TSTP Solution File: SET842-2 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET842-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n027.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 03:37:42 EDT 2022

% Result   : Unsatisfiable 0.13s 0.36s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   25 (   3 unt;  12 nHn;  16 RR)
%            Number of literals    :   51 (   0 equ;  15 neg)
%            Maximal clause size   :    3 (   2 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-3 aty)
%            Number of variables   :   45 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(cls_conjecture_3,negated_conjecture,
    ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ).

cnf(cls_conjecture_4,negated_conjecture,
    ( 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_Set_OUnionE_0,axiom,
    ( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
    | c_in(c_Main_OUnionE__1(V_A,V_C,T_a),V_C,tc_set(T_a)) ) ).

cnf(cls_Set_OUnionE_1,axiom,
    ( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
    | c_in(V_A,c_Main_OUnionE__1(V_A,V_C,T_a),T_a) ) ).

cnf(cls_Set_OsubsetD_0,axiom,
    ( ~ c_in(V_c,V_A,T_a)
    | ~ c_lessequals(V_A,V_B,tc_set(T_a))
    | c_in(V_c,V_B,T_a) ) ).

cnf(cls_Set_OsubsetI_0,axiom,
    ( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
    | c_lessequals(V_A,V_B,tc_set(T_a)) ) ).

cnf(cls_Set_OsubsetI_1,axiom,
    ( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
    | c_lessequals(V_A,V_B,tc_set(T_a)) ) ).

cnf(refute_0_0,plain,
    ( ~ c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_m,tc_set(t_a))
    | c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
    inference(subst,[],[cls_Set_OsubsetI_1:[bind(T_a,$fot(tc_set(t_a))),bind(V_A,$fot(c_Union(v_Y,tc_set(t_a)))),bind(V_B,$fot(v_m))]]) ).

cnf(refute_0_1,plain,
    ( ~ c_in(c_Main_OsubsetI__1(c_Union(V_C,X_4),X_6,X_4),c_Union(V_C,X_4),X_4)
    | c_in(c_Main_OsubsetI__1(c_Union(V_C,X_4),X_6,X_4),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(V_C,X_4),X_6,X_4),V_C,X_4),X_4) ),
    inference(subst,[],[cls_Set_OUnionE_1:[bind(T_a,$fot(X_4)),bind(V_A,$fot(c_Main_OsubsetI__1(c_Union(V_C,X_4),X_6,X_4)))]]) ).

cnf(refute_0_2,plain,
    ( c_in(c_Main_OsubsetI__1(c_Union(V_C,X_4),X_6,X_4),c_Union(V_C,X_4),X_4)
    | c_lessequals(c_Union(V_C,X_4),X_6,tc_set(X_4)) ),
    inference(subst,[],[cls_Set_OsubsetI_0:[bind(T_a,$fot(X_4)),bind(V_A,$fot(c_Union(V_C,X_4))),bind(V_B,$fot(X_6))]]) ).

cnf(refute_0_3,plain,
    ( c_in(c_Main_OsubsetI__1(c_Union(V_C,X_4),X_6,X_4),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(V_C,X_4),X_6,X_4),V_C,X_4),X_4)
    | c_lessequals(c_Union(V_C,X_4),X_6,tc_set(X_4)) ),
    inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(c_Union(V_C,X_4),X_6,X_4),c_Union(V_C,X_4),X_4) )],[refute_0_2,refute_0_1]) ).

cnf(refute_0_4,plain,
    ( c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_40,tc_set(t_a)),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_40,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a))
    | c_lessequals(c_Union(v_Y,tc_set(t_a)),X_40,tc_set(tc_set(t_a))) ),
    inference(subst,[],[refute_0_3:[bind(V_C,$fot(v_Y)),bind(X_4,$fot(tc_set(t_a))),bind(X_6,$fot(X_40))]]) ).

cnf(refute_0_5,plain,
    ( ~ c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_16,tc_set(t_a)),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a)))
    | c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_16,tc_set(t_a)),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
    inference(subst,[],[cls_conjecture_4:[bind(V_U,$fot(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_16,tc_set(t_a)),v_Y,tc_set(t_a))))]]) ).

cnf(refute_0_6,plain,
    ( c_in(c_Main_OsubsetI__1(c_Union(X_15,X_13),V_B,X_13),c_Union(X_15,X_13),X_13)
    | c_lessequals(c_Union(X_15,X_13),V_B,tc_set(X_13)) ),
    inference(subst,[],[cls_Set_OsubsetI_0:[bind(T_a,$fot(X_13)),bind(V_A,$fot(c_Union(X_15,X_13)))]]) ).

cnf(refute_0_7,plain,
    ( ~ c_in(c_Main_OsubsetI__1(c_Union(X_15,X_13),V_B,X_13),c_Union(X_15,X_13),X_13)
    | c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(X_15,X_13),V_B,X_13),X_15,X_13),X_15,tc_set(X_13)) ),
    inference(subst,[],[cls_Set_OUnionE_0:[bind(T_a,$fot(X_13)),bind(V_A,$fot(c_Main_OsubsetI__1(c_Union(X_15,X_13),V_B,X_13))),bind(V_C,$fot(X_15))]]) ).

cnf(refute_0_8,plain,
    ( c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(X_15,X_13),V_B,X_13),X_15,X_13),X_15,tc_set(X_13))
    | c_lessequals(c_Union(X_15,X_13),V_B,tc_set(X_13)) ),
    inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(c_Union(X_15,X_13),V_B,X_13),c_Union(X_15,X_13),X_13) )],[refute_0_6,refute_0_7]) ).

cnf(refute_0_9,plain,
    ( c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_16,tc_set(t_a)),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a)))
    | c_lessequals(c_Union(v_Y,tc_set(t_a)),X_16,tc_set(tc_set(t_a))) ),
    inference(subst,[],[refute_0_8:[bind(V_B,$fot(X_16)),bind(X_13,$fot(tc_set(t_a))),bind(X_15,$fot(v_Y))]]) ).

cnf(refute_0_10,plain,
    ( c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_16,tc_set(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)),X_16,tc_set(tc_set(t_a))) ),
    inference(resolve,[$cnf( c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_16,tc_set(t_a)),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a))) )],[refute_0_9,refute_0_5]) ).

cnf(refute_0_11,plain,
    ( ~ c_in(X_23,c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_16,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a))
    | ~ c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_16,tc_set(t_a)),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
    | c_in(X_23,v_m,tc_set(t_a)) ),
    inference(subst,[],[cls_Set_OsubsetD_0:[bind(T_a,$fot(tc_set(t_a))),bind(V_A,$fot(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_16,tc_set(t_a)),v_Y,tc_set(t_a)))),bind(V_B,$fot(v_m)),bind(V_c,$fot(X_23))]]) ).

cnf(refute_0_12,plain,
    ( ~ c_in(X_23,c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_16,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a))
    | c_in(X_23,v_m,tc_set(t_a))
    | c_lessequals(c_Union(v_Y,tc_set(t_a)),X_16,tc_set(tc_set(t_a))) ),
    inference(resolve,[$cnf( c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_16,tc_set(t_a)),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) )],[refute_0_10,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( ~ c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_40,tc_set(t_a)),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_40,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a))
    | c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_40,tc_set(t_a)),v_m,tc_set(t_a))
    | c_lessequals(c_Union(v_Y,tc_set(t_a)),X_40,tc_set(tc_set(t_a))) ),
    inference(subst,[],[refute_0_12:[bind(X_16,$fot(X_40)),bind(X_23,$fot(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_40,tc_set(t_a))))]]) ).

cnf(refute_0_14,plain,
    ( c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_40,tc_set(t_a)),v_m,tc_set(t_a))
    | c_lessequals(c_Union(v_Y,tc_set(t_a)),X_40,tc_set(tc_set(t_a))) ),
    inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_40,tc_set(t_a)),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_40,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a)) )],[refute_0_4,refute_0_13]) ).

cnf(refute_0_15,plain,
    ( c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_m,tc_set(t_a))
    | c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
    inference(subst,[],[refute_0_14:[bind(X_40,$fot(v_m))]]) ).

cnf(refute_0_16,plain,
    c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
    inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_m,tc_set(t_a)) )],[refute_0_15,refute_0_0]) ).

cnf(refute_0_17,plain,
    $false,
    inference(resolve,[$cnf( c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) )],[refute_0_16,cls_conjecture_3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SET842-2 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n027.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sun Jul 10 05:34:32 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36  
% 0.13/0.36  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.37  
%------------------------------------------------------------------------------