TSTP Solution File: SET852-2 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET852-2 : 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 : Tue Jul 19 03:37:49 EDT 2022

% Result   : Unsatisfiable 0.14s 0.35s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   18 (   4 unt;  14 nHn;  12 RR)
%            Number of literals    :   45 (   0 equ;   8 neg)
%            Maximal clause size   :    4 (   2 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-4 aty)
%            Number of variables   :   23 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(cls_conjecture_2,negated_conjecture,
    ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ).

cnf(cls_conjecture_3,negated_conjecture,
    ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ).

cnf(cls_conjecture_4,negated_conjecture,
    ( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),V_U,tc_set(tc_set(t_a)))
    | c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
    | ~ c_in(V_U,v_Y,tc_set(tc_set(t_a))) ) ).

cnf(cls_Zorn_OUnion__lemma0_0,axiom,
    ( c_in(c_Zorn_OUnion__lemma0__1(V_A,V_B,V_C,T_a),V_C,tc_set(T_a))
    | c_lessequals(V_B,c_Union(V_C,T_a),tc_set(T_a))
    | c_lessequals(c_Union(V_C,T_a),V_A,tc_set(T_a)) ) ).

cnf(cls_Zorn_OUnion__lemma0_1,axiom,
    ( ~ c_lessequals(c_Zorn_OUnion__lemma0__1(V_A,V_B,V_C,T_a),V_A,tc_set(T_a))
    | c_lessequals(V_B,c_Union(V_C,T_a),tc_set(T_a))
    | c_lessequals(c_Union(V_C,T_a),V_A,tc_set(T_a)) ) ).

cnf(cls_Zorn_OUnion__lemma0_2,axiom,
    ( ~ c_lessequals(V_B,c_Zorn_OUnion__lemma0__1(V_A,V_B,V_C,T_a),tc_set(T_a))
    | c_lessequals(V_B,c_Union(V_C,T_a),tc_set(T_a))
    | c_lessequals(c_Union(V_C,T_a),V_A,tc_set(T_a)) ) ).

cnf(refute_0_0,plain,
    ( ~ c_lessequals(c_Zorn_OUnion__lemma0__1(v_m,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
    | c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
    inference(subst,[],[cls_Zorn_OUnion__lemma0_1:[bind(T_a,$fot(tc_set(t_a))),bind(V_A,$fot(v_m)),bind(V_B,$fot(c_Zorn_Osucc(v_S,v_m,t_a))),bind(V_C,$fot(v_Y))]]) ).

cnf(refute_0_1,plain,
    ( ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OUnion__lemma0__1(X_13,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
    | c_lessequals(c_Union(v_Y,tc_set(t_a)),X_13,tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
    inference(subst,[],[cls_Zorn_OUnion__lemma0_2:[bind(T_a,$fot(tc_set(t_a))),bind(V_A,$fot(X_13)),bind(V_B,$fot(c_Zorn_Osucc(v_S,v_m,t_a))),bind(V_C,$fot(v_Y))]]) ).

cnf(refute_0_2,plain,
    ( ~ c_in(c_Zorn_OUnion__lemma0__1(X_2,X_3,v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_OUnion__lemma0__1(X_2,X_3,v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OUnion__lemma0__1(X_2,X_3,v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
    inference(subst,[],[cls_conjecture_4:[bind(V_U,$fot(c_Zorn_OUnion__lemma0__1(X_2,X_3,v_Y,tc_set(t_a))))]]) ).

cnf(refute_0_3,plain,
    ( c_in(c_Zorn_OUnion__lemma0__1(X_2,X_3,v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a)))
    | c_lessequals(X_3,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
    | c_lessequals(c_Union(v_Y,tc_set(t_a)),X_2,tc_set(tc_set(t_a))) ),
    inference(subst,[],[cls_Zorn_OUnion__lemma0_0:[bind(T_a,$fot(tc_set(t_a))),bind(V_A,$fot(X_2)),bind(V_B,$fot(X_3)),bind(V_C,$fot(v_Y))]]) ).

cnf(refute_0_4,plain,
    ( c_lessequals(X_3,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
    | c_lessequals(c_Union(v_Y,tc_set(t_a)),X_2,tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_OUnion__lemma0__1(X_2,X_3,v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OUnion__lemma0__1(X_2,X_3,v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
    inference(resolve,[$cnf( c_in(c_Zorn_OUnion__lemma0__1(X_2,X_3,v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a))) )],[refute_0_3,refute_0_2]) ).

cnf(refute_0_5,plain,
    ( c_lessequals(c_Union(v_Y,tc_set(t_a)),X_13,tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_OUnion__lemma0__1(X_13,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OUnion__lemma0__1(X_13,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
    inference(subst,[],[refute_0_4:[bind(X_2,$fot(X_13)),bind(X_3,$fot(c_Zorn_Osucc(v_S,v_m,t_a)))]]) ).

cnf(refute_0_6,plain,
    ( c_lessequals(c_Union(v_Y,tc_set(t_a)),X_13,tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_OUnion__lemma0__1(X_13,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
    inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OUnion__lemma0__1(X_13,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) )],[refute_0_5,refute_0_1]) ).

cnf(refute_0_7,plain,
    ( c_lessequals(c_Union(v_Y,tc_set(t_a)),X_13,tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_OUnion__lemma0__1(X_13,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
    inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) )],[refute_0_6,cls_conjecture_3]) ).

cnf(refute_0_8,plain,
    ( c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_OUnion__lemma0__1(v_m,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
    inference(subst,[],[refute_0_7:[bind(X_13,$fot(v_m))]]) ).

cnf(refute_0_9,plain,
    ( c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
    inference(resolve,[$cnf( c_lessequals(c_Zorn_OUnion__lemma0__1(v_m,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) )],[refute_0_8,refute_0_0]) ).

cnf(refute_0_10,plain,
    c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
    inference(resolve,[$cnf( c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) )],[refute_0_9,cls_conjecture_2]) ).

cnf(refute_0_11,plain,
    $false,
    inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) )],[refute_0_10,cls_conjecture_3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET852-2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13  % 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 : Sun Jul 10 05:23:57 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.35  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35  
% 0.14/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.14/0.36  
%------------------------------------------------------------------------------