TSTP Solution File: HEN004-5 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : HEN004-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 19.35s 19.57s
% Output : CNFRefutation 19.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 19
% Syntax : Number of clauses : 63 ( 27 unt; 0 nHn; 33 RR)
% Number of literals : 116 ( 115 equ; 55 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 71 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(quotient_smaller_than_numerator,axiom,
divide(divide(X,Y),X) = zero ).
cnf(quotient_property,axiom,
divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero ).
cnf(zero_is_smallest,axiom,
divide(zero,X) = zero ).
cnf(divide_and_equal,axiom,
( divide(X,Y) != zero
| divide(Y,X) != zero
| X = Y ) ).
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_75,divide(X_75,Y)) != zero
| divide(divide(X_75,Y),X_75) != zero
| X_75 = divide(X_75,Y) ),
inference(subst,[],[divide_and_equal:[bind(X,$fot(X_75)),bind(Y,$fot(divide(X_75,Y)))]]) ).
cnf(refute_0_1,plain,
divide(divide(X_75,Y),X_75) = zero,
inference(subst,[],[quotient_smaller_than_numerator:[bind(X,$fot(X_75))]]) ).
cnf(refute_0_2,plain,
( divide(divide(X_75,Y),X_75) != zero
| zero != zero
| divide(divide(X_75,Y),X_75) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(divide(X_75,Y),X_75),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_3,plain,
( zero != zero
| divide(divide(X_75,Y),X_75) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(X_75,Y),X_75),zero) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( divide(X_75,divide(X_75,Y)) != zero
| zero != zero
| X_75 = divide(X_75,Y) ),
inference(resolve,[$cnf( $equal(divide(divide(X_75,Y),X_75),zero) )],[refute_0_3,refute_0_0]) ).
cnf(refute_0_5,plain,
zero = zero,
introduced(tautology,[refl,[$fot(zero)]]) ).
cnf(refute_0_6,plain,
( divide(X_75,divide(X_75,Y)) != zero
| X_75 = divide(X_75,Y) ),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
( divide(X_855,divide(X_855,zero)) != zero
| X_855 = divide(X_855,zero) ),
inference(subst,[],[refute_0_6:[bind(Y,$fot(zero)),bind(X_75,$fot(X_855))]]) ).
cnf(refute_0_8,plain,
( divide(divide(X_82,divide(X_82,zero)),zero) != zero
| divide(zero,divide(X_82,divide(X_82,zero))) != zero
| divide(X_82,divide(X_82,zero)) = zero ),
inference(subst,[],[divide_and_equal:[bind(X,$fot(divide(X_82,divide(X_82,zero)))),bind(Y,$fot(zero))]]) ).
cnf(refute_0_9,plain,
( divide(divide(divide(X_10,divide(X_10,zero)),zero),zero) != zero
| divide(zero,divide(divide(X_10,divide(X_10,zero)),zero)) != zero
| zero = divide(divide(X_10,divide(X_10,zero)),zero) ),
inference(subst,[],[divide_and_equal:[bind(X,$fot(zero)),bind(Y,$fot(divide(divide(X_10,divide(X_10,zero)),zero)))]]) ).
cnf(refute_0_10,plain,
divide(divide(divide(X_5,X_7),divide(zero,X_7)),divide(divide(X_5,zero),X_7)) = zero,
inference(subst,[],[quotient_property:[bind(X,$fot(X_5)),bind(Y,$fot(zero)),bind(Z,$fot(X_7))]]) ).
cnf(refute_0_11,plain,
divide(zero,X_7) = zero,
inference(subst,[],[zero_is_smallest:[bind(X,$fot(X_7))]]) ).
cnf(refute_0_12,plain,
( divide(divide(divide(X_5,X_7),divide(zero,X_7)),divide(divide(X_5,zero),X_7)) != zero
| divide(zero,X_7) != zero
| divide(divide(divide(X_5,X_7),zero),divide(divide(X_5,zero),X_7)) = zero ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(divide(X_5,X_7),divide(zero,X_7)),divide(divide(X_5,zero),X_7)),zero) ),[0,0,1],$fot(zero)]]) ).
cnf(refute_0_13,plain,
( divide(divide(divide(X_5,X_7),divide(zero,X_7)),divide(divide(X_5,zero),X_7)) != zero
| divide(divide(divide(X_5,X_7),zero),divide(divide(X_5,zero),X_7)) = zero ),
inference(resolve,[$cnf( $equal(divide(zero,X_7),zero) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
divide(divide(divide(X_5,X_7),zero),divide(divide(X_5,zero),X_7)) = zero,
inference(resolve,[$cnf( $equal(divide(divide(divide(X_5,X_7),divide(zero,X_7)),divide(divide(X_5,zero),X_7)),zero) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
divide(divide(divide(X_10,divide(X_10,zero)),zero),divide(divide(X_10,zero),divide(X_10,zero))) = zero,
inference(subst,[],[refute_0_14:[bind(X_5,$fot(X_10)),bind(X_7,$fot(divide(X_10,zero)))]]) ).
cnf(refute_0_16,plain,
divide(divide(X_10,zero),divide(X_10,zero)) = zero,
inference(subst,[],[x_divide_x_is_zero:[bind(X,$fot(divide(X_10,zero)))]]) ).
cnf(refute_0_17,plain,
( divide(divide(X_10,zero),divide(X_10,zero)) != zero
| divide(divide(divide(X_10,divide(X_10,zero)),zero),divide(divide(X_10,zero),divide(X_10,zero))) != zero
| divide(divide(divide(X_10,divide(X_10,zero)),zero),zero) = zero ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(divide(X_10,divide(X_10,zero)),zero),divide(divide(X_10,zero),divide(X_10,zero))),zero) ),[0,1],$fot(zero)]]) ).
cnf(refute_0_18,plain,
( divide(divide(divide(X_10,divide(X_10,zero)),zero),divide(divide(X_10,zero),divide(X_10,zero))) != zero
| divide(divide(divide(X_10,divide(X_10,zero)),zero),zero) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(X_10,zero),divide(X_10,zero)),zero) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
divide(divide(divide(X_10,divide(X_10,zero)),zero),zero) = zero,
inference(resolve,[$cnf( $equal(divide(divide(divide(X_10,divide(X_10,zero)),zero),divide(divide(X_10,zero),divide(X_10,zero))),zero) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
( divide(divide(divide(X_10,divide(X_10,zero)),zero),zero) != zero
| zero != zero
| divide(divide(divide(X_10,divide(X_10,zero)),zero),zero) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(divide(divide(X_10,divide(X_10,zero)),zero),zero),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_21,plain,
( zero != zero
| divide(divide(divide(X_10,divide(X_10,zero)),zero),zero) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(divide(X_10,divide(X_10,zero)),zero),zero),zero) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( divide(zero,divide(divide(X_10,divide(X_10,zero)),zero)) != zero
| zero != zero
| zero = divide(divide(X_10,divide(X_10,zero)),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(divide(X_10,divide(X_10,zero)),zero),zero),zero) )],[refute_0_21,refute_0_9]) ).
cnf(refute_0_23,plain,
( divide(zero,divide(divide(X_10,divide(X_10,zero)),zero)) != zero
| zero = divide(divide(X_10,divide(X_10,zero)),zero) ),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_5,refute_0_22]) ).
cnf(refute_0_24,plain,
divide(zero,divide(divide(X_10,divide(X_10,zero)),zero)) = zero,
inference(subst,[],[zero_is_smallest:[bind(X,$fot(divide(divide(X_10,divide(X_10,zero)),zero)))]]) ).
cnf(refute_0_25,plain,
( divide(zero,divide(divide(X_10,divide(X_10,zero)),zero)) != zero
| zero != zero
| divide(zero,divide(divide(X_10,divide(X_10,zero)),zero)) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(zero,divide(divide(X_10,divide(X_10,zero)),zero)),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_26,plain,
( zero != zero
| divide(zero,divide(divide(X_10,divide(X_10,zero)),zero)) = zero ),
inference(resolve,[$cnf( $equal(divide(zero,divide(divide(X_10,divide(X_10,zero)),zero)),zero) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
( zero != zero
| zero = divide(divide(X_10,divide(X_10,zero)),zero) ),
inference(resolve,[$cnf( $equal(divide(zero,divide(divide(X_10,divide(X_10,zero)),zero)),zero) )],[refute_0_26,refute_0_23]) ).
cnf(refute_0_28,plain,
zero = divide(divide(X_10,divide(X_10,zero)),zero),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_5,refute_0_27]) ).
cnf(refute_0_29,plain,
zero = divide(divide(X_82,divide(X_82,zero)),zero),
inference(subst,[],[refute_0_28:[bind(X_10,$fot(X_82))]]) ).
cnf(refute_0_30,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_31,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_32,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
( zero != divide(divide(X_82,divide(X_82,zero)),zero)
| divide(divide(X_82,divide(X_82,zero)),zero) = zero ),
inference(subst,[],[refute_0_32:[bind(X0,$fot(zero)),bind(Y0,$fot(divide(divide(X_82,divide(X_82,zero)),zero)))]]) ).
cnf(refute_0_34,plain,
divide(divide(X_82,divide(X_82,zero)),zero) = zero,
inference(resolve,[$cnf( $equal(zero,divide(divide(X_82,divide(X_82,zero)),zero)) )],[refute_0_29,refute_0_33]) ).
cnf(refute_0_35,plain,
( divide(divide(X_82,divide(X_82,zero)),zero) != zero
| zero != zero
| divide(divide(X_82,divide(X_82,zero)),zero) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(divide(X_82,divide(X_82,zero)),zero),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_36,plain,
( zero != zero
| divide(divide(X_82,divide(X_82,zero)),zero) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(X_82,divide(X_82,zero)),zero),zero) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( divide(zero,divide(X_82,divide(X_82,zero))) != zero
| zero != zero
| divide(X_82,divide(X_82,zero)) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(X_82,divide(X_82,zero)),zero),zero) )],[refute_0_36,refute_0_8]) ).
cnf(refute_0_38,plain,
( divide(zero,divide(X_82,divide(X_82,zero))) != zero
| divide(X_82,divide(X_82,zero)) = zero ),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_5,refute_0_37]) ).
cnf(refute_0_39,plain,
divide(zero,divide(X_82,divide(X_82,zero))) = zero,
inference(subst,[],[zero_is_smallest:[bind(X,$fot(divide(X_82,divide(X_82,zero))))]]) ).
cnf(refute_0_40,plain,
( divide(zero,divide(X_82,divide(X_82,zero))) != zero
| zero != zero
| divide(zero,divide(X_82,divide(X_82,zero))) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(zero,divide(X_82,divide(X_82,zero))),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_41,plain,
( zero != zero
| divide(zero,divide(X_82,divide(X_82,zero))) = zero ),
inference(resolve,[$cnf( $equal(divide(zero,divide(X_82,divide(X_82,zero))),zero) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( zero != zero
| divide(X_82,divide(X_82,zero)) = zero ),
inference(resolve,[$cnf( $equal(divide(zero,divide(X_82,divide(X_82,zero))),zero) )],[refute_0_41,refute_0_38]) ).
cnf(refute_0_43,plain,
divide(X_82,divide(X_82,zero)) = zero,
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_5,refute_0_42]) ).
cnf(refute_0_44,plain,
divide(X_855,divide(X_855,zero)) = zero,
inference(subst,[],[refute_0_43:[bind(X_82,$fot(X_855))]]) ).
cnf(refute_0_45,plain,
( divide(X_855,divide(X_855,zero)) != zero
| zero != zero
| divide(X_855,divide(X_855,zero)) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(X_855,divide(X_855,zero)),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_46,plain,
( zero != zero
| divide(X_855,divide(X_855,zero)) = zero ),
inference(resolve,[$cnf( $equal(divide(X_855,divide(X_855,zero)),zero) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
( zero != zero
| X_855 = divide(X_855,zero) ),
inference(resolve,[$cnf( $equal(divide(X_855,divide(X_855,zero)),zero) )],[refute_0_46,refute_0_7]) ).
cnf(refute_0_48,plain,
X_855 = divide(X_855,zero),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_5,refute_0_47]) ).
cnf(refute_0_49,plain,
( X_855 != divide(X_855,zero)
| divide(X_855,zero) = X_855 ),
inference(subst,[],[refute_0_32:[bind(X0,$fot(X_855)),bind(Y0,$fot(divide(X_855,zero)))]]) ).
cnf(refute_0_50,plain,
divide(X_855,zero) = X_855,
inference(resolve,[$cnf( $equal(X_855,divide(X_855,zero)) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
divide(a,zero) = a,
inference(subst,[],[refute_0_50:[bind(X_855,$fot(a))]]) ).
cnf(refute_0_52,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_53,plain,
( a != a
| divide(a,zero) = a ),
inference(resolve,[$cnf( $equal(divide(a,zero),a) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
a != a,
inference(resolve,[$cnf( $equal(divide(a,zero),a) )],[refute_0_53,prove_x_divide_zero_is_x]) ).
cnf(refute_0_55,plain,
a = a,
introduced(tautology,[refl,[$fot(a)]]) ).
cnf(refute_0_56,plain,
$false,
inference(resolve,[$cnf( $equal(a,a) )],[refute_0_55,refute_0_54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HEN004-5 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n026.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 14:06:04 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 19.35/19.57 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.35/19.57
% 19.35/19.57 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 19.35/19.57
%------------------------------------------------------------------------------