TSTP Solution File: HEN003-5 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : HEN003-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 12:58:32 EDT 2022
% Result : Unsatisfiable 0.47s 0.67s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 15
% Syntax : Number of clauses : 47 ( 21 unt; 0 nHn; 25 RR)
% Number of literals : 86 ( 85 equ; 41 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 : 55 ( 7 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(prove_x_divide_x_is_zero,negated_conjecture,
divide(a,a) != zero ).
cnf(refute_0_0,plain,
( divide(divide(X_79,X_79),zero) != zero
| divide(zero,divide(X_79,X_79)) != zero
| divide(X_79,X_79) = zero ),
inference(subst,[],[divide_and_equal:[bind(X,$fot(divide(X_79,X_79))),bind(Y,$fot(zero))]]) ).
cnf(refute_0_1,plain,
( divide(divide(divide(X_10,X_10),zero),zero) != zero
| divide(zero,divide(divide(X_10,X_10),zero)) != zero
| zero = divide(divide(X_10,X_10),zero) ),
inference(subst,[],[divide_and_equal:[bind(X,$fot(zero)),bind(Y,$fot(divide(divide(X_10,X_10),zero)))]]) ).
cnf(refute_0_2,plain,
divide(divide(divide(X_6,X_6),divide(X_5,X_6)),divide(divide(X_6,X_5),X_6)) = zero,
inference(subst,[],[quotient_property:[bind(X,$fot(X_6)),bind(Y,$fot(X_5)),bind(Z,$fot(X_6))]]) ).
cnf(refute_0_3,plain,
divide(divide(X_6,X_5),X_6) = zero,
inference(subst,[],[quotient_smaller_than_numerator:[bind(X,$fot(X_6)),bind(Y,$fot(X_5))]]) ).
cnf(refute_0_4,plain,
( divide(divide(X_6,X_5),X_6) != zero
| divide(divide(divide(X_6,X_6),divide(X_5,X_6)),divide(divide(X_6,X_5),X_6)) != zero
| divide(divide(divide(X_6,X_6),divide(X_5,X_6)),zero) = zero ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(divide(X_6,X_6),divide(X_5,X_6)),divide(divide(X_6,X_5),X_6)),zero) ),[0,1],$fot(zero)]]) ).
cnf(refute_0_5,plain,
( divide(divide(divide(X_6,X_6),divide(X_5,X_6)),divide(divide(X_6,X_5),X_6)) != zero
| divide(divide(divide(X_6,X_6),divide(X_5,X_6)),zero) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(X_6,X_5),X_6),zero) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
divide(divide(divide(X_6,X_6),divide(X_5,X_6)),zero) = zero,
inference(resolve,[$cnf( $equal(divide(divide(divide(X_6,X_6),divide(X_5,X_6)),divide(divide(X_6,X_5),X_6)),zero) )],[refute_0_2,refute_0_5]) ).
cnf(refute_0_7,plain,
divide(divide(divide(X_10,X_10),divide(divide(X_10,Y),X_10)),zero) = zero,
inference(subst,[],[refute_0_6:[bind(X_5,$fot(divide(X_10,Y))),bind(X_6,$fot(X_10))]]) ).
cnf(refute_0_8,plain,
divide(divide(X_10,Y),X_10) = zero,
inference(subst,[],[quotient_smaller_than_numerator:[bind(X,$fot(X_10))]]) ).
cnf(refute_0_9,plain,
( divide(divide(X_10,Y),X_10) != zero
| divide(divide(divide(X_10,X_10),divide(divide(X_10,Y),X_10)),zero) != zero
| divide(divide(divide(X_10,X_10),zero),zero) = zero ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(divide(X_10,X_10),divide(divide(X_10,Y),X_10)),zero),zero) ),[0,0,1],$fot(zero)]]) ).
cnf(refute_0_10,plain,
( divide(divide(divide(X_10,X_10),divide(divide(X_10,Y),X_10)),zero) != zero
| divide(divide(divide(X_10,X_10),zero),zero) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(X_10,Y),X_10),zero) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
divide(divide(divide(X_10,X_10),zero),zero) = zero,
inference(resolve,[$cnf( $equal(divide(divide(divide(X_10,X_10),divide(divide(X_10,Y),X_10)),zero),zero) )],[refute_0_7,refute_0_10]) ).
cnf(refute_0_12,plain,
( divide(divide(divide(X_10,X_10),zero),zero) != zero
| zero != zero
| divide(divide(divide(X_10,X_10),zero),zero) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(divide(divide(X_10,X_10),zero),zero),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_13,plain,
( zero != zero
| divide(divide(divide(X_10,X_10),zero),zero) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(divide(X_10,X_10),zero),zero),zero) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( divide(zero,divide(divide(X_10,X_10),zero)) != zero
| zero != zero
| zero = divide(divide(X_10,X_10),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(divide(X_10,X_10),zero),zero),zero) )],[refute_0_13,refute_0_1]) ).
cnf(refute_0_15,plain,
zero = zero,
introduced(tautology,[refl,[$fot(zero)]]) ).
cnf(refute_0_16,plain,
( divide(zero,divide(divide(X_10,X_10),zero)) != zero
| zero = divide(divide(X_10,X_10),zero) ),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_15,refute_0_14]) ).
cnf(refute_0_17,plain,
divide(zero,divide(divide(X_10,X_10),zero)) = zero,
inference(subst,[],[zero_is_smallest:[bind(X,$fot(divide(divide(X_10,X_10),zero)))]]) ).
cnf(refute_0_18,plain,
( divide(zero,divide(divide(X_10,X_10),zero)) != zero
| zero != zero
| divide(zero,divide(divide(X_10,X_10),zero)) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(zero,divide(divide(X_10,X_10),zero)),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_19,plain,
( zero != zero
| divide(zero,divide(divide(X_10,X_10),zero)) = zero ),
inference(resolve,[$cnf( $equal(divide(zero,divide(divide(X_10,X_10),zero)),zero) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( zero != zero
| zero = divide(divide(X_10,X_10),zero) ),
inference(resolve,[$cnf( $equal(divide(zero,divide(divide(X_10,X_10),zero)),zero) )],[refute_0_19,refute_0_16]) ).
cnf(refute_0_21,plain,
zero = divide(divide(X_10,X_10),zero),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_15,refute_0_20]) ).
cnf(refute_0_22,plain,
zero = divide(divide(X_79,X_79),zero),
inference(subst,[],[refute_0_21:[bind(X_10,$fot(X_79))]]) ).
cnf(refute_0_23,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_24,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_25,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
( zero != divide(divide(X_79,X_79),zero)
| divide(divide(X_79,X_79),zero) = zero ),
inference(subst,[],[refute_0_25:[bind(X0,$fot(zero)),bind(Y0,$fot(divide(divide(X_79,X_79),zero)))]]) ).
cnf(refute_0_27,plain,
divide(divide(X_79,X_79),zero) = zero,
inference(resolve,[$cnf( $equal(zero,divide(divide(X_79,X_79),zero)) )],[refute_0_22,refute_0_26]) ).
cnf(refute_0_28,plain,
( divide(divide(X_79,X_79),zero) != zero
| zero != zero
| divide(divide(X_79,X_79),zero) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(divide(X_79,X_79),zero),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_29,plain,
( zero != zero
| divide(divide(X_79,X_79),zero) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(X_79,X_79),zero),zero) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( divide(zero,divide(X_79,X_79)) != zero
| zero != zero
| divide(X_79,X_79) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(X_79,X_79),zero),zero) )],[refute_0_29,refute_0_0]) ).
cnf(refute_0_31,plain,
( divide(zero,divide(X_79,X_79)) != zero
| divide(X_79,X_79) = zero ),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_15,refute_0_30]) ).
cnf(refute_0_32,plain,
divide(zero,divide(X_79,X_79)) = zero,
inference(subst,[],[zero_is_smallest:[bind(X,$fot(divide(X_79,X_79)))]]) ).
cnf(refute_0_33,plain,
( divide(zero,divide(X_79,X_79)) != zero
| zero != zero
| divide(zero,divide(X_79,X_79)) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(zero,divide(X_79,X_79)),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_34,plain,
( zero != zero
| divide(zero,divide(X_79,X_79)) = zero ),
inference(resolve,[$cnf( $equal(divide(zero,divide(X_79,X_79)),zero) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( zero != zero
| divide(X_79,X_79) = zero ),
inference(resolve,[$cnf( $equal(divide(zero,divide(X_79,X_79)),zero) )],[refute_0_34,refute_0_31]) ).
cnf(refute_0_36,plain,
divide(X_79,X_79) = zero,
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_15,refute_0_35]) ).
cnf(refute_0_37,plain,
divide(a,a) = zero,
inference(subst,[],[refute_0_36:[bind(X_79,$fot(a))]]) ).
cnf(refute_0_38,plain,
( divide(a,a) != zero
| zero != zero
| divide(a,a) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(a,a),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_39,plain,
( zero != zero
| divide(a,a) = zero ),
inference(resolve,[$cnf( $equal(divide(a,a),zero) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
zero != zero,
inference(resolve,[$cnf( $equal(divide(a,a),zero) )],[refute_0_39,prove_x_divide_x_is_zero]) ).
cnf(refute_0_41,plain,
$false,
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_15,refute_0_40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HEN003-5 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 1 14:46:31 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.47/0.67 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.47/0.67
% 0.47/0.67 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.47/0.67
%------------------------------------------------------------------------------