TSTP Solution File: SET841-2 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET841-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n024.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 : Tue Jul 19 03:37:41 EDT 2022

% Result   : Unsatisfiable 0.13s 0.35s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   13
% Syntax   : Number of clauses     :   32 (  15 unt;   6 nHn;  30 RR)
%            Number of literals    :   66 (  37 equ;  30 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-3 aty)
%            Number of variables   :   19 (   1 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(cls_Set_Osubset__refl_0,axiom,
    c_lessequals(V_A,V_A,tc_set(T_a)) ).

cnf(cls_Zorn_OTFin__subsetD_0,axiom,
    ( ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
    | ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
    | ~ c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
    | c_lessequals(c_Zorn_Osucc(V_S,V_n,T_a),V_m,tc_set(tc_set(T_a)))
    | V_n = V_m ) ).

cnf(cls_conjecture_0,negated_conjecture,
    c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ).

cnf(cls_conjecture_1,negated_conjecture,
    v_m = c_Zorn_Osucc(v_S,v_m,t_a) ).

cnf(cls_conjecture_2,negated_conjecture,
    c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ).

cnf(cls_conjecture_3,negated_conjecture,
    c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) ).

cnf(cls_conjecture_4,negated_conjecture,
    ~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))) ).

cnf(refute_0_0,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_1,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_2,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    ( v_m != c_Zorn_Osucc(v_S,v_m,t_a)
    | c_Zorn_Osucc(v_S,v_m,t_a) = v_m ),
    inference(subst,[],[refute_0_2:[bind(X,$fot(v_m)),bind(Y,$fot(c_Zorn_Osucc(v_S,v_m,t_a)))]]) ).

cnf(refute_0_4,plain,
    c_Zorn_Osucc(v_S,v_m,t_a) = v_m,
    inference(resolve,[$cnf( $equal(v_m,c_Zorn_Osucc(v_S,v_m,t_a)) )],[cls_conjecture_1,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( ~ c_in(X_5,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
    | ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
    | ~ c_lessequals(X_5,v_m,tc_set(tc_set(t_a)))
    | X_5 = v_m
    | c_lessequals(c_Zorn_Osucc(v_S,X_5,t_a),v_m,tc_set(tc_set(t_a))) ),
    inference(subst,[],[cls_Zorn_OTFin__subsetD_0:[bind(T_a,$fot(t_a)),bind(V_S,$fot(v_S)),bind(V_m,$fot(v_m)),bind(V_n,$fot(X_5))]]) ).

cnf(refute_0_6,plain,
    ( ~ c_in(X_5,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
    | ~ c_lessequals(X_5,v_m,tc_set(tc_set(t_a)))
    | X_5 = v_m
    | c_lessequals(c_Zorn_Osucc(v_S,X_5,t_a),v_m,tc_set(tc_set(t_a))) ),
    inference(resolve,[$cnf( c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_0,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
    | ~ c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
    | v_x = v_m
    | c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))) ),
    inference(subst,[],[refute_0_6:[bind(X_5,$fot(v_x))]]) ).

cnf(refute_0_8,plain,
    ( ~ c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
    | v_x = v_m
    | c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))) ),
    inference(resolve,[$cnf( c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_2,refute_0_7]) ).

cnf(refute_0_9,plain,
    ( v_x = v_m
    | c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))) ),
    inference(resolve,[$cnf( c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) )],[cls_conjecture_3,refute_0_8]) ).

cnf(refute_0_10,plain,
    v_x = v_m,
    inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))) )],[refute_0_9,cls_conjecture_4]) ).

cnf(refute_0_11,plain,
    c_Zorn_Osucc(v_S,v_x,t_a) = c_Zorn_Osucc(v_S,v_x,t_a),
    introduced(tautology,[refl,[$fot(c_Zorn_Osucc(v_S,v_x,t_a))]]) ).

cnf(refute_0_12,plain,
    ( c_Zorn_Osucc(v_S,v_x,t_a) != c_Zorn_Osucc(v_S,v_x,t_a)
    | v_x != v_m
    | c_Zorn_Osucc(v_S,v_x,t_a) = c_Zorn_Osucc(v_S,v_m,t_a) ),
    introduced(tautology,[equality,[$cnf( $equal(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_Osucc(v_S,v_x,t_a)) ),[1,1],$fot(v_m)]]) ).

cnf(refute_0_13,plain,
    ( v_x != v_m
    | c_Zorn_Osucc(v_S,v_x,t_a) = c_Zorn_Osucc(v_S,v_m,t_a) ),
    inference(resolve,[$cnf( $equal(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_Osucc(v_S,v_x,t_a)) )],[refute_0_11,refute_0_12]) ).

cnf(refute_0_14,plain,
    c_Zorn_Osucc(v_S,v_x,t_a) = c_Zorn_Osucc(v_S,v_m,t_a),
    inference(resolve,[$cnf( $equal(v_x,v_m) )],[refute_0_10,refute_0_13]) ).

cnf(refute_0_15,plain,
    ( Y != X
    | Y != Z
    | X = Z ),
    introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).

cnf(refute_0_16,plain,
    ( X != Y
    | Y != Z
    | X = Z ),
    inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_2,refute_0_15]) ).

cnf(refute_0_17,plain,
    ( c_Zorn_Osucc(v_S,v_m,t_a) != v_m
    | c_Zorn_Osucc(v_S,v_x,t_a) != c_Zorn_Osucc(v_S,v_m,t_a)
    | c_Zorn_Osucc(v_S,v_x,t_a) = v_m ),
    inference(subst,[],[refute_0_16:[bind(X,$fot(c_Zorn_Osucc(v_S,v_x,t_a))),bind(Y,$fot(c_Zorn_Osucc(v_S,v_m,t_a))),bind(Z,$fot(v_m))]]) ).

cnf(refute_0_18,plain,
    ( c_Zorn_Osucc(v_S,v_m,t_a) != v_m
    | c_Zorn_Osucc(v_S,v_x,t_a) = v_m ),
    inference(resolve,[$cnf( $equal(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_Osucc(v_S,v_m,t_a)) )],[refute_0_14,refute_0_17]) ).

cnf(refute_0_19,plain,
    c_Zorn_Osucc(v_S,v_x,t_a) = v_m,
    inference(resolve,[$cnf( $equal(c_Zorn_Osucc(v_S,v_m,t_a),v_m) )],[refute_0_4,refute_0_18]) ).

cnf(refute_0_20,plain,
    ( c_Zorn_Osucc(v_S,v_x,t_a) != v_m
    | ~ c_lessequals(v_m,v_m,tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))) ),
    introduced(tautology,[equality,[$cnf( ~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))) ),[0],$fot(v_m)]]) ).

cnf(refute_0_21,plain,
    ( ~ c_lessequals(v_m,v_m,tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))) ),
    inference(resolve,[$cnf( $equal(c_Zorn_Osucc(v_S,v_x,t_a),v_m) )],[refute_0_19,refute_0_20]) ).

cnf(refute_0_22,plain,
    ~ c_lessequals(v_m,v_m,tc_set(tc_set(t_a))),
    inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))) )],[refute_0_21,cls_conjecture_4]) ).

cnf(refute_0_23,plain,
    c_lessequals(v_m,v_m,tc_set(tc_set(t_a))),
    inference(subst,[],[cls_Set_Osubset__refl_0:[bind(T_a,$fot(tc_set(t_a))),bind(V_A,$fot(v_m))]]) ).

cnf(refute_0_24,plain,
    $false,
    inference(resolve,[$cnf( c_lessequals(v_m,v_m,tc_set(tc_set(t_a))) )],[refute_0_23,refute_0_22]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET841-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.33  % Computer : n024.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sun Jul 10 01:18:28 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35  
% 0.13/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.35  
%------------------------------------------------------------------------------