TSTP Solution File: HEN009-6 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : HEN009-6 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 12:58:44 EDT 2022
% Result : Unsatisfiable 14.23s 14.48s
% Output : CNFRefutation 14.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 23
% Syntax : Number of clauses : 70 ( 32 unt; 0 nHn; 58 RR)
% Number of literals : 121 ( 47 equ; 54 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 33 ( 1 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(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(x_divide_x_is_zero,axiom,
divide(X,X) = zero ).
cnf(property_of_divide1,axiom,
( ~ less_equal(divide(X,Y),Z)
| less_equal(divide(X,Z),Y) ) ).
cnf(property_of_divide3,axiom,
( ~ less_equal(X,Y)
| less_equal(divide(X,Z),divide(Y,Z)) ) ).
cnf(id_divide_a_is_b,hypothesis,
divide(identity,a) = b ).
cnf(id_divide_b_is_c,hypothesis,
divide(identity,b) = c ).
cnf(id_divide_c_is_d,hypothesis,
divide(identity,c) = d ).
cnf(prove_b_equals_d,negated_conjecture,
b != d ).
cnf(refute_0_0,plain,
( ~ less_equal(divide(identity,d),a)
| less_equal(divide(identity,a),d) ),
inference(subst,[],[property_of_divide1:[bind(X,$fot(identity)),bind(Y,$fot(d)),bind(Z,$fot(a))]]) ).
cnf(refute_0_1,plain,
( divide(divide(identity,d),a) != zero
| less_equal(divide(identity,d),a) ),
inference(subst,[],[quotient_less_equal2:[bind(X,$fot(divide(identity,d))),bind(Y,$fot(a))]]) ).
cnf(refute_0_2,plain,
( divide(X_12,X_12) != zero
| less_equal(X_12,X_12) ),
inference(subst,[],[quotient_less_equal2:[bind(X,$fot(X_12)),bind(Y,$fot(X_12))]]) ).
cnf(refute_0_3,plain,
divide(X_12,X_12) = zero,
inference(subst,[],[x_divide_x_is_zero:[bind(X,$fot(X_12))]]) ).
cnf(refute_0_4,plain,
( divide(X_12,X_12) != zero
| zero != zero
| divide(X_12,X_12) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(X_12,X_12),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_5,plain,
( zero != zero
| divide(X_12,X_12) = zero ),
inference(resolve,[$cnf( $equal(divide(X_12,X_12),zero) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( zero != zero
| less_equal(X_12,X_12) ),
inference(resolve,[$cnf( $equal(divide(X_12,X_12),zero) )],[refute_0_5,refute_0_2]) ).
cnf(refute_0_7,plain,
zero = zero,
introduced(tautology,[refl,[$fot(zero)]]) ).
cnf(refute_0_8,plain,
less_equal(X_12,X_12),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_7,refute_0_6]) ).
cnf(refute_0_9,plain,
less_equal(divide(X_106,X_107),divide(X_106,X_107)),
inference(subst,[],[refute_0_8:[bind(X_12,$fot(divide(X_106,X_107)))]]) ).
cnf(refute_0_10,plain,
( ~ less_equal(divide(X_106,X_107),divide(X_106,X_107))
| less_equal(divide(X_106,divide(X_106,X_107)),X_107) ),
inference(subst,[],[property_of_divide1:[bind(X,$fot(X_106)),bind(Y,$fot(X_107)),bind(Z,$fot(divide(X_106,X_107)))]]) ).
cnf(refute_0_11,plain,
less_equal(divide(X_106,divide(X_106,X_107)),X_107),
inference(resolve,[$cnf( less_equal(divide(X_106,X_107),divide(X_106,X_107)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
less_equal(divide(identity,divide(identity,c)),c),
inference(subst,[],[refute_0_11:[bind(X_106,$fot(identity)),bind(X_107,$fot(c))]]) ).
cnf(refute_0_13,plain,
( ~ less_equal(divide(identity,divide(identity,c)),c)
| divide(identity,c) != d
| less_equal(divide(identity,d),c) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(identity,divide(identity,c)),c) ),[0,1],$fot(d)]]) ).
cnf(refute_0_14,plain,
( ~ less_equal(divide(identity,divide(identity,c)),c)
| less_equal(divide(identity,d),c) ),
inference(resolve,[$cnf( $equal(divide(identity,c),d) )],[id_divide_c_is_d,refute_0_13]) ).
cnf(refute_0_15,plain,
less_equal(divide(identity,d),c),
inference(resolve,[$cnf( less_equal(divide(identity,divide(identity,c)),c) )],[refute_0_12,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ less_equal(divide(identity,d),c)
| less_equal(divide(divide(identity,d),X_399),divide(c,X_399)) ),
inference(subst,[],[property_of_divide3:[bind(X,$fot(divide(identity,d))),bind(Y,$fot(c)),bind(Z,$fot(X_399))]]) ).
cnf(refute_0_17,plain,
less_equal(divide(divide(identity,d),X_399),divide(c,X_399)),
inference(resolve,[$cnf( less_equal(divide(identity,d),c) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
less_equal(divide(divide(identity,d),a),divide(c,a)),
inference(subst,[],[refute_0_17:[bind(X_399,$fot(a))]]) ).
cnf(refute_0_19,plain,
( ~ less_equal(c,a)
| divide(c,a) = zero ),
inference(subst,[],[quotient_less_equal1:[bind(X,$fot(c)),bind(Y,$fot(a))]]) ).
cnf(refute_0_20,plain,
less_equal(divide(identity,divide(identity,a)),a),
inference(subst,[],[refute_0_11:[bind(X_106,$fot(identity)),bind(X_107,$fot(a))]]) ).
cnf(refute_0_21,plain,
( ~ less_equal(divide(identity,divide(identity,a)),a)
| divide(identity,a) != b
| less_equal(divide(identity,b),a) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(identity,divide(identity,a)),a) ),[0,1],$fot(b)]]) ).
cnf(refute_0_22,plain,
( ~ less_equal(divide(identity,divide(identity,a)),a)
| less_equal(divide(identity,b),a) ),
inference(resolve,[$cnf( $equal(divide(identity,a),b) )],[id_divide_a_is_b,refute_0_21]) ).
cnf(refute_0_23,plain,
less_equal(divide(identity,b),a),
inference(resolve,[$cnf( less_equal(divide(identity,divide(identity,a)),a) )],[refute_0_20,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ less_equal(divide(identity,b),a)
| divide(identity,b) != c
| less_equal(c,a) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(identity,b),a) ),[0],$fot(c)]]) ).
cnf(refute_0_25,plain,
( ~ less_equal(divide(identity,b),a)
| less_equal(c,a) ),
inference(resolve,[$cnf( $equal(divide(identity,b),c) )],[id_divide_b_is_c,refute_0_24]) ).
cnf(refute_0_26,plain,
less_equal(c,a),
inference(resolve,[$cnf( less_equal(divide(identity,b),a) )],[refute_0_23,refute_0_25]) ).
cnf(refute_0_27,plain,
divide(c,a) = zero,
inference(resolve,[$cnf( less_equal(c,a) )],[refute_0_26,refute_0_19]) ).
cnf(refute_0_28,plain,
( ~ less_equal(divide(divide(identity,d),a),divide(c,a))
| divide(c,a) != zero
| less_equal(divide(divide(identity,d),a),zero) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(identity,d),a),divide(c,a)) ),[1],$fot(zero)]]) ).
cnf(refute_0_29,plain,
( ~ less_equal(divide(divide(identity,d),a),divide(c,a))
| less_equal(divide(divide(identity,d),a),zero) ),
inference(resolve,[$cnf( $equal(divide(c,a),zero) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
less_equal(divide(divide(identity,d),a),zero),
inference(resolve,[$cnf( less_equal(divide(divide(identity,d),a),divide(c,a)) )],[refute_0_18,refute_0_29]) ).
cnf(refute_0_31,plain,
( ~ less_equal(divide(divide(identity,d),a),zero)
| ~ less_equal(zero,divide(divide(identity,d),a))
| divide(divide(identity,d),a) = zero ),
inference(subst,[],[less_equal_and_equal:[bind(X,$fot(divide(divide(identity,d),a))),bind(Y,$fot(zero))]]) ).
cnf(refute_0_32,plain,
( ~ less_equal(zero,divide(divide(identity,d),a))
| divide(divide(identity,d),a) = zero ),
inference(resolve,[$cnf( less_equal(divide(divide(identity,d),a),zero) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
less_equal(zero,divide(divide(identity,d),a)),
inference(subst,[],[zero_is_smallest:[bind(X,$fot(divide(divide(identity,d),a)))]]) ).
cnf(refute_0_34,plain,
divide(divide(identity,d),a) = zero,
inference(resolve,[$cnf( less_equal(zero,divide(divide(identity,d),a)) )],[refute_0_33,refute_0_32]) ).
cnf(refute_0_35,plain,
( divide(divide(identity,d),a) != zero
| zero != zero
| divide(divide(identity,d),a) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(divide(identity,d),a),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_36,plain,
( zero != zero
| divide(divide(identity,d),a) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(identity,d),a),zero) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( zero != zero
| less_equal(divide(identity,d),a) ),
inference(resolve,[$cnf( $equal(divide(divide(identity,d),a),zero) )],[refute_0_36,refute_0_1]) ).
cnf(refute_0_38,plain,
less_equal(divide(identity,d),a),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_7,refute_0_37]) ).
cnf(refute_0_39,plain,
less_equal(divide(identity,a),d),
inference(resolve,[$cnf( less_equal(divide(identity,d),a) )],[refute_0_38,refute_0_0]) ).
cnf(refute_0_40,plain,
( ~ less_equal(divide(identity,a),d)
| divide(identity,a) != b
| less_equal(b,d) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(identity,a),d) ),[0],$fot(b)]]) ).
cnf(refute_0_41,plain,
( ~ less_equal(divide(identity,a),d)
| less_equal(b,d) ),
inference(resolve,[$cnf( $equal(divide(identity,a),b) )],[id_divide_a_is_b,refute_0_40]) ).
cnf(refute_0_42,plain,
less_equal(b,d),
inference(resolve,[$cnf( less_equal(divide(identity,a),d) )],[refute_0_39,refute_0_41]) ).
cnf(refute_0_43,plain,
less_equal(divide(identity,divide(identity,b)),b),
inference(subst,[],[refute_0_11:[bind(X_106,$fot(identity)),bind(X_107,$fot(b))]]) ).
cnf(refute_0_44,plain,
( ~ less_equal(divide(identity,divide(identity,b)),b)
| divide(identity,b) != c
| less_equal(divide(identity,c),b) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(identity,divide(identity,b)),b) ),[0,1],$fot(c)]]) ).
cnf(refute_0_45,plain,
( ~ less_equal(divide(identity,divide(identity,b)),b)
| less_equal(divide(identity,c),b) ),
inference(resolve,[$cnf( $equal(divide(identity,b),c) )],[id_divide_b_is_c,refute_0_44]) ).
cnf(refute_0_46,plain,
less_equal(divide(identity,c),b),
inference(resolve,[$cnf( less_equal(divide(identity,divide(identity,b)),b) )],[refute_0_43,refute_0_45]) ).
cnf(refute_0_47,plain,
( ~ less_equal(divide(identity,c),b)
| divide(identity,c) != d
| less_equal(d,b) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(identity,c),b) ),[0],$fot(d)]]) ).
cnf(refute_0_48,plain,
( ~ less_equal(divide(identity,c),b)
| less_equal(d,b) ),
inference(resolve,[$cnf( $equal(divide(identity,c),d) )],[id_divide_c_is_d,refute_0_47]) ).
cnf(refute_0_49,plain,
less_equal(d,b),
inference(resolve,[$cnf( less_equal(divide(identity,c),b) )],[refute_0_46,refute_0_48]) ).
cnf(refute_0_50,plain,
( ~ less_equal(b,d)
| ~ less_equal(d,b)
| d = b ),
inference(subst,[],[less_equal_and_equal:[bind(X,$fot(d)),bind(Y,$fot(b))]]) ).
cnf(refute_0_51,plain,
( ~ less_equal(b,d)
| d = b ),
inference(resolve,[$cnf( less_equal(d,b) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_53,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_54,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
( d != b
| b = d ),
inference(subst,[],[refute_0_54:[bind(X0,$fot(d)),bind(Y0,$fot(b))]]) ).
cnf(refute_0_56,plain,
d != b,
inference(resolve,[$cnf( $equal(b,d) )],[refute_0_55,prove_b_equals_d]) ).
cnf(refute_0_57,plain,
~ less_equal(b,d),
inference(resolve,[$cnf( $equal(d,b) )],[refute_0_51,refute_0_56]) ).
cnf(refute_0_58,plain,
$false,
inference(resolve,[$cnf( less_equal(b,d) )],[refute_0_42,refute_0_57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : HEN009-6 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n018.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 14:16:02 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 14.23/14.48 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.23/14.48
% 14.23/14.48 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.33/14.48
%------------------------------------------------------------------------------