TSTP Solution File: SEU062+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SEU062+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n017.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 17:03:35 EDT 2023

% Result   : Theorem 0.48s 1.20s
% Output   : CNFRefutation 0.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   37 (   7 unt;   0 def)
%            Number of atoms       :  109 (  21 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  128 (  56   ~;  39   |;  21   &)
%                                         (   4 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   67 (   0 sgn;  41   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f5,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

fof(f25,axiom,
    ! [X0,X1] :
      ( relation(X1)
     => ( in(X0,relation_rng(X1))
      <=> empty_set != relation_inverse_image(X1,singleton(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t142_funct_1) ).

fof(f26,conjecture,
    ! [X0,X1] :
      ( relation(X1)
     => ( ! [X2] :
            ~ ( empty_set = relation_inverse_image(X1,singleton(X2))
              & in(X2,X0) )
       => subset(X0,relation_rng(X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t143_funct_1) ).

fof(f27,negated_conjecture,
    ~ ! [X0,X1] :
        ( relation(X1)
       => ( ! [X2] :
              ~ ( empty_set = relation_inverse_image(X1,singleton(X2))
                & in(X2,X0) )
         => subset(X0,relation_rng(X1)) ) ),
    inference(negated_conjecture,[],[f26]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( ( in(X0,relation_rng(X1))
      <=> empty_set != relation_inverse_image(X1,singleton(X0)) )
      | ~ relation(X1) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f52,plain,
    ? [X0,X1] :
      ( ~ subset(X0,relation_rng(X1))
      & ! [X2] :
          ( empty_set != relation_inverse_image(X1,singleton(X2))
          | ~ in(X2,X0) )
      & relation(X1) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f53,plain,
    ? [X0,X1] :
      ( ~ subset(X0,relation_rng(X1))
      & ! [X2] :
          ( empty_set != relation_inverse_image(X1,singleton(X2))
          | ~ in(X2,X0) )
      & relation(X1) ),
    inference(flattening,[],[f52]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f46]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f63]) ).

fof(f65,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK0(X0,X1),X1)
        & in(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f66,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK0(X0,X1),X1)
          & in(sK0(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f64,f65]) ).

fof(f89,plain,
    ! [X0,X1] :
      ( ( ( in(X0,relation_rng(X1))
          | empty_set = relation_inverse_image(X1,singleton(X0)) )
        & ( empty_set != relation_inverse_image(X1,singleton(X0))
          | ~ in(X0,relation_rng(X1)) ) )
      | ~ relation(X1) ),
    inference(nnf_transformation,[],[f51]) ).

fof(f90,plain,
    ( ? [X0,X1] :
        ( ~ subset(X0,relation_rng(X1))
        & ! [X2] :
            ( empty_set != relation_inverse_image(X1,singleton(X2))
            | ~ in(X2,X0) )
        & relation(X1) )
   => ( ~ subset(sK12,relation_rng(sK13))
      & ! [X2] :
          ( empty_set != relation_inverse_image(sK13,singleton(X2))
          | ~ in(X2,sK12) )
      & relation(sK13) ) ),
    introduced(choice_axiom,[]) ).

fof(f91,plain,
    ( ~ subset(sK12,relation_rng(sK13))
    & ! [X2] :
        ( empty_set != relation_inverse_image(sK13,singleton(X2))
        | ~ in(X2,sK12) )
    & relation(sK13) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13])],[f53,f90]) ).

fof(f99,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sK0(X0,X1),X0) ),
    inference(cnf_transformation,[],[f66]) ).

fof(f100,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ in(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f66]) ).

fof(f132,plain,
    ! [X0,X1] :
      ( in(X0,relation_rng(X1))
      | empty_set = relation_inverse_image(X1,singleton(X0))
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f133,plain,
    relation(sK13),
    inference(cnf_transformation,[],[f91]) ).

fof(f134,plain,
    ! [X2] :
      ( empty_set != relation_inverse_image(sK13,singleton(X2))
      | ~ in(X2,sK12) ),
    inference(cnf_transformation,[],[f91]) ).

fof(f135,plain,
    ~ subset(sK12,relation_rng(sK13)),
    inference(cnf_transformation,[],[f91]) ).

cnf(c_52,plain,
    ( ~ in(sK0(X0,X1),X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f100]) ).

cnf(c_53,plain,
    ( in(sK0(X0,X1),X0)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f99]) ).

cnf(c_85,plain,
    ( ~ relation(X0)
    | relation_inverse_image(X0,singleton(X1)) = empty_set
    | in(X1,relation_rng(X0)) ),
    inference(cnf_transformation,[],[f132]) ).

cnf(c_87,negated_conjecture,
    ~ subset(sK12,relation_rng(sK13)),
    inference(cnf_transformation,[],[f135]) ).

cnf(c_88,negated_conjecture,
    ( relation_inverse_image(sK13,singleton(X0)) != empty_set
    | ~ in(X0,sK12) ),
    inference(cnf_transformation,[],[f134]) ).

cnf(c_89,negated_conjecture,
    relation(sK13),
    inference(cnf_transformation,[],[f133]) ).

cnf(c_144,plain,
    ( ~ in(sK0(X0,X1),X1)
    | subset(X0,X1) ),
    inference(prop_impl_just,[status(thm)],[c_52]) ).

cnf(c_160,plain,
    ( subset(X0,X1)
    | in(sK0(X0,X1),X0) ),
    inference(prop_impl_just,[status(thm)],[c_53]) ).

cnf(c_161,plain,
    ( in(sK0(X0,X1),X0)
    | subset(X0,X1) ),
    inference(renaming,[status(thm)],[c_160]) ).

cnf(c_750,plain,
    ( relation_rng(sK13) != X1
    | X0 != sK12
    | in(sK0(X0,X1),X0) ),
    inference(resolution_lifted,[status(thm)],[c_161,c_87]) ).

cnf(c_751,plain,
    in(sK0(sK12,relation_rng(sK13)),sK12),
    inference(unflattening,[status(thm)],[c_750]) ).

cnf(c_755,plain,
    ( relation_rng(sK13) != X1
    | X0 != sK12
    | ~ in(sK0(X0,X1),X1) ),
    inference(resolution_lifted,[status(thm)],[c_144,c_87]) ).

cnf(c_756,plain,
    ~ in(sK0(sK12,relation_rng(sK13)),relation_rng(sK13)),
    inference(unflattening,[status(thm)],[c_755]) ).

cnf(c_3577,plain,
    ( relation_inverse_image(sK13,singleton(sK0(sK12,relation_rng(sK13)))) != empty_set
    | ~ in(sK0(sK12,relation_rng(sK13)),sK12) ),
    inference(instantiation,[status(thm)],[c_88]) ).

cnf(c_4387,plain,
    ( ~ relation(sK13)
    | relation_inverse_image(sK13,singleton(sK0(sK12,relation_rng(sK13)))) = empty_set
    | in(sK0(sK12,relation_rng(sK13)),relation_rng(sK13)) ),
    inference(instantiation,[status(thm)],[c_85]) ).

cnf(c_4388,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_4387,c_3577,c_756,c_751,c_89]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU062+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14  % Command  : run_iprover %s %d THM
% 0.13/0.36  % Computer : n017.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit : 300
% 0.13/0.36  % WCLimit  : 300
% 0.13/0.36  % DateTime : Wed Aug 23 19:23:08 EDT 2023
% 0.13/0.36  % CPUTime  : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.48/1.20  % SZS status Started for theBenchmark.p
% 0.48/1.20  % SZS status Theorem for theBenchmark.p
% 0.48/1.20  
% 0.48/1.20  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.48/1.20  
% 0.48/1.20  ------  iProver source info
% 0.48/1.20  
% 0.48/1.20  git: date: 2023-05-31 18:12:56 +0000
% 0.48/1.20  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.48/1.20  git: non_committed_changes: false
% 0.48/1.20  git: last_make_outside_of_git: false
% 0.48/1.20  
% 0.48/1.20  ------ Parsing...
% 0.48/1.20  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 0.48/1.20  
% 0.48/1.20  ------ Preprocessing... sup_sim: 0  sf_s  rm: 6 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e 
% 0.48/1.20  
% 0.48/1.20  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 0.48/1.20  
% 0.48/1.20  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 0.48/1.20  ------ Proving...
% 0.48/1.20  ------ Problem Properties 
% 0.48/1.20  
% 0.48/1.20  
% 0.48/1.20  clauses                                 43
% 0.48/1.20  conjectures                             3
% 0.48/1.20  EPR                                     25
% 0.48/1.20  Horn                                    39
% 0.48/1.20  unary                                   21
% 0.48/1.20  binary                                  14
% 0.48/1.20  lits                                    73
% 0.48/1.20  lits eq                                 5
% 0.48/1.20  fd_pure                                 0
% 0.48/1.20  fd_pseudo                               0
% 0.48/1.20  fd_cond                                 1
% 0.48/1.20  fd_pseudo_cond                          1
% 0.48/1.20  AC symbols                              0
% 0.48/1.20  
% 0.48/1.20  ------ Schedule dynamic 5 is on 
% 0.48/1.20  
% 0.48/1.20  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.48/1.20  
% 0.48/1.20  
% 0.48/1.20  ------ 
% 0.48/1.20  Current options:
% 0.48/1.20  ------ 
% 0.48/1.20  
% 0.48/1.20  
% 0.48/1.20  
% 0.48/1.20  
% 0.48/1.20  ------ Proving...
% 0.48/1.20  
% 0.48/1.20  
% 0.48/1.20  % SZS status Theorem for theBenchmark.p
% 0.48/1.20  
% 0.48/1.20  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.48/1.20  
% 0.48/1.20  
%------------------------------------------------------------------------------