TSTP Solution File: HEN007-3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : HEN007-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 12:58:39 EDT 2022
% Result : Unsatisfiable 0.17s 0.47s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 26
% Syntax : Number of clauses : 144 ( 76 unt; 0 nHn; 64 RR)
% Number of literals : 233 ( 114 equ; 90 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 170 ( 16 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(a_LE_b,hypothesis,
less_equal(a,b) ).
cnf(prove_c_divide_b_LE_c_divide_a,negated_conjecture,
~ less_equal(divide(c,b),divide(c,a)) ).
cnf(refute_0_0,plain,
( divide(divide(X_130,b),divide(X_130,a)) != zero
| less_equal(divide(X_130,b),divide(X_130,a)) ),
inference(subst,[],[quotient_less_equal2:[bind(X,$fot(divide(X_130,b))),bind(Y,$fot(divide(X_130,a)))]]) ).
cnf(refute_0_1,plain,
less_equal(zero,X_40),
inference(subst,[],[zero_is_smallest:[bind(X,$fot(X_40))]]) ).
cnf(refute_0_2,plain,
( ~ less_equal(X_40,zero)
| ~ less_equal(zero,X_40)
| zero = X_40 ),
inference(subst,[],[less_equal_and_equal:[bind(X,$fot(zero)),bind(Y,$fot(X_40))]]) ).
cnf(refute_0_3,plain,
( ~ less_equal(X_40,zero)
| zero = X_40 ),
inference(resolve,[$cnf( less_equal(zero,X_40) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ less_equal(divide(divide(X_129,b),divide(X_129,a)),zero)
| zero = divide(divide(X_129,b),divide(X_129,a)) ),
inference(subst,[],[refute_0_3:[bind(X_40,$fot(divide(divide(X_129,b),divide(X_129,a))))]]) ).
cnf(refute_0_5,plain,
( divide(X,divide(X,zero)) != zero
| less_equal(X,divide(X,zero)) ),
inference(subst,[],[quotient_less_equal2:[bind(Y,$fot(divide(X,zero)))]]) ).
cnf(refute_0_6,plain,
( ~ less_equal(divide(X_72,divide(X_72,zero)),zero)
| zero = divide(X_72,divide(X_72,zero)) ),
inference(subst,[],[refute_0_3:[bind(X_40,$fot(divide(X_72,divide(X_72,zero))))]]) ).
cnf(refute_0_7,plain,
( divide(divide(X_71,divide(X_71,zero)),zero) != zero
| less_equal(divide(X_71,divide(X_71,zero)),zero) ),
inference(subst,[],[quotient_less_equal2:[bind(X,$fot(divide(X_71,divide(X_71,zero)))),bind(Y,$fot(zero))]]) ).
cnf(refute_0_8,plain,
( ~ less_equal(divide(divide(X_64,divide(X_64,zero)),zero),zero)
| zero = divide(divide(X_64,divide(X_64,zero)),zero) ),
inference(subst,[],[refute_0_3:[bind(X_40,$fot(divide(divide(X_64,divide(X_64,zero)),zero)))]]) ).
cnf(refute_0_9,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,$fot(X_14))]]) ).
cnf(refute_0_10,plain,
less_equal(zero,X_7),
inference(subst,[],[zero_is_smallest:[bind(X,$fot(X_7))]]) ).
cnf(refute_0_11,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_12,plain,
divide(zero,X_7) = zero,
inference(resolve,[$cnf( less_equal(zero,X_7) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
divide(zero,X_14) = zero,
inference(subst,[],[refute_0_12:[bind(X_7,$fot(X_14))]]) ).
cnf(refute_0_14,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_15,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( $equal(divide(zero,X_14),zero) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
less_equal(divide(divide(X_12,X_14),zero),divide(divide(X_12,zero),X_14)),
inference(resolve,[$cnf( less_equal(divide(divide(X_12,X_14),divide(zero,X_14)),divide(divide(X_12,zero),X_14)) )],[refute_0_9,refute_0_15]) ).
cnf(refute_0_17,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_16:[bind(X_14,$fot(divide(X_12,zero)))]]) ).
cnf(refute_0_18,plain,
( ~ less_equal(divide(X_42,X_42),zero)
| ~ less_equal(zero,divide(X_42,X_42))
| zero = divide(X_42,X_42) ),
inference(subst,[],[less_equal_and_equal:[bind(X,$fot(zero)),bind(Y,$fot(divide(X_42,X_42)))]]) ).
cnf(refute_0_19,plain,
( divide(divide(X_41,X_41),zero) != zero
| less_equal(divide(X_41,X_41),zero) ),
inference(subst,[],[quotient_less_equal2:[bind(X,$fot(divide(X_41,X_41))),bind(Y,$fot(zero))]]) ).
cnf(refute_0_20,plain,
less_equal(divide(divide(X_14,X_14),divide(X_13,X_14)),divide(divide(X_14,X_13),X_14)),
inference(subst,[],[quotient_property:[bind(X,$fot(X_14)),bind(Y,$fot(X_13)),bind(Z,$fot(X_14))]]) ).
cnf(refute_0_21,plain,
less_equal(divide(X_7,Y),X_7),
inference(subst,[],[quotient_smaller_than_numerator:[bind(X,$fot(X_7))]]) ).
cnf(refute_0_22,plain,
( ~ less_equal(divide(X_7,Y),X_7)
| divide(divide(X_7,Y),X_7) = zero ),
inference(subst,[],[quotient_less_equal1:[bind(X,$fot(divide(X_7,Y))),bind(Y,$fot(X_7))]]) ).
cnf(refute_0_23,plain,
divide(divide(X_7,Y),X_7) = zero,
inference(resolve,[$cnf( less_equal(divide(X_7,Y),X_7) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
divide(divide(X_14,X_13),X_14) = zero,
inference(subst,[],[refute_0_23:[bind(Y,$fot(X_13)),bind(X_7,$fot(X_14))]]) ).
cnf(refute_0_25,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_26,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( $equal(divide(divide(X_14,X_13),X_14),zero) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
less_equal(divide(divide(X_14,X_14),divide(X_13,X_14)),zero),
inference(resolve,[$cnf( less_equal(divide(divide(X_14,X_14),divide(X_13,X_14)),divide(divide(X_14,X_13),X_14)) )],[refute_0_20,refute_0_26]) ).
cnf(refute_0_28,plain,
less_equal(divide(divide(X_22,X_22),divide(divide(X_22,Y),X_22)),zero),
inference(subst,[],[refute_0_27:[bind(X_13,$fot(divide(X_22,Y))),bind(X_14,$fot(X_22))]]) ).
cnf(refute_0_29,plain,
divide(divide(X_22,Y),X_22) = zero,
inference(subst,[],[refute_0_23:[bind(X_7,$fot(X_22))]]) ).
cnf(refute_0_30,plain,
( ~ less_equal(divide(divide(X_22,X_22),divide(divide(X_22,Y),X_22)),zero)
| divide(divide(X_22,Y),X_22) != zero
| less_equal(divide(divide(X_22,X_22),zero),zero) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(X_22,X_22),divide(divide(X_22,Y),X_22)),zero) ),[0,1],$fot(zero)]]) ).
cnf(refute_0_31,plain,
( ~ less_equal(divide(divide(X_22,X_22),divide(divide(X_22,Y),X_22)),zero)
| less_equal(divide(divide(X_22,X_22),zero),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(X_22,Y),X_22),zero) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
less_equal(divide(divide(X_22,X_22),zero),zero),
inference(resolve,[$cnf( less_equal(divide(divide(X_22,X_22),divide(divide(X_22,Y),X_22)),zero) )],[refute_0_28,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ less_equal(divide(divide(X_22,X_22),zero),zero)
| ~ less_equal(zero,divide(divide(X_22,X_22),zero))
| divide(divide(X_22,X_22),zero) = zero ),
inference(subst,[],[less_equal_and_equal:[bind(X,$fot(divide(divide(X_22,X_22),zero))),bind(Y,$fot(zero))]]) ).
cnf(refute_0_34,plain,
( ~ less_equal(zero,divide(divide(X_22,X_22),zero))
| divide(divide(X_22,X_22),zero) = zero ),
inference(resolve,[$cnf( less_equal(divide(divide(X_22,X_22),zero),zero) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
less_equal(zero,divide(divide(X_22,X_22),zero)),
inference(subst,[],[zero_is_smallest:[bind(X,$fot(divide(divide(X_22,X_22),zero)))]]) ).
cnf(refute_0_36,plain,
divide(divide(X_22,X_22),zero) = zero,
inference(resolve,[$cnf( less_equal(zero,divide(divide(X_22,X_22),zero)) )],[refute_0_35,refute_0_34]) ).
cnf(refute_0_37,plain,
divide(divide(X_41,X_41),zero) = zero,
inference(subst,[],[refute_0_36:[bind(X_22,$fot(X_41))]]) ).
cnf(refute_0_38,plain,
( divide(divide(X_41,X_41),zero) != zero
| zero != zero
| divide(divide(X_41,X_41),zero) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(divide(X_41,X_41),zero),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_39,plain,
( zero != zero
| divide(divide(X_41,X_41),zero) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(X_41,X_41),zero),zero) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( zero != zero
| less_equal(divide(X_41,X_41),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(X_41,X_41),zero),zero) )],[refute_0_39,refute_0_19]) ).
cnf(refute_0_41,plain,
zero = zero,
introduced(tautology,[refl,[$fot(zero)]]) ).
cnf(refute_0_42,plain,
less_equal(divide(X_41,X_41),zero),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_41,refute_0_40]) ).
cnf(refute_0_43,plain,
less_equal(divide(X_42,X_42),zero),
inference(subst,[],[refute_0_42:[bind(X_41,$fot(X_42))]]) ).
cnf(refute_0_44,plain,
( ~ less_equal(zero,divide(X_42,X_42))
| zero = divide(X_42,X_42) ),
inference(resolve,[$cnf( less_equal(divide(X_42,X_42),zero) )],[refute_0_43,refute_0_18]) ).
cnf(refute_0_45,plain,
less_equal(zero,divide(X_42,X_42)),
inference(subst,[],[zero_is_smallest:[bind(X,$fot(divide(X_42,X_42)))]]) ).
cnf(refute_0_46,plain,
zero = divide(X_42,X_42),
inference(resolve,[$cnf( less_equal(zero,divide(X_42,X_42)) )],[refute_0_45,refute_0_44]) ).
cnf(refute_0_47,plain,
zero = divide(divide(X_12,zero),divide(X_12,zero)),
inference(subst,[],[refute_0_46:[bind(X_42,$fot(divide(X_12,zero)))]]) ).
cnf(refute_0_48,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_49,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_50,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
( zero != divide(divide(X_12,zero),divide(X_12,zero))
| divide(divide(X_12,zero),divide(X_12,zero)) = zero ),
inference(subst,[],[refute_0_50:[bind(X0,$fot(zero)),bind(Y0,$fot(divide(divide(X_12,zero),divide(X_12,zero))))]]) ).
cnf(refute_0_52,plain,
divide(divide(X_12,zero),divide(X_12,zero)) = zero,
inference(resolve,[$cnf( $equal(zero,divide(divide(X_12,zero),divide(X_12,zero))) )],[refute_0_47,refute_0_51]) ).
cnf(refute_0_53,plain,
( ~ less_equal(divide(divide(X_12,divide(X_12,zero)),zero),divide(divide(X_12,zero),divide(X_12,zero)))
| divide(divide(X_12,zero),divide(X_12,zero)) != zero
| less_equal(divide(divide(X_12,divide(X_12,zero)),zero),zero) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(X_12,divide(X_12,zero)),zero),divide(divide(X_12,zero),divide(X_12,zero))) ),[1],$fot(zero)]]) ).
cnf(refute_0_54,plain,
( ~ less_equal(divide(divide(X_12,divide(X_12,zero)),zero),divide(divide(X_12,zero),divide(X_12,zero)))
| less_equal(divide(divide(X_12,divide(X_12,zero)),zero),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(X_12,zero),divide(X_12,zero)),zero) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
less_equal(divide(divide(X_12,divide(X_12,zero)),zero),zero),
inference(resolve,[$cnf( less_equal(divide(divide(X_12,divide(X_12,zero)),zero),divide(divide(X_12,zero),divide(X_12,zero))) )],[refute_0_17,refute_0_54]) ).
cnf(refute_0_56,plain,
less_equal(divide(divide(X_64,divide(X_64,zero)),zero),zero),
inference(subst,[],[refute_0_55:[bind(X_12,$fot(X_64))]]) ).
cnf(refute_0_57,plain,
zero = divide(divide(X_64,divide(X_64,zero)),zero),
inference(resolve,[$cnf( less_equal(divide(divide(X_64,divide(X_64,zero)),zero),zero) )],[refute_0_56,refute_0_8]) ).
cnf(refute_0_58,plain,
zero = divide(divide(X_71,divide(X_71,zero)),zero),
inference(subst,[],[refute_0_57:[bind(X_64,$fot(X_71))]]) ).
cnf(refute_0_59,plain,
( zero != divide(divide(X_71,divide(X_71,zero)),zero)
| divide(divide(X_71,divide(X_71,zero)),zero) = zero ),
inference(subst,[],[refute_0_50:[bind(X0,$fot(zero)),bind(Y0,$fot(divide(divide(X_71,divide(X_71,zero)),zero)))]]) ).
cnf(refute_0_60,plain,
divide(divide(X_71,divide(X_71,zero)),zero) = zero,
inference(resolve,[$cnf( $equal(zero,divide(divide(X_71,divide(X_71,zero)),zero)) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
( divide(divide(X_71,divide(X_71,zero)),zero) != zero
| zero != zero
| divide(divide(X_71,divide(X_71,zero)),zero) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(divide(X_71,divide(X_71,zero)),zero),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_62,plain,
( zero != zero
| divide(divide(X_71,divide(X_71,zero)),zero) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(X_71,divide(X_71,zero)),zero),zero) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
( zero != zero
| less_equal(divide(X_71,divide(X_71,zero)),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(X_71,divide(X_71,zero)),zero),zero) )],[refute_0_62,refute_0_7]) ).
cnf(refute_0_64,plain,
less_equal(divide(X_71,divide(X_71,zero)),zero),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_41,refute_0_63]) ).
cnf(refute_0_65,plain,
less_equal(divide(X_72,divide(X_72,zero)),zero),
inference(subst,[],[refute_0_64:[bind(X_71,$fot(X_72))]]) ).
cnf(refute_0_66,plain,
zero = divide(X_72,divide(X_72,zero)),
inference(resolve,[$cnf( less_equal(divide(X_72,divide(X_72,zero)),zero) )],[refute_0_65,refute_0_6]) ).
cnf(refute_0_67,plain,
zero = divide(X,divide(X,zero)),
inference(subst,[],[refute_0_66:[bind(X_72,$fot(X))]]) ).
cnf(refute_0_68,plain,
( zero != divide(X,divide(X,zero))
| divide(X,divide(X,zero)) = zero ),
inference(subst,[],[refute_0_50:[bind(X0,$fot(zero)),bind(Y0,$fot(divide(X,divide(X,zero))))]]) ).
cnf(refute_0_69,plain,
divide(X,divide(X,zero)) = zero,
inference(resolve,[$cnf( $equal(zero,divide(X,divide(X,zero))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
( divide(X,divide(X,zero)) != zero
| zero != zero
| divide(X,divide(X,zero)) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(X,divide(X,zero)),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_71,plain,
( zero != zero
| divide(X,divide(X,zero)) = zero ),
inference(resolve,[$cnf( $equal(divide(X,divide(X,zero)),zero) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
( zero != zero
| less_equal(X,divide(X,zero)) ),
inference(resolve,[$cnf( $equal(divide(X,divide(X,zero)),zero) )],[refute_0_71,refute_0_5]) ).
cnf(refute_0_73,plain,
less_equal(X,divide(X,zero)),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_41,refute_0_72]) ).
cnf(refute_0_74,plain,
less_equal(divide(divide(X_126,b),divide(X_126,a)),divide(divide(divide(X_126,b),divide(X_126,a)),zero)),
inference(subst,[],[refute_0_73:[bind(X,$fot(divide(divide(X_126,b),divide(X_126,a))))]]) ).
cnf(refute_0_75,plain,
( ~ less_equal(divide(divide(divide(X_112,b),divide(X_112,a)),zero),zero)
| zero = divide(divide(divide(X_112,b),divide(X_112,a)),zero) ),
inference(subst,[],[refute_0_3:[bind(X_40,$fot(divide(divide(divide(X_112,b),divide(X_112,a)),zero)))]]) ).
cnf(refute_0_76,plain,
less_equal(divide(divide(X_12,X_14),divide(divide(X_14,Y),X_14)),divide(divide(X_12,divide(X_14,Y)),X_14)),
inference(subst,[],[quotient_property:[bind(X,$fot(X_12)),bind(Y,$fot(divide(X_14,Y))),bind(Z,$fot(X_14))]]) ).
cnf(refute_0_77,plain,
divide(divide(X_14,Y),X_14) = zero,
inference(subst,[],[refute_0_23:[bind(X_7,$fot(X_14))]]) ).
cnf(refute_0_78,plain,
( ~ less_equal(divide(divide(X_12,X_14),divide(divide(X_14,Y),X_14)),divide(divide(X_12,divide(X_14,Y)),X_14))
| divide(divide(X_14,Y),X_14) != zero
| less_equal(divide(divide(X_12,X_14),zero),divide(divide(X_12,divide(X_14,Y)),X_14)) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(X_12,X_14),divide(divide(X_14,Y),X_14)),divide(divide(X_12,divide(X_14,Y)),X_14)) ),[0,1],$fot(zero)]]) ).
cnf(refute_0_79,plain,
( ~ less_equal(divide(divide(X_12,X_14),divide(divide(X_14,Y),X_14)),divide(divide(X_12,divide(X_14,Y)),X_14))
| less_equal(divide(divide(X_12,X_14),zero),divide(divide(X_12,divide(X_14,Y)),X_14)) ),
inference(resolve,[$cnf( $equal(divide(divide(X_14,Y),X_14),zero) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
less_equal(divide(divide(X_12,X_14),zero),divide(divide(X_12,divide(X_14,Y)),X_14)),
inference(resolve,[$cnf( less_equal(divide(divide(X_12,X_14),divide(divide(X_14,Y),X_14)),divide(divide(X_12,divide(X_14,Y)),X_14)) )],[refute_0_76,refute_0_79]) ).
cnf(refute_0_81,plain,
less_equal(divide(divide(divide(X_67,b),divide(X_67,a)),zero),divide(divide(divide(X_67,b),divide(divide(X_67,a),b)),divide(X_67,a))),
inference(subst,[],[refute_0_80:[bind(Y,$fot(b)),bind(X_12,$fot(divide(X_67,b))),bind(X_14,$fot(divide(X_67,a)))]]) ).
cnf(refute_0_82,plain,
( ~ less_equal(divide(divide(X_67,b),divide(divide(X_67,a),b)),zero)
| zero = divide(divide(X_67,b),divide(divide(X_67,a),b)) ),
inference(subst,[],[refute_0_3:[bind(X_40,$fot(divide(divide(X_67,b),divide(divide(X_67,a),b))))]]) ).
cnf(refute_0_83,plain,
( divide(divide(divide(X_54,b),divide(divide(X_54,a),b)),zero) != zero
| less_equal(divide(divide(X_54,b),divide(divide(X_54,a),b)),zero) ),
inference(subst,[],[quotient_less_equal2:[bind(X,$fot(divide(divide(X_54,b),divide(divide(X_54,a),b)))),bind(Y,$fot(zero))]]) ).
cnf(refute_0_84,plain,
less_equal(divide(divide(divide(X_16,b),divide(divide(X_16,a),b)),zero),divide(divide(divide(X_16,b),zero),divide(divide(X_16,a),b))),
inference(subst,[],[refute_0_16:[bind(X_12,$fot(divide(X_16,b))),bind(X_14,$fot(divide(divide(X_16,a),b)))]]) ).
cnf(refute_0_85,plain,
( ~ less_equal(divide(divide(X_16,b),zero),divide(divide(X_16,a),b))
| divide(divide(divide(X_16,b),zero),divide(divide(X_16,a),b)) = zero ),
inference(subst,[],[quotient_less_equal1:[bind(X,$fot(divide(divide(X_16,b),zero))),bind(Y,$fot(divide(divide(X_16,a),b)))]]) ).
cnf(refute_0_86,plain,
less_equal(divide(divide(X_12,b),divide(a,b)),divide(divide(X_12,a),b)),
inference(subst,[],[quotient_property:[bind(X,$fot(X_12)),bind(Y,$fot(a)),bind(Z,$fot(b))]]) ).
cnf(refute_0_87,plain,
( ~ less_equal(a,b)
| divide(a,b) = zero ),
inference(subst,[],[quotient_less_equal1:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).
cnf(refute_0_88,plain,
divide(a,b) = zero,
inference(resolve,[$cnf( less_equal(a,b) )],[a_LE_b,refute_0_87]) ).
cnf(refute_0_89,plain,
( ~ less_equal(divide(divide(X_12,b),divide(a,b)),divide(divide(X_12,a),b))
| divide(a,b) != zero
| less_equal(divide(divide(X_12,b),zero),divide(divide(X_12,a),b)) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(X_12,b),divide(a,b)),divide(divide(X_12,a),b)) ),[0,1],$fot(zero)]]) ).
cnf(refute_0_90,plain,
( ~ less_equal(divide(divide(X_12,b),divide(a,b)),divide(divide(X_12,a),b))
| less_equal(divide(divide(X_12,b),zero),divide(divide(X_12,a),b)) ),
inference(resolve,[$cnf( $equal(divide(a,b),zero) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
less_equal(divide(divide(X_12,b),zero),divide(divide(X_12,a),b)),
inference(resolve,[$cnf( less_equal(divide(divide(X_12,b),divide(a,b)),divide(divide(X_12,a),b)) )],[refute_0_86,refute_0_90]) ).
cnf(refute_0_92,plain,
less_equal(divide(divide(X_16,b),zero),divide(divide(X_16,a),b)),
inference(subst,[],[refute_0_91:[bind(X_12,$fot(X_16))]]) ).
cnf(refute_0_93,plain,
divide(divide(divide(X_16,b),zero),divide(divide(X_16,a),b)) = zero,
inference(resolve,[$cnf( less_equal(divide(divide(X_16,b),zero),divide(divide(X_16,a),b)) )],[refute_0_92,refute_0_85]) ).
cnf(refute_0_94,plain,
( ~ less_equal(divide(divide(divide(X_16,b),divide(divide(X_16,a),b)),zero),divide(divide(divide(X_16,b),zero),divide(divide(X_16,a),b)))
| divide(divide(divide(X_16,b),zero),divide(divide(X_16,a),b)) != zero
| less_equal(divide(divide(divide(X_16,b),divide(divide(X_16,a),b)),zero),zero) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(divide(X_16,b),divide(divide(X_16,a),b)),zero),divide(divide(divide(X_16,b),zero),divide(divide(X_16,a),b))) ),[1],$fot(zero)]]) ).
cnf(refute_0_95,plain,
( ~ less_equal(divide(divide(divide(X_16,b),divide(divide(X_16,a),b)),zero),divide(divide(divide(X_16,b),zero),divide(divide(X_16,a),b)))
| less_equal(divide(divide(divide(X_16,b),divide(divide(X_16,a),b)),zero),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(divide(X_16,b),zero),divide(divide(X_16,a),b)),zero) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
less_equal(divide(divide(divide(X_16,b),divide(divide(X_16,a),b)),zero),zero),
inference(resolve,[$cnf( less_equal(divide(divide(divide(X_16,b),divide(divide(X_16,a),b)),zero),divide(divide(divide(X_16,b),zero),divide(divide(X_16,a),b))) )],[refute_0_84,refute_0_95]) ).
cnf(refute_0_97,plain,
( ~ less_equal(divide(divide(divide(X_16,b),divide(divide(X_16,a),b)),zero),zero)
| ~ less_equal(zero,divide(divide(divide(X_16,b),divide(divide(X_16,a),b)),zero))
| divide(divide(divide(X_16,b),divide(divide(X_16,a),b)),zero) = zero ),
inference(subst,[],[less_equal_and_equal:[bind(X,$fot(divide(divide(divide(X_16,b),divide(divide(X_16,a),b)),zero))),bind(Y,$fot(zero))]]) ).
cnf(refute_0_98,plain,
( ~ less_equal(zero,divide(divide(divide(X_16,b),divide(divide(X_16,a),b)),zero))
| divide(divide(divide(X_16,b),divide(divide(X_16,a),b)),zero) = zero ),
inference(resolve,[$cnf( less_equal(divide(divide(divide(X_16,b),divide(divide(X_16,a),b)),zero),zero) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
less_equal(zero,divide(divide(divide(X_16,b),divide(divide(X_16,a),b)),zero)),
inference(subst,[],[zero_is_smallest:[bind(X,$fot(divide(divide(divide(X_16,b),divide(divide(X_16,a),b)),zero)))]]) ).
cnf(refute_0_100,plain,
divide(divide(divide(X_16,b),divide(divide(X_16,a),b)),zero) = zero,
inference(resolve,[$cnf( less_equal(zero,divide(divide(divide(X_16,b),divide(divide(X_16,a),b)),zero)) )],[refute_0_99,refute_0_98]) ).
cnf(refute_0_101,plain,
divide(divide(divide(X_54,b),divide(divide(X_54,a),b)),zero) = zero,
inference(subst,[],[refute_0_100:[bind(X_16,$fot(X_54))]]) ).
cnf(refute_0_102,plain,
( divide(divide(divide(X_54,b),divide(divide(X_54,a),b)),zero) != zero
| zero != zero
| divide(divide(divide(X_54,b),divide(divide(X_54,a),b)),zero) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(divide(divide(X_54,b),divide(divide(X_54,a),b)),zero),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_103,plain,
( zero != zero
| divide(divide(divide(X_54,b),divide(divide(X_54,a),b)),zero) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(divide(X_54,b),divide(divide(X_54,a),b)),zero),zero) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
( zero != zero
| less_equal(divide(divide(X_54,b),divide(divide(X_54,a),b)),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(divide(X_54,b),divide(divide(X_54,a),b)),zero),zero) )],[refute_0_103,refute_0_83]) ).
cnf(refute_0_105,plain,
less_equal(divide(divide(X_54,b),divide(divide(X_54,a),b)),zero),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_41,refute_0_104]) ).
cnf(refute_0_106,plain,
less_equal(divide(divide(X_67,b),divide(divide(X_67,a),b)),zero),
inference(subst,[],[refute_0_105:[bind(X_54,$fot(X_67))]]) ).
cnf(refute_0_107,plain,
zero = divide(divide(X_67,b),divide(divide(X_67,a),b)),
inference(resolve,[$cnf( less_equal(divide(divide(X_67,b),divide(divide(X_67,a),b)),zero) )],[refute_0_106,refute_0_82]) ).
cnf(refute_0_108,plain,
( zero != divide(divide(X_67,b),divide(divide(X_67,a),b))
| divide(divide(X_67,b),divide(divide(X_67,a),b)) = zero ),
inference(subst,[],[refute_0_50:[bind(X0,$fot(zero)),bind(Y0,$fot(divide(divide(X_67,b),divide(divide(X_67,a),b))))]]) ).
cnf(refute_0_109,plain,
divide(divide(X_67,b),divide(divide(X_67,a),b)) = zero,
inference(resolve,[$cnf( $equal(zero,divide(divide(X_67,b),divide(divide(X_67,a),b))) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
( ~ less_equal(divide(divide(divide(X_67,b),divide(X_67,a)),zero),divide(divide(divide(X_67,b),divide(divide(X_67,a),b)),divide(X_67,a)))
| divide(divide(X_67,b),divide(divide(X_67,a),b)) != zero
| less_equal(divide(divide(divide(X_67,b),divide(X_67,a)),zero),divide(zero,divide(X_67,a))) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(divide(X_67,b),divide(X_67,a)),zero),divide(divide(divide(X_67,b),divide(divide(X_67,a),b)),divide(X_67,a))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_111,plain,
( ~ less_equal(divide(divide(divide(X_67,b),divide(X_67,a)),zero),divide(divide(divide(X_67,b),divide(divide(X_67,a),b)),divide(X_67,a)))
| less_equal(divide(divide(divide(X_67,b),divide(X_67,a)),zero),divide(zero,divide(X_67,a))) ),
inference(resolve,[$cnf( $equal(divide(divide(X_67,b),divide(divide(X_67,a),b)),zero) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
less_equal(divide(divide(divide(X_67,b),divide(X_67,a)),zero),divide(zero,divide(X_67,a))),
inference(resolve,[$cnf( less_equal(divide(divide(divide(X_67,b),divide(X_67,a)),zero),divide(divide(divide(X_67,b),divide(divide(X_67,a),b)),divide(X_67,a))) )],[refute_0_81,refute_0_111]) ).
cnf(refute_0_113,plain,
divide(zero,divide(X_67,a)) = zero,
inference(subst,[],[refute_0_12:[bind(X_7,$fot(divide(X_67,a)))]]) ).
cnf(refute_0_114,plain,
( ~ less_equal(divide(divide(divide(X_67,b),divide(X_67,a)),zero),divide(zero,divide(X_67,a)))
| divide(zero,divide(X_67,a)) != zero
| less_equal(divide(divide(divide(X_67,b),divide(X_67,a)),zero),zero) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(divide(X_67,b),divide(X_67,a)),zero),divide(zero,divide(X_67,a))) ),[1],$fot(zero)]]) ).
cnf(refute_0_115,plain,
( ~ less_equal(divide(divide(divide(X_67,b),divide(X_67,a)),zero),divide(zero,divide(X_67,a)))
| less_equal(divide(divide(divide(X_67,b),divide(X_67,a)),zero),zero) ),
inference(resolve,[$cnf( $equal(divide(zero,divide(X_67,a)),zero) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
less_equal(divide(divide(divide(X_67,b),divide(X_67,a)),zero),zero),
inference(resolve,[$cnf( less_equal(divide(divide(divide(X_67,b),divide(X_67,a)),zero),divide(zero,divide(X_67,a))) )],[refute_0_112,refute_0_115]) ).
cnf(refute_0_117,plain,
less_equal(divide(divide(divide(X_112,b),divide(X_112,a)),zero),zero),
inference(subst,[],[refute_0_116:[bind(X_67,$fot(X_112))]]) ).
cnf(refute_0_118,plain,
zero = divide(divide(divide(X_112,b),divide(X_112,a)),zero),
inference(resolve,[$cnf( less_equal(divide(divide(divide(X_112,b),divide(X_112,a)),zero),zero) )],[refute_0_117,refute_0_75]) ).
cnf(refute_0_119,plain,
zero = divide(divide(divide(X_126,b),divide(X_126,a)),zero),
inference(subst,[],[refute_0_118:[bind(X_112,$fot(X_126))]]) ).
cnf(refute_0_120,plain,
( zero != divide(divide(divide(X_126,b),divide(X_126,a)),zero)
| divide(divide(divide(X_126,b),divide(X_126,a)),zero) = zero ),
inference(subst,[],[refute_0_50:[bind(X0,$fot(zero)),bind(Y0,$fot(divide(divide(divide(X_126,b),divide(X_126,a)),zero)))]]) ).
cnf(refute_0_121,plain,
divide(divide(divide(X_126,b),divide(X_126,a)),zero) = zero,
inference(resolve,[$cnf( $equal(zero,divide(divide(divide(X_126,b),divide(X_126,a)),zero)) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
( ~ less_equal(divide(divide(X_126,b),divide(X_126,a)),divide(divide(divide(X_126,b),divide(X_126,a)),zero))
| divide(divide(divide(X_126,b),divide(X_126,a)),zero) != zero
| less_equal(divide(divide(X_126,b),divide(X_126,a)),zero) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(X_126,b),divide(X_126,a)),divide(divide(divide(X_126,b),divide(X_126,a)),zero)) ),[1],$fot(zero)]]) ).
cnf(refute_0_123,plain,
( ~ less_equal(divide(divide(X_126,b),divide(X_126,a)),divide(divide(divide(X_126,b),divide(X_126,a)),zero))
| less_equal(divide(divide(X_126,b),divide(X_126,a)),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(divide(X_126,b),divide(X_126,a)),zero),zero) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
less_equal(divide(divide(X_126,b),divide(X_126,a)),zero),
inference(resolve,[$cnf( less_equal(divide(divide(X_126,b),divide(X_126,a)),divide(divide(divide(X_126,b),divide(X_126,a)),zero)) )],[refute_0_74,refute_0_123]) ).
cnf(refute_0_125,plain,
less_equal(divide(divide(X_129,b),divide(X_129,a)),zero),
inference(subst,[],[refute_0_124:[bind(X_126,$fot(X_129))]]) ).
cnf(refute_0_126,plain,
zero = divide(divide(X_129,b),divide(X_129,a)),
inference(resolve,[$cnf( less_equal(divide(divide(X_129,b),divide(X_129,a)),zero) )],[refute_0_125,refute_0_4]) ).
cnf(refute_0_127,plain,
zero = divide(divide(X_130,b),divide(X_130,a)),
inference(subst,[],[refute_0_126:[bind(X_129,$fot(X_130))]]) ).
cnf(refute_0_128,plain,
( zero != divide(divide(X_130,b),divide(X_130,a))
| divide(divide(X_130,b),divide(X_130,a)) = zero ),
inference(subst,[],[refute_0_50:[bind(X0,$fot(zero)),bind(Y0,$fot(divide(divide(X_130,b),divide(X_130,a))))]]) ).
cnf(refute_0_129,plain,
divide(divide(X_130,b),divide(X_130,a)) = zero,
inference(resolve,[$cnf( $equal(zero,divide(divide(X_130,b),divide(X_130,a))) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
( divide(divide(X_130,b),divide(X_130,a)) != zero
| zero != zero
| divide(divide(X_130,b),divide(X_130,a)) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(divide(X_130,b),divide(X_130,a)),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_131,plain,
( zero != zero
| divide(divide(X_130,b),divide(X_130,a)) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(X_130,b),divide(X_130,a)),zero) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
( zero != zero
| less_equal(divide(X_130,b),divide(X_130,a)) ),
inference(resolve,[$cnf( $equal(divide(divide(X_130,b),divide(X_130,a)),zero) )],[refute_0_131,refute_0_0]) ).
cnf(refute_0_133,plain,
less_equal(divide(X_130,b),divide(X_130,a)),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_41,refute_0_132]) ).
cnf(refute_0_134,plain,
less_equal(divide(c,b),divide(c,a)),
inference(subst,[],[refute_0_133:[bind(X_130,$fot(c))]]) ).
cnf(refute_0_135,plain,
$false,
inference(resolve,[$cnf( less_equal(divide(c,b),divide(c,a)) )],[refute_0_134,prove_c_divide_b_LE_c_divide_a]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : HEN007-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.11/0.33 % Computer : n009.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Fri Jul 1 14:46:22 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.17/0.47 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.47
% 0.17/0.47 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.17/0.49
%------------------------------------------------------------------------------