TSTP Solution File: HWV023-1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : HWV023-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n017.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 : Sat Jul 16 18:29:44 EDT 2022

% Result   : Unsatisfiable 219.96s 220.13s
% Output   : CNFRefutation 219.96s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   27
% Syntax   : Number of clauses     :   68 (  28 unt;  13 nHn;  56 RR)
%            Number of literals    :  137 (  81 equ;  57 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    9 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   40 (   1 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(axiom_2,axiom,
    gt(plus(X_1,n1),n0) ).

cnf(axiom_5,axiom,
    ( minus(X_3,Y_4) = Z_5
    | plus(Z_5,Y_4) != X_3
    | def_10(Y_4,X_3) ) ).

cnf(axiom_7,axiom,
    ( ~ def_10(Y_4,X_3)
    | X_3 != Y_4 ) ).

cnf(axiom_19,axiom,
    plus(n0,X_31) = X_31 ).

cnf(axiom_21,axiom,
    level(X_t_32) = int_level(X_t_32) ).

cnf(axiom_24,axiom,
    ( int_level(X_t_35) != n0
    | p_Empty(X_t_35) ) ).

cnf(axiom_71,axiom,
    ( p_Reset(X_t_42)
    | p_Wr(X_t_42)
    | ~ p_Rd(X_t_42)
    | ~ gt(int_level(X_t_42),n0)
    | int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) ).

cnf(quest_1,negated_conjecture,
    level(t_139) = n1 ).

cnf(quest_2,negated_conjecture,
    ~ p_Wr(t_139) ).

cnf(quest_3,negated_conjecture,
    p_Rd(t_139) ).

cnf(quest_4,negated_conjecture,
    ~ p_Reset(t_139) ).

cnf(quest_5,negated_conjecture,
    ~ p_Empty(plus(t_139,n1)) ).

cnf(refute_0_0,plain,
    ( int_level(plus(t_139,n1)) != n0
    | p_Empty(plus(t_139,n1)) ),
    inference(subst,[],[axiom_24:[bind(X_t_35,$fot(plus(t_139,n1)))]]) ).

cnf(refute_0_1,plain,
    ( ~ gt(int_level(t_139),n0)
    | ~ p_Rd(t_139)
    | int_level(plus(t_139,n1)) = minus(int_level(t_139),n1)
    | p_Reset(t_139)
    | p_Wr(t_139) ),
    inference(subst,[],[axiom_71:[bind(X_t_42,$fot(t_139))]]) ).

cnf(refute_0_2,plain,
    level(t_139) = int_level(t_139),
    inference(subst,[],[axiom_21:[bind(X_t_32,$fot(t_139))]]) ).

cnf(refute_0_3,plain,
    ( level(t_139) != int_level(t_139)
    | level(t_139) != n1
    | int_level(t_139) = n1 ),
    introduced(tautology,[equality,[$cnf( $equal(level(t_139),n1) ),[0],$fot(int_level(t_139))]]) ).

cnf(refute_0_4,plain,
    ( level(t_139) != n1
    | int_level(t_139) = n1 ),
    inference(resolve,[$cnf( $equal(level(t_139),int_level(t_139)) )],[refute_0_2,refute_0_3]) ).

cnf(refute_0_5,plain,
    int_level(t_139) = n1,
    inference(resolve,[$cnf( $equal(level(t_139),n1) )],[quest_1,refute_0_4]) ).

cnf(refute_0_6,plain,
    ( int_level(t_139) != n1
    | ~ gt(n1,n0)
    | gt(int_level(t_139),n0) ),
    introduced(tautology,[equality,[$cnf( ~ gt(int_level(t_139),n0) ),[0],$fot(n1)]]) ).

cnf(refute_0_7,plain,
    ( ~ gt(n1,n0)
    | gt(int_level(t_139),n0) ),
    inference(resolve,[$cnf( $equal(int_level(t_139),n1) )],[refute_0_5,refute_0_6]) ).

cnf(refute_0_8,plain,
    ( ~ gt(n1,n0)
    | ~ p_Rd(t_139)
    | int_level(plus(t_139,n1)) = minus(int_level(t_139),n1)
    | p_Reset(t_139)
    | p_Wr(t_139) ),
    inference(resolve,[$cnf( gt(int_level(t_139),n0) )],[refute_0_7,refute_0_1]) ).

cnf(refute_0_9,plain,
    ( plus(Z_5,Y_4) != plus(Z_5,Y_4)
    | minus(plus(Z_5,Y_4),Y_4) = Z_5
    | def_10(Y_4,plus(Z_5,Y_4)) ),
    inference(subst,[],[axiom_5:[bind(X_3,$fot(plus(Z_5,Y_4)))]]) ).

cnf(refute_0_10,plain,
    plus(Z_5,Y_4) = plus(Z_5,Y_4),
    introduced(tautology,[refl,[$fot(plus(Z_5,Y_4))]]) ).

cnf(refute_0_11,plain,
    ( minus(plus(Z_5,Y_4),Y_4) = Z_5
    | def_10(Y_4,plus(Z_5,Y_4)) ),
    inference(resolve,[$cnf( $equal(plus(Z_5,Y_4),plus(Z_5,Y_4)) )],[refute_0_10,refute_0_9]) ).

cnf(refute_0_12,plain,
    ( minus(plus(n0,X_87),X_87) = n0
    | def_10(X_87,plus(n0,X_87)) ),
    inference(subst,[],[refute_0_11:[bind(Y_4,$fot(X_87)),bind(Z_5,$fot(n0))]]) ).

cnf(refute_0_13,plain,
    plus(n0,X_87) = X_87,
    inference(subst,[],[axiom_19:[bind(X_31,$fot(X_87))]]) ).

cnf(refute_0_14,plain,
    ( minus(plus(n0,X_87),X_87) != n0
    | plus(n0,X_87) != X_87
    | minus(X_87,X_87) = n0 ),
    introduced(tautology,[equality,[$cnf( $equal(minus(plus(n0,X_87),X_87),n0) ),[0,0],$fot(X_87)]]) ).

cnf(refute_0_15,plain,
    ( minus(plus(n0,X_87),X_87) != n0
    | minus(X_87,X_87) = n0 ),
    inference(resolve,[$cnf( $equal(plus(n0,X_87),X_87) )],[refute_0_13,refute_0_14]) ).

cnf(refute_0_16,plain,
    ( minus(X_87,X_87) = n0
    | def_10(X_87,plus(n0,X_87)) ),
    inference(resolve,[$cnf( $equal(minus(plus(n0,X_87),X_87),n0) )],[refute_0_12,refute_0_15]) ).

cnf(refute_0_17,plain,
    ( plus(n0,X_87) != X_87
    | ~ def_10(X_87,plus(n0,X_87))
    | def_10(X_87,X_87) ),
    introduced(tautology,[equality,[$cnf( def_10(X_87,plus(n0,X_87)) ),[1],$fot(X_87)]]) ).

cnf(refute_0_18,plain,
    ( ~ def_10(X_87,plus(n0,X_87))
    | def_10(X_87,X_87) ),
    inference(resolve,[$cnf( $equal(plus(n0,X_87),X_87) )],[refute_0_13,refute_0_17]) ).

cnf(refute_0_19,plain,
    ( minus(X_87,X_87) = n0
    | def_10(X_87,X_87) ),
    inference(resolve,[$cnf( def_10(X_87,plus(n0,X_87)) )],[refute_0_16,refute_0_18]) ).

cnf(refute_0_20,plain,
    ( Y_4 != Y_4
    | ~ def_10(Y_4,Y_4) ),
    inference(subst,[],[axiom_7:[bind(X_3,$fot(Y_4))]]) ).

cnf(refute_0_21,plain,
    Y_4 = Y_4,
    introduced(tautology,[refl,[$fot(Y_4)]]) ).

cnf(refute_0_22,plain,
    ~ def_10(Y_4,Y_4),
    inference(resolve,[$cnf( $equal(Y_4,Y_4) )],[refute_0_21,refute_0_20]) ).

cnf(refute_0_23,plain,
    ~ def_10(X_87,X_87),
    inference(subst,[],[refute_0_22:[bind(Y_4,$fot(X_87))]]) ).

cnf(refute_0_24,plain,
    minus(X_87,X_87) = n0,
    inference(resolve,[$cnf( def_10(X_87,X_87) )],[refute_0_19,refute_0_23]) ).

cnf(refute_0_25,plain,
    minus(n1,n1) = n0,
    inference(subst,[],[refute_0_24:[bind(X_87,$fot(n1))]]) ).

cnf(refute_0_26,plain,
    minus(int_level(t_139),n1) = minus(int_level(t_139),n1),
    introduced(tautology,[refl,[$fot(minus(int_level(t_139),n1))]]) ).

cnf(refute_0_27,plain,
    ( int_level(t_139) != n1
    | minus(int_level(t_139),n1) != minus(int_level(t_139),n1)
    | minus(int_level(t_139),n1) = minus(n1,n1) ),
    introduced(tautology,[equality,[$cnf( $equal(minus(int_level(t_139),n1),minus(int_level(t_139),n1)) ),[1,0],$fot(n1)]]) ).

cnf(refute_0_28,plain,
    ( int_level(t_139) != n1
    | minus(int_level(t_139),n1) = minus(n1,n1) ),
    inference(resolve,[$cnf( $equal(minus(int_level(t_139),n1),minus(int_level(t_139),n1)) )],[refute_0_26,refute_0_27]) ).

cnf(refute_0_29,plain,
    minus(int_level(t_139),n1) = minus(n1,n1),
    inference(resolve,[$cnf( $equal(int_level(t_139),n1) )],[refute_0_5,refute_0_28]) ).

cnf(refute_0_30,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_31,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_32,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_30,refute_0_31]) ).

cnf(refute_0_33,plain,
    ( Y != X
    | Y != Z
    | X = Z ),
    introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).

cnf(refute_0_34,plain,
    ( X != Y
    | Y != Z
    | X = Z ),
    inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_32,refute_0_33]) ).

cnf(refute_0_35,plain,
    ( minus(int_level(t_139),n1) != minus(n1,n1)
    | minus(n1,n1) != n0
    | minus(int_level(t_139),n1) = n0 ),
    inference(subst,[],[refute_0_34:[bind(X,$fot(minus(int_level(t_139),n1))),bind(Y,$fot(minus(n1,n1))),bind(Z,$fot(n0))]]) ).

cnf(refute_0_36,plain,
    ( minus(n1,n1) != n0
    | minus(int_level(t_139),n1) = n0 ),
    inference(resolve,[$cnf( $equal(minus(int_level(t_139),n1),minus(n1,n1)) )],[refute_0_29,refute_0_35]) ).

cnf(refute_0_37,plain,
    minus(int_level(t_139),n1) = n0,
    inference(resolve,[$cnf( $equal(minus(n1,n1),n0) )],[refute_0_25,refute_0_36]) ).

cnf(refute_0_38,plain,
    ( int_level(plus(t_139,n1)) != minus(int_level(t_139),n1)
    | minus(int_level(t_139),n1) != n0
    | int_level(plus(t_139,n1)) = n0 ),
    introduced(tautology,[equality,[$cnf( ~ $equal(int_level(plus(t_139,n1)),n0) ),[0],$fot(minus(int_level(t_139),n1))]]) ).

cnf(refute_0_39,plain,
    ( int_level(plus(t_139,n1)) != minus(int_level(t_139),n1)
    | int_level(plus(t_139,n1)) = n0 ),
    inference(resolve,[$cnf( $equal(minus(int_level(t_139),n1),n0) )],[refute_0_37,refute_0_38]) ).

cnf(refute_0_40,plain,
    ( ~ gt(n1,n0)
    | ~ p_Rd(t_139)
    | int_level(plus(t_139,n1)) = n0
    | p_Reset(t_139)
    | p_Wr(t_139) ),
    inference(resolve,[$cnf( $equal(int_level(plus(t_139,n1)),minus(int_level(t_139),n1)) )],[refute_0_8,refute_0_39]) ).

cnf(refute_0_41,plain,
    gt(plus(n0,n1),n0),
    inference(subst,[],[axiom_2:[bind(X_1,$fot(n0))]]) ).

cnf(refute_0_42,plain,
    plus(n0,n1) = n1,
    inference(subst,[],[axiom_19:[bind(X_31,$fot(n1))]]) ).

cnf(refute_0_43,plain,
    ( plus(n0,n1) != n1
    | ~ gt(plus(n0,n1),n0)
    | gt(n1,n0) ),
    introduced(tautology,[equality,[$cnf( gt(plus(n0,n1),n0) ),[0],$fot(n1)]]) ).

cnf(refute_0_44,plain,
    ( ~ gt(plus(n0,n1),n0)
    | gt(n1,n0) ),
    inference(resolve,[$cnf( $equal(plus(n0,n1),n1) )],[refute_0_42,refute_0_43]) ).

cnf(refute_0_45,plain,
    gt(n1,n0),
    inference(resolve,[$cnf( gt(plus(n0,n1),n0) )],[refute_0_41,refute_0_44]) ).

cnf(refute_0_46,plain,
    ( ~ p_Rd(t_139)
    | int_level(plus(t_139,n1)) = n0
    | p_Reset(t_139)
    | p_Wr(t_139) ),
    inference(resolve,[$cnf( gt(n1,n0) )],[refute_0_45,refute_0_40]) ).

cnf(refute_0_47,plain,
    ( int_level(plus(t_139,n1)) = n0
    | p_Reset(t_139)
    | p_Wr(t_139) ),
    inference(resolve,[$cnf( p_Rd(t_139) )],[quest_3,refute_0_46]) ).

cnf(refute_0_48,plain,
    ( int_level(plus(t_139,n1)) = n0
    | p_Wr(t_139) ),
    inference(resolve,[$cnf( p_Reset(t_139) )],[refute_0_47,quest_4]) ).

cnf(refute_0_49,plain,
    int_level(plus(t_139,n1)) = n0,
    inference(resolve,[$cnf( p_Wr(t_139) )],[refute_0_48,quest_2]) ).

cnf(refute_0_50,plain,
    ( int_level(plus(t_139,n1)) != n0
    | n0 != n0
    | int_level(plus(t_139,n1)) = n0 ),
    introduced(tautology,[equality,[$cnf( ~ $equal(int_level(plus(t_139,n1)),n0) ),[0],$fot(n0)]]) ).

cnf(refute_0_51,plain,
    ( n0 != n0
    | int_level(plus(t_139,n1)) = n0 ),
    inference(resolve,[$cnf( $equal(int_level(plus(t_139,n1)),n0) )],[refute_0_49,refute_0_50]) ).

cnf(refute_0_52,plain,
    ( n0 != n0
    | p_Empty(plus(t_139,n1)) ),
    inference(resolve,[$cnf( $equal(int_level(plus(t_139,n1)),n0) )],[refute_0_51,refute_0_0]) ).

cnf(refute_0_53,plain,
    n0 = n0,
    introduced(tautology,[refl,[$fot(n0)]]) ).

cnf(refute_0_54,plain,
    p_Empty(plus(t_139,n1)),
    inference(resolve,[$cnf( $equal(n0,n0) )],[refute_0_53,refute_0_52]) ).

cnf(refute_0_55,plain,
    $false,
    inference(resolve,[$cnf( p_Empty(plus(t_139,n1)) )],[refute_0_54,quest_5]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : HWV023-1 : TPTP v8.1.0. Released v2.5.0.
% 0.08/0.14  % Command  : metis --show proof --show saturation %s
% 0.15/0.36  % Computer : n017.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 600
% 0.15/0.36  % DateTime : Thu Jun 16 22:50:41 EDT 2022
% 0.15/0.36  % CPUTime  : 
% 0.15/0.36  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 219.96/220.13  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 219.96/220.13  
% 219.96/220.13  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 219.96/220.13  
%------------------------------------------------------------------------------