TSTP Solution File: HEN004-4 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : HEN004-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n006.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 12:58:33 EDT 2022
% Result : Unsatisfiable 0.39s 0.56s
% Output : CNFRefutation 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 17
% Syntax : Number of clauses : 57 ( 31 unt; 0 nHn; 28 RR)
% Number of literals : 93 ( 53 equ; 38 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 : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 63 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
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(prove_x_divide_zero_is_x,negated_conjecture,
divide(a,zero) != a ).
cnf(refute_0_0,plain,
( divide(X,divide(X,zero)) != zero
| less_equal(X,divide(X,zero)) ),
inference(subst,[],[quotient_less_equal2:[bind(Y,$fot(divide(X,zero)))]]) ).
cnf(refute_0_1,plain,
( ~ less_equal(divide(X_40,divide(X_40,zero)),zero)
| ~ less_equal(zero,divide(X_40,divide(X_40,zero)))
| zero = divide(X_40,divide(X_40,zero)) ),
inference(subst,[],[less_equal_and_equal:[bind(X,$fot(zero)),bind(Y,$fot(divide(X_40,divide(X_40,zero))))]]) ).
cnf(refute_0_2,plain,
( divide(divide(X_39,divide(X_39,zero)),zero) != zero
| less_equal(divide(X_39,divide(X_39,zero)),zero) ),
inference(subst,[],[quotient_less_equal2:[bind(X,$fot(divide(X_39,divide(X_39,zero)))),bind(Y,$fot(zero))]]) ).
cnf(refute_0_3,plain,
less_equal(divide(divide(X_14,X_16),divide(zero,X_16)),divide(divide(X_14,zero),X_16)),
inference(subst,[],[quotient_property:[bind(X,$fot(X_14)),bind(Y,$fot(zero)),bind(Z,$fot(X_16))]]) ).
cnf(refute_0_4,plain,
divide(zero,X_16) = zero,
inference(subst,[],[zero_divide_anything_is_zero:[bind(X,$fot(X_16))]]) ).
cnf(refute_0_5,plain,
( ~ less_equal(divide(divide(X_14,X_16),divide(zero,X_16)),divide(divide(X_14,zero),X_16))
| divide(zero,X_16) != zero
| less_equal(divide(divide(X_14,X_16),zero),divide(divide(X_14,zero),X_16)) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(X_14,X_16),divide(zero,X_16)),divide(divide(X_14,zero),X_16)) ),[0,1],$fot(zero)]]) ).
cnf(refute_0_6,plain,
( ~ less_equal(divide(divide(X_14,X_16),divide(zero,X_16)),divide(divide(X_14,zero),X_16))
| less_equal(divide(divide(X_14,X_16),zero),divide(divide(X_14,zero),X_16)) ),
inference(resolve,[$cnf( $equal(divide(zero,X_16),zero) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
less_equal(divide(divide(X_14,X_16),zero),divide(divide(X_14,zero),X_16)),
inference(resolve,[$cnf( less_equal(divide(divide(X_14,X_16),divide(zero,X_16)),divide(divide(X_14,zero),X_16)) )],[refute_0_3,refute_0_6]) ).
cnf(refute_0_8,plain,
less_equal(divide(divide(X_19,divide(X_19,zero)),zero),divide(divide(X_19,zero),divide(X_19,zero))),
inference(subst,[],[refute_0_7:[bind(X_14,$fot(X_19)),bind(X_16,$fot(divide(X_19,zero)))]]) ).
cnf(refute_0_9,plain,
divide(divide(X_19,zero),divide(X_19,zero)) = zero,
inference(subst,[],[x_divide_x_is_zero:[bind(X,$fot(divide(X_19,zero)))]]) ).
cnf(refute_0_10,plain,
( ~ less_equal(divide(divide(X_19,divide(X_19,zero)),zero),divide(divide(X_19,zero),divide(X_19,zero)))
| divide(divide(X_19,zero),divide(X_19,zero)) != zero
| less_equal(divide(divide(X_19,divide(X_19,zero)),zero),zero) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(X_19,divide(X_19,zero)),zero),divide(divide(X_19,zero),divide(X_19,zero))) ),[1],$fot(zero)]]) ).
cnf(refute_0_11,plain,
( ~ less_equal(divide(divide(X_19,divide(X_19,zero)),zero),divide(divide(X_19,zero),divide(X_19,zero)))
| less_equal(divide(divide(X_19,divide(X_19,zero)),zero),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(X_19,zero),divide(X_19,zero)),zero) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
less_equal(divide(divide(X_19,divide(X_19,zero)),zero),zero),
inference(resolve,[$cnf( less_equal(divide(divide(X_19,divide(X_19,zero)),zero),divide(divide(X_19,zero),divide(X_19,zero))) )],[refute_0_8,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ less_equal(divide(divide(X_19,divide(X_19,zero)),zero),zero)
| ~ less_equal(zero,divide(divide(X_19,divide(X_19,zero)),zero))
| divide(divide(X_19,divide(X_19,zero)),zero) = zero ),
inference(subst,[],[less_equal_and_equal:[bind(X,$fot(divide(divide(X_19,divide(X_19,zero)),zero))),bind(Y,$fot(zero))]]) ).
cnf(refute_0_14,plain,
( ~ less_equal(zero,divide(divide(X_19,divide(X_19,zero)),zero))
| divide(divide(X_19,divide(X_19,zero)),zero) = zero ),
inference(resolve,[$cnf( less_equal(divide(divide(X_19,divide(X_19,zero)),zero),zero) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
less_equal(zero,divide(divide(X_19,divide(X_19,zero)),zero)),
inference(subst,[],[zero_is_smallest:[bind(X,$fot(divide(divide(X_19,divide(X_19,zero)),zero)))]]) ).
cnf(refute_0_16,plain,
divide(divide(X_19,divide(X_19,zero)),zero) = zero,
inference(resolve,[$cnf( less_equal(zero,divide(divide(X_19,divide(X_19,zero)),zero)) )],[refute_0_15,refute_0_14]) ).
cnf(refute_0_17,plain,
divide(divide(X_39,divide(X_39,zero)),zero) = zero,
inference(subst,[],[refute_0_16:[bind(X_19,$fot(X_39))]]) ).
cnf(refute_0_18,plain,
( divide(divide(X_39,divide(X_39,zero)),zero) != zero
| zero != zero
| divide(divide(X_39,divide(X_39,zero)),zero) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(divide(X_39,divide(X_39,zero)),zero),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_19,plain,
( zero != zero
| divide(divide(X_39,divide(X_39,zero)),zero) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(X_39,divide(X_39,zero)),zero),zero) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( zero != zero
| less_equal(divide(X_39,divide(X_39,zero)),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(X_39,divide(X_39,zero)),zero),zero) )],[refute_0_19,refute_0_2]) ).
cnf(refute_0_21,plain,
zero = zero,
introduced(tautology,[refl,[$fot(zero)]]) ).
cnf(refute_0_22,plain,
less_equal(divide(X_39,divide(X_39,zero)),zero),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_21,refute_0_20]) ).
cnf(refute_0_23,plain,
less_equal(divide(X_40,divide(X_40,zero)),zero),
inference(subst,[],[refute_0_22:[bind(X_39,$fot(X_40))]]) ).
cnf(refute_0_24,plain,
( ~ less_equal(zero,divide(X_40,divide(X_40,zero)))
| zero = divide(X_40,divide(X_40,zero)) ),
inference(resolve,[$cnf( less_equal(divide(X_40,divide(X_40,zero)),zero) )],[refute_0_23,refute_0_1]) ).
cnf(refute_0_25,plain,
less_equal(zero,divide(X_40,divide(X_40,zero))),
inference(subst,[],[zero_is_smallest:[bind(X,$fot(divide(X_40,divide(X_40,zero))))]]) ).
cnf(refute_0_26,plain,
zero = divide(X_40,divide(X_40,zero)),
inference(resolve,[$cnf( less_equal(zero,divide(X_40,divide(X_40,zero))) )],[refute_0_25,refute_0_24]) ).
cnf(refute_0_27,plain,
zero = divide(X,divide(X,zero)),
inference(subst,[],[refute_0_26:[bind(X_40,$fot(X))]]) ).
cnf(refute_0_28,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_29,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_30,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( zero != divide(X,divide(X,zero))
| divide(X,divide(X,zero)) = zero ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(zero)),bind(Y0,$fot(divide(X,divide(X,zero))))]]) ).
cnf(refute_0_32,plain,
divide(X,divide(X,zero)) = zero,
inference(resolve,[$cnf( $equal(zero,divide(X,divide(X,zero))) )],[refute_0_27,refute_0_31]) ).
cnf(refute_0_33,plain,
( divide(X,divide(X,zero)) != zero
| zero != zero
| divide(X,divide(X,zero)) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(X,divide(X,zero)),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_34,plain,
( zero != zero
| divide(X,divide(X,zero)) = zero ),
inference(resolve,[$cnf( $equal(divide(X,divide(X,zero)),zero) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( zero != zero
| less_equal(X,divide(X,zero)) ),
inference(resolve,[$cnf( $equal(divide(X,divide(X,zero)),zero) )],[refute_0_34,refute_0_0]) ).
cnf(refute_0_36,plain,
less_equal(X,divide(X,zero)),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_21,refute_0_35]) ).
cnf(refute_0_37,plain,
less_equal(X_158,divide(X_158,zero)),
inference(subst,[],[refute_0_36:[bind(X,$fot(X_158))]]) ).
cnf(refute_0_38,plain,
less_equal(divide(X_37,Y),X_37),
inference(subst,[],[quotient_smaller_than_numerator:[bind(X,$fot(X_37))]]) ).
cnf(refute_0_39,plain,
( ~ less_equal(X_37,divide(X_37,Y))
| ~ less_equal(divide(X_37,Y),X_37)
| divide(X_37,Y) = X_37 ),
inference(subst,[],[less_equal_and_equal:[bind(X,$fot(divide(X_37,Y))),bind(Y,$fot(X_37))]]) ).
cnf(refute_0_40,plain,
( ~ less_equal(X_37,divide(X_37,Y))
| divide(X_37,Y) = X_37 ),
inference(resolve,[$cnf( less_equal(divide(X_37,Y),X_37) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( ~ less_equal(X_158,divide(X_158,zero))
| divide(X_158,zero) = X_158 ),
inference(subst,[],[refute_0_40:[bind(Y,$fot(zero)),bind(X_37,$fot(X_158))]]) ).
cnf(refute_0_42,plain,
divide(X_158,zero) = X_158,
inference(resolve,[$cnf( less_equal(X_158,divide(X_158,zero)) )],[refute_0_37,refute_0_41]) ).
cnf(refute_0_43,plain,
divide(a,zero) = a,
inference(subst,[],[refute_0_42:[bind(X_158,$fot(a))]]) ).
cnf(refute_0_44,plain,
( divide(a,zero) != a
| a != a
| divide(a,zero) = a ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(a,zero),a) ),[0],$fot(a)]]) ).
cnf(refute_0_45,plain,
( a != a
| divide(a,zero) = a ),
inference(resolve,[$cnf( $equal(divide(a,zero),a) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
a != a,
inference(resolve,[$cnf( $equal(divide(a,zero),a) )],[refute_0_45,prove_x_divide_zero_is_x]) ).
cnf(refute_0_47,plain,
a = a,
introduced(tautology,[refl,[$fot(a)]]) ).
cnf(refute_0_48,plain,
$false,
inference(resolve,[$cnf( $equal(a,a) )],[refute_0_47,refute_0_46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : HEN004-4 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.31 % Computer : n006.cluster.edu
% 0.13/0.31 % Model : x86_64 x86_64
% 0.13/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31 % Memory : 8042.1875MB
% 0.13/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.31 % CPULimit : 300
% 0.13/0.31 % WCLimit : 600
% 0.13/0.31 % DateTime : Fri Jul 1 14:54:07 EDT 2022
% 0.17/0.31 % CPUTime :
% 0.17/0.31 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.39/0.56 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.39/0.56
% 0.39/0.56 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.42/0.57
%------------------------------------------------------------------------------