TSTP Solution File: LCL445-2 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : LCL445-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n011.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 12:52:21 EDT 2022

% Result   : Unsatisfiable 0.13s 0.35s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   19 (  10 unt;   0 nHn;  17 RR)
%            Number of literals    :   31 (   0 equ;  13 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-3 aty)
%            Number of variables   :   24 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
    c_in(v_q,c_PropLog_Othms(c_insert(v_p,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ).

cnf(cls_conjecture_1,negated_conjecture,
    c_in(v_q,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ).

cnf(cls_conjecture_2,negated_conjecture,
    ~ c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ).

cnf(cls_PropLog_Odeduction_0,axiom,
    ( ~ c_in(V_q,c_PropLog_Othms(c_insert(V_p,V_H,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a))
    | c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ) ).

cnf(cls_PropLog_Othms_OMP_0,axiom,
    ( ~ c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
    | ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
    | c_in(V_q,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ) ).

cnf(cls_PropLog_Othms__excluded__middle_0,axiom,
    c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Ofalse,T_a),V_q,T_a),V_q,T_a),T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ).

cnf(refute_0_0,plain,
    ( ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_q,t_a),v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a))
    | ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a))
    | c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
    inference(subst,[],[cls_PropLog_Othms_OMP_0:[bind(T_a,$fot(t_a)),bind(V_H,$fot(v_H)),bind(V_p,$fot(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_q,t_a))),bind(V_q,$fot(v_q))]]) ).

cnf(refute_0_1,plain,
    ( ~ c_in(v_q,c_PropLog_Othms(c_insert(v_p,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
    | c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
    inference(subst,[],[cls_PropLog_Odeduction_0:[bind(T_a,$fot(t_a)),bind(V_H,$fot(v_H)),bind(V_p,$fot(v_p)),bind(V_q,$fot(v_q))]]) ).

cnf(refute_0_2,plain,
    c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
    inference(resolve,[$cnf( c_in(v_q,c_PropLog_Othms(c_insert(v_p,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) )],[cls_conjecture_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,X_26),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Ofalse,X_26),V_q,X_26),V_q,X_26),X_26),c_PropLog_Othms(X_27,X_26),tc_PropLog_Opl(X_26)),
    inference(subst,[],[cls_PropLog_Othms__excluded__middle_0:[bind(T_a,$fot(X_26)),bind(V_H,$fot(X_27))]]) ).

cnf(refute_0_4,plain,
    ( ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,X_26),c_PropLog_Othms(X_27,X_26),tc_PropLog_Opl(X_26))
    | ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,X_26),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Ofalse,X_26),V_q,X_26),V_q,X_26),X_26),c_PropLog_Othms(X_27,X_26),tc_PropLog_Opl(X_26))
    | c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Ofalse,X_26),V_q,X_26),V_q,X_26),c_PropLog_Othms(X_27,X_26),tc_PropLog_Opl(X_26)) ),
    inference(subst,[],[cls_PropLog_Othms_OMP_0:[bind(T_a,$fot(X_26)),bind(V_H,$fot(X_27)),bind(V_p,$fot(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,X_26))),bind(V_q,$fot(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Ofalse,X_26),V_q,X_26),V_q,X_26)))]]) ).

cnf(refute_0_5,plain,
    ( ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,X_26),c_PropLog_Othms(X_27,X_26),tc_PropLog_Opl(X_26))
    | c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Ofalse,X_26),V_q,X_26),V_q,X_26),c_PropLog_Othms(X_27,X_26),tc_PropLog_Opl(X_26)) ),
    inference(resolve,[$cnf( c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,X_26),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Ofalse,X_26),V_q,X_26),V_q,X_26),X_26),c_PropLog_Othms(X_27,X_26),tc_PropLog_Opl(X_26)) )],[refute_0_3,refute_0_4]) ).

cnf(refute_0_6,plain,
    ( ~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a))
    | c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_q,t_a),v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
    inference(subst,[],[refute_0_5:[bind(V_p,$fot(v_p)),bind(V_q,$fot(v_q)),bind(X_26,$fot(t_a)),bind(X_27,$fot(v_H))]]) ).

cnf(refute_0_7,plain,
    c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_q,t_a),v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
    inference(resolve,[$cnf( c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) )],[refute_0_2,refute_0_6]) ).

cnf(refute_0_8,plain,
    ( ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a))
    | c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
    inference(resolve,[$cnf( c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_q,t_a),v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) )],[refute_0_7,refute_0_0]) ).

cnf(refute_0_9,plain,
    ( ~ c_in(v_q,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
    | c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
    inference(subst,[],[cls_PropLog_Odeduction_0:[bind(T_a,$fot(t_a)),bind(V_H,$fot(v_H)),bind(V_p,$fot(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a))),bind(V_q,$fot(v_q))]]) ).

cnf(refute_0_10,plain,
    c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
    inference(resolve,[$cnf( c_in(v_q,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) )],[cls_conjecture_1,refute_0_9]) ).

cnf(refute_0_11,plain,
    c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
    inference(resolve,[$cnf( c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) )],[refute_0_10,refute_0_8]) ).

cnf(refute_0_12,plain,
    $false,
    inference(resolve,[$cnf( c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) )],[refute_0_11,cls_conjecture_2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : LCL445-2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n011.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 : Sat Jul  2 13:00:34 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35  
% 0.13/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.35  
%------------------------------------------------------------------------------