TSTP Solution File: ALG226+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : ALG226+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% 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 : Fri May  3 02:04:22 EDT 2024

% Result   : Theorem 184.47s 24.92s
% Output   : CNFRefutation 184.47s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,conjecture,
    ! [X0] :
      ( ~ v1_xboole_0(X0)
     => ! [X1] :
          ( ( m1_pboole(X1,X0)
            & v2_relat_1(X1) )
         => ! [X2] :
              ( ( m1_pboole(X2,X0)
                & v2_relat_1(X2) )
             => ( ( k7_relat_1(X1,k1_closure3(X0,X1)) = k7_relat_1(X2,k1_closure3(X0,X2))
                  & k1_closure3(X0,X1) = k1_closure3(X0,X2) )
               => r6_pboole(X0,X1,X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_closure3) ).

fof(f2,negated_conjecture,
    ~ ! [X0] :
        ( ~ v1_xboole_0(X0)
       => ! [X1] :
            ( ( m1_pboole(X1,X0)
              & v2_relat_1(X1) )
           => ! [X2] :
                ( ( m1_pboole(X2,X0)
                  & v2_relat_1(X2) )
               => ( ( k7_relat_1(X1,k1_closure3(X0,X1)) = k7_relat_1(X2,k1_closure3(X0,X2))
                    & k1_closure3(X0,X1) = k1_closure3(X0,X2) )
                 => r6_pboole(X0,X1,X2) ) ) ) ),
    inference(negated_conjecture,[],[f1]) ).

fof(f11,axiom,
    ! [X0,X1] : k3_xboole_0(X0,X1) = k3_xboole_0(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

fof(f13,axiom,
    ! [X0] :
      ( ~ v1_xboole_0(X0)
     => ! [X1] :
          ( m1_pboole(X1,X0)
         => ! [X2] :
              ( k1_closure3(X0,X1) = X2
            <=> a_2_0_closure3(X0,X1) = X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_closure3) ).

fof(f14,axiom,
    ! [X0,X1] :
      ( ( v1_funct_1(X1)
        & v1_relat_1(X1) )
     => ( m1_pboole(X1,X0)
      <=> k1_relat_1(X1) = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_pboole) ).

fof(f15,axiom,
    ! [X0,X1,X2] :
      ( k3_xboole_0(X0,X1) = X2
    <=> ! [X3] :
          ( r2_hidden(X3,X2)
        <=> ( r2_hidden(X3,X1)
            & r2_hidden(X3,X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).

fof(f22,axiom,
    ! [X0,X1] :
      ( m1_pboole(X1,X0)
     => ( v1_funct_1(X1)
        & v1_relat_1(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_pboole) ).

fof(f28,axiom,
    v1_xboole_0(k1_xboole_0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).

fof(f29,axiom,
    ! [X0,X1,X2] :
      ( ( m1_subset_1(X2,X0)
        & m1_pboole(X1,X0)
        & v2_relat_1(X1)
        & ~ v1_xboole_0(X0) )
     => ~ v1_xboole_0(k1_funct_1(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_pboole) ).

fof(f31,axiom,
    ! [X0,X1,X2] :
      ( ( m1_pboole(X2,X1)
        & ~ v1_xboole_0(X1) )
     => ( r2_hidden(X0,a_2_0_closure3(X1,X2))
      <=> ? [X3] :
            ( k1_xboole_0 != k1_funct_1(X2,X3)
            & X0 = X3
            & m1_subset_1(X3,X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_closure3) ).

fof(f33,axiom,
    ! [X0,X1] : k3_xboole_0(X0,X0) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).

fof(f49,axiom,
    ! [X0,X1] :
      ( r2_hidden(X0,X1)
     => m1_subset_1(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).

fof(f51,axiom,
    ! [X0,X1] :
      ( m1_subset_1(X0,X1)
     => ( r2_hidden(X0,X1)
        | v1_xboole_0(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).

fof(f54,axiom,
    ! [X0,X1,X2] :
      ( ( v1_funct_1(X2)
        & v1_relat_1(X2) )
     => ( r2_hidden(X1,k1_relat_1(k7_relat_1(X2,X0)))
       => k1_funct_1(k7_relat_1(X2,X0),X1) = k1_funct_1(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_funct_1) ).

fof(f57,axiom,
    ! [X0,X1] :
      ( v1_relat_1(X1)
     => k1_relat_1(k7_relat_1(X1,X0)) = k3_xboole_0(k1_relat_1(X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_relat_1) ).

fof(f58,axiom,
    ! [X0] :
      ( ( v1_funct_1(X0)
        & v1_relat_1(X0) )
     => ! [X1] :
          ( ( v1_funct_1(X1)
            & v1_relat_1(X1) )
         => ( ( ! [X2] :
                  ( r2_hidden(X2,k1_relat_1(X0))
                 => k1_funct_1(X1,X2) = k1_funct_1(X0,X2) )
              & k1_relat_1(X1) = k1_relat_1(X0) )
           => X0 = X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_funct_1) ).

fof(f59,plain,
    ! [X0] : k3_xboole_0(X0,X0) = X0,
    inference(rectify,[],[f33]) ).

fof(f66,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ~ r6_pboole(X0,X1,X2)
              & k7_relat_1(X1,k1_closure3(X0,X1)) = k7_relat_1(X2,k1_closure3(X0,X2))
              & k1_closure3(X0,X1) = k1_closure3(X0,X2)
              & m1_pboole(X2,X0)
              & v2_relat_1(X2) )
          & m1_pboole(X1,X0)
          & v2_relat_1(X1) )
      & ~ v1_xboole_0(X0) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f67,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ~ r6_pboole(X0,X1,X2)
              & k7_relat_1(X1,k1_closure3(X0,X1)) = k7_relat_1(X2,k1_closure3(X0,X2))
              & k1_closure3(X0,X1) = k1_closure3(X0,X2)
              & m1_pboole(X2,X0)
              & v2_relat_1(X2) )
          & m1_pboole(X1,X0)
          & v2_relat_1(X1) )
      & ~ v1_xboole_0(X0) ),
    inference(flattening,[],[f66]) ).

fof(f78,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( k1_closure3(X0,X1) = X2
            <=> a_2_0_closure3(X0,X1) = X2 )
          | ~ m1_pboole(X1,X0) )
      | v1_xboole_0(X0) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f79,plain,
    ! [X0,X1] :
      ( ( m1_pboole(X1,X0)
      <=> k1_relat_1(X1) = X0 )
      | ~ v1_funct_1(X1)
      | ~ v1_relat_1(X1) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f80,plain,
    ! [X0,X1] :
      ( ( m1_pboole(X1,X0)
      <=> k1_relat_1(X1) = X0 )
      | ~ v1_funct_1(X1)
      | ~ v1_relat_1(X1) ),
    inference(flattening,[],[f79]) ).

fof(f82,plain,
    ! [X0,X1] :
      ( ( v1_funct_1(X1)
        & v1_relat_1(X1) )
      | ~ m1_pboole(X1,X0) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f85,plain,
    ! [X0,X1,X2] :
      ( ~ v1_xboole_0(k1_funct_1(X1,X2))
      | ~ m1_subset_1(X2,X0)
      | ~ m1_pboole(X1,X0)
      | ~ v2_relat_1(X1)
      | v1_xboole_0(X0) ),
    inference(ennf_transformation,[],[f29]) ).

fof(f86,plain,
    ! [X0,X1,X2] :
      ( ~ v1_xboole_0(k1_funct_1(X1,X2))
      | ~ m1_subset_1(X2,X0)
      | ~ m1_pboole(X1,X0)
      | ~ v2_relat_1(X1)
      | v1_xboole_0(X0) ),
    inference(flattening,[],[f85]) ).

fof(f89,plain,
    ! [X0,X1,X2] :
      ( ( r2_hidden(X0,a_2_0_closure3(X1,X2))
      <=> ? [X3] :
            ( k1_xboole_0 != k1_funct_1(X2,X3)
            & X0 = X3
            & m1_subset_1(X3,X1) ) )
      | ~ m1_pboole(X2,X1)
      | v1_xboole_0(X1) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f90,plain,
    ! [X0,X1,X2] :
      ( ( r2_hidden(X0,a_2_0_closure3(X1,X2))
      <=> ? [X3] :
            ( k1_xboole_0 != k1_funct_1(X2,X3)
            & X0 = X3
            & m1_subset_1(X3,X1) ) )
      | ~ m1_pboole(X2,X1)
      | v1_xboole_0(X1) ),
    inference(flattening,[],[f89]) ).

fof(f99,plain,
    ! [X0,X1] :
      ( m1_subset_1(X0,X1)
      | ~ r2_hidden(X0,X1) ),
    inference(ennf_transformation,[],[f49]) ).

fof(f100,plain,
    ! [X0,X1] :
      ( r2_hidden(X0,X1)
      | v1_xboole_0(X1)
      | ~ m1_subset_1(X0,X1) ),
    inference(ennf_transformation,[],[f51]) ).

fof(f101,plain,
    ! [X0,X1] :
      ( r2_hidden(X0,X1)
      | v1_xboole_0(X1)
      | ~ m1_subset_1(X0,X1) ),
    inference(flattening,[],[f100]) ).

fof(f104,plain,
    ! [X0,X1,X2] :
      ( k1_funct_1(k7_relat_1(X2,X0),X1) = k1_funct_1(X2,X1)
      | ~ r2_hidden(X1,k1_relat_1(k7_relat_1(X2,X0)))
      | ~ v1_funct_1(X2)
      | ~ v1_relat_1(X2) ),
    inference(ennf_transformation,[],[f54]) ).

fof(f105,plain,
    ! [X0,X1,X2] :
      ( k1_funct_1(k7_relat_1(X2,X0),X1) = k1_funct_1(X2,X1)
      | ~ r2_hidden(X1,k1_relat_1(k7_relat_1(X2,X0)))
      | ~ v1_funct_1(X2)
      | ~ v1_relat_1(X2) ),
    inference(flattening,[],[f104]) ).

fof(f108,plain,
    ! [X0,X1] :
      ( k1_relat_1(k7_relat_1(X1,X0)) = k3_xboole_0(k1_relat_1(X1),X0)
      | ~ v1_relat_1(X1) ),
    inference(ennf_transformation,[],[f57]) ).

fof(f109,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ? [X2] :
              ( k1_funct_1(X1,X2) != k1_funct_1(X0,X2)
              & r2_hidden(X2,k1_relat_1(X0)) )
          | k1_relat_1(X1) != k1_relat_1(X0)
          | ~ v1_funct_1(X1)
          | ~ v1_relat_1(X1) )
      | ~ v1_funct_1(X0)
      | ~ v1_relat_1(X0) ),
    inference(ennf_transformation,[],[f58]) ).

fof(f110,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ? [X2] :
              ( k1_funct_1(X1,X2) != k1_funct_1(X0,X2)
              & r2_hidden(X2,k1_relat_1(X0)) )
          | k1_relat_1(X1) != k1_relat_1(X0)
          | ~ v1_funct_1(X1)
          | ~ v1_relat_1(X1) )
      | ~ v1_funct_1(X0)
      | ~ v1_relat_1(X0) ),
    inference(flattening,[],[f109]) ).

fof(f111,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ~ r6_pboole(X0,X1,X2)
                & k7_relat_1(X1,k1_closure3(X0,X1)) = k7_relat_1(X2,k1_closure3(X0,X2))
                & k1_closure3(X0,X1) = k1_closure3(X0,X2)
                & m1_pboole(X2,X0)
                & v2_relat_1(X2) )
            & m1_pboole(X1,X0)
            & v2_relat_1(X1) )
        & ~ v1_xboole_0(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ~ r6_pboole(sK0,X1,X2)
              & k7_relat_1(X1,k1_closure3(sK0,X1)) = k7_relat_1(X2,k1_closure3(sK0,X2))
              & k1_closure3(sK0,X1) = k1_closure3(sK0,X2)
              & m1_pboole(X2,sK0)
              & v2_relat_1(X2) )
          & m1_pboole(X1,sK0)
          & v2_relat_1(X1) )
      & ~ v1_xboole_0(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f112,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ~ r6_pboole(sK0,X1,X2)
            & k7_relat_1(X1,k1_closure3(sK0,X1)) = k7_relat_1(X2,k1_closure3(sK0,X2))
            & k1_closure3(sK0,X1) = k1_closure3(sK0,X2)
            & m1_pboole(X2,sK0)
            & v2_relat_1(X2) )
        & m1_pboole(X1,sK0)
        & v2_relat_1(X1) )
   => ( ? [X2] :
          ( ~ r6_pboole(sK0,sK1,X2)
          & k7_relat_1(X2,k1_closure3(sK0,X2)) = k7_relat_1(sK1,k1_closure3(sK0,sK1))
          & k1_closure3(sK0,X2) = k1_closure3(sK0,sK1)
          & m1_pboole(X2,sK0)
          & v2_relat_1(X2) )
      & m1_pboole(sK1,sK0)
      & v2_relat_1(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f113,plain,
    ( ? [X2] :
        ( ~ r6_pboole(sK0,sK1,X2)
        & k7_relat_1(X2,k1_closure3(sK0,X2)) = k7_relat_1(sK1,k1_closure3(sK0,sK1))
        & k1_closure3(sK0,X2) = k1_closure3(sK0,sK1)
        & m1_pboole(X2,sK0)
        & v2_relat_1(X2) )
   => ( ~ r6_pboole(sK0,sK1,sK2)
      & k7_relat_1(sK1,k1_closure3(sK0,sK1)) = k7_relat_1(sK2,k1_closure3(sK0,sK2))
      & k1_closure3(sK0,sK1) = k1_closure3(sK0,sK2)
      & m1_pboole(sK2,sK0)
      & v2_relat_1(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f114,plain,
    ( ~ r6_pboole(sK0,sK1,sK2)
    & k7_relat_1(sK1,k1_closure3(sK0,sK1)) = k7_relat_1(sK2,k1_closure3(sK0,sK2))
    & k1_closure3(sK0,sK1) = k1_closure3(sK0,sK2)
    & m1_pboole(sK2,sK0)
    & v2_relat_1(sK2)
    & m1_pboole(sK1,sK0)
    & v2_relat_1(sK1)
    & ~ v1_xboole_0(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f67,f113,f112,f111]) ).

fof(f119,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( k1_closure3(X0,X1) = X2
                | a_2_0_closure3(X0,X1) != X2 )
              & ( a_2_0_closure3(X0,X1) = X2
                | k1_closure3(X0,X1) != X2 ) )
          | ~ m1_pboole(X1,X0) )
      | v1_xboole_0(X0) ),
    inference(nnf_transformation,[],[f78]) ).

fof(f120,plain,
    ! [X0,X1] :
      ( ( ( m1_pboole(X1,X0)
          | k1_relat_1(X1) != X0 )
        & ( k1_relat_1(X1) = X0
          | ~ m1_pboole(X1,X0) ) )
      | ~ v1_funct_1(X1)
      | ~ v1_relat_1(X1) ),
    inference(nnf_transformation,[],[f80]) ).

fof(f121,plain,
    ! [X0,X1,X2] :
      ( ( k3_xboole_0(X0,X1) = X2
        | ? [X3] :
            ( ( ~ r2_hidden(X3,X1)
              | ~ r2_hidden(X3,X0)
              | ~ r2_hidden(X3,X2) )
            & ( ( r2_hidden(X3,X1)
                & r2_hidden(X3,X0) )
              | r2_hidden(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( r2_hidden(X3,X2)
              | ~ r2_hidden(X3,X1)
              | ~ r2_hidden(X3,X0) )
            & ( ( r2_hidden(X3,X1)
                & r2_hidden(X3,X0) )
              | ~ r2_hidden(X3,X2) ) )
        | k3_xboole_0(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f15]) ).

fof(f122,plain,
    ! [X0,X1,X2] :
      ( ( k3_xboole_0(X0,X1) = X2
        | ? [X3] :
            ( ( ~ r2_hidden(X3,X1)
              | ~ r2_hidden(X3,X0)
              | ~ r2_hidden(X3,X2) )
            & ( ( r2_hidden(X3,X1)
                & r2_hidden(X3,X0) )
              | r2_hidden(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( r2_hidden(X3,X2)
              | ~ r2_hidden(X3,X1)
              | ~ r2_hidden(X3,X0) )
            & ( ( r2_hidden(X3,X1)
                & r2_hidden(X3,X0) )
              | ~ r2_hidden(X3,X2) ) )
        | k3_xboole_0(X0,X1) != X2 ) ),
    inference(flattening,[],[f121]) ).

fof(f123,plain,
    ! [X0,X1,X2] :
      ( ( k3_xboole_0(X0,X1) = X2
        | ? [X3] :
            ( ( ~ r2_hidden(X3,X1)
              | ~ r2_hidden(X3,X0)
              | ~ r2_hidden(X3,X2) )
            & ( ( r2_hidden(X3,X1)
                & r2_hidden(X3,X0) )
              | r2_hidden(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( r2_hidden(X4,X2)
              | ~ r2_hidden(X4,X1)
              | ~ r2_hidden(X4,X0) )
            & ( ( r2_hidden(X4,X1)
                & r2_hidden(X4,X0) )
              | ~ r2_hidden(X4,X2) ) )
        | k3_xboole_0(X0,X1) != X2 ) ),
    inference(rectify,[],[f122]) ).

fof(f124,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ r2_hidden(X3,X1)
            | ~ r2_hidden(X3,X0)
            | ~ r2_hidden(X3,X2) )
          & ( ( r2_hidden(X3,X1)
              & r2_hidden(X3,X0) )
            | r2_hidden(X3,X2) ) )
     => ( ( ~ r2_hidden(sK4(X0,X1,X2),X1)
          | ~ r2_hidden(sK4(X0,X1,X2),X0)
          | ~ r2_hidden(sK4(X0,X1,X2),X2) )
        & ( ( r2_hidden(sK4(X0,X1,X2),X1)
            & r2_hidden(sK4(X0,X1,X2),X0) )
          | r2_hidden(sK4(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f125,plain,
    ! [X0,X1,X2] :
      ( ( k3_xboole_0(X0,X1) = X2
        | ( ( ~ r2_hidden(sK4(X0,X1,X2),X1)
            | ~ r2_hidden(sK4(X0,X1,X2),X0)
            | ~ r2_hidden(sK4(X0,X1,X2),X2) )
          & ( ( r2_hidden(sK4(X0,X1,X2),X1)
              & r2_hidden(sK4(X0,X1,X2),X0) )
            | r2_hidden(sK4(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( r2_hidden(X4,X2)
              | ~ r2_hidden(X4,X1)
              | ~ r2_hidden(X4,X0) )
            & ( ( r2_hidden(X4,X1)
                & r2_hidden(X4,X0) )
              | ~ r2_hidden(X4,X2) ) )
        | k3_xboole_0(X0,X1) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f123,f124]) ).

fof(f130,plain,
    ! [X0,X1,X2] :
      ( ( ( r2_hidden(X0,a_2_0_closure3(X1,X2))
          | ! [X3] :
              ( k1_xboole_0 = k1_funct_1(X2,X3)
              | X0 != X3
              | ~ m1_subset_1(X3,X1) ) )
        & ( ? [X3] :
              ( k1_xboole_0 != k1_funct_1(X2,X3)
              & X0 = X3
              & m1_subset_1(X3,X1) )
          | ~ r2_hidden(X0,a_2_0_closure3(X1,X2)) ) )
      | ~ m1_pboole(X2,X1)
      | v1_xboole_0(X1) ),
    inference(nnf_transformation,[],[f90]) ).

fof(f131,plain,
    ! [X0,X1,X2] :
      ( ( ( r2_hidden(X0,a_2_0_closure3(X1,X2))
          | ! [X3] :
              ( k1_xboole_0 = k1_funct_1(X2,X3)
              | X0 != X3
              | ~ m1_subset_1(X3,X1) ) )
        & ( ? [X4] :
              ( k1_xboole_0 != k1_funct_1(X2,X4)
              & X0 = X4
              & m1_subset_1(X4,X1) )
          | ~ r2_hidden(X0,a_2_0_closure3(X1,X2)) ) )
      | ~ m1_pboole(X2,X1)
      | v1_xboole_0(X1) ),
    inference(rectify,[],[f130]) ).

fof(f132,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( k1_xboole_0 != k1_funct_1(X2,X4)
          & X0 = X4
          & m1_subset_1(X4,X1) )
     => ( k1_xboole_0 != k1_funct_1(X2,sK7(X0,X1,X2))
        & sK7(X0,X1,X2) = X0
        & m1_subset_1(sK7(X0,X1,X2),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f133,plain,
    ! [X0,X1,X2] :
      ( ( ( r2_hidden(X0,a_2_0_closure3(X1,X2))
          | ! [X3] :
              ( k1_xboole_0 = k1_funct_1(X2,X3)
              | X0 != X3
              | ~ m1_subset_1(X3,X1) ) )
        & ( ( k1_xboole_0 != k1_funct_1(X2,sK7(X0,X1,X2))
            & sK7(X0,X1,X2) = X0
            & m1_subset_1(sK7(X0,X1,X2),X1) )
          | ~ r2_hidden(X0,a_2_0_closure3(X1,X2)) ) )
      | ~ m1_pboole(X2,X1)
      | v1_xboole_0(X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f131,f132]) ).

fof(f166,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( k1_funct_1(X1,X2) != k1_funct_1(X0,X2)
          & r2_hidden(X2,k1_relat_1(X0)) )
     => ( k1_funct_1(X1,sK22(X0,X1)) != k1_funct_1(X0,sK22(X0,X1))
        & r2_hidden(sK22(X0,X1),k1_relat_1(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f167,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ( k1_funct_1(X1,sK22(X0,X1)) != k1_funct_1(X0,sK22(X0,X1))
            & r2_hidden(sK22(X0,X1),k1_relat_1(X0)) )
          | k1_relat_1(X1) != k1_relat_1(X0)
          | ~ v1_funct_1(X1)
          | ~ v1_relat_1(X1) )
      | ~ v1_funct_1(X0)
      | ~ v1_relat_1(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f110,f166]) ).

fof(f168,plain,
    ~ v1_xboole_0(sK0),
    inference(cnf_transformation,[],[f114]) ).

fof(f169,plain,
    v2_relat_1(sK1),
    inference(cnf_transformation,[],[f114]) ).

fof(f170,plain,
    m1_pboole(sK1,sK0),
    inference(cnf_transformation,[],[f114]) ).

fof(f172,plain,
    m1_pboole(sK2,sK0),
    inference(cnf_transformation,[],[f114]) ).

fof(f173,plain,
    k1_closure3(sK0,sK1) = k1_closure3(sK0,sK2),
    inference(cnf_transformation,[],[f114]) ).

fof(f174,plain,
    k7_relat_1(sK1,k1_closure3(sK0,sK1)) = k7_relat_1(sK2,k1_closure3(sK0,sK2)),
    inference(cnf_transformation,[],[f114]) ).

fof(f175,plain,
    ~ r6_pboole(sK0,sK1,sK2),
    inference(cnf_transformation,[],[f114]) ).

fof(f183,plain,
    ! [X0,X1] : k3_xboole_0(X0,X1) = k3_xboole_0(X1,X0),
    inference(cnf_transformation,[],[f11]) ).

fof(f187,plain,
    ! [X2,X0,X1] :
      ( a_2_0_closure3(X0,X1) = X2
      | k1_closure3(X0,X1) != X2
      | ~ m1_pboole(X1,X0)
      | v1_xboole_0(X0) ),
    inference(cnf_transformation,[],[f119]) ).

fof(f189,plain,
    ! [X0,X1] :
      ( k1_relat_1(X1) = X0
      | ~ m1_pboole(X1,X0)
      | ~ v1_funct_1(X1)
      | ~ v1_relat_1(X1) ),
    inference(cnf_transformation,[],[f120]) ).

fof(f192,plain,
    ! [X2,X0,X1,X4] :
      ( r2_hidden(X4,X1)
      | ~ r2_hidden(X4,X2)
      | k3_xboole_0(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f125]) ).

fof(f193,plain,
    ! [X2,X0,X1,X4] :
      ( r2_hidden(X4,X2)
      | ~ r2_hidden(X4,X1)
      | ~ r2_hidden(X4,X0)
      | k3_xboole_0(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f125]) ).

fof(f194,plain,
    ! [X2,X0,X1] :
      ( k3_xboole_0(X0,X1) = X2
      | r2_hidden(sK4(X0,X1,X2),X0)
      | r2_hidden(sK4(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f125]) ).

fof(f196,plain,
    ! [X2,X0,X1] :
      ( k3_xboole_0(X0,X1) = X2
      | ~ r2_hidden(sK4(X0,X1,X2),X1)
      | ~ r2_hidden(sK4(X0,X1,X2),X0)
      | ~ r2_hidden(sK4(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f125]) ).

fof(f198,plain,
    ! [X0,X1] :
      ( v1_relat_1(X1)
      | ~ m1_pboole(X1,X0) ),
    inference(cnf_transformation,[],[f82]) ).

fof(f199,plain,
    ! [X0,X1] :
      ( v1_funct_1(X1)
      | ~ m1_pboole(X1,X0) ),
    inference(cnf_transformation,[],[f82]) ).

fof(f204,plain,
    v1_xboole_0(k1_xboole_0),
    inference(cnf_transformation,[],[f28]) ).

fof(f205,plain,
    ! [X2,X0,X1] :
      ( ~ v1_xboole_0(k1_funct_1(X1,X2))
      | ~ m1_subset_1(X2,X0)
      | ~ m1_pboole(X1,X0)
      | ~ v2_relat_1(X1)
      | v1_xboole_0(X0) ),
    inference(cnf_transformation,[],[f86]) ).

fof(f208,plain,
    ! [X2,X0,X1] :
      ( m1_subset_1(sK7(X0,X1,X2),X1)
      | ~ r2_hidden(X0,a_2_0_closure3(X1,X2))
      | ~ m1_pboole(X2,X1)
      | v1_xboole_0(X1) ),
    inference(cnf_transformation,[],[f133]) ).

fof(f209,plain,
    ! [X2,X0,X1] :
      ( sK7(X0,X1,X2) = X0
      | ~ r2_hidden(X0,a_2_0_closure3(X1,X2))
      | ~ m1_pboole(X2,X1)
      | v1_xboole_0(X1) ),
    inference(cnf_transformation,[],[f133]) ).

fof(f211,plain,
    ! [X2,X3,X0,X1] :
      ( r2_hidden(X0,a_2_0_closure3(X1,X2))
      | k1_xboole_0 = k1_funct_1(X2,X3)
      | X0 != X3
      | ~ m1_subset_1(X3,X1)
      | ~ m1_pboole(X2,X1)
      | v1_xboole_0(X1) ),
    inference(cnf_transformation,[],[f133]) ).

fof(f216,plain,
    ! [X0] : k3_xboole_0(X0,X0) = X0,
    inference(cnf_transformation,[],[f59]) ).

fof(f253,plain,
    ! [X0,X1] :
      ( m1_subset_1(X0,X1)
      | ~ r2_hidden(X0,X1) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f255,plain,
    ! [X0,X1] :
      ( r2_hidden(X0,X1)
      | v1_xboole_0(X1)
      | ~ m1_subset_1(X0,X1) ),
    inference(cnf_transformation,[],[f101]) ).

fof(f259,plain,
    ! [X2,X0,X1] :
      ( k1_funct_1(k7_relat_1(X2,X0),X1) = k1_funct_1(X2,X1)
      | ~ r2_hidden(X1,k1_relat_1(k7_relat_1(X2,X0)))
      | ~ v1_funct_1(X2)
      | ~ v1_relat_1(X2) ),
    inference(cnf_transformation,[],[f105]) ).

fof(f262,plain,
    ! [X0,X1] :
      ( k1_relat_1(k7_relat_1(X1,X0)) = k3_xboole_0(k1_relat_1(X1),X0)
      | ~ v1_relat_1(X1) ),
    inference(cnf_transformation,[],[f108]) ).

fof(f263,plain,
    ! [X0,X1] :
      ( X0 = X1
      | r2_hidden(sK22(X0,X1),k1_relat_1(X0))
      | k1_relat_1(X1) != k1_relat_1(X0)
      | ~ v1_funct_1(X1)
      | ~ v1_relat_1(X1)
      | ~ v1_funct_1(X0)
      | ~ v1_relat_1(X0) ),
    inference(cnf_transformation,[],[f167]) ).

fof(f264,plain,
    ! [X0,X1] :
      ( X0 = X1
      | k1_funct_1(X1,sK22(X0,X1)) != k1_funct_1(X0,sK22(X0,X1))
      | k1_relat_1(X1) != k1_relat_1(X0)
      | ~ v1_funct_1(X1)
      | ~ v1_relat_1(X1)
      | ~ v1_funct_1(X0)
      | ~ v1_relat_1(X0) ),
    inference(cnf_transformation,[],[f167]) ).

fof(f266,plain,
    ! [X0,X1] :
      ( k1_closure3(X0,X1) = a_2_0_closure3(X0,X1)
      | ~ m1_pboole(X1,X0)
      | v1_xboole_0(X0) ),
    inference(equality_resolution,[],[f187]) ).

fof(f268,plain,
    ! [X0,X1,X4] :
      ( r2_hidden(X4,k3_xboole_0(X0,X1))
      | ~ r2_hidden(X4,X1)
      | ~ r2_hidden(X4,X0) ),
    inference(equality_resolution,[],[f193]) ).

fof(f269,plain,
    ! [X0,X1,X4] :
      ( r2_hidden(X4,X1)
      | ~ r2_hidden(X4,k3_xboole_0(X0,X1)) ),
    inference(equality_resolution,[],[f192]) ).

fof(f271,plain,
    ! [X2,X3,X1] :
      ( r2_hidden(X3,a_2_0_closure3(X1,X2))
      | k1_xboole_0 = k1_funct_1(X2,X3)
      | ~ m1_subset_1(X3,X1)
      | ~ m1_pboole(X2,X1)
      | v1_xboole_0(X1) ),
    inference(equality_resolution,[],[f211]) ).

cnf(c_49,negated_conjecture,
    ~ r6_pboole(sK0,sK1,sK2),
    inference(cnf_transformation,[],[f175]) ).

cnf(c_50,negated_conjecture,
    k7_relat_1(sK1,k1_closure3(sK0,sK1)) = k7_relat_1(sK2,k1_closure3(sK0,sK2)),
    inference(cnf_transformation,[],[f174]) ).

cnf(c_51,negated_conjecture,
    k1_closure3(sK0,sK1) = k1_closure3(sK0,sK2),
    inference(cnf_transformation,[],[f173]) ).

cnf(c_52,negated_conjecture,
    m1_pboole(sK2,sK0),
    inference(cnf_transformation,[],[f172]) ).

cnf(c_54,negated_conjecture,
    m1_pboole(sK1,sK0),
    inference(cnf_transformation,[],[f170]) ).

cnf(c_55,negated_conjecture,
    v2_relat_1(sK1),
    inference(cnf_transformation,[],[f169]) ).

cnf(c_56,negated_conjecture,
    ~ v1_xboole_0(sK0),
    inference(cnf_transformation,[],[f168]) ).

cnf(c_62,plain,
    k3_xboole_0(X0,X1) = k3_xboole_0(X1,X0),
    inference(cnf_transformation,[],[f183]) ).

cnf(c_67,plain,
    ( ~ m1_pboole(X0,X1)
    | k1_closure3(X1,X0) = a_2_0_closure3(X1,X0)
    | v1_xboole_0(X1) ),
    inference(cnf_transformation,[],[f266]) ).

cnf(c_69,plain,
    ( ~ m1_pboole(X0,X1)
    | ~ v1_funct_1(X0)
    | ~ v1_relat_1(X0)
    | k1_relat_1(X0) = X1 ),
    inference(cnf_transformation,[],[f189]) ).

cnf(c_70,plain,
    ( ~ r2_hidden(sK4(X0,X1,X2),X0)
    | ~ r2_hidden(sK4(X0,X1,X2),X1)
    | ~ r2_hidden(sK4(X0,X1,X2),X2)
    | k3_xboole_0(X0,X1) = X2 ),
    inference(cnf_transformation,[],[f196]) ).

cnf(c_72,plain,
    ( k3_xboole_0(X0,X1) = X2
    | r2_hidden(sK4(X0,X1,X2),X0)
    | r2_hidden(sK4(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f194]) ).

cnf(c_73,plain,
    ( ~ r2_hidden(X0,X1)
    | ~ r2_hidden(X0,X2)
    | r2_hidden(X0,k3_xboole_0(X2,X1)) ),
    inference(cnf_transformation,[],[f268]) ).

cnf(c_74,plain,
    ( ~ r2_hidden(X0,k3_xboole_0(X1,X2))
    | r2_hidden(X0,X2) ),
    inference(cnf_transformation,[],[f269]) ).

cnf(c_77,plain,
    ( ~ m1_pboole(X0,X1)
    | v1_funct_1(X0) ),
    inference(cnf_transformation,[],[f199]) ).

cnf(c_78,plain,
    ( ~ m1_pboole(X0,X1)
    | v1_relat_1(X0) ),
    inference(cnf_transformation,[],[f198]) ).

cnf(c_83,plain,
    v1_xboole_0(k1_xboole_0),
    inference(cnf_transformation,[],[f204]) ).

cnf(c_84,plain,
    ( ~ v1_xboole_0(k1_funct_1(X0,X1))
    | ~ m1_pboole(X0,X2)
    | ~ m1_subset_1(X1,X2)
    | ~ v2_relat_1(X0)
    | v1_xboole_0(X2) ),
    inference(cnf_transformation,[],[f205]) ).

cnf(c_87,plain,
    ( ~ m1_pboole(X0,X1)
    | ~ m1_subset_1(X2,X1)
    | k1_funct_1(X0,X2) = k1_xboole_0
    | r2_hidden(X2,a_2_0_closure3(X1,X0))
    | v1_xboole_0(X1) ),
    inference(cnf_transformation,[],[f271]) ).

cnf(c_89,plain,
    ( ~ r2_hidden(X0,a_2_0_closure3(X1,X2))
    | ~ m1_pboole(X2,X1)
    | sK7(X0,X1,X2) = X0
    | v1_xboole_0(X1) ),
    inference(cnf_transformation,[],[f209]) ).

cnf(c_90,plain,
    ( ~ r2_hidden(X0,a_2_0_closure3(X1,X2))
    | ~ m1_pboole(X2,X1)
    | m1_subset_1(sK7(X0,X1,X2),X1)
    | v1_xboole_0(X1) ),
    inference(cnf_transformation,[],[f208]) ).

cnf(c_95,plain,
    k3_xboole_0(X0,X0) = X0,
    inference(cnf_transformation,[],[f216]) ).

cnf(c_128,plain,
    ( ~ m1_pboole(X0,X1)
    | r6_pboole(X1,X0,X0) ),
    inference(cnf_transformation,[],[f274]) ).

cnf(c_132,plain,
    ( ~ r2_hidden(X0,X1)
    | m1_subset_1(X0,X1) ),
    inference(cnf_transformation,[],[f253]) ).

cnf(c_134,plain,
    ( ~ m1_subset_1(X0,X1)
    | r2_hidden(X0,X1)
    | v1_xboole_0(X1) ),
    inference(cnf_transformation,[],[f255]) ).

cnf(c_138,plain,
    ( ~ r2_hidden(X0,k1_relat_1(k7_relat_1(X1,X2)))
    | ~ v1_funct_1(X1)
    | ~ v1_relat_1(X1)
    | k1_funct_1(k7_relat_1(X1,X2),X0) = k1_funct_1(X1,X0) ),
    inference(cnf_transformation,[],[f259]) ).

cnf(c_141,plain,
    ( ~ v1_relat_1(X0)
    | k3_xboole_0(k1_relat_1(X0),X1) = k1_relat_1(k7_relat_1(X0,X1)) ),
    inference(cnf_transformation,[],[f262]) ).

cnf(c_142,plain,
    ( k1_funct_1(X0,sK22(X0,X1)) != k1_funct_1(X1,sK22(X0,X1))
    | k1_relat_1(X0) != k1_relat_1(X1)
    | ~ v1_funct_1(X0)
    | ~ v1_funct_1(X1)
    | ~ v1_relat_1(X0)
    | ~ v1_relat_1(X1)
    | X0 = X1 ),
    inference(cnf_transformation,[],[f264]) ).

cnf(c_143,plain,
    ( k1_relat_1(X0) != k1_relat_1(X1)
    | ~ v1_funct_1(X0)
    | ~ v1_funct_1(X1)
    | ~ v1_relat_1(X0)
    | ~ v1_relat_1(X1)
    | X0 = X1
    | r2_hidden(sK22(X1,X0),k1_relat_1(X1)) ),
    inference(cnf_transformation,[],[f263]) ).

cnf(c_184,plain,
    ( ~ m1_pboole(X0,X1)
    | k1_relat_1(X0) = X1 ),
    inference(global_subsumption_just,[status(thm)],[c_69,c_78,c_77,c_69]) ).

cnf(c_679,plain,
    k7_relat_1(sK1,k1_closure3(sK0,sK1)) = k7_relat_1(sK2,k1_closure3(sK0,sK1)),
    inference(light_normalisation,[status(thm)],[c_50,c_51]) ).

cnf(c_4304,plain,
    k1_closure3(sK0,sK1) = sP0_iProver_def,
    definition ).

cnf(c_4306,negated_conjecture,
    ~ v1_xboole_0(sK0),
    inference(demodulation,[status(thm)],[c_56]) ).

cnf(c_4308,negated_conjecture,
    m1_pboole(sK1,sK0),
    inference(demodulation,[status(thm)],[c_54]) ).

cnf(c_4310,negated_conjecture,
    m1_pboole(sK2,sK0),
    inference(demodulation,[status(thm)],[c_52]) ).

cnf(c_4313,plain,
    X0 = X0,
    theory(equality) ).

cnf(c_4316,plain,
    ( X0 != X1
    | X2 != X3
    | X4 != X5
    | ~ r6_pboole(X1,X3,X5)
    | r6_pboole(X0,X2,X4) ),
    theory(equality) ).

cnf(c_4321,plain,
    ( X0 != X1
    | ~ v1_xboole_0(X1)
    | v1_xboole_0(X0) ),
    theory(equality) ).

cnf(c_5878,plain,
    ( k1_closure3(sK0,sK1) = a_2_0_closure3(sK0,sK1)
    | v1_xboole_0(sK0) ),
    inference(superposition,[status(thm)],[c_4308,c_67]) ).

cnf(c_5888,plain,
    ( a_2_0_closure3(sK0,sK1) = sP0_iProver_def
    | v1_xboole_0(sK0) ),
    inference(light_normalisation,[status(thm)],[c_5878,c_4304]) ).

cnf(c_5889,plain,
    a_2_0_closure3(sK0,sK1) = sP0_iProver_def,
    inference(forward_subsumption_resolution,[status(thm)],[c_5888,c_4306]) ).

cnf(c_6233,plain,
    ( ~ m1_pboole(sK2,sK0)
    | r6_pboole(sK0,sK2,sK2) ),
    inference(instantiation,[status(thm)],[c_128]) ).

cnf(c_6392,plain,
    ( ~ v1_xboole_0(k1_funct_1(X0,X1))
    | ~ m1_pboole(X0,sK0)
    | ~ m1_subset_1(X1,sK0)
    | ~ v2_relat_1(X0)
    | v1_xboole_0(sK0) ),
    inference(instantiation,[status(thm)],[c_84]) ).

cnf(c_6667,plain,
    ( ~ m1_subset_1(X0,sK0)
    | ~ m1_pboole(sK1,sK0)
    | k1_funct_1(sK1,X0) = k1_xboole_0
    | r2_hidden(X0,sP0_iProver_def)
    | v1_xboole_0(sK0) ),
    inference(superposition,[status(thm)],[c_5889,c_87]) ).

cnf(c_6675,plain,
    ( ~ m1_subset_1(X0,sK0)
    | k1_funct_1(sK1,X0) = k1_xboole_0
    | r2_hidden(X0,sP0_iProver_def) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_6667,c_4306,c_4308]) ).

cnf(c_6952,plain,
    ( X0 != sK0
    | X1 != sK2
    | X2 != sK2
    | ~ r6_pboole(sK0,sK2,sK2)
    | r6_pboole(X0,X1,X2) ),
    inference(instantiation,[status(thm)],[c_4316]) ).

cnf(c_7291,plain,
    sK2 = sK2,
    inference(instantiation,[status(thm)],[c_4313]) ).

cnf(c_7670,plain,
    ( ~ v1_xboole_0(k1_funct_1(sK1,X0))
    | ~ m1_subset_1(X0,sK0)
    | ~ m1_pboole(sK1,sK0)
    | ~ v2_relat_1(sK1)
    | v1_xboole_0(sK0) ),
    inference(instantiation,[status(thm)],[c_6392]) ).

cnf(c_13629,plain,
    sK0 = sK0,
    inference(instantiation,[status(thm)],[c_4313]) ).

cnf(c_14631,plain,
    ( sK0 != sK0
    | sK1 != sK2
    | sK2 != sK2
    | ~ r6_pboole(sK0,sK2,sK2)
    | r6_pboole(sK0,sK1,sK2) ),
    inference(instantiation,[status(thm)],[c_6952]) ).

cnf(c_49169,plain,
    ( k1_closure3(sK0,sK1) = a_2_0_closure3(sK0,sK1)
    | v1_xboole_0(sK0) ),
    inference(superposition,[status(thm)],[c_4308,c_67]) ).

cnf(c_49174,plain,
    ( a_2_0_closure3(sK0,sK1) = sP0_iProver_def
    | v1_xboole_0(sK0) ),
    inference(light_normalisation,[status(thm)],[c_49169,c_4304]) ).

cnf(c_49175,plain,
    a_2_0_closure3(sK0,sK1) = sP0_iProver_def,
    inference(forward_subsumption_resolution,[status(thm)],[c_49174,c_4306]) ).

cnf(c_49783,plain,
    ( k3_xboole_0(X0,X1) = X0
    | r2_hidden(sK4(X0,X1,X0),X0) ),
    inference(equality_factoring,[status(thm)],[c_72]) ).

cnf(c_50069,plain,
    ( ~ r2_hidden(X0,sP0_iProver_def)
    | ~ m1_pboole(sK1,sK0)
    | sK7(X0,sK0,sK1) = X0
    | v1_xboole_0(sK0) ),
    inference(superposition,[status(thm)],[c_49175,c_89]) ).

cnf(c_50072,plain,
    ( ~ r2_hidden(X0,sP0_iProver_def)
    | sK7(X0,sK0,sK1) = X0 ),
    inference(forward_subsumption_resolution,[status(thm)],[c_50069,c_4306,c_4308]) ).

cnf(c_50282,plain,
    ( sK7(sK4(sP0_iProver_def,X0,sP0_iProver_def),sK0,sK1) = sK4(sP0_iProver_def,X0,sP0_iProver_def)
    | k3_xboole_0(sP0_iProver_def,X0) = sP0_iProver_def ),
    inference(superposition,[status(thm)],[c_49783,c_50072]) ).

cnf(c_63412,plain,
    ( ~ r2_hidden(sK4(sP0_iProver_def,X0,sP0_iProver_def),a_2_0_closure3(sK0,sK1))
    | ~ m1_pboole(sK1,sK0)
    | k3_xboole_0(sP0_iProver_def,X0) = sP0_iProver_def
    | m1_subset_1(sK4(sP0_iProver_def,X0,sP0_iProver_def),sK0)
    | v1_xboole_0(sK0) ),
    inference(superposition,[status(thm)],[c_50282,c_90]) ).

cnf(c_63415,plain,
    ( ~ r2_hidden(sK4(sP0_iProver_def,X0,sP0_iProver_def),sP0_iProver_def)
    | ~ m1_pboole(sK1,sK0)
    | k3_xboole_0(sP0_iProver_def,X0) = sP0_iProver_def
    | m1_subset_1(sK4(sP0_iProver_def,X0,sP0_iProver_def),sK0)
    | v1_xboole_0(sK0) ),
    inference(light_normalisation,[status(thm)],[c_63412,c_49175]) ).

cnf(c_63416,plain,
    ( ~ r2_hidden(sK4(sP0_iProver_def,X0,sP0_iProver_def),sP0_iProver_def)
    | k3_xboole_0(sP0_iProver_def,X0) = sP0_iProver_def
    | m1_subset_1(sK4(sP0_iProver_def,X0,sP0_iProver_def),sK0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_63415,c_4306,c_4308]) ).

cnf(c_63480,plain,
    ( k3_xboole_0(sP0_iProver_def,X0) = sP0_iProver_def
    | m1_subset_1(sK4(sP0_iProver_def,X0,sP0_iProver_def),sK0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_63416,c_49783]) ).

cnf(c_63483,plain,
    ( k3_xboole_0(sP0_iProver_def,X0) = sP0_iProver_def
    | r2_hidden(sK4(sP0_iProver_def,X0,sP0_iProver_def),sK0)
    | v1_xboole_0(sK0) ),
    inference(superposition,[status(thm)],[c_63480,c_134]) ).

cnf(c_63486,plain,
    ( k3_xboole_0(sP0_iProver_def,X0) = sP0_iProver_def
    | r2_hidden(sK4(sP0_iProver_def,X0,sP0_iProver_def),sK0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_63483,c_4306]) ).

cnf(c_63532,plain,
    ( ~ r2_hidden(sK4(sP0_iProver_def,sK0,sP0_iProver_def),sP0_iProver_def)
    | k3_xboole_0(sP0_iProver_def,sK0) = sP0_iProver_def ),
    inference(superposition,[status(thm)],[c_63486,c_70]) ).

cnf(c_71320,plain,
    k3_xboole_0(sP0_iProver_def,sK0) = sP0_iProver_def,
    inference(forward_subsumption_resolution,[status(thm)],[c_63532,c_49783]) ).

cnf(c_71361,plain,
    ( ~ r2_hidden(X0,sP0_iProver_def)
    | r2_hidden(X0,sK0) ),
    inference(superposition,[status(thm)],[c_71320,c_74]) ).

cnf(c_114191,plain,
    ( k1_funct_1(sK1,X0) != X1
    | ~ v1_xboole_0(X1)
    | v1_xboole_0(k1_funct_1(sK1,X0)) ),
    inference(instantiation,[status(thm)],[c_4321]) ).

cnf(c_114204,plain,
    ( ~ r2_hidden(X0,sK0)
    | m1_subset_1(X0,sK0) ),
    inference(instantiation,[status(thm)],[c_132]) ).

cnf(c_117179,plain,
    ( k1_funct_1(sK1,X0) != k1_xboole_0
    | ~ v1_xboole_0(k1_xboole_0)
    | v1_xboole_0(k1_funct_1(sK1,X0)) ),
    inference(instantiation,[status(thm)],[c_114191]) ).

cnf(c_182383,plain,
    k7_relat_1(sK1,sP0_iProver_def) = k7_relat_1(sK2,sP0_iProver_def),
    inference(light_normalisation,[status(thm)],[c_679,c_4304]) ).

cnf(c_182395,plain,
    k1_relat_1(sK2) = sK0,
    inference(superposition,[status(thm)],[c_4310,c_184]) ).

cnf(c_182396,plain,
    k1_relat_1(sK1) = sK0,
    inference(superposition,[status(thm)],[c_4308,c_184]) ).

cnf(c_182404,plain,
    v1_funct_1(sK2),
    inference(superposition,[status(thm)],[c_4310,c_77]) ).

cnf(c_182405,plain,
    v1_funct_1(sK1),
    inference(superposition,[status(thm)],[c_4308,c_77]) ).

cnf(c_182413,plain,
    v1_relat_1(sK2),
    inference(superposition,[status(thm)],[c_4310,c_78]) ).

cnf(c_182414,plain,
    v1_relat_1(sK1),
    inference(superposition,[status(thm)],[c_4308,c_78]) ).

cnf(c_182733,plain,
    ( ~ r2_hidden(X0,X1)
    | ~ r2_hidden(X0,X2)
    | m1_subset_1(X0,k3_xboole_0(X2,X1)) ),
    inference(superposition,[status(thm)],[c_73,c_132]) ).

cnf(c_182758,plain,
    k3_xboole_0(k1_relat_1(sK2),X0) = k1_relat_1(k7_relat_1(sK2,X0)),
    inference(superposition,[status(thm)],[c_182413,c_141]) ).

cnf(c_182759,plain,
    k3_xboole_0(k1_relat_1(sK1),X0) = k1_relat_1(k7_relat_1(sK1,X0)),
    inference(superposition,[status(thm)],[c_182414,c_141]) ).

cnf(c_182762,plain,
    k1_relat_1(k7_relat_1(sK1,X0)) = k3_xboole_0(sK0,X0),
    inference(light_normalisation,[status(thm)],[c_182759,c_182396]) ).

cnf(c_182763,plain,
    k1_relat_1(k7_relat_1(sK2,X0)) = k3_xboole_0(sK0,X0),
    inference(light_normalisation,[status(thm)],[c_182758,c_182395]) ).

cnf(c_182906,plain,
    ( k1_closure3(sK0,sK1) = a_2_0_closure3(sK0,sK1)
    | v1_xboole_0(sK0) ),
    inference(superposition,[status(thm)],[c_4308,c_67]) ).

cnf(c_182916,plain,
    ( a_2_0_closure3(sK0,sK1) = sP0_iProver_def
    | v1_xboole_0(sK0) ),
    inference(light_normalisation,[status(thm)],[c_182906,c_4304]) ).

cnf(c_182917,plain,
    a_2_0_closure3(sK0,sK1) = sP0_iProver_def,
    inference(forward_subsumption_resolution,[status(thm)],[c_182916,c_4306]) ).

cnf(c_183308,plain,
    ( k3_xboole_0(X0,X1) = X0
    | r2_hidden(sK4(X0,X1,X0),X0) ),
    inference(equality_factoring,[status(thm)],[c_72]) ).

cnf(c_183729,plain,
    ( ~ m1_subset_1(X0,sK0)
    | ~ m1_pboole(sK1,sK0)
    | k1_funct_1(sK1,X0) = k1_xboole_0
    | r2_hidden(X0,sP0_iProver_def)
    | v1_xboole_0(sK0) ),
    inference(superposition,[status(thm)],[c_182917,c_87]) ).

cnf(c_183737,plain,
    ( ~ m1_subset_1(X0,sK0)
    | k1_funct_1(sK1,X0) = k1_xboole_0
    | r2_hidden(X0,sP0_iProver_def) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_183729,c_4306,c_4308]) ).

cnf(c_183898,plain,
    ( ~ m1_subset_1(X0,sK0)
    | r2_hidden(X0,sP0_iProver_def) ),
    inference(global_subsumption_just,[status(thm)],[c_183737,c_55,c_83,c_56,c_54,c_6675,c_7670,c_117179]) ).

cnf(c_184258,plain,
    ( ~ r2_hidden(X0,k3_xboole_0(sK0,X1))
    | ~ v1_funct_1(sK2)
    | ~ v1_relat_1(sK2)
    | k1_funct_1(k7_relat_1(sK2,X1),X0) = k1_funct_1(sK2,X0) ),
    inference(superposition,[status(thm)],[c_182763,c_138]) ).

cnf(c_184259,plain,
    ( ~ r2_hidden(X0,k3_xboole_0(sK0,X1))
    | ~ v1_funct_1(sK1)
    | ~ v1_relat_1(sK1)
    | k1_funct_1(k7_relat_1(sK1,X1),X0) = k1_funct_1(sK1,X0) ),
    inference(superposition,[status(thm)],[c_182762,c_138]) ).

cnf(c_184262,plain,
    ( ~ r2_hidden(X0,k3_xboole_0(sK0,X1))
    | k1_funct_1(k7_relat_1(sK1,X1),X0) = k1_funct_1(sK1,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_184259,c_182414,c_182405]) ).

cnf(c_184265,plain,
    ( ~ r2_hidden(X0,k3_xboole_0(sK0,X1))
    | k1_funct_1(k7_relat_1(sK2,X1),X0) = k1_funct_1(sK2,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_184258,c_182413,c_182404]) ).

cnf(c_184970,plain,
    ( ~ r2_hidden(X0,sK0)
    | k1_funct_1(k7_relat_1(sK1,sK0),X0) = k1_funct_1(sK1,X0) ),
    inference(superposition,[status(thm)],[c_95,c_184262]) ).

cnf(c_185038,plain,
    ( ~ r2_hidden(X0,sK0)
    | k1_funct_1(k7_relat_1(sK2,sK0),X0) = k1_funct_1(sK2,X0) ),
    inference(superposition,[status(thm)],[c_95,c_184265]) ).

cnf(c_193883,plain,
    ( k3_xboole_0(X0,X1) = X0
    | m1_subset_1(sK4(X0,X1,X0),X0) ),
    inference(superposition,[status(thm)],[c_183308,c_132]) ).

cnf(c_198435,plain,
    ( k3_xboole_0(sK0,X0) = sK0
    | r2_hidden(sK4(sK0,X0,sK0),sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_193883,c_183898]) ).

cnf(c_203039,plain,
    ( ~ r2_hidden(sK4(sK0,sP0_iProver_def,sK0),sK0)
    | k3_xboole_0(sK0,sP0_iProver_def) = sK0 ),
    inference(superposition,[status(thm)],[c_198435,c_70]) ).

cnf(c_219743,plain,
    ( ~ r2_hidden(sK4(sK0,sP0_iProver_def,sK0),sK0)
    | k3_xboole_0(sP0_iProver_def,sK0) = sK0 ),
    inference(demodulation,[status(thm)],[c_203039,c_62]) ).

cnf(c_219751,plain,
    ( k3_xboole_0(sK0,sP0_iProver_def) = sK0
    | k3_xboole_0(sP0_iProver_def,sK0) = sK0 ),
    inference(superposition,[status(thm)],[c_183308,c_219743]) ).

cnf(c_225476,plain,
    k3_xboole_0(sP0_iProver_def,sK0) = sK0,
    inference(demodulation,[status(thm)],[c_219751,c_62]) ).

cnf(c_225524,plain,
    ( ~ r2_hidden(X0,sK0)
    | ~ r2_hidden(X0,sP0_iProver_def)
    | m1_subset_1(X0,sK0) ),
    inference(superposition,[status(thm)],[c_225476,c_182733]) ).

cnf(c_227653,plain,
    ( ~ r2_hidden(X0,sP0_iProver_def)
    | m1_subset_1(X0,sK0) ),
    inference(global_subsumption_just,[status(thm)],[c_225524,c_71361,c_114204]) ).

cnf(c_227680,plain,
    ( k3_xboole_0(sP0_iProver_def,X0) = sP0_iProver_def
    | m1_subset_1(sK4(sP0_iProver_def,X0,sP0_iProver_def),sK0) ),
    inference(superposition,[status(thm)],[c_183308,c_227653]) ).

cnf(c_248877,plain,
    ( k3_xboole_0(sP0_iProver_def,X0) = sP0_iProver_def
    | r2_hidden(sK4(sP0_iProver_def,X0,sP0_iProver_def),sK0)
    | v1_xboole_0(sK0) ),
    inference(superposition,[status(thm)],[c_227680,c_134]) ).

cnf(c_248931,plain,
    ( k3_xboole_0(sP0_iProver_def,X0) = sP0_iProver_def
    | r2_hidden(sK4(sP0_iProver_def,X0,sP0_iProver_def),sK0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_248877,c_4306]) ).

cnf(c_249194,plain,
    ( ~ r2_hidden(sK4(sP0_iProver_def,sK0,sP0_iProver_def),sP0_iProver_def)
    | k3_xboole_0(sP0_iProver_def,sK0) = sP0_iProver_def ),
    inference(superposition,[status(thm)],[c_248931,c_70]) ).

cnf(c_249196,plain,
    ( ~ r2_hidden(sK4(sP0_iProver_def,sK0,sP0_iProver_def),sP0_iProver_def)
    | sK0 = sP0_iProver_def ),
    inference(light_normalisation,[status(thm)],[c_249194,c_225476]) ).

cnf(c_249778,plain,
    ( k3_xboole_0(sP0_iProver_def,sK0) = sP0_iProver_def
    | sK0 = sP0_iProver_def ),
    inference(superposition,[status(thm)],[c_183308,c_249196]) ).

cnf(c_249779,plain,
    sK0 = sP0_iProver_def,
    inference(light_normalisation,[status(thm)],[c_249778,c_225476]) ).

cnf(c_250174,plain,
    k1_relat_1(sK1) = sP0_iProver_def,
    inference(demodulation,[status(thm)],[c_182396,c_249779]) ).

cnf(c_250175,plain,
    k1_relat_1(sK2) = sP0_iProver_def,
    inference(demodulation,[status(thm)],[c_182395,c_249779]) ).

cnf(c_253324,plain,
    ( ~ r2_hidden(X0,sP0_iProver_def)
    | k1_funct_1(k7_relat_1(sK1,sP0_iProver_def),X0) = k1_funct_1(sK1,X0) ),
    inference(light_normalisation,[status(thm)],[c_184970,c_249779]) ).

cnf(c_253512,plain,
    ( ~ r2_hidden(X0,sP0_iProver_def)
    | k1_funct_1(k7_relat_1(sK1,sP0_iProver_def),X0) = k1_funct_1(sK2,X0) ),
    inference(light_normalisation,[status(thm)],[c_185038,c_182383,c_249779]) ).

cnf(c_253896,plain,
    ( k1_relat_1(X0) != sP0_iProver_def
    | ~ v1_funct_1(X0)
    | ~ v1_relat_1(X0)
    | ~ v1_funct_1(sK1)
    | ~ v1_relat_1(sK1)
    | X0 = sK1
    | r2_hidden(sK22(sK1,X0),k1_relat_1(sK1)) ),
    inference(superposition,[status(thm)],[c_250174,c_143]) ).

cnf(c_253897,plain,
    ( k1_relat_1(X0) != sP0_iProver_def
    | ~ v1_funct_1(X0)
    | ~ v1_relat_1(X0)
    | ~ v1_funct_1(sK1)
    | ~ v1_relat_1(sK1)
    | X0 = sK1
    | r2_hidden(sK22(sK1,X0),sP0_iProver_def) ),
    inference(light_normalisation,[status(thm)],[c_253896,c_250174]) ).

cnf(c_253898,plain,
    ( k1_relat_1(X0) != sP0_iProver_def
    | ~ v1_funct_1(X0)
    | ~ v1_relat_1(X0)
    | X0 = sK1
    | r2_hidden(sK22(sK1,X0),sP0_iProver_def) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_253897,c_182414,c_182405]) ).

cnf(c_272713,plain,
    ( ~ v1_funct_1(sK2)
    | ~ v1_relat_1(sK2)
    | sK1 = sK2
    | r2_hidden(sK22(sK1,sK2),sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_250175,c_253898]) ).

cnf(c_272730,plain,
    ( sK1 = sK2
    | r2_hidden(sK22(sK1,sK2),sP0_iProver_def) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_272713,c_182413,c_182404]) ).

cnf(c_272820,plain,
    r2_hidden(sK22(sK1,sK2),sP0_iProver_def),
    inference(global_subsumption_just,[status(thm)],[c_272730,c_52,c_49,c_6233,c_7291,c_13629,c_14631,c_272730]) ).

cnf(c_272827,plain,
    k1_funct_1(k7_relat_1(sK1,sP0_iProver_def),sK22(sK1,sK2)) = k1_funct_1(sK2,sK22(sK1,sK2)),
    inference(superposition,[status(thm)],[c_272820,c_253512]) ).

cnf(c_272828,plain,
    k1_funct_1(k7_relat_1(sK1,sP0_iProver_def),sK22(sK1,sK2)) = k1_funct_1(sK1,sK22(sK1,sK2)),
    inference(superposition,[status(thm)],[c_272820,c_253324]) ).

cnf(c_380010,plain,
    k1_funct_1(sK1,sK22(sK1,sK2)) = k1_funct_1(sK2,sK22(sK1,sK2)),
    inference(demodulation,[status(thm)],[c_272827,c_272828]) ).

cnf(c_380014,plain,
    ( k1_relat_1(sK1) != k1_relat_1(sK2)
    | ~ v1_funct_1(sK1)
    | ~ v1_funct_1(sK2)
    | ~ v1_relat_1(sK1)
    | ~ v1_relat_1(sK2)
    | sK1 = sK2 ),
    inference(superposition,[status(thm)],[c_380010,c_142]) ).

cnf(c_380024,plain,
    ( sP0_iProver_def != sP0_iProver_def
    | ~ v1_funct_1(sK1)
    | ~ v1_funct_1(sK2)
    | ~ v1_relat_1(sK1)
    | ~ v1_relat_1(sK2)
    | sK1 = sK2 ),
    inference(light_normalisation,[status(thm)],[c_380014,c_250174,c_250175]) ).

cnf(c_380025,plain,
    ( ~ v1_funct_1(sK1)
    | ~ v1_funct_1(sK2)
    | ~ v1_relat_1(sK1)
    | ~ v1_relat_1(sK2)
    | sK1 = sK2 ),
    inference(equality_resolution_simp,[status(thm)],[c_380024]) ).

cnf(c_380026,plain,
    sK1 = sK2,
    inference(forward_subsumption_resolution,[status(thm)],[c_380025,c_182413,c_182414,c_182404,c_182405]) ).

cnf(c_380160,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_380026,c_14631,c_13629,c_7291,c_6233,c_49,c_52]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : ALG226+1 : TPTP v8.1.2. Released v3.4.0.
% 0.03/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n014.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  : 300
% 0.13/0.34  % DateTime : Thu May  2 22:42:32 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.20/0.47  Running first-order theorem proving
% 0.20/0.47  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 184.47/24.92  % SZS status Started for theBenchmark.p
% 184.47/24.92  % SZS status Theorem for theBenchmark.p
% 184.47/24.92  
% 184.47/24.92  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 184.47/24.92  
% 184.47/24.92  ------  iProver source info
% 184.47/24.92  
% 184.47/24.92  git: date: 2024-05-02 19:28:25 +0000
% 184.47/24.92  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 184.47/24.92  git: non_committed_changes: false
% 184.47/24.92  
% 184.47/24.92  ------ Parsing...
% 184.47/24.92  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 184.47/24.92  
% 184.47/24.92  ------ Preprocessing... sup_sim: 1  sf_s  rm: 7 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 0  sf_s  rm: 3 0s  sf_e  pe_s  pe_e 
% 184.47/24.92  
% 184.47/24.92  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 184.47/24.92  
% 184.47/24.92  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 184.47/24.92  ------ Proving...
% 184.47/24.92  ------ Problem Properties 
% 184.47/24.92  
% 184.47/24.92  
% 184.47/24.92  clauses                                 87
% 184.47/24.92  conjectures                             7
% 184.47/24.92  EPR                                     42
% 184.47/24.92  Horn                                    73
% 184.47/24.92  unary                                   43
% 184.47/24.92  binary                                  13
% 184.47/24.92  lits                                    191
% 184.47/24.92  lits eq                                 30
% 184.47/24.92  fd_pure                                 0
% 184.47/24.92  fd_pseudo                               0
% 184.47/24.92  fd_cond                                 1
% 184.47/24.92  fd_pseudo_cond                          10
% 184.47/24.92  AC symbols                              0
% 184.47/24.92  
% 184.47/24.92  ------ Schedule dynamic 5 is on 
% 184.47/24.92  
% 184.47/24.92  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 184.47/24.92  
% 184.47/24.92  
% 184.47/24.92  ------ 
% 184.47/24.92  Current options:
% 184.47/24.92  ------ 
% 184.47/24.92  
% 184.47/24.92  
% 184.47/24.92  
% 184.47/24.92  
% 184.47/24.92  ------ Proving...
% 184.47/24.92  Proof_search_loop: time out after: 7245 full_loop iterations
% 184.47/24.92  
% 184.47/24.92  ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 184.47/24.92  
% 184.47/24.92  
% 184.47/24.92  ------ 
% 184.47/24.92  Current options:
% 184.47/24.92  ------ 
% 184.47/24.92  
% 184.47/24.92  
% 184.47/24.92  
% 184.47/24.92  
% 184.47/24.92  ------ Proving...
% 184.47/24.92  
% 184.47/24.92  
% 184.47/24.92  % SZS status Theorem for theBenchmark.p
% 184.47/24.92  
% 184.47/24.92  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 184.47/24.93  
% 184.47/24.93  
%------------------------------------------------------------------------------