TSTP Solution File: SWV019-1 by Metis---2.4

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%------------------------------------------------------------------------------
% 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  
%------------------------------------------------------------------------------