TSTP Solution File: HEN006-6 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : HEN006-6 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.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 12:58:37 EDT 2022
% Result : Unsatisfiable 0.21s 0.48s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 23
% Syntax : Number of clauses : 94 ( 48 unt; 0 nHn; 61 RR)
% Number of literals : 156 ( 74 equ; 63 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 73 ( 8 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(zero_divide_anything_is_zero,axiom,
divide(zero,X) = zero ).
cnf(x_divide_x_is_zero,axiom,
divide(X,X) = zero ).
cnf(a_divide_b_LE_d,hypothesis,
less_equal(divide(a,b),d) ).
cnf(prove_a_divide_d_LE_b,negated_conjecture,
~ less_equal(divide(a,d),b) ).
cnf(refute_0_0,plain,
( divide(divide(a,d),b) != zero
| less_equal(divide(a,d),b) ),
inference(subst,[],[quotient_less_equal2:[bind(X,$fot(divide(a,d))),bind(Y,$fot(b))]]) ).
cnf(refute_0_1,plain,
less_equal(zero,X_46),
inference(subst,[],[zero_is_smallest:[bind(X,$fot(X_46))]]) ).
cnf(refute_0_2,plain,
( ~ less_equal(X_46,zero)
| ~ less_equal(zero,X_46)
| zero = X_46 ),
inference(subst,[],[less_equal_and_equal:[bind(X,$fot(zero)),bind(Y,$fot(X_46))]]) ).
cnf(refute_0_3,plain,
( ~ less_equal(X_46,zero)
| zero = X_46 ),
inference(resolve,[$cnf( less_equal(zero,X_46) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ less_equal(divide(divide(a,d),b),zero)
| zero = divide(divide(a,d),b) ),
inference(subst,[],[refute_0_3:[bind(X_46,$fot(divide(divide(a,d),b)))]]) ).
cnf(refute_0_5,plain,
( divide(X,divide(X,zero)) != zero
| less_equal(X,divide(X,zero)) ),
inference(subst,[],[quotient_less_equal2:[bind(Y,$fot(divide(X,zero)))]]) ).
cnf(refute_0_6,plain,
( ~ less_equal(divide(X_49,divide(X_49,zero)),zero)
| ~ less_equal(zero,divide(X_49,divide(X_49,zero)))
| zero = divide(X_49,divide(X_49,zero)) ),
inference(subst,[],[less_equal_and_equal:[bind(X,$fot(zero)),bind(Y,$fot(divide(X_49,divide(X_49,zero))))]]) ).
cnf(refute_0_7,plain,
( divide(divide(X_48,divide(X_48,zero)),zero) != zero
| less_equal(divide(X_48,divide(X_48,zero)),zero) ),
inference(subst,[],[quotient_less_equal2:[bind(X,$fot(divide(X_48,divide(X_48,zero)))),bind(Y,$fot(zero))]]) ).
cnf(refute_0_8,plain,
less_equal(divide(divide(X_14,X_16),divide(zero,X_16)),divide(divide(X_14,zero),X_16)),
inference(subst,[],[quotient_property:[bind(X,$fot(X_14)),bind(Y,$fot(zero)),bind(Z,$fot(X_16))]]) ).
cnf(refute_0_9,plain,
divide(zero,X_16) = zero,
inference(subst,[],[zero_divide_anything_is_zero:[bind(X,$fot(X_16))]]) ).
cnf(refute_0_10,plain,
( ~ less_equal(divide(divide(X_14,X_16),divide(zero,X_16)),divide(divide(X_14,zero),X_16))
| divide(zero,X_16) != zero
| less_equal(divide(divide(X_14,X_16),zero),divide(divide(X_14,zero),X_16)) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(X_14,X_16),divide(zero,X_16)),divide(divide(X_14,zero),X_16)) ),[0,1],$fot(zero)]]) ).
cnf(refute_0_11,plain,
( ~ less_equal(divide(divide(X_14,X_16),divide(zero,X_16)),divide(divide(X_14,zero),X_16))
| less_equal(divide(divide(X_14,X_16),zero),divide(divide(X_14,zero),X_16)) ),
inference(resolve,[$cnf( $equal(divide(zero,X_16),zero) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
less_equal(divide(divide(X_14,X_16),zero),divide(divide(X_14,zero),X_16)),
inference(resolve,[$cnf( less_equal(divide(divide(X_14,X_16),divide(zero,X_16)),divide(divide(X_14,zero),X_16)) )],[refute_0_8,refute_0_11]) ).
cnf(refute_0_13,plain,
less_equal(divide(divide(X_25,divide(X_25,zero)),zero),divide(divide(X_25,zero),divide(X_25,zero))),
inference(subst,[],[refute_0_12:[bind(X_14,$fot(X_25)),bind(X_16,$fot(divide(X_25,zero)))]]) ).
cnf(refute_0_14,plain,
divide(divide(X_25,zero),divide(X_25,zero)) = zero,
inference(subst,[],[x_divide_x_is_zero:[bind(X,$fot(divide(X_25,zero)))]]) ).
cnf(refute_0_15,plain,
( ~ less_equal(divide(divide(X_25,divide(X_25,zero)),zero),divide(divide(X_25,zero),divide(X_25,zero)))
| divide(divide(X_25,zero),divide(X_25,zero)) != zero
| less_equal(divide(divide(X_25,divide(X_25,zero)),zero),zero) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(X_25,divide(X_25,zero)),zero),divide(divide(X_25,zero),divide(X_25,zero))) ),[1],$fot(zero)]]) ).
cnf(refute_0_16,plain,
( ~ less_equal(divide(divide(X_25,divide(X_25,zero)),zero),divide(divide(X_25,zero),divide(X_25,zero)))
| less_equal(divide(divide(X_25,divide(X_25,zero)),zero),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(X_25,zero),divide(X_25,zero)),zero) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
less_equal(divide(divide(X_25,divide(X_25,zero)),zero),zero),
inference(resolve,[$cnf( less_equal(divide(divide(X_25,divide(X_25,zero)),zero),divide(divide(X_25,zero),divide(X_25,zero))) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ less_equal(divide(divide(X_25,divide(X_25,zero)),zero),zero)
| ~ less_equal(zero,divide(divide(X_25,divide(X_25,zero)),zero))
| divide(divide(X_25,divide(X_25,zero)),zero) = zero ),
inference(subst,[],[less_equal_and_equal:[bind(X,$fot(divide(divide(X_25,divide(X_25,zero)),zero))),bind(Y,$fot(zero))]]) ).
cnf(refute_0_19,plain,
( ~ less_equal(zero,divide(divide(X_25,divide(X_25,zero)),zero))
| divide(divide(X_25,divide(X_25,zero)),zero) = zero ),
inference(resolve,[$cnf( less_equal(divide(divide(X_25,divide(X_25,zero)),zero),zero) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
less_equal(zero,divide(divide(X_25,divide(X_25,zero)),zero)),
inference(subst,[],[zero_is_smallest:[bind(X,$fot(divide(divide(X_25,divide(X_25,zero)),zero)))]]) ).
cnf(refute_0_21,plain,
divide(divide(X_25,divide(X_25,zero)),zero) = zero,
inference(resolve,[$cnf( less_equal(zero,divide(divide(X_25,divide(X_25,zero)),zero)) )],[refute_0_20,refute_0_19]) ).
cnf(refute_0_22,plain,
divide(divide(X_48,divide(X_48,zero)),zero) = zero,
inference(subst,[],[refute_0_21:[bind(X_25,$fot(X_48))]]) ).
cnf(refute_0_23,plain,
( divide(divide(X_48,divide(X_48,zero)),zero) != zero
| zero != zero
| divide(divide(X_48,divide(X_48,zero)),zero) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(divide(X_48,divide(X_48,zero)),zero),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_24,plain,
( zero != zero
| divide(divide(X_48,divide(X_48,zero)),zero) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(X_48,divide(X_48,zero)),zero),zero) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( zero != zero
| less_equal(divide(X_48,divide(X_48,zero)),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(X_48,divide(X_48,zero)),zero),zero) )],[refute_0_24,refute_0_7]) ).
cnf(refute_0_26,plain,
zero = zero,
introduced(tautology,[refl,[$fot(zero)]]) ).
cnf(refute_0_27,plain,
less_equal(divide(X_48,divide(X_48,zero)),zero),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_26,refute_0_25]) ).
cnf(refute_0_28,plain,
less_equal(divide(X_49,divide(X_49,zero)),zero),
inference(subst,[],[refute_0_27:[bind(X_48,$fot(X_49))]]) ).
cnf(refute_0_29,plain,
( ~ less_equal(zero,divide(X_49,divide(X_49,zero)))
| zero = divide(X_49,divide(X_49,zero)) ),
inference(resolve,[$cnf( less_equal(divide(X_49,divide(X_49,zero)),zero) )],[refute_0_28,refute_0_6]) ).
cnf(refute_0_30,plain,
less_equal(zero,divide(X_49,divide(X_49,zero))),
inference(subst,[],[zero_is_smallest:[bind(X,$fot(divide(X_49,divide(X_49,zero))))]]) ).
cnf(refute_0_31,plain,
zero = divide(X_49,divide(X_49,zero)),
inference(resolve,[$cnf( less_equal(zero,divide(X_49,divide(X_49,zero))) )],[refute_0_30,refute_0_29]) ).
cnf(refute_0_32,plain,
zero = divide(X,divide(X,zero)),
inference(subst,[],[refute_0_31:[bind(X_49,$fot(X))]]) ).
cnf(refute_0_33,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_34,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_35,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
( zero != divide(X,divide(X,zero))
| divide(X,divide(X,zero)) = zero ),
inference(subst,[],[refute_0_35:[bind(X0,$fot(zero)),bind(Y0,$fot(divide(X,divide(X,zero))))]]) ).
cnf(refute_0_37,plain,
divide(X,divide(X,zero)) = zero,
inference(resolve,[$cnf( $equal(zero,divide(X,divide(X,zero))) )],[refute_0_32,refute_0_36]) ).
cnf(refute_0_38,plain,
( divide(X,divide(X,zero)) != zero
| zero != zero
| divide(X,divide(X,zero)) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(X,divide(X,zero)),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_39,plain,
( zero != zero
| divide(X,divide(X,zero)) = zero ),
inference(resolve,[$cnf( $equal(divide(X,divide(X,zero)),zero) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( zero != zero
| less_equal(X,divide(X,zero)) ),
inference(resolve,[$cnf( $equal(divide(X,divide(X,zero)),zero) )],[refute_0_39,refute_0_5]) ).
cnf(refute_0_41,plain,
less_equal(X,divide(X,zero)),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_26,refute_0_40]) ).
cnf(refute_0_42,plain,
less_equal(divide(divide(a,d),b),divide(divide(divide(a,d),b),zero)),
inference(subst,[],[refute_0_41:[bind(X,$fot(divide(divide(a,d),b)))]]) ).
cnf(refute_0_43,plain,
( ~ less_equal(divide(divide(divide(a,d),b),zero),zero)
| zero = divide(divide(divide(a,d),b),zero) ),
inference(subst,[],[refute_0_3:[bind(X_46,$fot(divide(divide(divide(a,d),b),zero)))]]) ).
cnf(refute_0_44,plain,
less_equal(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(divide(divide(a,d),divide(b,d)),Z)),
inference(subst,[],[quotient_property:[bind(X,$fot(divide(a,d))),bind(Y,$fot(divide(b,d)))]]) ).
cnf(refute_0_45,plain,
less_equal(divide(divide(a,d),divide(b,d)),divide(divide(a,b),d)),
inference(subst,[],[quotient_property:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(d))]]) ).
cnf(refute_0_46,plain,
( ~ less_equal(divide(a,b),d)
| divide(divide(a,b),d) = zero ),
inference(subst,[],[quotient_less_equal1:[bind(X,$fot(divide(a,b))),bind(Y,$fot(d))]]) ).
cnf(refute_0_47,plain,
divide(divide(a,b),d) = zero,
inference(resolve,[$cnf( less_equal(divide(a,b),d) )],[a_divide_b_LE_d,refute_0_46]) ).
cnf(refute_0_48,plain,
( ~ less_equal(divide(divide(a,d),divide(b,d)),divide(divide(a,b),d))
| divide(divide(a,b),d) != zero
| less_equal(divide(divide(a,d),divide(b,d)),zero) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(a,d),divide(b,d)),divide(divide(a,b),d)) ),[1],$fot(zero)]]) ).
cnf(refute_0_49,plain,
( ~ less_equal(divide(divide(a,d),divide(b,d)),divide(divide(a,b),d))
| less_equal(divide(divide(a,d),divide(b,d)),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(a,b),d),zero) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
less_equal(divide(divide(a,d),divide(b,d)),zero),
inference(resolve,[$cnf( less_equal(divide(divide(a,d),divide(b,d)),divide(divide(a,b),d)) )],[refute_0_45,refute_0_49]) ).
cnf(refute_0_51,plain,
( ~ less_equal(divide(divide(a,d),divide(b,d)),zero)
| ~ less_equal(zero,divide(divide(a,d),divide(b,d)))
| divide(divide(a,d),divide(b,d)) = zero ),
inference(subst,[],[less_equal_and_equal:[bind(X,$fot(divide(divide(a,d),divide(b,d)))),bind(Y,$fot(zero))]]) ).
cnf(refute_0_52,plain,
( ~ less_equal(zero,divide(divide(a,d),divide(b,d)))
| divide(divide(a,d),divide(b,d)) = zero ),
inference(resolve,[$cnf( less_equal(divide(divide(a,d),divide(b,d)),zero) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
less_equal(zero,divide(divide(a,d),divide(b,d))),
inference(subst,[],[zero_is_smallest:[bind(X,$fot(divide(divide(a,d),divide(b,d))))]]) ).
cnf(refute_0_54,plain,
divide(divide(a,d),divide(b,d)) = zero,
inference(resolve,[$cnf( less_equal(zero,divide(divide(a,d),divide(b,d))) )],[refute_0_53,refute_0_52]) ).
cnf(refute_0_55,plain,
( ~ less_equal(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(divide(divide(a,d),divide(b,d)),Z))
| divide(divide(a,d),divide(b,d)) != zero
| less_equal(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(zero,Z)) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(divide(divide(a,d),divide(b,d)),Z)) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_56,plain,
( ~ less_equal(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(divide(divide(a,d),divide(b,d)),Z))
| less_equal(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(zero,Z)) ),
inference(resolve,[$cnf( $equal(divide(divide(a,d),divide(b,d)),zero) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
less_equal(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(zero,Z)),
inference(resolve,[$cnf( less_equal(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(divide(divide(a,d),divide(b,d)),Z)) )],[refute_0_44,refute_0_56]) ).
cnf(refute_0_58,plain,
divide(zero,Z) = zero,
inference(subst,[],[zero_divide_anything_is_zero:[bind(X,$fot(Z))]]) ).
cnf(refute_0_59,plain,
( ~ less_equal(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(zero,Z))
| divide(zero,Z) != zero
| less_equal(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),zero) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(zero,Z)) ),[1],$fot(zero)]]) ).
cnf(refute_0_60,plain,
( ~ less_equal(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(zero,Z))
| less_equal(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),zero) ),
inference(resolve,[$cnf( $equal(divide(zero,Z),zero) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
less_equal(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),zero),
inference(resolve,[$cnf( less_equal(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(zero,Z)) )],[refute_0_57,refute_0_60]) ).
cnf(refute_0_62,plain,
less_equal(divide(divide(divide(a,d),b),divide(divide(b,d),b)),zero),
inference(subst,[],[refute_0_61:[bind(Z,$fot(b))]]) ).
cnf(refute_0_63,plain,
less_equal(divide(X_8,Y),X_8),
inference(subst,[],[quotient_smaller_than_numerator:[bind(X,$fot(X_8))]]) ).
cnf(refute_0_64,plain,
( ~ less_equal(divide(X_8,Y),X_8)
| divide(divide(X_8,Y),X_8) = zero ),
inference(subst,[],[quotient_less_equal1:[bind(X,$fot(divide(X_8,Y))),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_65,plain,
divide(divide(X_8,Y),X_8) = zero,
inference(resolve,[$cnf( less_equal(divide(X_8,Y),X_8) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
divide(divide(b,d),b) = zero,
inference(subst,[],[refute_0_65:[bind(Y,$fot(d)),bind(X_8,$fot(b))]]) ).
cnf(refute_0_67,plain,
( ~ less_equal(divide(divide(divide(a,d),b),divide(divide(b,d),b)),zero)
| divide(divide(b,d),b) != zero
| less_equal(divide(divide(divide(a,d),b),zero),zero) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(divide(a,d),b),divide(divide(b,d),b)),zero) ),[0,1],$fot(zero)]]) ).
cnf(refute_0_68,plain,
( ~ less_equal(divide(divide(divide(a,d),b),divide(divide(b,d),b)),zero)
| less_equal(divide(divide(divide(a,d),b),zero),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(b,d),b),zero) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
less_equal(divide(divide(divide(a,d),b),zero),zero),
inference(resolve,[$cnf( less_equal(divide(divide(divide(a,d),b),divide(divide(b,d),b)),zero) )],[refute_0_62,refute_0_68]) ).
cnf(refute_0_70,plain,
zero = divide(divide(divide(a,d),b),zero),
inference(resolve,[$cnf( less_equal(divide(divide(divide(a,d),b),zero),zero) )],[refute_0_69,refute_0_43]) ).
cnf(refute_0_71,plain,
( zero != divide(divide(divide(a,d),b),zero)
| divide(divide(divide(a,d),b),zero) = zero ),
inference(subst,[],[refute_0_35:[bind(X0,$fot(zero)),bind(Y0,$fot(divide(divide(divide(a,d),b),zero)))]]) ).
cnf(refute_0_72,plain,
divide(divide(divide(a,d),b),zero) = zero,
inference(resolve,[$cnf( $equal(zero,divide(divide(divide(a,d),b),zero)) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
( ~ less_equal(divide(divide(a,d),b),divide(divide(divide(a,d),b),zero))
| divide(divide(divide(a,d),b),zero) != zero
| less_equal(divide(divide(a,d),b),zero) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(a,d),b),divide(divide(divide(a,d),b),zero)) ),[1],$fot(zero)]]) ).
cnf(refute_0_74,plain,
( ~ less_equal(divide(divide(a,d),b),divide(divide(divide(a,d),b),zero))
| less_equal(divide(divide(a,d),b),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(divide(a,d),b),zero),zero) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
less_equal(divide(divide(a,d),b),zero),
inference(resolve,[$cnf( less_equal(divide(divide(a,d),b),divide(divide(divide(a,d),b),zero)) )],[refute_0_42,refute_0_74]) ).
cnf(refute_0_76,plain,
zero = divide(divide(a,d),b),
inference(resolve,[$cnf( less_equal(divide(divide(a,d),b),zero) )],[refute_0_75,refute_0_4]) ).
cnf(refute_0_77,plain,
( zero != divide(divide(a,d),b)
| divide(divide(a,d),b) = zero ),
inference(subst,[],[refute_0_35:[bind(X0,$fot(zero)),bind(Y0,$fot(divide(divide(a,d),b)))]]) ).
cnf(refute_0_78,plain,
divide(divide(a,d),b) = zero,
inference(resolve,[$cnf( $equal(zero,divide(divide(a,d),b)) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
( divide(divide(a,d),b) != zero
| zero != zero
| divide(divide(a,d),b) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(divide(a,d),b),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_80,plain,
( zero != zero
| divide(divide(a,d),b) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(a,d),b),zero) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
( zero != zero
| less_equal(divide(a,d),b) ),
inference(resolve,[$cnf( $equal(divide(divide(a,d),b),zero) )],[refute_0_80,refute_0_0]) ).
cnf(refute_0_82,plain,
less_equal(divide(a,d),b),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_26,refute_0_81]) ).
cnf(refute_0_83,plain,
$false,
inference(resolve,[$cnf( less_equal(divide(a,d),b) )],[refute_0_82,prove_a_divide_d_LE_b]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : HEN006-6 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n015.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Fri Jul 1 15:02:43 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.48 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.48
% 0.21/0.48 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.21/0.49
%------------------------------------------------------------------------------