TSTP Solution File: SWV019-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWV019-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.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 : Wed Jul 20 20:29:52 EDT 2022
% Result : Unsatisfiable 0.20s 0.41s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of clauses : 50 ( 13 unt; 20 nHn; 46 RR)
% Number of literals : 130 ( 27 equ; 46 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(in_bounds,axiom,
( less_than(X1,lower_bound)
| less_than(upper_bound,X1)
| in_array_bounds(array,X1) ) ).
cnf(predecessor_less,axiom,
( ~ less_than(successor(X),successor(Y))
| less_than(X,Y) ) ).
cnf(transitivity_of_less,axiom,
( ~ less_than(X,Y)
| ~ less_than(Y,Z)
| less_than(X,Z) ) ).
cnf(successor_greater,axiom,
less_than(X,successor(X)) ).
cnf(this_is_maximal,axiom,
( ~ in_array_bounds(array,index_of_maximal)
| maximal_value = array_value_at(array,index_of_maximal) ) ).
cnf(maximal_before_somewhere,axiom,
less_than(index_of_maximal,an_index) ).
cnf(somewhere_above_lower_bound,axiom,
~ less_than(an_index,lower_bound) ).
cnf(somewhere_below_upper_bound,axiom,
~ less_than(upper_bound,an_index) ).
cnf(maximal_above_lower_bound,axiom,
~ less_than(index_of_maximal,lower_bound) ).
cnf(prove_this,negated_conjecture,
( ~ in_array_bounds(array,an_index)
| less_than(successor(an_index),lower_bound)
| less_than(successor(upper_bound),successor(an_index))
| less_than(index_of_maximal,lower_bound)
| ~ less_than(index_of_maximal,successor(an_index))
| ~ in_array_bounds(array,index_of_maximal)
| maximal_value != array_value_at(array,index_of_maximal) ) ).
cnf(refute_0_0,plain,
( ~ less_than(X_4,index_of_maximal)
| ~ less_than(index_of_maximal,an_index)
| less_than(X_4,an_index) ),
inference(subst,[],[transitivity_of_less:[bind(X,$fot(X_4)),bind(Y,$fot(index_of_maximal)),bind(Z,$fot(an_index))]]) ).
cnf(refute_0_1,plain,
( ~ less_than(X_4,index_of_maximal)
| less_than(X_4,an_index) ),
inference(resolve,[$cnf( less_than(index_of_maximal,an_index) )],[maximal_before_somewhere,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ less_than(upper_bound,index_of_maximal)
| less_than(upper_bound,an_index) ),
inference(subst,[],[refute_0_1:[bind(X_4,$fot(upper_bound))]]) ).
cnf(refute_0_3,plain,
less_than(X_4,successor(X_4)),
inference(subst,[],[successor_greater:[bind(X,$fot(X_4))]]) ).
cnf(refute_0_4,plain,
( ~ less_than(X_4,successor(X_4))
| ~ less_than(successor(X_4),X_6)
| less_than(X_4,X_6) ),
inference(subst,[],[transitivity_of_less:[bind(X,$fot(X_4)),bind(Y,$fot(successor(X_4))),bind(Z,$fot(X_6))]]) ).
cnf(refute_0_5,plain,
( ~ less_than(successor(X_4),X_6)
| less_than(X_4,X_6) ),
inference(resolve,[$cnf( less_than(X_4,successor(X_4)) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ less_than(successor(an_index),lower_bound)
| less_than(an_index,lower_bound) ),
inference(subst,[],[refute_0_5:[bind(X_4,$fot(an_index)),bind(X_6,$fot(lower_bound))]]) ).
cnf(refute_0_7,plain,
( ~ less_than(successor(upper_bound),successor(an_index))
| less_than(upper_bound,an_index) ),
inference(subst,[],[predecessor_less:[bind(X,$fot(upper_bound)),bind(Y,$fot(an_index))]]) ).
cnf(refute_0_8,plain,
( less_than(an_index,lower_bound)
| less_than(upper_bound,an_index)
| in_array_bounds(array,an_index) ),
inference(subst,[],[in_bounds:[bind(X1,$fot(an_index))]]) ).
cnf(refute_0_9,plain,
( less_than(index_of_maximal,lower_bound)
| less_than(upper_bound,index_of_maximal)
| in_array_bounds(array,index_of_maximal) ),
inference(subst,[],[in_bounds:[bind(X1,$fot(index_of_maximal))]]) ).
cnf(refute_0_10,plain,
( ~ less_than(index_of_maximal,successor(an_index))
| maximal_value != array_value_at(array,index_of_maximal)
| ~ in_array_bounds(array,an_index)
| ~ in_array_bounds(array,index_of_maximal)
| less_than(successor(an_index),lower_bound)
| less_than(successor(upper_bound),successor(an_index)) ),
inference(resolve,[$cnf( less_than(index_of_maximal,lower_bound) )],[prove_this,maximal_above_lower_bound]) ).
cnf(refute_0_11,plain,
less_than(an_index,successor(an_index)),
inference(subst,[],[successor_greater:[bind(X,$fot(an_index))]]) ).
cnf(refute_0_12,plain,
( ~ less_than(an_index,X_6)
| ~ less_than(index_of_maximal,an_index)
| less_than(index_of_maximal,X_6) ),
inference(subst,[],[transitivity_of_less:[bind(X,$fot(index_of_maximal)),bind(Y,$fot(an_index)),bind(Z,$fot(X_6))]]) ).
cnf(refute_0_13,plain,
( ~ less_than(an_index,X_6)
| less_than(index_of_maximal,X_6) ),
inference(resolve,[$cnf( less_than(index_of_maximal,an_index) )],[maximal_before_somewhere,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ less_than(an_index,successor(an_index))
| less_than(index_of_maximal,successor(an_index)) ),
inference(subst,[],[refute_0_13:[bind(X_6,$fot(successor(an_index)))]]) ).
cnf(refute_0_15,plain,
less_than(index_of_maximal,successor(an_index)),
inference(resolve,[$cnf( less_than(an_index,successor(an_index)) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
( maximal_value != array_value_at(array,index_of_maximal)
| ~ in_array_bounds(array,an_index)
| ~ in_array_bounds(array,index_of_maximal)
| less_than(successor(an_index),lower_bound)
| less_than(successor(upper_bound),successor(an_index)) ),
inference(resolve,[$cnf( less_than(index_of_maximal,successor(an_index)) )],[refute_0_15,refute_0_10]) ).
cnf(refute_0_17,plain,
( maximal_value != array_value_at(array,index_of_maximal)
| ~ in_array_bounds(array,an_index)
| less_than(index_of_maximal,lower_bound)
| less_than(successor(an_index),lower_bound)
| less_than(successor(upper_bound),successor(an_index))
| less_than(upper_bound,index_of_maximal) ),
inference(resolve,[$cnf( in_array_bounds(array,index_of_maximal) )],[refute_0_9,refute_0_16]) ).
cnf(refute_0_18,plain,
( maximal_value != array_value_at(array,index_of_maximal)
| ~ in_array_bounds(array,an_index)
| less_than(successor(an_index),lower_bound)
| less_than(successor(upper_bound),successor(an_index))
| less_than(upper_bound,index_of_maximal) ),
inference(resolve,[$cnf( less_than(index_of_maximal,lower_bound) )],[refute_0_17,maximal_above_lower_bound]) ).
cnf(refute_0_19,plain,
( maximal_value != array_value_at(array,index_of_maximal)
| less_than(an_index,lower_bound)
| less_than(successor(an_index),lower_bound)
| less_than(successor(upper_bound),successor(an_index))
| less_than(upper_bound,an_index)
| less_than(upper_bound,index_of_maximal) ),
inference(resolve,[$cnf( in_array_bounds(array,an_index) )],[refute_0_8,refute_0_18]) ).
cnf(refute_0_20,plain,
( maximal_value != array_value_at(array,index_of_maximal)
| less_than(successor(an_index),lower_bound)
| less_than(successor(upper_bound),successor(an_index))
| less_than(upper_bound,an_index)
| less_than(upper_bound,index_of_maximal) ),
inference(resolve,[$cnf( less_than(an_index,lower_bound) )],[refute_0_19,somewhere_above_lower_bound]) ).
cnf(refute_0_21,plain,
( maximal_value != array_value_at(array,index_of_maximal)
| less_than(successor(an_index),lower_bound)
| less_than(successor(upper_bound),successor(an_index))
| less_than(upper_bound,index_of_maximal) ),
inference(resolve,[$cnf( less_than(upper_bound,an_index) )],[refute_0_20,somewhere_below_upper_bound]) ).
cnf(refute_0_22,plain,
( less_than(index_of_maximal,lower_bound)
| less_than(upper_bound,index_of_maximal)
| maximal_value = array_value_at(array,index_of_maximal) ),
inference(resolve,[$cnf( in_array_bounds(array,index_of_maximal) )],[refute_0_9,this_is_maximal]) ).
cnf(refute_0_23,plain,
( less_than(upper_bound,index_of_maximal)
| maximal_value = array_value_at(array,index_of_maximal) ),
inference(resolve,[$cnf( less_than(index_of_maximal,lower_bound) )],[refute_0_22,maximal_above_lower_bound]) ).
cnf(refute_0_24,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_25,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_26,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
( maximal_value != array_value_at(array,index_of_maximal)
| array_value_at(array,index_of_maximal) = maximal_value ),
inference(subst,[],[refute_0_26:[bind(X0,$fot(maximal_value)),bind(Y0,$fot(array_value_at(array,index_of_maximal)))]]) ).
cnf(refute_0_28,plain,
( less_than(upper_bound,index_of_maximal)
| array_value_at(array,index_of_maximal) = maximal_value ),
inference(resolve,[$cnf( $equal(maximal_value,array_value_at(array,index_of_maximal)) )],[refute_0_23,refute_0_27]) ).
cnf(refute_0_29,plain,
( array_value_at(array,index_of_maximal) != maximal_value
| maximal_value != maximal_value
| maximal_value = array_value_at(array,index_of_maximal) ),
introduced(tautology,[equality,[$cnf( ~ $equal(maximal_value,array_value_at(array,index_of_maximal)) ),[1],$fot(maximal_value)]]) ).
cnf(refute_0_30,plain,
( maximal_value != maximal_value
| less_than(upper_bound,index_of_maximal)
| maximal_value = array_value_at(array,index_of_maximal) ),
inference(resolve,[$cnf( $equal(array_value_at(array,index_of_maximal),maximal_value) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( maximal_value != maximal_value
| less_than(successor(an_index),lower_bound)
| less_than(successor(upper_bound),successor(an_index))
| less_than(upper_bound,index_of_maximal) ),
inference(resolve,[$cnf( $equal(maximal_value,array_value_at(array,index_of_maximal)) )],[refute_0_30,refute_0_21]) ).
cnf(refute_0_32,plain,
maximal_value = maximal_value,
introduced(tautology,[refl,[$fot(maximal_value)]]) ).
cnf(refute_0_33,plain,
( less_than(successor(an_index),lower_bound)
| less_than(successor(upper_bound),successor(an_index))
| less_than(upper_bound,index_of_maximal) ),
inference(resolve,[$cnf( $equal(maximal_value,maximal_value) )],[refute_0_32,refute_0_31]) ).
cnf(refute_0_34,plain,
( less_than(successor(an_index),lower_bound)
| less_than(upper_bound,an_index)
| less_than(upper_bound,index_of_maximal) ),
inference(resolve,[$cnf( less_than(successor(upper_bound),successor(an_index)) )],[refute_0_33,refute_0_7]) ).
cnf(refute_0_35,plain,
( less_than(successor(an_index),lower_bound)
| less_than(upper_bound,index_of_maximal) ),
inference(resolve,[$cnf( less_than(upper_bound,an_index) )],[refute_0_34,somewhere_below_upper_bound]) ).
cnf(refute_0_36,plain,
( less_than(an_index,lower_bound)
| less_than(upper_bound,index_of_maximal) ),
inference(resolve,[$cnf( less_than(successor(an_index),lower_bound) )],[refute_0_35,refute_0_6]) ).
cnf(refute_0_37,plain,
less_than(upper_bound,index_of_maximal),
inference(resolve,[$cnf( less_than(an_index,lower_bound) )],[refute_0_36,somewhere_above_lower_bound]) ).
cnf(refute_0_38,plain,
less_than(upper_bound,an_index),
inference(resolve,[$cnf( less_than(upper_bound,index_of_maximal) )],[refute_0_37,refute_0_2]) ).
cnf(refute_0_39,plain,
$false,
inference(resolve,[$cnf( less_than(upper_bound,an_index) )],[refute_0_38,somewhere_below_upper_bound]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWV019-1 : TPTP v8.1.0. Released v2.4.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 22:08:55 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.41 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.41
% 0.20/0.41 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.41
%------------------------------------------------------------------------------