TSTP Solution File: ANA009-2 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : ANA009-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n003.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 : Thu Jul 14 19:14:29 EDT 2022

% Result   : Unsatisfiable 0.17s 0.33s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   23 (  12 unt;   0 nHn;  12 RR)
%            Number of literals    :   37 (   5 equ;  15 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    7 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-3 aty)
%            Number of variables   :   22 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(cls_OrderedGroup_Oadd__le__cancel__right_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
    | ~ c_lessequals(V_a,V_b,T_a)
    | c_lessequals(c_plus(V_a,V_c,T_a),c_plus(V_b,V_c,T_a),T_a) ) ).

cnf(cls_OrderedGroup_Oright__minus_0,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | c_plus(V_a,c_uminus(V_a,T_a),T_a) = c_0 ) ).

cnf(cls_conjecture_0,negated_conjecture,
    c_lessequals(v_lb(V_U),v_f(V_U),t_b) ).

cnf(cls_conjecture_2,negated_conjecture,
    ~ c_lessequals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b) ).

cnf(clsrel_Ring__and__Field_Oordered__idom_37,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T) ) ).

cnf(clsrel_Ring__and__Field_Oordered__idom_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T)
    | class_OrderedGroup_Oab__group__add(T) ) ).

cnf(tfree_tcs,negated_conjecture,
    class_Ring__and__Field_Oordered__idom(t_b) ).

cnf(refute_0_0,plain,
    ( ~ c_lessequals(v_lb(V_U),v_f(V_U),t_b)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)
    | c_lessequals(c_plus(v_lb(V_U),X_9,t_b),c_plus(v_f(V_U),X_9,t_b),t_b) ),
    inference(subst,[],[cls_OrderedGroup_Oadd__le__cancel__right_1:[bind(T_a,$fot(t_b)),bind(V_a,$fot(v_lb(V_U))),bind(V_b,$fot(v_f(V_U))),bind(V_c,$fot(X_9))]]) ).

cnf(refute_0_1,plain,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)
    | c_lessequals(c_plus(v_lb(V_U),X_9,t_b),c_plus(v_f(V_U),X_9,t_b),t_b) ),
    inference(resolve,[$cnf( c_lessequals(v_lb(V_U),v_f(V_U),t_b) )],[cls_conjecture_0,refute_0_0]) ).

cnf(refute_0_2,plain,
    ( ~ class_Ring__and__Field_Oordered__idom(t_b)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b) ),
    inference(subst,[],[clsrel_Ring__and__Field_Oordered__idom_37:[bind(T,$fot(t_b))]]) ).

cnf(refute_0_3,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b),
    inference(resolve,[$cnf( class_Ring__and__Field_Oordered__idom(t_b) )],[tfree_tcs,refute_0_2]) ).

cnf(refute_0_4,plain,
    c_lessequals(c_plus(v_lb(V_U),X_9,t_b),c_plus(v_f(V_U),X_9,t_b),t_b),
    inference(resolve,[$cnf( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b) )],[refute_0_3,refute_0_1]) ).

cnf(refute_0_5,plain,
    c_lessequals(c_plus(v_lb(X_10),c_uminus(v_lb(X_10),t_b),t_b),c_plus(v_f(X_10),c_uminus(v_lb(X_10),t_b),t_b),t_b),
    inference(subst,[],[refute_0_4:[bind(V_U,$fot(X_10)),bind(X_9,$fot(c_uminus(v_lb(X_10),t_b)))]]) ).

cnf(refute_0_6,plain,
    ( ~ class_Ring__and__Field_Oordered__idom(t_b)
    | class_OrderedGroup_Oab__group__add(t_b) ),
    inference(subst,[],[clsrel_Ring__and__Field_Oordered__idom_4:[bind(T,$fot(t_b))]]) ).

cnf(refute_0_7,plain,
    class_OrderedGroup_Oab__group__add(t_b),
    inference(resolve,[$cnf( class_Ring__and__Field_Oordered__idom(t_b) )],[tfree_tcs,refute_0_6]) ).

cnf(refute_0_8,plain,
    ( ~ class_OrderedGroup_Oab__group__add(t_b)
    | c_plus(X_4,c_uminus(X_4,t_b),t_b) = c_0 ),
    inference(subst,[],[cls_OrderedGroup_Oright__minus_0:[bind(T_a,$fot(t_b)),bind(V_a,$fot(X_4))]]) ).

cnf(refute_0_9,plain,
    c_plus(X_4,c_uminus(X_4,t_b),t_b) = c_0,
    inference(resolve,[$cnf( class_OrderedGroup_Oab__group__add(t_b) )],[refute_0_7,refute_0_8]) ).

cnf(refute_0_10,plain,
    c_plus(v_lb(X_10),c_uminus(v_lb(X_10),t_b),t_b) = c_0,
    inference(subst,[],[refute_0_9:[bind(X_4,$fot(v_lb(X_10)))]]) ).

cnf(refute_0_11,plain,
    ( c_plus(v_lb(X_10),c_uminus(v_lb(X_10),t_b),t_b) != c_0
    | ~ c_lessequals(c_plus(v_lb(X_10),c_uminus(v_lb(X_10),t_b),t_b),c_plus(v_f(X_10),c_uminus(v_lb(X_10),t_b),t_b),t_b)
    | c_lessequals(c_0,c_plus(v_f(X_10),c_uminus(v_lb(X_10),t_b),t_b),t_b) ),
    introduced(tautology,[equality,[$cnf( c_lessequals(c_plus(v_lb(X_10),c_uminus(v_lb(X_10),t_b),t_b),c_plus(v_f(X_10),c_uminus(v_lb(X_10),t_b),t_b),t_b) ),[0],$fot(c_0)]]) ).

cnf(refute_0_12,plain,
    ( ~ c_lessequals(c_plus(v_lb(X_10),c_uminus(v_lb(X_10),t_b),t_b),c_plus(v_f(X_10),c_uminus(v_lb(X_10),t_b),t_b),t_b)
    | c_lessequals(c_0,c_plus(v_f(X_10),c_uminus(v_lb(X_10),t_b),t_b),t_b) ),
    inference(resolve,[$cnf( $equal(c_plus(v_lb(X_10),c_uminus(v_lb(X_10),t_b),t_b),c_0) )],[refute_0_10,refute_0_11]) ).

cnf(refute_0_13,plain,
    c_lessequals(c_0,c_plus(v_f(X_10),c_uminus(v_lb(X_10),t_b),t_b),t_b),
    inference(resolve,[$cnf( c_lessequals(c_plus(v_lb(X_10),c_uminus(v_lb(X_10),t_b),t_b),c_plus(v_f(X_10),c_uminus(v_lb(X_10),t_b),t_b),t_b) )],[refute_0_5,refute_0_12]) ).

cnf(refute_0_14,plain,
    c_lessequals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b),
    inference(subst,[],[refute_0_13:[bind(X_10,$fot(v_x))]]) ).

cnf(refute_0_15,plain,
    $false,
    inference(resolve,[$cnf( c_lessequals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b) )],[refute_0_14,cls_conjecture_2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : ANA009-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.32  % Computer : n003.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 600
% 0.12/0.32  % DateTime : Fri Jul  8 04:16:42 EDT 2022
% 0.12/0.32  % CPUTime  : 
% 0.12/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.17/0.33  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.33  
% 0.17/0.33  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.17/0.33  
%------------------------------------------------------------------------------