TSTP Solution File: SEU245+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SEU245+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n008.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 : Thu Aug 31 17:05:09 EDT 2023

% Result   : Theorem 2.78s 1.14s
% Output   : CNFRefutation 2.78s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   48 (  10 unt;   0 def)
%            Number of atoms       :  189 (  20 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  225 (  84   ~;  87   |;  44   &)
%                                         (   4 <=>;   5  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-3 aty)
%            Number of variables   :   99 (   3 sgn;  60   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f16,axiom,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

fof(f24,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X1] : relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_wellord1) ).

fof(f25,conjecture,
    ! [X0,X1,X2] :
      ( relation(X2)
     => ( in(X0,relation_restriction(X2,X1))
      <=> ( in(X0,cartesian_product2(X1,X1))
          & in(X0,X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_wellord1) ).

fof(f26,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( relation(X2)
       => ( in(X0,relation_restriction(X2,X1))
        <=> ( in(X0,cartesian_product2(X1,X1))
            & in(X0,X2) ) ) ),
    inference(negated_conjecture,[],[f25]) ).

fof(f27,axiom,
    ! [X0,X1,X2] :
      ( set_intersection2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            & in(X3,X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).

fof(f42,plain,
    ! [X0] :
      ( ! [X1] : relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1))
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f43,plain,
    ? [X0,X1,X2] :
      ( ( in(X0,relation_restriction(X2,X1))
      <~> ( in(X0,cartesian_product2(X1,X1))
          & in(X0,X2) ) )
      & relation(X2) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f56,plain,
    ? [X0,X1,X2] :
      ( ( ~ in(X0,cartesian_product2(X1,X1))
        | ~ in(X0,X2)
        | ~ in(X0,relation_restriction(X2,X1)) )
      & ( ( in(X0,cartesian_product2(X1,X1))
          & in(X0,X2) )
        | in(X0,relation_restriction(X2,X1)) )
      & relation(X2) ),
    inference(nnf_transformation,[],[f43]) ).

fof(f57,plain,
    ? [X0,X1,X2] :
      ( ( ~ in(X0,cartesian_product2(X1,X1))
        | ~ in(X0,X2)
        | ~ in(X0,relation_restriction(X2,X1)) )
      & ( ( in(X0,cartesian_product2(X1,X1))
          & in(X0,X2) )
        | in(X0,relation_restriction(X2,X1)) )
      & relation(X2) ),
    inference(flattening,[],[f56]) ).

fof(f58,plain,
    ( ? [X0,X1,X2] :
        ( ( ~ in(X0,cartesian_product2(X1,X1))
          | ~ in(X0,X2)
          | ~ in(X0,relation_restriction(X2,X1)) )
        & ( ( in(X0,cartesian_product2(X1,X1))
            & in(X0,X2) )
          | in(X0,relation_restriction(X2,X1)) )
        & relation(X2) )
   => ( ( ~ in(sK6,cartesian_product2(sK7,sK7))
        | ~ in(sK6,sK8)
        | ~ in(sK6,relation_restriction(sK8,sK7)) )
      & ( ( in(sK6,cartesian_product2(sK7,sK7))
          & in(sK6,sK8) )
        | in(sK6,relation_restriction(sK8,sK7)) )
      & relation(sK8) ) ),
    introduced(choice_axiom,[]) ).

fof(f59,plain,
    ( ( ~ in(sK6,cartesian_product2(sK7,sK7))
      | ~ in(sK6,sK8)
      | ~ in(sK6,relation_restriction(sK8,sK7)) )
    & ( ( in(sK6,cartesian_product2(sK7,sK7))
        & in(sK6,sK8) )
      | in(sK6,relation_restriction(sK8,sK7)) )
    & relation(sK8) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f57,f58]) ).

fof(f60,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) = X2
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ~ in(X3,X1)
              | ~ in(X3,X0) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | ~ in(X3,X2) ) )
        | set_intersection2(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f27]) ).

fof(f61,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) = X2
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ~ in(X3,X1)
              | ~ in(X3,X0) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | ~ in(X3,X2) ) )
        | set_intersection2(X0,X1) != X2 ) ),
    inference(flattening,[],[f60]) ).

fof(f62,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) = X2
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ~ in(X4,X1)
              | ~ in(X4,X0) )
            & ( ( in(X4,X1)
                & in(X4,X0) )
              | ~ in(X4,X2) ) )
        | set_intersection2(X0,X1) != X2 ) ),
    inference(rectify,[],[f61]) ).

fof(f63,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ in(X3,X1)
            | ~ in(X3,X0)
            | ~ in(X3,X2) )
          & ( ( in(X3,X1)
              & in(X3,X0) )
            | in(X3,X2) ) )
     => ( ( ~ in(sK9(X0,X1,X2),X1)
          | ~ in(sK9(X0,X1,X2),X0)
          | ~ in(sK9(X0,X1,X2),X2) )
        & ( ( in(sK9(X0,X1,X2),X1)
            & in(sK9(X0,X1,X2),X0) )
          | in(sK9(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f64,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) = X2
        | ( ( ~ in(sK9(X0,X1,X2),X1)
            | ~ in(sK9(X0,X1,X2),X0)
            | ~ in(sK9(X0,X1,X2),X2) )
          & ( ( in(sK9(X0,X1,X2),X1)
              & in(sK9(X0,X1,X2),X0) )
            | in(sK9(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ~ in(X4,X1)
              | ~ in(X4,X0) )
            & ( ( in(X4,X1)
                & in(X4,X0) )
              | ~ in(X4,X2) ) )
        | set_intersection2(X0,X1) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f62,f63]) ).

fof(f83,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[],[f16]) ).

fof(f89,plain,
    ! [X0,X1] :
      ( relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1))
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f42]) ).

fof(f90,plain,
    relation(sK8),
    inference(cnf_transformation,[],[f59]) ).

fof(f91,plain,
    ( in(sK6,sK8)
    | in(sK6,relation_restriction(sK8,sK7)) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f92,plain,
    ( in(sK6,cartesian_product2(sK7,sK7))
    | in(sK6,relation_restriction(sK8,sK7)) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f93,plain,
    ( ~ in(sK6,cartesian_product2(sK7,sK7))
    | ~ in(sK6,sK8)
    | ~ in(sK6,relation_restriction(sK8,sK7)) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f94,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X0)
      | ~ in(X4,X2)
      | set_intersection2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f64]) ).

fof(f95,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X1)
      | ~ in(X4,X2)
      | set_intersection2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f64]) ).

fof(f96,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X2)
      | ~ in(X4,X1)
      | ~ in(X4,X0)
      | set_intersection2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f64]) ).

fof(f100,plain,
    ! [X0,X1,X4] :
      ( in(X4,set_intersection2(X0,X1))
      | ~ in(X4,X1)
      | ~ in(X4,X0) ),
    inference(equality_resolution,[],[f96]) ).

fof(f101,plain,
    ! [X0,X1,X4] :
      ( in(X4,X1)
      | ~ in(X4,set_intersection2(X0,X1)) ),
    inference(equality_resolution,[],[f95]) ).

fof(f102,plain,
    ! [X0,X1,X4] :
      ( in(X4,X0)
      | ~ in(X4,set_intersection2(X0,X1)) ),
    inference(equality_resolution,[],[f94]) ).

cnf(c_65,plain,
    set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[],[f83]) ).

cnf(c_71,plain,
    ( ~ relation(X0)
    | set_intersection2(X0,cartesian_product2(X1,X1)) = relation_restriction(X0,X1) ),
    inference(cnf_transformation,[],[f89]) ).

cnf(c_72,negated_conjecture,
    ( ~ in(sK6,relation_restriction(sK8,sK7))
    | ~ in(sK6,cartesian_product2(sK7,sK7))
    | ~ in(sK6,sK8) ),
    inference(cnf_transformation,[],[f93]) ).

cnf(c_73,negated_conjecture,
    ( in(sK6,relation_restriction(sK8,sK7))
    | in(sK6,cartesian_product2(sK7,sK7)) ),
    inference(cnf_transformation,[],[f92]) ).

cnf(c_74,negated_conjecture,
    ( in(sK6,relation_restriction(sK8,sK7))
    | in(sK6,sK8) ),
    inference(cnf_transformation,[],[f91]) ).

cnf(c_75,negated_conjecture,
    relation(sK8),
    inference(cnf_transformation,[],[f90]) ).

cnf(c_79,plain,
    ( ~ in(X0,X1)
    | ~ in(X0,X2)
    | in(X0,set_intersection2(X1,X2)) ),
    inference(cnf_transformation,[],[f100]) ).

cnf(c_80,plain,
    ( ~ in(X0,set_intersection2(X1,X2))
    | in(X0,X2) ),
    inference(cnf_transformation,[],[f101]) ).

cnf(c_81,plain,
    ( ~ in(X0,set_intersection2(X1,X2))
    | in(X0,X1) ),
    inference(cnf_transformation,[],[f102]) ).

cnf(c_885,plain,
    set_intersection2(sK8,cartesian_product2(X0,X0)) = relation_restriction(sK8,X0),
    inference(superposition,[status(thm)],[c_75,c_71]) ).

cnf(c_967,plain,
    ( ~ in(X0,relation_restriction(sK8,X1))
    | in(X0,sK8) ),
    inference(superposition,[status(thm)],[c_885,c_81]) ).

cnf(c_968,plain,
    ( ~ in(X0,relation_restriction(sK8,X1))
    | in(X0,cartesian_product2(X1,X1)) ),
    inference(superposition,[status(thm)],[c_885,c_80]) ).

cnf(c_983,plain,
    in(sK6,sK8),
    inference(backward_subsumption_resolution,[status(thm)],[c_74,c_967]) ).

cnf(c_984,plain,
    ( ~ in(sK6,relation_restriction(sK8,sK7))
    | ~ in(sK6,cartesian_product2(sK7,sK7)) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_72,c_967]) ).

cnf(c_1018,plain,
    ( ~ in(X0,X1)
    | ~ in(X0,X2)
    | in(X0,set_intersection2(X2,X1)) ),
    inference(superposition,[status(thm)],[c_65,c_79]) ).

cnf(c_1340,plain,
    in(sK6,cartesian_product2(sK7,sK7)),
    inference(backward_subsumption_resolution,[status(thm)],[c_73,c_968]) ).

cnf(c_1341,plain,
    ~ in(sK6,relation_restriction(sK8,sK7)),
    inference(backward_subsumption_resolution,[status(thm)],[c_984,c_968]) ).

cnf(c_2078,plain,
    ( ~ in(X0,cartesian_product2(X1,X1))
    | ~ in(X0,sK8)
    | in(X0,relation_restriction(sK8,X1)) ),
    inference(superposition,[status(thm)],[c_885,c_1018]) ).

cnf(c_2386,plain,
    ( ~ in(sK6,sK8)
    | in(sK6,relation_restriction(sK8,sK7)) ),
    inference(superposition,[status(thm)],[c_1340,c_2078]) ).

cnf(c_2401,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_2386,c_1341,c_983]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU245+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n008.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 Aug 24 01:10:02 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.47  Running first-order theorem proving
% 0.19/0.47  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.78/1.14  % SZS status Started for theBenchmark.p
% 2.78/1.14  % SZS status Theorem for theBenchmark.p
% 2.78/1.14  
% 2.78/1.14  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.78/1.14  
% 2.78/1.14  ------  iProver source info
% 2.78/1.14  
% 2.78/1.14  git: date: 2023-05-31 18:12:56 +0000
% 2.78/1.14  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.78/1.14  git: non_committed_changes: false
% 2.78/1.14  git: last_make_outside_of_git: false
% 2.78/1.14  
% 2.78/1.14  ------ Parsing...
% 2.78/1.14  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 2.78/1.14  
% 2.78/1.14  ------ Preprocessing... sup_sim: 0  sf_s  rm: 6 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 0  sf_s  rm: 3 0s  sf_e  pe_s  pe_e 
% 2.78/1.14  
% 2.78/1.14  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 2.78/1.14  
% 2.78/1.14  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.78/1.14  ------ Proving...
% 2.78/1.14  ------ Problem Properties 
% 2.78/1.14  
% 2.78/1.14  
% 2.78/1.14  clauses                                 27
% 2.78/1.14  conjectures                             4
% 2.78/1.14  EPR                                     12
% 2.78/1.14  Horn                                    22
% 2.78/1.14  unary                                   11
% 2.78/1.14  binary                                  10
% 2.78/1.14  lits                                    50
% 2.78/1.14  lits eq                                 9
% 2.78/1.14  fd_pure                                 0
% 2.78/1.14  fd_pseudo                               0
% 2.78/1.14  fd_cond                                 1
% 2.78/1.14  fd_pseudo_cond                          4
% 2.78/1.14  AC symbols                              0
% 2.78/1.14  
% 2.78/1.14  ------ Schedule dynamic 5 is on 
% 2.78/1.14  
% 2.78/1.14  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.78/1.14  
% 2.78/1.14  
% 2.78/1.14  ------ 
% 2.78/1.14  Current options:
% 2.78/1.14  ------ 
% 2.78/1.14  
% 2.78/1.14  
% 2.78/1.14  
% 2.78/1.14  
% 2.78/1.14  ------ Proving...
% 2.78/1.14  
% 2.78/1.14  
% 2.78/1.14  % SZS status Theorem for theBenchmark.p
% 2.78/1.14  
% 2.78/1.14  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.78/1.14  
% 2.78/1.14  
%------------------------------------------------------------------------------