TSTP Solution File: CSR002+2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : CSR002+2 : TPTP v8.1.2. Bugfixed v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %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  : 300s
% DateTime : Sun May  5 04:54:56 EDT 2024

% Result   : Theorem 0.21s 0.53s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   68
%            Number of leaves      :   30
% Syntax   : Number of formulae    :  214 (  47 unt;   0 def)
%            Number of atoms       :  707 ( 263 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  761 ( 268   ~; 326   |; 128   &)
%                                         (  26 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   15 (  13 usr;   1 prp; 0-3 aty)
%            Number of functors    :   15 (  15 usr;  10 con; 0-2 aty)
%            Number of variables   :  286 ( 265   !;  21   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f11326,plain,
    $false,
    inference(resolution,[],[f11068,f10441]) ).

fof(f10441,plain,
    holdsAt(filling,n1),
    inference(backward_demodulation,[],[f177,f10440]) ).

fof(f10440,plain,
    n1 = n4,
    inference(forward_demodulation,[],[f10027,f420]) ).

fof(f420,plain,
    n1 = plus(n1,n0),
    inference(superposition,[],[f220,f195]) ).

fof(f195,plain,
    n1 = plus(n0,n1),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,axiom,
    n1 = plus(n0,n1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus0_1) ).

fof(f220,plain,
    ! [X0,X1] : plus(X0,X1) = plus(X1,X0),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,plain,
    ! [X0,X1] : plus(X0,X1) = plus(X1,X0),
    inference(rectify,[],[f36]) ).

fof(f36,axiom,
    ! [X11,X12] : plus(X11,X12) = plus(X12,X11),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_plus) ).

fof(f10027,plain,
    n4 = plus(n1,n0),
    inference(backward_demodulation,[],[f198,f10020]) ).

fof(f10020,plain,
    n0 = n3,
    inference(resolution,[],[f10019,f177]) ).

fof(f10019,plain,
    ( ~ holdsAt(filling,n4)
    | n0 = n3 ),
    inference(resolution,[],[f10018,f9613]) ).

fof(f9613,plain,
    ~ holdsAt(filling,n3),
    inference(resolution,[],[f9609,f177]) ).

fof(f9609,plain,
    ( ~ holdsAt(filling,n4)
    | ~ holdsAt(filling,n3) ),
    inference(resolution,[],[f9607,f182]) ).

fof(f182,plain,
    holdsAt(waterLevel(n3),n3),
    inference(cnf_transformation,[],[f55]) ).

fof(f55,axiom,
    holdsAt(waterLevel(n3),n3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',waterLevel_3) ).

fof(f9607,plain,
    ( ~ holdsAt(waterLevel(n3),n3)
    | ~ holdsAt(filling,n3)
    | ~ holdsAt(filling,n4) ),
    inference(superposition,[],[f8839,f198]) ).

fof(f8839,plain,
    ! [X0] :
      ( ~ holdsAt(filling,plus(n1,X0))
      | ~ holdsAt(filling,X0)
      | ~ holdsAt(waterLevel(n3),X0) ),
    inference(superposition,[],[f7048,f220]) ).

fof(f7048,plain,
    ! [X0] :
      ( ~ holdsAt(filling,plus(X0,n1))
      | ~ holdsAt(filling,X0)
      | ~ holdsAt(waterLevel(n3),X0) ),
    inference(resolution,[],[f7046,f288]) ).

fof(f288,plain,
    ! [X1] :
      ( sP0(overflow,X1)
      | ~ holdsAt(filling,X1)
      | ~ holdsAt(waterLevel(n3),X1) ),
    inference(equality_resolution,[],[f238]) ).

fof(f238,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | overflow != X0
      | ~ holdsAt(filling,X1)
      | ~ holdsAt(waterLevel(n3),X1) ),
    inference(cnf_transformation,[],[f151]) ).

fof(f151,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | overflow != X0
        | ~ holdsAt(filling,X1)
        | ~ holdsAt(waterLevel(n3),X1) )
      & ( ( overflow = X0
          & holdsAt(filling,X1)
          & holdsAt(waterLevel(n3),X1) )
        | ~ sP0(X0,X1) ) ),
    inference(flattening,[],[f150]) ).

fof(f150,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | overflow != X0
        | ~ holdsAt(filling,X1)
        | ~ holdsAt(waterLevel(n3),X1) )
      & ( ( overflow = X0
          & holdsAt(filling,X1)
          & holdsAt(waterLevel(n3),X1) )
        | ~ sP0(X0,X1) ) ),
    inference(nnf_transformation,[],[f121]) ).

fof(f121,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
    <=> ( overflow = X0
        & holdsAt(filling,X1)
        & holdsAt(waterLevel(n3),X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f7046,plain,
    ! [X0] :
      ( ~ sP0(overflow,X0)
      | ~ holdsAt(filling,plus(X0,n1)) ),
    inference(resolution,[],[f7043,f242]) ).

fof(f242,plain,
    ! [X0,X1] :
      ( happens(X0,X1)
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f153]) ).

fof(f153,plain,
    ! [X0,X1] :
      ( ( happens(X0,X1)
        | ( ~ sP0(X0,X1)
          & ( n0 != X1
            | tapOn != X0 ) ) )
      & ( sP0(X0,X1)
        | ( n0 = X1
          & tapOn = X0 )
        | ~ happens(X0,X1) ) ),
    inference(flattening,[],[f152]) ).

fof(f152,plain,
    ! [X0,X1] :
      ( ( happens(X0,X1)
        | ( ~ sP0(X0,X1)
          & ( n0 != X1
            | tapOn != X0 ) ) )
      & ( sP0(X0,X1)
        | ( n0 = X1
          & tapOn = X0 )
        | ~ happens(X0,X1) ) ),
    inference(nnf_transformation,[],[f122]) ).

fof(f122,plain,
    ! [X0,X1] :
      ( happens(X0,X1)
    <=> ( sP0(X0,X1)
        | ( n0 = X1
          & tapOn = X0 ) ) ),
    inference(definition_folding,[],[f79,f121]) ).

fof(f79,plain,
    ! [X0,X1] :
      ( happens(X0,X1)
    <=> ( ( overflow = X0
          & holdsAt(filling,X1)
          & holdsAt(waterLevel(n3),X1) )
        | ( n0 = X1
          & tapOn = X0 ) ) ),
    inference(rectify,[],[f16]) ).

fof(f16,axiom,
    ! [X3,X4] :
      ( happens(X3,X4)
    <=> ( ( overflow = X3
          & holdsAt(filling,X4)
          & holdsAt(waterLevel(n3),X4) )
        | ( n0 = X4
          & tapOn = X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',happens_all_defn) ).

fof(f7043,plain,
    ! [X0] :
      ( ~ happens(overflow,X0)
      | ~ holdsAt(filling,plus(X0,n1)) ),
    inference(resolution,[],[f4410,f295]) ).

fof(f295,plain,
    sP1(filling,overflow),
    inference(equality_resolution,[],[f294]) ).

fof(f294,plain,
    ! [X1] :
      ( sP1(filling,X1)
      | overflow != X1 ),
    inference(equality_resolution,[],[f263]) ).

fof(f263,plain,
    ! [X0,X1] :
      ( sP1(X0,X1)
      | filling != X0
      | overflow != X1 ),
    inference(cnf_transformation,[],[f163]) ).

fof(f163,plain,
    ! [X0,X1] :
      ( ( sP1(X0,X1)
        | ( ( filling != X0
            | overflow != X1 )
          & ( filling != X0
            | tapOff != X1 ) ) )
      & ( ( filling = X0
          & overflow = X1 )
        | ( filling = X0
          & tapOff = X1 )
        | ~ sP1(X0,X1) ) ),
    inference(rectify,[],[f162]) ).

fof(f162,plain,
    ! [X1,X0] :
      ( ( sP1(X1,X0)
        | ( ( filling != X1
            | overflow != X0 )
          & ( filling != X1
            | tapOff != X0 ) ) )
      & ( ( filling = X1
          & overflow = X0 )
        | ( filling = X1
          & tapOff = X0 )
        | ~ sP1(X1,X0) ) ),
    inference(flattening,[],[f161]) ).

fof(f161,plain,
    ! [X1,X0] :
      ( ( sP1(X1,X0)
        | ( ( filling != X1
            | overflow != X0 )
          & ( filling != X1
            | tapOff != X0 ) ) )
      & ( ( filling = X1
          & overflow = X0 )
        | ( filling = X1
          & tapOff = X0 )
        | ~ sP1(X1,X0) ) ),
    inference(nnf_transformation,[],[f123]) ).

fof(f123,plain,
    ! [X1,X0] :
      ( sP1(X1,X0)
    <=> ( ( filling = X1
          & overflow = X0 )
        | ( filling = X1
          & tapOff = X0 ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f4410,plain,
    ! [X2,X0,X1] :
      ( ~ sP1(X0,X2)
      | ~ happens(X2,X1)
      | ~ holdsAt(X0,plus(X1,n1)) ),
    inference(resolution,[],[f246,f265]) ).

fof(f265,plain,
    ! [X2,X0,X1] :
      ( terminates(X0,X1,X2)
      | ~ sP1(X1,X0) ),
    inference(cnf_transformation,[],[f164]) ).

fof(f164,plain,
    ! [X0,X1,X2] :
      ( ( terminates(X0,X1,X2)
        | ~ sP1(X1,X0) )
      & ( sP1(X1,X0)
        | ~ terminates(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f124]) ).

fof(f124,plain,
    ! [X0,X1,X2] :
      ( terminates(X0,X1,X2)
    <=> sP1(X1,X0) ),
    inference(definition_folding,[],[f88,f123]) ).

fof(f88,plain,
    ! [X0,X1,X2] :
      ( terminates(X0,X1,X2)
    <=> ( ( filling = X1
          & overflow = X0 )
        | ( filling = X1
          & tapOff = X0 ) ) ),
    inference(rectify,[],[f14]) ).

fof(f14,axiom,
    ! [X3,X1,X4] :
      ( terminates(X3,X1,X4)
    <=> ( ( filling = X1
          & overflow = X3 )
        | ( filling = X1
          & tapOff = X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',terminates_all_defn) ).

fof(f246,plain,
    ! [X2,X0,X1] :
      ( ~ terminates(X0,X2,X1)
      | ~ holdsAt(X2,plus(X1,n1))
      | ~ happens(X0,X1) ),
    inference(cnf_transformation,[],[f109]) ).

fof(f109,plain,
    ! [X0,X1,X2] :
      ( ~ holdsAt(X2,plus(X1,n1))
      | ~ terminates(X0,X2,X1)
      | ~ happens(X0,X1) ),
    inference(flattening,[],[f108]) ).

fof(f108,plain,
    ! [X0,X1,X2] :
      ( ~ holdsAt(X2,plus(X1,n1))
      | ~ terminates(X0,X2,X1)
      | ~ happens(X0,X1) ),
    inference(ennf_transformation,[],[f82]) ).

fof(f82,plain,
    ! [X0,X1,X2] :
      ( ( terminates(X0,X2,X1)
        & happens(X0,X1) )
     => ~ holdsAt(X2,plus(X1,n1)) ),
    inference(rectify,[],[f10]) ).

fof(f10,axiom,
    ! [X3,X4,X1] :
      ( ( terminates(X3,X1,X4)
        & happens(X3,X4) )
     => ~ holdsAt(X1,plus(X4,n1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',happens_terminates_not_holds) ).

fof(f10018,plain,
    ( holdsAt(filling,n3)
    | ~ holdsAt(filling,n4)
    | n0 = n3 ),
    inference(duplicate_literal_removal,[],[f10014]) ).

fof(f10014,plain,
    ( n0 = n3
    | ~ holdsAt(filling,n4)
    | holdsAt(filling,n3)
    | n0 = n3 ),
    inference(resolution,[],[f10001,f9829]) ).

fof(f9829,plain,
    ! [X0] :
      ( releasedAt(X0,n4)
      | ~ holdsAt(X0,n4)
      | holdsAt(X0,n3)
      | n0 = n3 ),
    inference(resolution,[],[f9819,f9621]) ).

fof(f9621,plain,
    ! [X0] :
      ( ~ happens(X0,n3)
      | n0 = n3 ),
    inference(resolution,[],[f9616,f240]) ).

fof(f240,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | n0 = X1
      | ~ happens(X0,X1) ),
    inference(cnf_transformation,[],[f153]) ).

fof(f9616,plain,
    ! [X0] : ~ sP0(X0,n3),
    inference(resolution,[],[f9613,f236]) ).

fof(f236,plain,
    ! [X0,X1] :
      ( holdsAt(filling,X1)
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f151]) ).

fof(f9819,plain,
    ! [X0] :
      ( happens(sK6(X0,n3),n3)
      | releasedAt(X0,n4)
      | ~ holdsAt(X0,n4)
      | holdsAt(X0,n3) ),
    inference(superposition,[],[f6977,f198]) ).

fof(f6977,plain,
    ! [X0,X1] :
      ( releasedAt(X1,plus(n1,X0))
      | happens(sK6(X1,X0),X0)
      | ~ holdsAt(X1,plus(n1,X0))
      | holdsAt(X1,X0) ),
    inference(superposition,[],[f223,f220]) ).

fof(f223,plain,
    ! [X0,X1] :
      ( releasedAt(X0,plus(X1,n1))
      | happens(sK6(X0,X1),X1)
      | ~ holdsAt(X0,plus(X1,n1))
      | holdsAt(X0,X1) ),
    inference(cnf_transformation,[],[f141]) ).

fof(f141,plain,
    ! [X0,X1] :
      ( ~ holdsAt(X0,plus(X1,n1))
      | ( initiates(sK6(X0,X1),X0,X1)
        & happens(sK6(X0,X1),X1) )
      | releasedAt(X0,plus(X1,n1))
      | holdsAt(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f101,f140]) ).

fof(f140,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( initiates(X2,X0,X1)
          & happens(X2,X1) )
     => ( initiates(sK6(X0,X1),X0,X1)
        & happens(sK6(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f101,plain,
    ! [X0,X1] :
      ( ~ holdsAt(X0,plus(X1,n1))
      | ? [X2] :
          ( initiates(X2,X0,X1)
          & happens(X2,X1) )
      | releasedAt(X0,plus(X1,n1))
      | holdsAt(X0,X1) ),
    inference(flattening,[],[f100]) ).

fof(f100,plain,
    ! [X0,X1] :
      ( ~ holdsAt(X0,plus(X1,n1))
      | ? [X2] :
          ( initiates(X2,X0,X1)
          & happens(X2,X1) )
      | releasedAt(X0,plus(X1,n1))
      | holdsAt(X0,X1) ),
    inference(ennf_transformation,[],[f74]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( ( ~ ? [X2] :
              ( initiates(X2,X0,X1)
              & happens(X2,X1) )
        & ~ releasedAt(X0,plus(X1,n1))
        & ~ holdsAt(X0,X1) )
     => ~ holdsAt(X0,plus(X1,n1)) ),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X1,X4] :
      ( ( ~ ? [X3] :
              ( initiates(X3,X1,X4)
              & happens(X3,X4) )
        & ~ releasedAt(X1,plus(X4,n1))
        & ~ holdsAt(X1,X4) )
     => ~ holdsAt(X1,plus(X4,n1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',keep_not_holding) ).

fof(f10001,plain,
    ( ~ releasedAt(filling,n4)
    | n0 = n3 ),
    inference(duplicate_literal_removal,[],[f10000]) ).

fof(f10000,plain,
    ( n0 = n3
    | n0 = n3
    | ~ releasedAt(filling,n4) ),
    inference(resolution,[],[f9986,f9630]) ).

fof(f9630,plain,
    ! [X0] :
      ( releasedAt(X0,n3)
      | n0 = n3
      | ~ releasedAt(X0,n4) ),
    inference(forward_demodulation,[],[f9629,f198]) ).

fof(f9629,plain,
    ! [X0] :
      ( ~ releasedAt(X0,plus(n1,n3))
      | n0 = n3
      | releasedAt(X0,n3) ),
    inference(forward_demodulation,[],[f9627,f220]) ).

fof(f9627,plain,
    ! [X0] :
      ( n0 = n3
      | ~ releasedAt(X0,plus(n3,n1))
      | releasedAt(X0,n3) ),
    inference(resolution,[],[f9621,f221]) ).

fof(f221,plain,
    ! [X0,X1] :
      ( happens(sK5(X0,X1),X1)
      | ~ releasedAt(X0,plus(X1,n1))
      | releasedAt(X0,X1) ),
    inference(cnf_transformation,[],[f139]) ).

fof(f139,plain,
    ! [X0,X1] :
      ( ~ releasedAt(X0,plus(X1,n1))
      | ( releases(sK5(X0,X1),X0,X1)
        & happens(sK5(X0,X1),X1) )
      | releasedAt(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f99,f138]) ).

fof(f138,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( releases(X2,X0,X1)
          & happens(X2,X1) )
     => ( releases(sK5(X0,X1),X0,X1)
        & happens(sK5(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f99,plain,
    ! [X0,X1] :
      ( ~ releasedAt(X0,plus(X1,n1))
      | ? [X2] :
          ( releases(X2,X0,X1)
          & happens(X2,X1) )
      | releasedAt(X0,X1) ),
    inference(flattening,[],[f98]) ).

fof(f98,plain,
    ! [X0,X1] :
      ( ~ releasedAt(X0,plus(X1,n1))
      | ? [X2] :
          ( releases(X2,X0,X1)
          & happens(X2,X1) )
      | releasedAt(X0,X1) ),
    inference(ennf_transformation,[],[f73]) ).

fof(f73,plain,
    ! [X0,X1] :
      ( ( ~ ? [X2] :
              ( releases(X2,X0,X1)
              & happens(X2,X1) )
        & ~ releasedAt(X0,X1) )
     => ~ releasedAt(X0,plus(X1,n1)) ),
    inference(rectify,[],[f8]) ).

fof(f8,axiom,
    ! [X1,X4] :
      ( ( ~ ? [X3] :
              ( releases(X3,X1,X4)
              & happens(X3,X4) )
        & ~ releasedAt(X1,X4) )
     => ~ releasedAt(X1,plus(X4,n1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',keep_not_released) ).

fof(f9986,plain,
    ( ~ releasedAt(filling,n3)
    | n0 = n3 ),
    inference(resolution,[],[f9985,f9615]) ).

fof(f9615,plain,
    ~ happens(tapOn,n2),
    inference(resolution,[],[f9613,f7159]) ).

fof(f7159,plain,
    ( holdsAt(filling,n3)
    | ~ happens(tapOn,n2) ),
    inference(resolution,[],[f7146,f301]) ).

fof(f301,plain,
    ! [X0] : sP4(X0,tapOn,filling),
    inference(equality_resolution,[],[f300]) ).

fof(f300,plain,
    ! [X0,X1] :
      ( sP4(X0,X1,filling)
      | tapOn != X1 ),
    inference(equality_resolution,[],[f270]) ).

fof(f270,plain,
    ! [X2,X0,X1] :
      ( sP4(X0,X1,X2)
      | filling != X2
      | tapOn != X1 ),
    inference(cnf_transformation,[],[f167]) ).

fof(f167,plain,
    ! [X0,X1,X2] :
      ( ( sP4(X0,X1,X2)
        | ( ~ sP3(X2,X1,X0)
          & ~ sP2(X2,X1,X0)
          & ( spilling != X2
            | overflow != X1 )
          & ( filling != X2
            | tapOn != X1 ) ) )
      & ( sP3(X2,X1,X0)
        | sP2(X2,X1,X0)
        | ( spilling = X2
          & overflow = X1 )
        | ( filling = X2
          & tapOn = X1 )
        | ~ sP4(X0,X1,X2) ) ),
    inference(rectify,[],[f166]) ).

fof(f166,plain,
    ! [X2,X0,X1] :
      ( ( sP4(X2,X0,X1)
        | ( ~ sP3(X1,X0,X2)
          & ~ sP2(X1,X0,X2)
          & ( spilling != X1
            | overflow != X0 )
          & ( filling != X1
            | tapOn != X0 ) ) )
      & ( sP3(X1,X0,X2)
        | sP2(X1,X0,X2)
        | ( spilling = X1
          & overflow = X0 )
        | ( filling = X1
          & tapOn = X0 )
        | ~ sP4(X2,X0,X1) ) ),
    inference(flattening,[],[f165]) ).

fof(f165,plain,
    ! [X2,X0,X1] :
      ( ( sP4(X2,X0,X1)
        | ( ~ sP3(X1,X0,X2)
          & ~ sP2(X1,X0,X2)
          & ( spilling != X1
            | overflow != X0 )
          & ( filling != X1
            | tapOn != X0 ) ) )
      & ( sP3(X1,X0,X2)
        | sP2(X1,X0,X2)
        | ( spilling = X1
          & overflow = X0 )
        | ( filling = X1
          & tapOn = X0 )
        | ~ sP4(X2,X0,X1) ) ),
    inference(nnf_transformation,[],[f127]) ).

fof(f127,plain,
    ! [X2,X0,X1] :
      ( sP4(X2,X0,X1)
    <=> ( sP3(X1,X0,X2)
        | sP2(X1,X0,X2)
        | ( spilling = X1
          & overflow = X0 )
        | ( filling = X1
          & tapOn = X0 ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).

fof(f7146,plain,
    ! [X0,X1] :
      ( ~ sP4(n2,X1,X0)
      | ~ happens(X1,n2)
      | holdsAt(X0,n3) ),
    inference(resolution,[],[f7138,f283]) ).

fof(f283,plain,
    ! [X2,X0,X1] :
      ( initiates(X0,X1,X2)
      | ~ sP4(X2,X0,X1) ),
    inference(cnf_transformation,[],[f176]) ).

fof(f176,plain,
    ! [X0,X1,X2] :
      ( ( initiates(X0,X1,X2)
        | ~ sP4(X2,X0,X1) )
      & ( sP4(X2,X0,X1)
        | ~ initiates(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f128]) ).

fof(f128,plain,
    ! [X0,X1,X2] :
      ( initiates(X0,X1,X2)
    <=> sP4(X2,X0,X1) ),
    inference(definition_folding,[],[f89,f127,f126,f125]) ).

fof(f125,plain,
    ! [X1,X0,X2] :
      ( sP2(X1,X0,X2)
    <=> ? [X4] :
          ( waterLevel(X4) = X1
          & tapOff = X0
          & holdsAt(waterLevel(X4),X2) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f126,plain,
    ! [X1,X0,X2] :
      ( sP3(X1,X0,X2)
    <=> ? [X3] :
          ( waterLevel(X3) = X1
          & overflow = X0
          & holdsAt(waterLevel(X3),X2) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).

fof(f89,plain,
    ! [X0,X1,X2] :
      ( initiates(X0,X1,X2)
    <=> ( ? [X3] :
            ( waterLevel(X3) = X1
            & overflow = X0
            & holdsAt(waterLevel(X3),X2) )
        | ? [X4] :
            ( waterLevel(X4) = X1
            & tapOff = X0
            & holdsAt(waterLevel(X4),X2) )
        | ( spilling = X1
          & overflow = X0 )
        | ( filling = X1
          & tapOn = X0 ) ) ),
    inference(rectify,[],[f13]) ).

fof(f13,axiom,
    ! [X3,X1,X4] :
      ( initiates(X3,X1,X4)
    <=> ( ? [X8] :
            ( waterLevel(X8) = X1
            & overflow = X3
            & holdsAt(waterLevel(X8),X4) )
        | ? [X8] :
            ( waterLevel(X8) = X1
            & tapOff = X3
            & holdsAt(waterLevel(X8),X4) )
        | ( spilling = X1
          & overflow = X3 )
        | ( filling = X1
          & tapOn = X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',initiates_all_defn) ).

fof(f7138,plain,
    ! [X0,X1] :
      ( ~ initiates(X1,X0,n2)
      | holdsAt(X0,n3)
      | ~ happens(X1,n2) ),
    inference(superposition,[],[f4589,f192]) ).

fof(f192,plain,
    n3 = plus(n1,n2),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,axiom,
    n3 = plus(n1,n2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus1_2) ).

fof(f4589,plain,
    ! [X2,X0,X1] :
      ( holdsAt(X1,plus(n1,X0))
      | ~ initiates(X2,X1,X0)
      | ~ happens(X2,X0) ),
    inference(superposition,[],[f247,f220]) ).

fof(f247,plain,
    ! [X2,X0,X1] :
      ( holdsAt(X2,plus(X1,n1))
      | ~ initiates(X0,X2,X1)
      | ~ happens(X0,X1) ),
    inference(cnf_transformation,[],[f111]) ).

fof(f111,plain,
    ! [X0,X1,X2] :
      ( holdsAt(X2,plus(X1,n1))
      | ~ initiates(X0,X2,X1)
      | ~ happens(X0,X1) ),
    inference(flattening,[],[f110]) ).

fof(f110,plain,
    ! [X0,X1,X2] :
      ( holdsAt(X2,plus(X1,n1))
      | ~ initiates(X0,X2,X1)
      | ~ happens(X0,X1) ),
    inference(ennf_transformation,[],[f83]) ).

fof(f83,plain,
    ! [X0,X1,X2] :
      ( ( initiates(X0,X2,X1)
        & happens(X0,X1) )
     => holdsAt(X2,plus(X1,n1)) ),
    inference(rectify,[],[f9]) ).

fof(f9,axiom,
    ! [X3,X4,X1] :
      ( ( initiates(X3,X1,X4)
        & happens(X3,X4) )
     => holdsAt(X1,plus(X4,n1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',happens_holds) ).

fof(f9985,plain,
    ( happens(tapOn,n2)
    | ~ releasedAt(filling,n3)
    | n0 = n3 ),
    inference(duplicate_literal_removal,[],[f9981]) ).

fof(f9981,plain,
    ( happens(tapOn,n2)
    | ~ releasedAt(filling,n3)
    | n0 = n3
    | n0 = n3 ),
    inference(resolution,[],[f9980,f9955]) ).

fof(f9955,plain,
    ( ~ releasedAt(filling,n2)
    | n0 = n3 ),
    inference(duplicate_literal_removal,[],[f9954]) ).

fof(f9954,plain,
    ( ~ releasedAt(filling,n2)
    | ~ releasedAt(filling,n2)
    | n0 = n3 ),
    inference(forward_demodulation,[],[f9947,f191]) ).

fof(f191,plain,
    n2 = plus(n1,n1),
    inference(cnf_transformation,[],[f30]) ).

fof(f30,axiom,
    n2 = plus(n1,n1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus1_1) ).

fof(f9947,plain,
    ( ~ releasedAt(filling,n2)
    | n0 = n3
    | ~ releasedAt(filling,plus(n1,n1)) ),
    inference(resolution,[],[f9946,f7167]) ).

fof(f7167,plain,
    ! [X0] :
      ( ~ happens(tapOn,X0)
      | ~ releasedAt(filling,plus(X0,n1)) ),
    inference(resolution,[],[f5059,f301]) ).

fof(f5059,plain,
    ! [X2,X0,X1] :
      ( ~ sP4(X1,X2,X0)
      | ~ happens(X2,X1)
      | ~ releasedAt(X0,plus(X1,n1)) ),
    inference(resolution,[],[f248,f283]) ).

fof(f248,plain,
    ! [X2,X0,X1] :
      ( ~ initiates(X0,X2,X1)
      | ~ releasedAt(X2,plus(X1,n1))
      | ~ happens(X0,X1) ),
    inference(cnf_transformation,[],[f113]) ).

fof(f113,plain,
    ! [X0,X1,X2] :
      ( ~ releasedAt(X2,plus(X1,n1))
      | ( ~ terminates(X0,X2,X1)
        & ~ initiates(X0,X2,X1) )
      | ~ happens(X0,X1) ),
    inference(flattening,[],[f112]) ).

fof(f112,plain,
    ! [X0,X1,X2] :
      ( ~ releasedAt(X2,plus(X1,n1))
      | ( ~ terminates(X0,X2,X1)
        & ~ initiates(X0,X2,X1) )
      | ~ happens(X0,X1) ),
    inference(ennf_transformation,[],[f84]) ).

fof(f84,plain,
    ! [X0,X1,X2] :
      ( ( ( terminates(X0,X2,X1)
          | initiates(X0,X2,X1) )
        & happens(X0,X1) )
     => ~ releasedAt(X2,plus(X1,n1)) ),
    inference(rectify,[],[f12]) ).

fof(f12,axiom,
    ! [X3,X4,X1] :
      ( ( ( terminates(X3,X1,X4)
          | initiates(X3,X1,X4) )
        & happens(X3,X4) )
     => ~ releasedAt(X1,plus(X4,n1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',happens_not_released) ).

fof(f9946,plain,
    ( happens(tapOn,n1)
    | ~ releasedAt(filling,n2)
    | n0 = n3 ),
    inference(resolution,[],[f9945,f7174]) ).

fof(f7174,plain,
    ~ releasedAt(filling,n1),
    inference(forward_demodulation,[],[f7172,f195]) ).

fof(f7172,plain,
    ~ releasedAt(filling,plus(n0,n1)),
    inference(resolution,[],[f7167,f290]) ).

fof(f290,plain,
    happens(tapOn,n0),
    inference(equality_resolution,[],[f289]) ).

fof(f289,plain,
    ! [X0] :
      ( happens(X0,n0)
      | tapOn != X0 ),
    inference(equality_resolution,[],[f241]) ).

fof(f241,plain,
    ! [X0,X1] :
      ( happens(X0,X1)
      | n0 != X1
      | tapOn != X0 ),
    inference(cnf_transformation,[],[f153]) ).

fof(f9945,plain,
    ( releasedAt(filling,n1)
    | happens(tapOn,n1)
    | ~ releasedAt(filling,n2)
    | n0 = n3 ),
    inference(forward_demodulation,[],[f9943,f191]) ).

fof(f9943,plain,
    ( happens(tapOn,n1)
    | ~ releasedAt(filling,plus(n1,n1))
    | releasedAt(filling,n1)
    | n0 = n3 ),
    inference(superposition,[],[f221,f9940]) ).

fof(f9940,plain,
    ( tapOn = sK5(filling,n1)
    | n0 = n3 ),
    inference(resolution,[],[f9939,f177]) ).

fof(f9939,plain,
    ( ~ holdsAt(filling,n4)
    | tapOn = sK5(filling,n1)
    | n0 = n3 ),
    inference(resolution,[],[f9938,f9613]) ).

fof(f9938,plain,
    ( holdsAt(filling,n3)
    | tapOn = sK5(filling,n1)
    | ~ holdsAt(filling,n4)
    | n0 = n3 ),
    inference(duplicate_literal_removal,[],[f9934]) ).

fof(f9934,plain,
    ( n0 = n3
    | tapOn = sK5(filling,n1)
    | ~ holdsAt(filling,n4)
    | holdsAt(filling,n3)
    | n0 = n3 ),
    inference(resolution,[],[f9931,f9829]) ).

fof(f9931,plain,
    ( ~ releasedAt(filling,n4)
    | n0 = n3
    | tapOn = sK5(filling,n1) ),
    inference(duplicate_literal_removal,[],[f9930]) ).

fof(f9930,plain,
    ( tapOn = sK5(filling,n1)
    | n0 = n3
    | n0 = n3
    | ~ releasedAt(filling,n4) ),
    inference(resolution,[],[f9915,f9630]) ).

fof(f9915,plain,
    ( ~ releasedAt(filling,n3)
    | tapOn = sK5(filling,n1)
    | n0 = n3 ),
    inference(resolution,[],[f9914,f9615]) ).

fof(f9914,plain,
    ( happens(tapOn,n2)
    | ~ releasedAt(filling,n3)
    | tapOn = sK5(filling,n1)
    | n0 = n3 ),
    inference(duplicate_literal_removal,[],[f9913]) ).

fof(f9913,plain,
    ( happens(tapOn,n2)
    | ~ releasedAt(filling,n3)
    | tapOn = sK5(filling,n1)
    | n0 = n3
    | tapOn = sK5(filling,n1) ),
    inference(resolution,[],[f9910,f7537]) ).

fof(f7537,plain,
    ( ~ releasedAt(filling,n2)
    | tapOn = sK5(filling,n1) ),
    inference(resolution,[],[f7532,f7174]) ).

fof(f7532,plain,
    ! [X0] :
      ( releasedAt(X0,n1)
      | ~ releasedAt(X0,n2)
      | tapOn = sK5(X0,n1) ),
    inference(superposition,[],[f6956,f191]) ).

fof(f6956,plain,
    ! [X0,X1] :
      ( ~ releasedAt(X0,plus(X1,n1))
      | releasedAt(X0,X1)
      | tapOn = sK5(X0,X1) ),
    inference(resolution,[],[f222,f255]) ).

fof(f255,plain,
    ! [X2,X0,X1] :
      ( ~ releases(X0,X1,X2)
      | tapOn = X0 ),
    inference(cnf_transformation,[],[f160]) ).

fof(f160,plain,
    ! [X0,X1,X2] :
      ( ( releases(X0,X1,X2)
        | ! [X3] :
            ( waterLevel(X3) != X1
            | tapOn != X0 ) )
      & ( ( waterLevel(sK11(X0,X1)) = X1
          & tapOn = X0 )
        | ~ releases(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f158,f159]) ).

fof(f159,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( waterLevel(X4) = X1
          & tapOn = X0 )
     => ( waterLevel(sK11(X0,X1)) = X1
        & tapOn = X0 ) ),
    introduced(choice_axiom,[]) ).

fof(f158,plain,
    ! [X0,X1,X2] :
      ( ( releases(X0,X1,X2)
        | ! [X3] :
            ( waterLevel(X3) != X1
            | tapOn != X0 ) )
      & ( ? [X4] :
            ( waterLevel(X4) = X1
            & tapOn = X0 )
        | ~ releases(X0,X1,X2) ) ),
    inference(rectify,[],[f157]) ).

fof(f157,plain,
    ! [X0,X1,X2] :
      ( ( releases(X0,X1,X2)
        | ! [X3] :
            ( waterLevel(X3) != X1
            | tapOn != X0 ) )
      & ( ? [X3] :
            ( waterLevel(X3) = X1
            & tapOn = X0 )
        | ~ releases(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f87]) ).

fof(f87,plain,
    ! [X0,X1,X2] :
      ( releases(X0,X1,X2)
    <=> ? [X3] :
          ( waterLevel(X3) = X1
          & tapOn = X0 ) ),
    inference(rectify,[],[f15]) ).

fof(f15,axiom,
    ! [X3,X1,X4] :
      ( releases(X3,X1,X4)
    <=> ? [X8] :
          ( waterLevel(X8) = X1
          & tapOn = X3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',releases_all_defn) ).

fof(f222,plain,
    ! [X0,X1] :
      ( releases(sK5(X0,X1),X0,X1)
      | ~ releasedAt(X0,plus(X1,n1))
      | releasedAt(X0,X1) ),
    inference(cnf_transformation,[],[f139]) ).

fof(f9910,plain,
    ( releasedAt(filling,n2)
    | happens(tapOn,n2)
    | ~ releasedAt(filling,n3)
    | tapOn = sK5(filling,n1)
    | n0 = n3 ),
    inference(forward_demodulation,[],[f9909,f192]) ).

fof(f9909,plain,
    ( ~ releasedAt(filling,plus(n1,n2))
    | happens(tapOn,n2)
    | releasedAt(filling,n2)
    | tapOn = sK5(filling,n1)
    | n0 = n3 ),
    inference(forward_demodulation,[],[f9906,f220]) ).

fof(f9906,plain,
    ( happens(tapOn,n2)
    | ~ releasedAt(filling,plus(n2,n1))
    | releasedAt(filling,n2)
    | tapOn = sK5(filling,n1)
    | n0 = n3 ),
    inference(superposition,[],[f221,f9903]) ).

fof(f9903,plain,
    ( tapOn = sK5(filling,n2)
    | tapOn = sK5(filling,n1)
    | n0 = n3 ),
    inference(resolution,[],[f9902,f177]) ).

fof(f9902,plain,
    ( ~ holdsAt(filling,n4)
    | n0 = n3
    | tapOn = sK5(filling,n1)
    | tapOn = sK5(filling,n2) ),
    inference(resolution,[],[f9839,f9613]) ).

fof(f9839,plain,
    ( holdsAt(filling,n3)
    | ~ holdsAt(filling,n4)
    | n0 = n3
    | tapOn = sK5(filling,n1)
    | tapOn = sK5(filling,n2) ),
    inference(duplicate_literal_removal,[],[f9834]) ).

fof(f9834,plain,
    ( ~ holdsAt(filling,n4)
    | holdsAt(filling,n3)
    | n0 = n3
    | tapOn = sK5(filling,n1)
    | n0 = n3
    | tapOn = sK5(filling,n2) ),
    inference(resolution,[],[f9829,f9783]) ).

fof(f9783,plain,
    ( ~ releasedAt(filling,n4)
    | tapOn = sK5(filling,n1)
    | n0 = n3
    | tapOn = sK5(filling,n2) ),
    inference(resolution,[],[f9746,f9630]) ).

fof(f9746,plain,
    ( ~ releasedAt(filling,n3)
    | tapOn = sK5(filling,n2)
    | tapOn = sK5(filling,n1) ),
    inference(resolution,[],[f9742,f7537]) ).

fof(f9742,plain,
    ! [X0] :
      ( releasedAt(X0,n2)
      | ~ releasedAt(X0,n3)
      | tapOn = sK5(X0,n2) ),
    inference(superposition,[],[f7534,f192]) ).

fof(f7534,plain,
    ! [X0,X1] :
      ( ~ releasedAt(X1,plus(n1,X0))
      | releasedAt(X1,X0)
      | tapOn = sK5(X1,X0) ),
    inference(superposition,[],[f6956,f220]) ).

fof(f9980,plain,
    ( releasedAt(filling,n2)
    | happens(tapOn,n2)
    | ~ releasedAt(filling,n3)
    | n0 = n3 ),
    inference(forward_demodulation,[],[f9979,f192]) ).

fof(f9979,plain,
    ( ~ releasedAt(filling,plus(n1,n2))
    | happens(tapOn,n2)
    | releasedAt(filling,n2)
    | n0 = n3 ),
    inference(forward_demodulation,[],[f9976,f220]) ).

fof(f9976,plain,
    ( happens(tapOn,n2)
    | ~ releasedAt(filling,plus(n2,n1))
    | releasedAt(filling,n2)
    | n0 = n3 ),
    inference(superposition,[],[f221,f9973]) ).

fof(f9973,plain,
    ( tapOn = sK5(filling,n2)
    | n0 = n3 ),
    inference(resolution,[],[f9972,f177]) ).

fof(f9972,plain,
    ( ~ holdsAt(filling,n4)
    | n0 = n3
    | tapOn = sK5(filling,n2) ),
    inference(resolution,[],[f9971,f9613]) ).

fof(f9971,plain,
    ( holdsAt(filling,n3)
    | n0 = n3
    | ~ holdsAt(filling,n4)
    | tapOn = sK5(filling,n2) ),
    inference(duplicate_literal_removal,[],[f9967]) ).

fof(f9967,plain,
    ( tapOn = sK5(filling,n2)
    | n0 = n3
    | ~ holdsAt(filling,n4)
    | holdsAt(filling,n3)
    | n0 = n3 ),
    inference(resolution,[],[f9964,f9829]) ).

fof(f9964,plain,
    ( ~ releasedAt(filling,n4)
    | tapOn = sK5(filling,n2)
    | n0 = n3 ),
    inference(duplicate_literal_removal,[],[f9963]) ).

fof(f9963,plain,
    ( n0 = n3
    | tapOn = sK5(filling,n2)
    | n0 = n3
    | ~ releasedAt(filling,n4) ),
    inference(resolution,[],[f9958,f9630]) ).

fof(f9958,plain,
    ( ~ releasedAt(filling,n3)
    | n0 = n3
    | tapOn = sK5(filling,n2) ),
    inference(resolution,[],[f9955,f9742]) ).

fof(f198,plain,
    plus(n1,n3) = n4,
    inference(cnf_transformation,[],[f32]) ).

fof(f32,axiom,
    plus(n1,n3) = n4,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus1_3) ).

fof(f177,plain,
    holdsAt(filling,n4),
    inference(cnf_transformation,[],[f58]) ).

fof(f58,plain,
    holdsAt(filling,n4),
    inference(flattening,[],[f57]) ).

fof(f57,negated_conjecture,
    ~ ~ holdsAt(filling,n4),
    inference(negated_conjecture,[],[f56]) ).

fof(f56,conjecture,
    ~ holdsAt(filling,n4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_filling_4) ).

fof(f11068,plain,
    ~ holdsAt(filling,n1),
    inference(backward_demodulation,[],[f181,f11064]) ).

fof(f11064,plain,
    n0 = n1,
    inference(forward_demodulation,[],[f10943,f10848]) ).

fof(f10848,plain,
    n1 = plus(n1,n1),
    inference(backward_demodulation,[],[f191,f10837]) ).

fof(f10837,plain,
    n1 = n2,
    inference(resolution,[],[f10449,f1050]) ).

fof(f1050,plain,
    ( less(n1,n2)
    | n1 = n2 ),
    inference(resolution,[],[f234,f328]) ).

fof(f328,plain,
    ~ less(n2,n1),
    inference(resolution,[],[f230,f320]) ).

fof(f320,plain,
    ~ less_or_equal(n2,n1),
    inference(resolution,[],[f215,f287]) ).

fof(f287,plain,
    ! [X1] : ~ less(X1,X1),
    inference(equality_resolution,[],[f233]) ).

fof(f233,plain,
    ! [X0,X1] :
      ( X0 != X1
      | ~ less(X0,X1) ),
    inference(cnf_transformation,[],[f149]) ).

fof(f149,plain,
    ! [X0,X1] :
      ( ( less(X0,X1)
        | X0 = X1
        | less(X1,X0) )
      & ( ( X0 != X1
          & ~ less(X1,X0) )
        | ~ less(X0,X1) ) ),
    inference(flattening,[],[f148]) ).

fof(f148,plain,
    ! [X0,X1] :
      ( ( less(X0,X1)
        | X0 = X1
        | less(X1,X0) )
      & ( ( X0 != X1
          & ~ less(X1,X0) )
        | ~ less(X0,X1) ) ),
    inference(nnf_transformation,[],[f78]) ).

fof(f78,plain,
    ! [X0,X1] :
      ( less(X0,X1)
    <=> ( X0 != X1
        & ~ less(X1,X0) ) ),
    inference(rectify,[],[f48]) ).

fof(f48,axiom,
    ! [X11,X12] :
      ( less(X11,X12)
    <=> ( X11 != X12
        & ~ less(X12,X11) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_property) ).

fof(f215,plain,
    ! [X0] :
      ( less(X0,n2)
      | ~ less_or_equal(X0,n1) ),
    inference(cnf_transformation,[],[f135]) ).

fof(f135,plain,
    ! [X0] :
      ( ( less(X0,n2)
        | ~ less_or_equal(X0,n1) )
      & ( less_or_equal(X0,n1)
        | ~ less(X0,n2) ) ),
    inference(nnf_transformation,[],[f69]) ).

fof(f69,plain,
    ! [X0] :
      ( less(X0,n2)
    <=> less_or_equal(X0,n1) ),
    inference(rectify,[],[f40]) ).

fof(f40,axiom,
    ! [X11] :
      ( less(X11,n2)
    <=> less_or_equal(X11,n1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',less2) ).

fof(f230,plain,
    ! [X0,X1] :
      ( less_or_equal(X0,X1)
      | ~ less(X0,X1) ),
    inference(cnf_transformation,[],[f147]) ).

fof(f147,plain,
    ! [X0,X1] :
      ( ( less_or_equal(X0,X1)
        | ( X0 != X1
          & ~ less(X0,X1) ) )
      & ( X0 = X1
        | less(X0,X1)
        | ~ less_or_equal(X0,X1) ) ),
    inference(flattening,[],[f146]) ).

fof(f146,plain,
    ! [X0,X1] :
      ( ( less_or_equal(X0,X1)
        | ( X0 != X1
          & ~ less(X0,X1) ) )
      & ( X0 = X1
        | less(X0,X1)
        | ~ less_or_equal(X0,X1) ) ),
    inference(nnf_transformation,[],[f77]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( less_or_equal(X0,X1)
    <=> ( X0 = X1
        | less(X0,X1) ) ),
    inference(rectify,[],[f37]) ).

fof(f37,axiom,
    ! [X11,X12] :
      ( less_or_equal(X11,X12)
    <=> ( X11 = X12
        | less(X11,X12) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal) ).

fof(f234,plain,
    ! [X0,X1] :
      ( less(X1,X0)
      | X0 = X1
      | less(X0,X1) ),
    inference(cnf_transformation,[],[f149]) ).

fof(f10449,plain,
    ~ less(n1,n2),
    inference(backward_demodulation,[],[f367,f10440]) ).

fof(f367,plain,
    ~ less(n4,n2),
    inference(resolution,[],[f337,f230]) ).

fof(f337,plain,
    ~ less_or_equal(n4,n2),
    inference(resolution,[],[f329,f217]) ).

fof(f217,plain,
    ! [X0] :
      ( less(X0,n3)
      | ~ less_or_equal(X0,n2) ),
    inference(cnf_transformation,[],[f136]) ).

fof(f136,plain,
    ! [X0] :
      ( ( less(X0,n3)
        | ~ less_or_equal(X0,n2) )
      & ( less_or_equal(X0,n2)
        | ~ less(X0,n3) ) ),
    inference(nnf_transformation,[],[f70]) ).

fof(f70,plain,
    ! [X0] :
      ( less(X0,n3)
    <=> less_or_equal(X0,n2) ),
    inference(rectify,[],[f41]) ).

fof(f41,axiom,
    ! [X11] :
      ( less(X11,n3)
    <=> less_or_equal(X11,n2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',less3) ).

fof(f329,plain,
    ~ less(n4,n3),
    inference(resolution,[],[f230,f318]) ).

fof(f318,plain,
    ~ less_or_equal(n4,n3),
    inference(resolution,[],[f213,f287]) ).

fof(f213,plain,
    ! [X0] :
      ( less(X0,n4)
      | ~ less_or_equal(X0,n3) ),
    inference(cnf_transformation,[],[f134]) ).

fof(f134,plain,
    ! [X0] :
      ( ( less(X0,n4)
        | ~ less_or_equal(X0,n3) )
      & ( less_or_equal(X0,n3)
        | ~ less(X0,n4) ) ),
    inference(nnf_transformation,[],[f68]) ).

fof(f68,plain,
    ! [X0] :
      ( less(X0,n4)
    <=> less_or_equal(X0,n3) ),
    inference(rectify,[],[f42]) ).

fof(f42,axiom,
    ! [X11] :
      ( less(X11,n4)
    <=> less_or_equal(X11,n3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',less4) ).

fof(f10943,plain,
    n0 = plus(n1,n1),
    inference(backward_demodulation,[],[f10023,f10837]) ).

fof(f10023,plain,
    n0 = plus(n1,n2),
    inference(backward_demodulation,[],[f192,f10020]) ).

fof(f181,plain,
    ~ holdsAt(filling,n0),
    inference(cnf_transformation,[],[f50]) ).

fof(f50,axiom,
    ~ holdsAt(filling,n0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_filling_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : CSR002+2 : TPTP v8.1.2. Bugfixed v3.1.0.
% 0.12/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n014.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Fri May  3 20:22:53 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.36  % (17359)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38  % (17362)WARNING: value z3 for option sas not known
% 0.14/0.38  % (17363)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38  % (17360)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38  % (17361)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38  % (17364)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.38  % (17362)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38  % (17365)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.38  % (17366)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.38  Detected minimum model sizes of [3]
% 0.14/0.38  Detected maximum model sizes of [max]
% 0.14/0.38  TRYING [3]
% 0.14/0.40  TRYING [4]
% 0.21/0.42  Detected minimum model sizes of [3]
% 0.21/0.42  Detected maximum model sizes of [max]
% 0.21/0.43  TRYING [3]
% 0.21/0.44  TRYING [5]
% 0.21/0.51  TRYING [6]
% 0.21/0.53  % (17365)First to succeed.
% 0.21/0.53  % (17365)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-17359"
% 0.21/0.53  % (17365)Refutation found. Thanks to Tanya!
% 0.21/0.53  % SZS status Theorem for theBenchmark
% 0.21/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.53  % (17365)------------------------------
% 0.21/0.53  % (17365)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.53  % (17365)Termination reason: Refutation
% 0.21/0.53  
% 0.21/0.53  % (17365)Memory used [KB]: 1961
% 0.21/0.53  % (17365)Time elapsed: 0.155 s
% 0.21/0.53  % (17365)Instructions burned: 308 (million)
% 0.21/0.53  % (17359)Success in time 0.173 s
%------------------------------------------------------------------------------