TSTP Solution File: SWC027-1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SWC027-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n014.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 21:26:09 EDT 2022

% Result   : Unsatisfiable 7.94s 8.11s
% Output   : CNFRefutation 7.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   25
% Syntax   : Number of clauses     :   66 (  16 unt;  15 nHn;  64 RR)
%            Number of literals    :  135 (  82 equ;  61 neg)
%            Maximal clause size   :    4 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :   11 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(clause8,axiom,
    ssList(nil) ).

cnf(clause11,axiom,
    ~ singletonP(nil) ).

cnf(clause71,axiom,
    ( ~ memberP(nil,U)
    | ~ ssItem(U) ) ).

cnf(clause116,axiom,
    ( cons(U,nil) != V
    | ~ ssItem(U)
    | ~ ssList(V)
    | singletonP(V) ) ).

cnf(co1_5,negated_conjecture,
    sk2 = sk4 ).

cnf(co1_6,negated_conjecture,
    sk1 = sk3 ).

cnf(co1_7,negated_conjecture,
    ( ssItem(sk5)
    | nil = sk4 ) ).

cnf(co1_8,negated_conjecture,
    ( ssItem(sk5)
    | nil = sk3 ) ).

cnf(co1_9,negated_conjecture,
    ( cons(sk5,nil) = sk3
    | nil = sk4 ) ).

cnf(co1_13,negated_conjecture,
    ( memberP(sk4,sk5)
    | nil = sk3 ) ).

cnf(co1_15,negated_conjecture,
    ( nil = sk2
    | nil = sk1 ) ).

cnf(co1_18,negated_conjecture,
    ( nil != sk1
    | nil != sk2 ) ).

cnf(refute_0_0,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_1,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_2,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    ( sk2 != sk4
    | sk4 = sk2 ),
    inference(subst,[],[refute_0_2:[bind(X,$fot(sk2)),bind(Y,$fot(sk4))]]) ).

cnf(refute_0_4,plain,
    sk4 = sk2,
    inference(resolve,[$cnf( $equal(sk2,sk4) )],[co1_5,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( nil != sk4
    | sk4 != sk2
    | nil = sk2 ),
    introduced(tautology,[equality,[$cnf( ~ $equal(nil,sk2) ),[0],$fot(sk4)]]) ).

cnf(refute_0_6,plain,
    ( nil != sk4
    | nil = sk2 ),
    inference(resolve,[$cnf( $equal(sk4,sk2) )],[refute_0_4,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( nil = sk2
    | ssItem(sk5) ),
    inference(resolve,[$cnf( $equal(nil,sk4) )],[co1_7,refute_0_6]) ).

cnf(refute_0_8,plain,
    ( cons(U,nil) != cons(U,nil)
    | ~ ssItem(U)
    | ~ ssList(cons(U,nil))
    | singletonP(cons(U,nil)) ),
    inference(subst,[],[clause116:[bind(V,$fot(cons(U,nil)))]]) ).

cnf(refute_0_9,plain,
    cons(U,nil) = cons(U,nil),
    introduced(tautology,[refl,[$fot(cons(U,nil))]]) ).

cnf(refute_0_10,plain,
    ( ~ ssItem(U)
    | ~ ssList(cons(U,nil))
    | singletonP(cons(U,nil)) ),
    inference(resolve,[$cnf( $equal(cons(U,nil),cons(U,nil)) )],[refute_0_9,refute_0_8]) ).

cnf(refute_0_11,plain,
    ( ~ ssItem(sk5)
    | ~ ssList(cons(sk5,nil))
    | singletonP(cons(sk5,nil)) ),
    inference(subst,[],[refute_0_10:[bind(U,$fot(sk5))]]) ).

cnf(refute_0_12,plain,
    ( sk1 != sk3
    | sk3 = sk1 ),
    inference(subst,[],[refute_0_2:[bind(X,$fot(sk1)),bind(Y,$fot(sk3))]]) ).

cnf(refute_0_13,plain,
    sk3 = sk1,
    inference(resolve,[$cnf( $equal(sk1,sk3) )],[co1_6,refute_0_12]) ).

cnf(refute_0_14,plain,
    ( cons(sk5,nil) != sk3
    | sk3 != sk1
    | cons(sk5,nil) = sk1 ),
    introduced(tautology,[equality,[$cnf( ~ $equal(cons(sk5,nil),sk1) ),[0],$fot(sk3)]]) ).

cnf(refute_0_15,plain,
    ( cons(sk5,nil) != sk3
    | cons(sk5,nil) = sk1 ),
    inference(resolve,[$cnf( $equal(sk3,sk1) )],[refute_0_13,refute_0_14]) ).

cnf(refute_0_16,plain,
    ( cons(sk5,nil) = sk1
    | nil = sk4 ),
    inference(resolve,[$cnf( $equal(cons(sk5,nil),sk3) )],[co1_9,refute_0_15]) ).

cnf(refute_0_17,plain,
    ( cons(sk5,nil) = sk1
    | nil = sk2 ),
    inference(resolve,[$cnf( $equal(nil,sk4) )],[refute_0_16,refute_0_6]) ).

cnf(refute_0_18,plain,
    ( nil != sk3
    | sk3 != sk1
    | nil = sk1 ),
    introduced(tautology,[equality,[$cnf( ~ $equal(nil,sk1) ),[0],$fot(sk3)]]) ).

cnf(refute_0_19,plain,
    ( nil != sk3
    | nil = sk1 ),
    inference(resolve,[$cnf( $equal(sk3,sk1) )],[refute_0_13,refute_0_18]) ).

cnf(refute_0_20,plain,
    ( nil = sk1
    | ssItem(sk5) ),
    inference(resolve,[$cnf( $equal(nil,sk3) )],[co1_8,refute_0_19]) ).

cnf(refute_0_21,plain,
    ( nil = sk1
    | memberP(sk4,sk5) ),
    inference(resolve,[$cnf( $equal(nil,sk3) )],[co1_13,refute_0_19]) ).

cnf(refute_0_22,plain,
    ( sk4 != sk2
    | ~ memberP(sk4,sk5)
    | memberP(sk2,sk5) ),
    introduced(tautology,[equality,[$cnf( memberP(sk4,sk5) ),[0],$fot(sk2)]]) ).

cnf(refute_0_23,plain,
    ( ~ memberP(sk4,sk5)
    | memberP(sk2,sk5) ),
    inference(resolve,[$cnf( $equal(sk4,sk2) )],[refute_0_4,refute_0_22]) ).

cnf(refute_0_24,plain,
    ( nil = sk1
    | memberP(sk2,sk5) ),
    inference(resolve,[$cnf( memberP(sk4,sk5) )],[refute_0_21,refute_0_23]) ).

cnf(refute_0_25,plain,
    ( nil != sk2
    | sk2 = nil ),
    inference(subst,[],[refute_0_2:[bind(X,$fot(nil)),bind(Y,$fot(sk2))]]) ).

cnf(refute_0_26,plain,
    ( nil = sk1
    | sk2 = nil ),
    inference(resolve,[$cnf( $equal(nil,sk2) )],[co1_15,refute_0_25]) ).

cnf(refute_0_27,plain,
    ( sk2 != nil
    | ~ memberP(sk2,sk5)
    | memberP(nil,sk5) ),
    introduced(tautology,[equality,[$cnf( memberP(sk2,sk5) ),[0],$fot(nil)]]) ).

cnf(refute_0_28,plain,
    ( ~ memberP(sk2,sk5)
    | nil = sk1
    | memberP(nil,sk5) ),
    inference(resolve,[$cnf( $equal(sk2,nil) )],[refute_0_26,refute_0_27]) ).

cnf(refute_0_29,plain,
    ( nil = sk1
    | memberP(nil,sk5) ),
    inference(resolve,[$cnf( memberP(sk2,sk5) )],[refute_0_24,refute_0_28]) ).

cnf(refute_0_30,plain,
    ( ~ memberP(nil,sk5)
    | ~ ssItem(sk5) ),
    inference(subst,[],[clause71:[bind(U,$fot(sk5))]]) ).

cnf(refute_0_31,plain,
    ( ~ ssItem(sk5)
    | nil = sk1 ),
    inference(resolve,[$cnf( memberP(nil,sk5) )],[refute_0_29,refute_0_30]) ).

cnf(refute_0_32,plain,
    nil = sk1,
    inference(resolve,[$cnf( ssItem(sk5) )],[refute_0_20,refute_0_31]) ).

cnf(refute_0_33,plain,
    ( nil != sk1
    | sk1 = nil ),
    inference(subst,[],[refute_0_2:[bind(X,$fot(nil)),bind(Y,$fot(sk1))]]) ).

cnf(refute_0_34,plain,
    sk1 = nil,
    inference(resolve,[$cnf( $equal(nil,sk1) )],[refute_0_32,refute_0_33]) ).

cnf(refute_0_35,plain,
    ( cons(sk5,nil) != sk1
    | sk1 != nil
    | cons(sk5,nil) = nil ),
    introduced(tautology,[equality,[$cnf( ~ $equal(cons(sk5,nil),nil) ),[0],$fot(sk1)]]) ).

cnf(refute_0_36,plain,
    ( cons(sk5,nil) != sk1
    | cons(sk5,nil) = nil ),
    inference(resolve,[$cnf( $equal(sk1,nil) )],[refute_0_34,refute_0_35]) ).

cnf(refute_0_37,plain,
    ( cons(sk5,nil) = nil
    | nil = sk2 ),
    inference(resolve,[$cnf( $equal(cons(sk5,nil),sk1) )],[refute_0_17,refute_0_36]) ).

cnf(refute_0_38,plain,
    ( nil != nil
    | sk1 != nil
    | nil = sk1 ),
    introduced(tautology,[equality,[$cnf( ~ $equal(nil,sk1) ),[1],$fot(nil)]]) ).

cnf(refute_0_39,plain,
    ( nil != nil
    | nil = sk1 ),
    inference(resolve,[$cnf( $equal(sk1,nil) )],[refute_0_34,refute_0_38]) ).

cnf(refute_0_40,plain,
    ( nil != nil
    | nil != sk2 ),
    inference(resolve,[$cnf( $equal(nil,sk1) )],[refute_0_39,co1_18]) ).

cnf(refute_0_41,plain,
    nil = nil,
    introduced(tautology,[refl,[$fot(nil)]]) ).

cnf(refute_0_42,plain,
    nil != sk2,
    inference(resolve,[$cnf( $equal(nil,nil) )],[refute_0_41,refute_0_40]) ).

cnf(refute_0_43,plain,
    cons(sk5,nil) = nil,
    inference(resolve,[$cnf( $equal(nil,sk2) )],[refute_0_37,refute_0_42]) ).

cnf(refute_0_44,plain,
    ( cons(sk5,nil) != nil
    | ~ ssList(nil)
    | ssList(cons(sk5,nil)) ),
    introduced(tautology,[equality,[$cnf( ~ ssList(cons(sk5,nil)) ),[0],$fot(nil)]]) ).

cnf(refute_0_45,plain,
    ( ~ ssList(nil)
    | ssList(cons(sk5,nil)) ),
    inference(resolve,[$cnf( $equal(cons(sk5,nil),nil) )],[refute_0_43,refute_0_44]) ).

cnf(refute_0_46,plain,
    ( ~ ssItem(sk5)
    | ~ ssList(nil)
    | singletonP(cons(sk5,nil)) ),
    inference(resolve,[$cnf( ssList(cons(sk5,nil)) )],[refute_0_45,refute_0_11]) ).

cnf(refute_0_47,plain,
    ( cons(sk5,nil) != nil
    | ~ singletonP(cons(sk5,nil))
    | singletonP(nil) ),
    introduced(tautology,[equality,[$cnf( singletonP(cons(sk5,nil)) ),[0],$fot(nil)]]) ).

cnf(refute_0_48,plain,
    ( ~ singletonP(cons(sk5,nil))
    | singletonP(nil) ),
    inference(resolve,[$cnf( $equal(cons(sk5,nil),nil) )],[refute_0_43,refute_0_47]) ).

cnf(refute_0_49,plain,
    ( ~ ssItem(sk5)
    | ~ ssList(nil)
    | singletonP(nil) ),
    inference(resolve,[$cnf( singletonP(cons(sk5,nil)) )],[refute_0_46,refute_0_48]) ).

cnf(refute_0_50,plain,
    ( ~ ssItem(sk5)
    | singletonP(nil) ),
    inference(resolve,[$cnf( ssList(nil) )],[clause8,refute_0_49]) ).

cnf(refute_0_51,plain,
    ~ ssItem(sk5),
    inference(resolve,[$cnf( singletonP(nil) )],[refute_0_50,clause11]) ).

cnf(refute_0_52,plain,
    nil = sk2,
    inference(resolve,[$cnf( ssItem(sk5) )],[refute_0_7,refute_0_51]) ).

cnf(refute_0_53,plain,
    $false,
    inference(resolve,[$cnf( $equal(nil,sk2) )],[refute_0_52,refute_0_42]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : SWC027-1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12  % Command  : metis --show proof --show saturation %s
% 0.11/0.33  % Computer : n014.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 600
% 0.11/0.33  % DateTime : Sun Jun 12 06:14:38 EDT 2022
% 0.11/0.33  % CPUTime  : 
% 0.11/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 7.94/8.11  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.94/8.11  
% 7.94/8.11  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.94/8.12  
%------------------------------------------------------------------------------