TSTP Solution File: LAT259-2 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : LAT259-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n006.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 : Sun Jul 17 06:01:46 EDT 2022

% Result   : Unsatisfiable 0.12s 0.34s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   10
% Syntax   : Number of clauses     :   24 (  12 unt;   0 nHn;  23 RR)
%            Number of literals    :   43 (  20 equ;  21 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-4 aty)
%            Number of variables   :   11 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
    c_in(c_Pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) ).

cnf(cls_conjecture_1,negated_conjecture,
    c_in(c_Pair(v_b,v_a,t_a,t_a),v_r,tc_prod(t_a,t_a)) ).

cnf(cls_conjecture_2,negated_conjecture,
    v_a != v_b ).

cnf(cls_Relation_Oantisym__def_0,axiom,
    ( ~ c_Relation_Oantisym(V_r,T_a)
    | ~ c_in(c_Pair(V_V,V_U,T_a,T_a),V_r,tc_prod(T_a,T_a))
    | ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
    | V_U = V_V ) ).

cnf(cls_Tarski_OPartialOrder__iff_1,axiom,
    ( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
    | c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) ) ).

cnf(cls_Tarski_Ocl_A_58_APartialOrder_0,axiom,
    c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ).

cnf(cls_Tarski_Or_A_61_61_Aorder_Acl_0,axiom,
    v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) ).

cnf(refute_0_0,plain,
    ( ~ c_Relation_Oantisym(v_r,t_a)
    | ~ c_in(c_Pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
    | ~ c_in(c_Pair(v_b,v_a,t_a,t_a),v_r,tc_prod(t_a,t_a))
    | v_b = v_a ),
    inference(subst,[],[cls_Relation_Oantisym__def_0:[bind(T_a,$fot(t_a)),bind(V_U,$fot(v_b)),bind(V_V,$fot(v_a)),bind(V_r,$fot(v_r))]]) ).

cnf(refute_0_1,plain,
    ( ~ c_Relation_Oantisym(v_r,t_a)
    | ~ c_in(c_Pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
    | v_b = v_a ),
    inference(resolve,[$cnf( c_in(c_Pair(v_b,v_a,t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[cls_conjecture_1,refute_0_0]) ).

cnf(refute_0_2,plain,
    ( ~ c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
    | c_Relation_Oantisym(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
    inference(subst,[],[cls_Tarski_OPartialOrder__iff_1:[bind(T_a,$fot(t_a)),bind(V_P,$fot(v_cl))]]) ).

cnf(refute_0_3,plain,
    c_Relation_Oantisym(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a),
    inference(resolve,[$cnf( c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) )],[cls_Tarski_Ocl_A_58_APartialOrder_0,refute_0_2]) ).

cnf(refute_0_4,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_5,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_6,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_4,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( v_r != c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit)
    | c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) = v_r ),
    inference(subst,[],[refute_0_6:[bind(X,$fot(v_r)),bind(Y,$fot(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit)))]]) ).

cnf(refute_0_8,plain,
    c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) = v_r,
    inference(resolve,[$cnf( $equal(v_r,c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit)) )],[cls_Tarski_Or_A_61_61_Aorder_Acl_0,refute_0_7]) ).

cnf(refute_0_9,plain,
    ( c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) != v_r
    | ~ c_Relation_Oantisym(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a)
    | c_Relation_Oantisym(v_r,t_a) ),
    introduced(tautology,[equality,[$cnf( c_Relation_Oantisym(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),[0],$fot(v_r)]]) ).

cnf(refute_0_10,plain,
    ( ~ c_Relation_Oantisym(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a)
    | c_Relation_Oantisym(v_r,t_a) ),
    inference(resolve,[$cnf( $equal(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),v_r) )],[refute_0_8,refute_0_9]) ).

cnf(refute_0_11,plain,
    c_Relation_Oantisym(v_r,t_a),
    inference(resolve,[$cnf( c_Relation_Oantisym(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a) )],[refute_0_3,refute_0_10]) ).

cnf(refute_0_12,plain,
    ( ~ c_in(c_Pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
    | v_b = v_a ),
    inference(resolve,[$cnf( c_Relation_Oantisym(v_r,t_a) )],[refute_0_11,refute_0_1]) ).

cnf(refute_0_13,plain,
    v_b = v_a,
    inference(resolve,[$cnf( c_in(c_Pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[cls_conjecture_0,refute_0_12]) ).

cnf(refute_0_14,plain,
    ( v_b != v_a
    | v_a = v_b ),
    inference(subst,[],[refute_0_6:[bind(X,$fot(v_b)),bind(Y,$fot(v_a))]]) ).

cnf(refute_0_15,plain,
    v_b != v_a,
    inference(resolve,[$cnf( $equal(v_a,v_b) )],[refute_0_14,cls_conjecture_2]) ).

cnf(refute_0_16,plain,
    $false,
    inference(resolve,[$cnf( $equal(v_b,v_a) )],[refute_0_13,refute_0_15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LAT259-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n006.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 : Thu Jun 30 12:12:08 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34  
% 0.12/0.34  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.34  
%------------------------------------------------------------------------------