal(divide(divide(identity,c),divide(X_13,c)),divide(divide(identity,X_13),c))
| less_equal(divide(d,divide(X_13,c)),divide(divide(identity,X_13),c)) ),
inference(resolve,[$cnf( $equal(divide(identity,c),d) )],[id_divide_c_is_d,refute_0_157]) ).
cnf(refute_0_159,plain,
less_equal(divide(d,divide(X_13,c)),divide(divide(identity,X_13),c)),
inference(resolve,[$cnf( less_equal(divide(divide(identity,c),divide(X_13,c)),divide(divide(identity,X_13),c)) )],[refute_0_156,refute_0_158]) ).
cnf(refute_0_160,plain,
less_equal(divide(d,divide(b,c)),divide(divide(identity,b),c)),
inference(subst,[],[refute_0_159:[bind(X_13,$fot(b))]]) ).
cnf(refute_0_161,plain,
( ~ less_equal(divide(d,divide(b,c)),divide(divide(identity,b),c))
| divide(identity,b) != c
| less_equal(divide(d,divide(b,c)),divide(c,c)) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(d,divide(b,c)),divide(divide(identity,b),c)) ),[1,0],$fot(c)]]) ).
cnf(refute_0_162,plain,
( ~ less_equal(divide(d,divide(b,c)),divide(divide(identity,b),c))
| less_equal(divide(d,divide(b,c)),divide(c,c)) ),
inference(resolve,[$cnf( $equal(divide(identity,b),c) )],[id_divide_b_is_c,refute_0_161]) ).
cnf(refute_0_163,plain,
less_equal(divide(d,divide(b,c)),divide(c,c)),
inference(resolve,[$cnf( less_equal(divide(d,divide(b,c)),divide(divide(identity,b),c)) )],[refute_0_160,refute_0_162]) ).
cnf(refute_0_164,plain,
( ~ less_equal(divide(c,c),divide(d,divide(b,c)))
| ~ less_equal(divide(d,divide(b,c)),divide(c,c))
| divide(d,divide(b,c)) = divide(c,c) ),
inference(subst,[],[less_equal_and_equal:[bind(X,$fot(divide(d,divide(b,c)))),bind(Y,$fot(divide(c,c)))]]) ).
cnf(refute_0_165,plain,
( ~ less_equal(divide(c,c),divide(d,divide(b,c)))
| divide(d,divide(b,c)) = divide(c,c) ),
inference(resolve,[$cnf( less_equal(divide(d,divide(b,c)),divide(c,c)) )],[refute_0_163,refute_0_164]) ).
cnf(refute_0_166,plain,
less_equal(divide(divide(X_12,b),divide(identity,b)),divide(divide(X_12,identity),b)),
inference(subst,[],[quotient_property:[bind(X,$fot(X_12)),bind(Y,$fot(identity)),bind(Z,$fot(b))]]) ).
cnf(refute_0_167,plain,
( ~ less_equal(divide(divide(X_12,b),divide(identity,b)),divide(divide(X_12,identity),b))
| divide(identity,b) != c
| less_equal(divide(divide(X_12,b),c),divide(divide(X_12,identity),b)) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(X_12,b),divide(identity,b)),divide(divide(X_12,identity),b)) ),[0,1],$fot(c)]]) ).
cnf(refute_0_168,plain,
( ~ less_equal(divide(divide(X_12,b),divide(identity,b)),divide(divide(X_12,identity),b))
| less_equal(divide(divide(X_12,b),c),divide(divide(X_12,identity),b)) ),
inference(resolve,[$cnf( $equal(divide(identity,b),c) )],[id_divide_b_is_c,refute_0_167]) ).
cnf(refute_0_169,plain,
less_equal(divide(divide(X_12,b),c),divide(divide(X_12,identity),b)),
inference(resolve,[$cnf( less_equal(divide(divide(X_12,b),divide(identity,b)),divide(divide(X_12,identity),b)) )],[refute_0_166,refute_0_168]) ).
cnf(refute_0_170,plain,
divide(zero,b) = zero,
inference(subst,[],[refute_0_32:[bind(X_5,$fot(b))]]) ).
cnf(refute_0_171,plain,
divide(divide(X_12,identity),b) = divide(divide(X_12,identity),b),
introduced(tautology,[refl,[$fot(divide(divide(X_12,identity),b))]]) ).
cnf(refute_0_172,plain,
( divide(X_12,identity) != zero
| divide(divide(X_12,identity),b) != divide(divide(X_12,identity),b)
| divide(divide(X_12,identity),b) = divide(zero,b) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(X_12,identity),b),divide(divide(X_12,identity),b)) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_173,plain,
( divide(X_12,identity) != zero
| divide(divide(X_12,identity),b) = divide(zero,b) ),
inference(resolve,[$cnf( $equal(divide(divide(X_12,identity),b),divide(divide(X_12,identity),b)) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
divide(divide(X_12,identity),b) = divide(zero,b),
inference(resolve,[$cnf( $equal(divide(X_12,identity),zero) )],[refute_0_56,refute_0_173]) ).
cnf(refute_0_175,plain,
( divide(divide(X_12,identity),b) != divide(zero,b)
| divide(zero,b) != zero
| divide(divide(X_12,identity),b) = zero ),
inference(subst,[],[refute_0_65:[bind(X0,$fot(divide(divide(X_12,identity),b))),bind(Y0,$fot(divide(zero,b))),bind(Z0,$fot(zero))]]) ).
cnf(refute_0_176,plain,
( divide(zero,b) != zero
| divide(divide(X_12,identity),b) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(X_12,identity),b),divide(zero,b)) )],[refute_0_174,refute_0_175]) ).
cnf(refute_0_177,plain,
divide(divide(X_12,identity),b) = zero,
inference(resolve,[$cnf( $equal(divide(zero,b),zero) )],[refute_0_170,refute_0_176]) ).
cnf(refute_0_178,plain,
( ~ less_equal(divide(divide(X_12,b),c),divide(divide(X_12,identity),b))
| divide(divide(X_12,identity),b) != zero
| less_equal(divide(divide(X_12,b),c),zero) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(X_12,b),c),divide(divide(X_12,identity),b)) ),[1],$fot(zero)]]) ).
cnf(refute_0_179,plain,
( ~ less_equal(divide(divide(X_12,b),c),divide(divide(X_12,identity),b))
| less_equal(divide(divide(X_12,b),c),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(X_12,identity),b),zero) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
less_equal(divide(divide(X_12,b),c),zero),
inference(resolve,[$cnf( less_equal(divide(divide(X_12,b),c),divide(divide(X_12,identity),b)) )],[refute_0_169,refute_0_179]) ).
cnf(refute_0_181,plain,
less_equal(divide(divide(identity,b),c),zero),
inference(subst,[],[refute_0_180:[bind(X_12,$fot(identity))]]) ).
cnf(refute_0_182,plain,
( ~ less_equal(divide(divide(identity,b),c),zero)
| divide(identity,b) != c
| less_equal(divide(c,c),zero) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(identity,b),c),zero) ),[0,0],$fot(c)]]) ).
cnf(refute_0_183,plain,
( ~ less_equal(divide(divide(identity,b),c),zero)
| less_equal(divide(c,c),zero) ),
inference(resolve,[$cnf( $equal(divide(identity,b),c) )],[id_divide_b_is_c,refute_0_182]) ).
cnf(refute_0_184,plain,
less_equal(divide(c,c),zero),
inference(resolve,[$cnf( less_equal(divide(divide(identity,b),c),zero) )],[refute_0_181,refute_0_183]) ).
cnf(refute_0_185,plain,
( ~ less_equal(divide(c,c),zero)
| ~ less_equal(zero,divide(c,c))
| divide(c,c) = zero ),
inference(subst,[],[less_equal_and_equal:[bind(X,$fot(divide(c,c))),bind(Y,$fot(zero))]]) ).
cnf(refute_0_186,plain,
( ~ less_equal(zero,divide(c,c))
| divide(c,c) = zero ),
inference(resolve,[$cnf( less_equal(divide(c,c),zero) )],[refute_0_184,refute_0_185]) ).
cnf(refute_0_187,plain,
less_equal(zero,divide(c,c)),
inference(subst,[],[zero_is_smallest:[bind(X,$fot(divide(c,c)))]]) ).
cnf(refute_0_188,plain,
divide(c,c) = zero,
inference(resolve,[$cnf( less_equal(zero,divide(c,c)) )],[refute_0_187,refute_0_186]) ).
cnf(refute_0_189,plain,
( ~ less_equal(zero,divide(d,divide(b,c)))
| divide(c,c) != zero
| less_equal(divide(c,c),divide(d,divide(b,c))) ),
introduced(tautology,[equality,[$cnf( ~ less_equal(divide(c,c),divide(d,divide(b,c))) ),[0],$fot(zero)]]) ).
cnf(refute_0_190,plain,
( ~ less_equal(zero,divide(d,divide(b,c)))
| less_equal(divide(c,c),divide(d,divide(b,c))) ),
inference(resolve,[$cnf( $equal(divide(c,c),zero) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
( ~ less_equal(zero,divide(d,divide(b,c)))
| divide(d,divide(b,c)) = divide(c,c) ),
inference(resolve,[$cnf( less_equal(divide(c,c),divide(d,divide(b,c))) )],[refute_0_190,refute_0_165]) ).
cnf(refute_0_192,plain,
( divide(c,c) != zero
| divide(d,divide(b,c)) != divide(c,c)
| divide(d,divide(b,c)) = zero ),
introduced(tautology,[equality,[$cnf( $equal(divide(d,divide(b,c)),divide(c,c)) ),[1],$fot(zero)]]) ).
cnf(refute_0_193,plain,
( divide(d,divide(b,c)) != divide(c,c)
| divide(d,divide(b,c)) = zero ),
inference(resolve,[$cnf( $equal(divide(c,c),zero) )],[refute_0_188,refute_0_192]) ).
cnf(refute_0_194,plain,
( ~ less_equal(zero,divide(d,divide(b,c)))
| divide(d,divide(b,c)) = zero ),
inference(resolve,[$cnf( $equal(divide(d,divide(b,c)),divide(c,c)) )],[refute_0_191,refute_0_193]) ).
cnf(refute_0_195,plain,
less_equal(zero,divide(d,divide(b,c))),
inference(subst,[],[zero_is_smallest:[bind(X,$fot(divide(d,divide(b,c))))]]) ).
cnf(refute_0_196,plain,
divide(d,divide(b,c)) = zero,
inference(resolve,[$cnf( less_equal(zero,divide(d,divide(b,c))) )],[refute_0_195,refute_0_194]) ).
cnf(refute_0_197,plain,
( ~ less_equal(divide(divide(d,Z),divide(divide(b,c),Z)),divide(divide(d,divide(b,c)),Z))
| divide(d,divide(b,c)) != zero
| less_equal(divide(divide(d,Z),divide(divide(b,c),Z)),divide(zero,Z)) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(d,Z),divide(divide(b,c),Z)),divide(divide(d,divide(b,c)),Z)) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_198,plain,
( ~ less_equal(divide(divide(d,Z),divide(divide(b,c),Z)),divide(divide(d,divide(b,c)),Z))
| less_equal(divide(divide(d,Z),divide(divide(b,c),Z)),divide(zero,Z)) ),
inference(resolve,[$cnf( $equal(divide(d,divide(b,c)),zero) )],[refute_0_196,refute_0_197]) ).
cnf(refute_0_199,plain,
less_equal(divide(divide(d,Z),divide(divide(b,c),Z)),divide(zero,Z)),
inference(resolve,[$cnf( less_equal(divide(divide(d,Z),divide(divide(b,c),Z)),divide(divide(d,divide(b,c)),Z)) )],[refute_0_155,refute_0_198]) ).
cnf(refute_0_200,plain,
( ~ less_equal(divide(divide(d,Z),divide(divide(b,c),Z)),divide(zero,Z))
| divide(zero,Z) != zero
| less_equal(divide(divide(d,Z),divide(divide(b,c),Z)),zero) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(d,Z),divide(divide(b,c),Z)),divide(zero,Z)) ),[1],$fot(zero)]]) ).
cnf(refute_0_201,plain,
( ~ less_equal(divide(divide(d,Z),divide(divide(b,c),Z)),divide(zero,Z))
| less_equal(divide(divide(d,Z),divide(divide(b,c),Z)),zero) ),
inference(resolve,[$cnf( $equal(divide(zero,Z),zero) )],[refute_0_91,refute_0_200]) ).
cnf(refute_0_202,plain,
less_equal(divide(divide(d,Z),divide(divide(b,c),Z)),zero),
inference(resolve,[$cnf( less_equal(divide(divide(d,Z),divide(divide(b,c),Z)),divide(zero,Z)) )],[refute_0_199,refute_0_201]) ).
cnf(refute_0_203,plain,
less_equal(divide(divide(d,b),divide(divide(b,c),b)),zero),
inference(subst,[],[refute_0_202:[bind(Z,$fot(b))]]) ).
cnf(refute_0_204,plain,
divide(divide(b,c),b) = zero,
inference(subst,[],[refute_0_98:[bind(Y,$fot(c)),bind(X_5,$fot(b))]]) ).
cnf(refute_0_205,plain,
( ~ less_equal(divide(divide(d,b),divide(divide(b,c),b)),zero)
| divide(divide(b,c),b) != zero
| less_equal(divide(divide(d,b),zero),zero) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(d,b),divide(divide(b,c),b)),zero) ),[0,1],$fot(zero)]]) ).
cnf(refute_0_206,plain,
( ~ less_equal(divide(divide(d,b),divide(divide(b,c),b)),zero)
| less_equal(divide(divide(d,b),zero),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(b,c),b),zero) )],[refute_0_204,refute_0_205]) ).
cnf(refute_0_207,plain,
less_equal(divide(divide(d,b),zero),zero),
inference(resolve,[$cnf( less_equal(divide(divide(d,b),divide(divide(b,c),b)),zero) )],[refute_0_203,refute_0_206]) ).
cnf(refute_0_208,plain,
zero = divide(divide(d,b),zero),
inference(resolve,[$cnf( less_equal(divide(divide(d,b),zero),zero) )],[refute_0_207,refute_0_154]) ).
cnf(refute_0_209,plain,
( zero != divide(divide(d,b),zero)
| divide(divide(d,b),zero) = zero ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(zero)),bind(Y0,$fot(divide(divide(d,b),zero)))]]) ).
cnf(refute_0_210,plain,
divide(divide(d,b),zero) = zero,
inference(resolve,[$cnf( $equal(zero,divide(divide(d,b),zero)) )],[refute_0_208,refute_0_209]) ).
cnf(refute_0_211,plain,
( divide(divide(d,b),zero) != zero
| zero != zero
| divide(divide(d,b),zero) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(divide(d,b),zero),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_212,plain,
( zero != zero
| divide(divide(d,b),zero) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(d,b),zero),zero) )],[refute_0_210,refute_0_211]) ).
cnf(refute_0_213,plain,
( zero != zero
| less_equal(divide(d,b),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(d,b),zero),zero) )],[refute_0_212,refute_0_153]) ).
cnf(refute_0_214,plain,
less_equal(divide(d,b),zero),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_28,refute_0_213]) ).
cnf(refute_0_215,plain,
zero = divide(d,b),
inference(resolve,[$cnf( less_equal(divide(d,b),zero) )],[refute_0_214,refute_0_152]) ).
cnf(refute_0_216,plain,
( zero != divide(d,b)
| divide(d,b) = zero ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(zero)),bind(Y0,$fot(divide(d,b)))]]) ).
cnf(refute_0_217,plain,
divide(d,b) = zero,
inference(resolve,[$cnf( $equal(zero,divide(d,b)) )],[refute_0_215,refute_0_216]) ).
cnf(refute_0_218,plain,
( divide(d,b) != zero
| zero != zero
| divide(d,b) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(d,b),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_219,plain,
( zero != zero
| divide(d,b) = zero ),
inference(resolve,[$cnf( $equal(divide(d,b),zero) )],[refute_0_217,refute_0_218]) ).
cnf(refute_0_220,plain,
( zero != zero
| less_equal(d,b) ),
inference(resolve,[$cnf( $equal(divide(d,b),zero) )],[refute_0_219,refute_0_151]) ).
cnf(refute_0_221,plain,
less_equal(d,b),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_28,refute_0_220]) ).
cnf(refute_0_222,plain,
( ~ less_equal(b,d)
| b = d ),
inference(resolve,[$cnf( less_equal(d,b) )],[refute_0_221,refute_0_150]) ).
cnf(refute_0_223,plain,
~ less_equal(b,d),
inference(resolve,[$cnf( $equal(b,d) )],[refute_0_222,prove_b_equals_d]) ).
cnf(refute_0_224,plain,
$false,
inference(resolve,[$cnf( less_equal(b,d) )],[refute_0_149,refute_0_223]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HEN009-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jul 1 13:31:08 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.17/1.34 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.17/1.34
% 1.17/1.34 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.17/1.36
%------------------------------------------------------------------------------