TSTP Solution File: CSR023+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : CSR023+1 : TPTP v8.1.0. Bugfixed v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n018.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 : Fri Jul 15 21:56:34 EDT 2022

% Result   : Theorem 0.18s 0.48s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   69 (  25 unt;   2 def)
%            Number of atoms       :  284 ( 155 equ)
%            Maximal formula atoms :   46 (   4 avg)
%            Number of connectives :  371 ( 156   ~; 152   |;  50   &)
%                                         (  12 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    8 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   9 con; 0-2 aty)
%            Number of variables   :   87 (   0 sgn  57   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(happens_holds,axiom,
    ! [Event,Time,Fluent] :
      ( ( happens(Event,Time)
        & initiates(Event,Fluent,Time) )
     => holdsAt(Fluent,plus(Time,n1)) ) ).

fof(initiates_all_defn,axiom,
    ! [Event,Fluent,Time] :
      ( initiates(Event,Fluent,Time)
    <=> ( ( Event = push
          & Fluent = forwards
          & ~ happens(pull,Time) )
        | ( Event = pull
          & Fluent = backwards
          & ~ happens(push,Time) )
        | ( Event = pull
          & Fluent = spinning
          & happens(push,Time) ) ) ) ).

fof(happens_all_defn,axiom,
    ! [Event,Time] :
      ( happens(Event,Time)
    <=> ( ( Event = push
          & Time = n0 )
        | ( Event = pull
          & Time = n1 )
        | ( Event = pull
          & Time = n2 )
        | ( Event = push
          & Time = n2 ) ) ) ).

fof(plus1_2,axiom,
    plus(n1,n2) = n3 ).

fof(symmetry_of_plus,axiom,
    ! [X,Y] : plus(X,Y) = plus(Y,X) ).

fof(spinning_3,conjecture,
    holdsAt(spinning,n3) ).

fof(definition_0,definition,
    ! [Event,Fluent,Time] :
      ( definitionFOFtoCNF_0(Event,Fluent,Time)
    <=> ( Event != pull
        | Fluent != backwards
        | happens(push,Time) ) ) ).

fof(definition_1,definition,
    ! [Event,Time] :
      ( definitionFOFtoCNF_4(Event,Time)
    <=> ( Event != pull
        | Time != n1 ) ) ).

fof(subgoal_0,plain,
    holdsAt(spinning,n3),
    inference(strip,[],[spinning_3]) ).

fof(negate_0_0,plain,
    ~ holdsAt(spinning,n3),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ! [Event,Time] :
      ( ~ happens(Event,Time)
    <=> ( ( Event != pull
          | Time != n1 )
        & ( Event != pull
          | Time != n2 )
        & ( Event != push
          | Time != n0 )
        & ( Event != push
          | Time != n2 ) ) ),
    inference(canonicalize,[],[happens_all_defn]) ).

fof(normalize_0_1,plain,
    ! [Event,Time] :
      ( ~ happens(Event,Time)
    <=> ( ( Event != pull
          | Time != n1 )
        & ( Event != pull
          | Time != n2 )
        & ( Event != push
          | Time != n0 )
        & ( Event != push
          | Time != n2 ) ) ),
    inference(specialize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [Event,Time] :
      ( ~ definitionFOFtoCNF_4(Event,Time)
    <=> ( Event = pull
        & Time = n1 ) ),
    inference(canonicalize,[],[definition_1]) ).

fof(normalize_0_3,plain,
    ! [Event,Time] :
      ( ~ happens(Event,Time)
    <=> ( definitionFOFtoCNF_4(Event,Time)
        & ( Event != pull
          | Time != n2 )
        & ( Event != push
          | Time != n0 )
        & ( Event != push
          | Time != n2 ) ) ),
    inference(simplify,[],[normalize_0_1,normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [Event,Time] :
      ( ( definitionFOFtoCNF_4(Event,Time)
        | happens(Event,Time) )
      & ( Event != pull
        | Time != n2
        | happens(Event,Time) )
      & ( Event != push
        | Time != n0
        | happens(Event,Time) )
      & ( Event != push
        | Time != n2
        | happens(Event,Time) )
      & ( ~ definitionFOFtoCNF_4(Event,Time)
        | ~ happens(Event,Time)
        | Event = pull
        | Event = push )
      & ( ~ definitionFOFtoCNF_4(Event,Time)
        | ~ happens(Event,Time)
        | Event = push
        | Time = n2 )
      & ( ~ definitionFOFtoCNF_4(Event,Time)
        | ~ happens(Event,Time)
        | Time = n0
        | Time = n2 )
      & ( ~ definitionFOFtoCNF_4(Event,Time)
        | ~ happens(Event,Time)
        | Event = pull
        | Event = push
        | Time = n0 )
      & ( ~ definitionFOFtoCNF_4(Event,Time)
        | ~ happens(Event,Time)
        | Event = pull
        | Event = push
        | Time = n2 )
      & ( ~ definitionFOFtoCNF_4(Event,Time)
        | ~ happens(Event,Time)
        | Event = pull
        | Time = n0
        | Time = n2 )
      & ( ~ definitionFOFtoCNF_4(Event,Time)
        | ~ happens(Event,Time)
        | Event = push
        | Time = n0
        | Time = n2 ) ),
    inference(clausify,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [Event,Time] :
      ( Event != push
      | Time != n2
      | happens(Event,Time) ),
    inference(conjunct,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [Event,Fluent,Time] :
      ( ~ initiates(Event,Fluent,Time)
    <=> ( ( Event != pull
          | Fluent != backwards
          | happens(push,Time) )
        & ( Event != pull
          | Fluent != spinning
          | ~ happens(push,Time) )
        & ( Event != push
          | Fluent != forwards
          | happens(pull,Time) ) ) ),
    inference(canonicalize,[],[initiates_all_defn]) ).

fof(normalize_0_7,plain,
    ! [Event,Fluent,Time] :
      ( ~ initiates(Event,Fluent,Time)
    <=> ( ( Event != pull
          | Fluent != backwards
          | happens(push,Time) )
        & ( Event != pull
          | Fluent != spinning
          | ~ happens(push,Time) )
        & ( Event != push
          | Fluent != forwards
          | happens(pull,Time) ) ) ),
    inference(specialize,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    ! [Event,Fluent,Time] :
      ( ~ definitionFOFtoCNF_0(Event,Fluent,Time)
    <=> ( ~ happens(push,Time)
        & Event = pull
        & Fluent = backwards ) ),
    inference(canonicalize,[],[definition_0]) ).

fof(normalize_0_9,plain,
    ! [Event,Fluent,Time] :
      ( ~ initiates(Event,Fluent,Time)
    <=> ( definitionFOFtoCNF_0(Event,Fluent,Time)
        & ( Event != pull
          | Fluent != spinning
          | ~ happens(push,Time) )
        & ( Event != push
          | Fluent != forwards
          | happens(pull,Time) ) ) ),
    inference(simplify,[],[normalize_0_7,normalize_0_8]) ).

fof(normalize_0_10,plain,
    ! [Event,Fluent,Time] :
      ( ( definitionFOFtoCNF_0(Event,Fluent,Time)
        | initiates(Event,Fluent,Time) )
      & ( Event != pull
        | Fluent != spinning
        | ~ happens(push,Time)
        | initiates(Event,Fluent,Time) )
      & ( Event != push
        | Fluent != forwards
        | happens(pull,Time)
        | initiates(Event,Fluent,Time) )
      & ( ~ definitionFOFtoCNF_0(Event,Fluent,Time)
        | ~ happens(pull,Time)
        | ~ initiates(Event,Fluent,Time)
        | Event = pull )
      & ( ~ definitionFOFtoCNF_0(Event,Fluent,Time)
        | ~ happens(pull,Time)
        | ~ initiates(Event,Fluent,Time)
        | Fluent = spinning )
      & ( ~ definitionFOFtoCNF_0(Event,Fluent,Time)
        | ~ happens(pull,Time)
        | ~ initiates(Event,Fluent,Time)
        | happens(push,Time) )
      & ( ~ definitionFOFtoCNF_0(Event,Fluent,Time)
        | ~ initiates(Event,Fluent,Time)
        | Event = pull
        | Event = push )
      & ( ~ definitionFOFtoCNF_0(Event,Fluent,Time)
        | ~ initiates(Event,Fluent,Time)
        | Event = pull
        | Fluent = forwards )
      & ( ~ definitionFOFtoCNF_0(Event,Fluent,Time)
        | ~ initiates(Event,Fluent,Time)
        | Event = push
        | Fluent = spinning )
      & ( ~ definitionFOFtoCNF_0(Event,Fluent,Time)
        | ~ initiates(Event,Fluent,Time)
        | Event = push
        | happens(push,Time) )
      & ( ~ definitionFOFtoCNF_0(Event,Fluent,Time)
        | ~ initiates(Event,Fluent,Time)
        | Fluent = forwards
        | Fluent = spinning )
      & ( ~ definitionFOFtoCNF_0(Event,Fluent,Time)
        | ~ initiates(Event,Fluent,Time)
        | Fluent = forwards
        | happens(push,Time) ) ),
    inference(clausify,[],[normalize_0_9]) ).

fof(normalize_0_11,plain,
    ! [Event,Fluent,Time] :
      ( Event != pull
      | Fluent != spinning
      | ~ happens(push,Time)
      | initiates(Event,Fluent,Time) ),
    inference(conjunct,[],[normalize_0_10]) ).

fof(normalize_0_12,plain,
    ! [Event,Fluent,Time] :
      ( ~ happens(Event,Time)
      | ~ initiates(Event,Fluent,Time)
      | holdsAt(Fluent,plus(Time,n1)) ),
    inference(canonicalize,[],[happens_holds]) ).

fof(normalize_0_13,plain,
    ! [Event,Fluent,Time] :
      ( ~ happens(Event,Time)
      | ~ initiates(Event,Fluent,Time)
      | holdsAt(Fluent,plus(Time,n1)) ),
    inference(specialize,[],[normalize_0_12]) ).

fof(normalize_0_14,plain,
    plus(n1,n2) = n3,
    inference(canonicalize,[],[plus1_2]) ).

fof(normalize_0_15,plain,
    ! [X,Y] : plus(X,Y) = plus(Y,X),
    inference(canonicalize,[],[symmetry_of_plus]) ).

fof(normalize_0_16,plain,
    ! [X,Y] : plus(X,Y) = plus(Y,X),
    inference(specialize,[],[normalize_0_15]) ).

fof(normalize_0_17,plain,
    ! [Event,Time] :
      ( Event != pull
      | Time != n2
      | happens(Event,Time) ),
    inference(conjunct,[],[normalize_0_4]) ).

fof(normalize_0_18,plain,
    ~ holdsAt(spinning,n3),
    inference(canonicalize,[],[negate_0_0]) ).

cnf(refute_0_0,plain,
    ( Event != push
    | Time != n2
    | happens(Event,Time) ),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_1,plain,
    ( n2 != n2
    | push != push
    | happens(push,n2) ),
    inference(subst,[],[refute_0_0:[bind(Event,$fot(push)),bind(Time,$fot(n2))]]) ).

cnf(refute_0_2,plain,
    n2 = n2,
    introduced(tautology,[refl,[$fot(n2)]]) ).

cnf(refute_0_3,plain,
    ( push != push
    | happens(push,n2) ),
    inference(resolve,[$cnf( $equal(n2,n2) )],[refute_0_2,refute_0_1]) ).

cnf(refute_0_4,plain,
    push = push,
    introduced(tautology,[refl,[$fot(push)]]) ).

cnf(refute_0_5,plain,
    happens(push,n2),
    inference(resolve,[$cnf( $equal(push,push) )],[refute_0_4,refute_0_3]) ).

cnf(refute_0_6,plain,
    ( Event != pull
    | Fluent != spinning
    | ~ happens(push,Time)
    | initiates(Event,Fluent,Time) ),
    inference(canonicalize,[],[normalize_0_11]) ).

cnf(refute_0_7,plain,
    ( pull != pull
    | spinning != spinning
    | ~ happens(push,Time)
    | initiates(pull,spinning,Time) ),
    inference(subst,[],[refute_0_6:[bind(Event,$fot(pull)),bind(Fluent,$fot(spinning))]]) ).

cnf(refute_0_8,plain,
    pull = pull,
    introduced(tautology,[refl,[$fot(pull)]]) ).

cnf(refute_0_9,plain,
    ( spinning != spinning
    | ~ happens(push,Time)
    | initiates(pull,spinning,Time) ),
    inference(resolve,[$cnf( $equal(pull,pull) )],[refute_0_8,refute_0_7]) ).

cnf(refute_0_10,plain,
    spinning = spinning,
    introduced(tautology,[refl,[$fot(spinning)]]) ).

cnf(refute_0_11,plain,
    ( ~ happens(push,Time)
    | initiates(pull,spinning,Time) ),
    inference(resolve,[$cnf( $equal(spinning,spinning) )],[refute_0_10,refute_0_9]) ).

cnf(refute_0_12,plain,
    ( ~ happens(push,n2)
    | initiates(pull,spinning,n2) ),
    inference(subst,[],[refute_0_11:[bind(Time,$fot(n2))]]) ).

cnf(refute_0_13,plain,
    initiates(pull,spinning,n2),
    inference(resolve,[$cnf( happens(push,n2) )],[refute_0_5,refute_0_12]) ).

cnf(refute_0_14,plain,
    ( ~ happens(Event,Time)
    | ~ initiates(Event,Fluent,Time)
    | holdsAt(Fluent,plus(Time,n1)) ),
    inference(canonicalize,[],[normalize_0_13]) ).

cnf(refute_0_15,plain,
    ( ~ happens(pull,n2)
    | ~ initiates(pull,spinning,n2)
    | holdsAt(spinning,plus(n2,n1)) ),
    inference(subst,[],[refute_0_14:[bind(Event,$fot(pull)),bind(Fluent,$fot(spinning)),bind(Time,$fot(n2))]]) ).

cnf(refute_0_16,plain,
    ( ~ happens(pull,n2)
    | holdsAt(spinning,plus(n2,n1)) ),
    inference(resolve,[$cnf( initiates(pull,spinning,n2) )],[refute_0_13,refute_0_15]) ).

cnf(refute_0_17,plain,
    plus(n1,n2) = n3,
    inference(canonicalize,[],[normalize_0_14]) ).

cnf(refute_0_18,plain,
    plus(X,Y) = plus(Y,X),
    inference(canonicalize,[],[normalize_0_16]) ).

cnf(refute_0_19,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_20,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_21,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_19,refute_0_20]) ).

cnf(refute_0_22,plain,
    ( plus(X,Y) != plus(Y,X)
    | plus(Y,X) = plus(X,Y) ),
    inference(subst,[],[refute_0_21:[bind(X0,$fot(plus(X,Y))),bind(Y0,$fot(plus(Y,X)))]]) ).

cnf(refute_0_23,plain,
    plus(Y,X) = plus(X,Y),
    inference(resolve,[$cnf( $equal(plus(X,Y),plus(Y,X)) )],[refute_0_18,refute_0_22]) ).

cnf(refute_0_24,plain,
    plus(n2,n1) = plus(n1,n2),
    inference(subst,[],[refute_0_23:[bind(X,$fot(n1)),bind(Y,$fot(n2))]]) ).

cnf(refute_0_25,plain,
    ( Y0 != X0
    | Y0 != Z
    | X0 = Z ),
    introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).

cnf(refute_0_26,plain,
    ( X0 != Y0
    | Y0 != Z
    | X0 = Z ),
    inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_21,refute_0_25]) ).

cnf(refute_0_27,plain,
    ( plus(n1,n2) != n3
    | plus(n2,n1) != plus(n1,n2)
    | plus(n2,n1) = n3 ),
    inference(subst,[],[refute_0_26:[bind(X0,$fot(plus(n2,n1))),bind(Y0,$fot(plus(n1,n2))),bind(Z,$fot(n3))]]) ).

cnf(refute_0_28,plain,
    ( plus(n1,n2) != n3
    | plus(n2,n1) = n3 ),
    inference(resolve,[$cnf( $equal(plus(n2,n1),plus(n1,n2)) )],[refute_0_24,refute_0_27]) ).

cnf(refute_0_29,plain,
    plus(n2,n1) = n3,
    inference(resolve,[$cnf( $equal(plus(n1,n2),n3) )],[refute_0_17,refute_0_28]) ).

cnf(refute_0_30,plain,
    ( plus(n2,n1) != n3
    | ~ holdsAt(spinning,plus(n2,n1))
    | holdsAt(spinning,n3) ),
    introduced(tautology,[equality,[$cnf( holdsAt(spinning,plus(n2,n1)) ),[1],$fot(n3)]]) ).

cnf(refute_0_31,plain,
    ( ~ holdsAt(spinning,plus(n2,n1))
    | holdsAt(spinning,n3) ),
    inference(resolve,[$cnf( $equal(plus(n2,n1),n3) )],[refute_0_29,refute_0_30]) ).

cnf(refute_0_32,plain,
    ( ~ happens(pull,n2)
    | holdsAt(spinning,n3) ),
    inference(resolve,[$cnf( holdsAt(spinning,plus(n2,n1)) )],[refute_0_16,refute_0_31]) ).

cnf(refute_0_33,plain,
    ( Event != pull
    | Time != n2
    | happens(Event,Time) ),
    inference(canonicalize,[],[normalize_0_17]) ).

cnf(refute_0_34,plain,
    ( n2 != n2
    | pull != pull
    | happens(pull,n2) ),
    inference(subst,[],[refute_0_33:[bind(Event,$fot(pull)),bind(Time,$fot(n2))]]) ).

cnf(refute_0_35,plain,
    ( pull != pull
    | happens(pull,n2) ),
    inference(resolve,[$cnf( $equal(n2,n2) )],[refute_0_2,refute_0_34]) ).

cnf(refute_0_36,plain,
    happens(pull,n2),
    inference(resolve,[$cnf( $equal(pull,pull) )],[refute_0_8,refute_0_35]) ).

cnf(refute_0_37,plain,
    holdsAt(spinning,n3),
    inference(resolve,[$cnf( happens(pull,n2) )],[refute_0_36,refute_0_32]) ).

cnf(refute_0_38,plain,
    ~ holdsAt(spinning,n3),
    inference(canonicalize,[],[normalize_0_18]) ).

cnf(refute_0_39,plain,
    $false,
    inference(resolve,[$cnf( holdsAt(spinning,n3) )],[refute_0_37,refute_0_38]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : CSR023+1 : TPTP v8.1.0. Bugfixed v3.1.0.
% 0.06/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n018.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 : Thu Jun  9 19:20:53 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.48  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.48  
% 0.18/0.48  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.18/0.49  
%------------------------------------------------------------------------------