TSTP Solution File: SET855-2 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET855-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n008.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 03:37:51 EDT 2022

% Result   : Unsatisfiable 0.12s 0.34s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   13 (   7 unt;   0 nHn;  12 RR)
%            Number of literals    :   22 (  14 equ;  11 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :    8 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(cls_Set_Osubset__antisym_0,axiom,
    ( ~ c_lessequals(V_B,V_A,tc_set(T_a))
    | ~ c_lessequals(V_A,V_B,tc_set(T_a))
    | V_A = V_B ) ).

cnf(cls_conjecture_2,negated_conjecture,
    c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ).

cnf(cls_conjecture_3,negated_conjecture,
    c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a))) ).

cnf(cls_conjecture_4,negated_conjecture,
    v_n != c_Union(v_Y,tc_set(t_a)) ).

cnf(refute_0_0,plain,
    ( ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a)))
    | ~ c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
    | c_Union(v_Y,tc_set(t_a)) = v_n ),
    inference(subst,[],[cls_Set_Osubset__antisym_0:[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_n))]]) ).

cnf(refute_0_1,plain,
    ( ~ c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
    | c_Union(v_Y,tc_set(t_a)) = v_n ),
    inference(resolve,[$cnf( c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a))) )],[cls_conjecture_3,refute_0_0]) ).

cnf(refute_0_2,plain,
    c_Union(v_Y,tc_set(t_a)) = v_n,
    inference(resolve,[$cnf( c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) )],[cls_conjecture_2,refute_0_1]) ).

cnf(refute_0_3,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_4,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_5,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_3,refute_0_4]) ).

cnf(refute_0_6,plain,
    ( c_Union(v_Y,tc_set(t_a)) != v_n
    | v_n = c_Union(v_Y,tc_set(t_a)) ),
    inference(subst,[],[refute_0_5:[bind(X,$fot(c_Union(v_Y,tc_set(t_a)))),bind(Y,$fot(v_n))]]) ).

cnf(refute_0_7,plain,
    c_Union(v_Y,tc_set(t_a)) != v_n,
    inference(resolve,[$cnf( $equal(v_n,c_Union(v_Y,tc_set(t_a))) )],[refute_0_6,cls_conjecture_4]) ).

cnf(refute_0_8,plain,
    $false,
    inference(resolve,[$cnf( $equal(c_Union(v_Y,tc_set(t_a)),v_n) )],[refute_0_2,refute_0_7]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SET855-2 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n008.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 : Sun Jul 10 10:49:23 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.34  
% 0.12/0.34  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.34  
%------------------------------------------------------------------------------