TSTP Solution File: ANA027-2 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : ANA027-2 : TPTP v8.1.0. Released v3.2.0.
% 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 : Thu Jul 14 19:14:42 EDT 2022

% Result   : Unsatisfiable 2.39s 2.55s
% Output   : CNFRefutation 2.39s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   15
% Syntax   : Number of clauses     :   46 (  16 unt;   0 nHn;  42 RR)
%            Number of literals    :   88 (   7 equ;  43 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   10 (   7 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   3 con; 0-3 aty)
%            Number of variables   :   35 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(cls_conjecture_1,negated_conjecture,
    c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b) ).

cnf(cls_conjecture_2,negated_conjecture,
    c_lessequals(v_g(v_x),v_k(v_x),t_b) ).

cnf(cls_conjecture_3,negated_conjecture,
    ~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) ).

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

cnf(cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | c_plus(c_0,V_y,T_a) = V_y ) ).

cnf(cls_OrderedGroup_Ocompare__rls__9_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | ~ c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
    | c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) ) ).

cnf(cls_OrderedGroup_Ocompare__rls__9_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
    | c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a) ) ).

cnf(cls_Orderings_Oorder__class_Oorder__trans_0,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | ~ c_lessequals(V_y,V_z,T_a)
    | ~ c_lessequals(V_x,V_y,T_a)
    | c_lessequals(V_x,V_z,T_a) ) ).

cnf(clsrel_LOrder_Ojoin__semilorder_1,axiom,
    ( ~ class_LOrder_Ojoin__semilorder(T)
    | class_Orderings_Oorder(T) ) ).

cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(T)
    | class_OrderedGroup_Opordered__ab__group__add(T) ) ).

cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_15,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(T)
    | class_LOrder_Ojoin__semilorder(T) ) ).

cnf(clsrel_Ring__and__Field_Oordered__idom_23,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T)
    | class_OrderedGroup_Ocomm__monoid__add(T) ) ).

cnf(clsrel_Ring__and__Field_Oordered__idom_50,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T)
    | class_OrderedGroup_Olordered__ab__group__abs(T) ) ).

cnf(refute_0_0,plain,
    ( ~ c_lessequals(c_plus(c_0,X_14,t_b),X_15,t_b)
    | ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
    | c_lessequals(c_0,c_minus(X_15,X_14,t_b),t_b) ),
    inference(subst,[],[cls_OrderedGroup_Ocompare__rls__9_1:[bind(T_a,$fot(t_b)),bind(V_a,$fot(c_0)),bind(V_b,$fot(X_14)),bind(V_c,$fot(X_15))]]) ).

cnf(refute_0_1,plain,
    ( ~ class_Ring__and__Field_Oordered__idom(t_b)
    | class_OrderedGroup_Ocomm__monoid__add(t_b) ),
    inference(subst,[],[clsrel_Ring__and__Field_Oordered__idom_23:[bind(T,$fot(t_b))]]) ).

cnf(refute_0_2,plain,
    class_OrderedGroup_Ocomm__monoid__add(t_b),
    inference(resolve,[$cnf( class_Ring__and__Field_Oordered__idom(t_b) )],[tfree_tcs,refute_0_1]) ).

cnf(refute_0_3,plain,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(t_b)
    | c_plus(c_0,X_6,t_b) = X_6 ),
    inference(subst,[],[cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0:[bind(T_a,$fot(t_b)),bind(V_y,$fot(X_6))]]) ).

cnf(refute_0_4,plain,
    c_plus(c_0,X_6,t_b) = X_6,
    inference(resolve,[$cnf( class_OrderedGroup_Ocomm__monoid__add(t_b) )],[refute_0_2,refute_0_3]) ).

cnf(refute_0_5,plain,
    c_plus(c_0,X_14,t_b) = X_14,
    inference(subst,[],[refute_0_4:[bind(X_6,$fot(X_14))]]) ).

cnf(refute_0_6,plain,
    ( c_plus(c_0,X_14,t_b) != X_14
    | ~ c_lessequals(X_14,X_15,t_b)
    | c_lessequals(c_plus(c_0,X_14,t_b),X_15,t_b) ),
    introduced(tautology,[equality,[$cnf( ~ c_lessequals(c_plus(c_0,X_14,t_b),X_15,t_b) ),[0],$fot(X_14)]]) ).

cnf(refute_0_7,plain,
    ( ~ c_lessequals(X_14,X_15,t_b)
    | c_lessequals(c_plus(c_0,X_14,t_b),X_15,t_b) ),
    inference(resolve,[$cnf( $equal(c_plus(c_0,X_14,t_b),X_14) )],[refute_0_5,refute_0_6]) ).

cnf(refute_0_8,plain,
    ( ~ c_lessequals(X_14,X_15,t_b)
    | ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
    | c_lessequals(c_0,c_minus(X_15,X_14,t_b),t_b) ),
    inference(resolve,[$cnf( c_lessequals(c_plus(c_0,X_14,t_b),X_15,t_b) )],[refute_0_7,refute_0_0]) ).

cnf(refute_0_9,plain,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
    | class_OrderedGroup_Opordered__ab__group__add(t_b) ),
    inference(subst,[],[clsrel_OrderedGroup_Olordered__ab__group__abs_1:[bind(T,$fot(t_b))]]) ).

cnf(refute_0_10,plain,
    ( ~ class_Ring__and__Field_Oordered__idom(t_b)
    | class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
    inference(subst,[],[clsrel_Ring__and__Field_Oordered__idom_50:[bind(T,$fot(t_b))]]) ).

cnf(refute_0_11,plain,
    class_OrderedGroup_Olordered__ab__group__abs(t_b),
    inference(resolve,[$cnf( class_Ring__and__Field_Oordered__idom(t_b) )],[tfree_tcs,refute_0_10]) ).

cnf(refute_0_12,plain,
    class_OrderedGroup_Opordered__ab__group__add(t_b),
    inference(resolve,[$cnf( class_OrderedGroup_Olordered__ab__group__abs(t_b) )],[refute_0_11,refute_0_9]) ).

cnf(refute_0_13,plain,
    ( ~ c_lessequals(X_14,X_15,t_b)
    | c_lessequals(c_0,c_minus(X_15,X_14,t_b),t_b) ),
    inference(resolve,[$cnf( class_OrderedGroup_Opordered__ab__group__add(t_b) )],[refute_0_12,refute_0_8]) ).

cnf(refute_0_14,plain,
    ( ~ c_lessequals(v_g(v_x),v_f(v_x),t_b)
    | c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) ),
    inference(subst,[],[refute_0_13:[bind(X_14,$fot(v_g(v_x))),bind(X_15,$fot(v_f(v_x)))]]) ).

cnf(refute_0_15,plain,
    ( ~ c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b)
    | ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
    | c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b) ),
    inference(subst,[],[cls_OrderedGroup_Ocompare__rls__9_0:[bind(T_a,$fot(t_b)),bind(V_a,$fot(c_0)),bind(V_b,$fot(v_k(v_x))),bind(V_c,$fot(v_f(v_x)))]]) ).

cnf(refute_0_16,plain,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
    | c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b) ),
    inference(resolve,[$cnf( c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b) )],[cls_conjecture_1,refute_0_15]) ).

cnf(refute_0_17,plain,
    c_plus(c_0,v_k(v_x),t_b) = v_k(v_x),
    inference(subst,[],[refute_0_4:[bind(X_6,$fot(v_k(v_x)))]]) ).

cnf(refute_0_18,plain,
    ( c_plus(c_0,v_k(v_x),t_b) != v_k(v_x)
    | ~ c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b)
    | c_lessequals(v_k(v_x),v_f(v_x),t_b) ),
    introduced(tautology,[equality,[$cnf( c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b) ),[0],$fot(v_k(v_x))]]) ).

cnf(refute_0_19,plain,
    ( ~ c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b)
    | c_lessequals(v_k(v_x),v_f(v_x),t_b) ),
    inference(resolve,[$cnf( $equal(c_plus(c_0,v_k(v_x),t_b),v_k(v_x)) )],[refute_0_17,refute_0_18]) ).

cnf(refute_0_20,plain,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
    | c_lessequals(v_k(v_x),v_f(v_x),t_b) ),
    inference(resolve,[$cnf( c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b) )],[refute_0_16,refute_0_19]) ).

cnf(refute_0_21,plain,
    c_lessequals(v_k(v_x),v_f(v_x),t_b),
    inference(resolve,[$cnf( class_OrderedGroup_Opordered__ab__group__add(t_b) )],[refute_0_12,refute_0_20]) ).

cnf(refute_0_22,plain,
    ( ~ c_lessequals(v_g(v_x),v_k(v_x),t_b)
    | ~ c_lessequals(v_k(v_x),X_21,t_b)
    | ~ class_Orderings_Oorder(t_b)
    | c_lessequals(v_g(v_x),X_21,t_b) ),
    inference(subst,[],[cls_Orderings_Oorder__class_Oorder__trans_0:[bind(T_a,$fot(t_b)),bind(V_x,$fot(v_g(v_x))),bind(V_y,$fot(v_k(v_x))),bind(V_z,$fot(X_21))]]) ).

cnf(refute_0_23,plain,
    ( ~ c_lessequals(v_k(v_x),X_21,t_b)
    | ~ class_Orderings_Oorder(t_b)
    | c_lessequals(v_g(v_x),X_21,t_b) ),
    inference(resolve,[$cnf( c_lessequals(v_g(v_x),v_k(v_x),t_b) )],[cls_conjecture_2,refute_0_22]) ).

cnf(refute_0_24,plain,
    ( ~ class_LOrder_Ojoin__semilorder(t_b)
    | class_Orderings_Oorder(t_b) ),
    inference(subst,[],[clsrel_LOrder_Ojoin__semilorder_1:[bind(T,$fot(t_b))]]) ).

cnf(refute_0_25,plain,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
    | class_LOrder_Ojoin__semilorder(t_b) ),
    inference(subst,[],[clsrel_OrderedGroup_Olordered__ab__group__abs_15:[bind(T,$fot(t_b))]]) ).

cnf(refute_0_26,plain,
    class_LOrder_Ojoin__semilorder(t_b),
    inference(resolve,[$cnf( class_OrderedGroup_Olordered__ab__group__abs(t_b) )],[refute_0_11,refute_0_25]) ).

cnf(refute_0_27,plain,
    class_Orderings_Oorder(t_b),
    inference(resolve,[$cnf( class_LOrder_Ojoin__semilorder(t_b) )],[refute_0_26,refute_0_24]) ).

cnf(refute_0_28,plain,
    ( ~ c_lessequals(v_k(v_x),X_21,t_b)
    | c_lessequals(v_g(v_x),X_21,t_b) ),
    inference(resolve,[$cnf( class_Orderings_Oorder(t_b) )],[refute_0_27,refute_0_23]) ).

cnf(refute_0_29,plain,
    ( ~ c_lessequals(v_k(v_x),v_f(v_x),t_b)
    | c_lessequals(v_g(v_x),v_f(v_x),t_b) ),
    inference(subst,[],[refute_0_28:[bind(X_21,$fot(v_f(v_x)))]]) ).

cnf(refute_0_30,plain,
    c_lessequals(v_g(v_x),v_f(v_x),t_b),
    inference(resolve,[$cnf( c_lessequals(v_k(v_x),v_f(v_x),t_b) )],[refute_0_21,refute_0_29]) ).

cnf(refute_0_31,plain,
    c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
    inference(resolve,[$cnf( c_lessequals(v_g(v_x),v_f(v_x),t_b) )],[refute_0_30,refute_0_14]) ).

cnf(refute_0_32,plain,
    $false,
    inference(resolve,[$cnf( c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) )],[refute_0_31,cls_conjecture_3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ANA027-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.14/0.34  % Computer : n018.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Fri Jul  8 06:55:40 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.39/2.55  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.39/2.55  
% 2.39/2.55  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.39/2.55  
%------------------------------------------------------------------------------