TSTP Solution File: SET679+3 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SET679+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n004.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 15:09:05 EDT 2023

% Result   : Theorem 2.94s 1.14s
% Output   : CNFRefutation 2.94s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named f140)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( member(X1,X0)
          <=> member(ordered_pair(X1,X1),identity_relation_of(X0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).

fof(f2,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ~ member(X0,empty_set) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).

fof(f8,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( not_equal(X0,X1)
          <=> X0 != X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7) ).

fof(f9,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ( empty(X0)
      <=> ! [X1] :
            ( ilf_type(X1,set_type)
           => ~ member(X1,X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8) ).

fof(f23,axiom,
    ! [X0] : ilf_type(X0,set_type),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22) ).

fof(f24,conjecture,
    ! [X0] :
      ( ( ilf_type(X0,set_type)
        & ~ empty(X0) )
     => not_equal(identity_relation_of(X0),empty_set) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_46) ).

fof(f25,negated_conjecture,
    ~ ! [X0] :
        ( ( ilf_type(X0,set_type)
          & ~ empty(X0) )
       => not_equal(identity_relation_of(X0),empty_set) ),
    inference(negated_conjecture,[],[f24]) ).

fof(f27,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( member(X1,X0)
          <=> member(ordered_pair(X1,X1),identity_relation_of(X0)) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f28,plain,
    ! [X0] :
      ( ~ member(X0,empty_set)
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f32,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( not_equal(X0,X1)
          <=> X0 != X1 )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f33,plain,
    ! [X0] :
      ( ( empty(X0)
      <=> ! [X1] :
            ( ~ member(X1,X0)
            | ~ ilf_type(X1,set_type) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f51,plain,
    ? [X0] :
      ( ~ not_equal(identity_relation_of(X0),empty_set)
      & ilf_type(X0,set_type)
      & ~ empty(X0) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f52,plain,
    ? [X0] :
      ( ~ not_equal(identity_relation_of(X0),empty_set)
      & ilf_type(X0,set_type)
      & ~ empty(X0) ),
    inference(flattening,[],[f51]) ).

fof(f53,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( member(X1,X0)
              | ~ member(ordered_pair(X1,X1),identity_relation_of(X0)) )
            & ( member(ordered_pair(X1,X1),identity_relation_of(X0))
              | ~ member(X1,X0) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f27]) ).

fof(f61,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( not_equal(X0,X1)
              | X0 = X1 )
            & ( X0 != X1
              | ~ not_equal(X0,X1) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f32]) ).

fof(f62,plain,
    ! [X0] :
      ( ( ( empty(X0)
          | ? [X1] :
              ( member(X1,X0)
              & ilf_type(X1,set_type) ) )
        & ( ! [X1] :
              ( ~ member(X1,X0)
              | ~ ilf_type(X1,set_type) )
          | ~ empty(X0) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f33]) ).

fof(f63,plain,
    ! [X0] :
      ( ( ( empty(X0)
          | ? [X1] :
              ( member(X1,X0)
              & ilf_type(X1,set_type) ) )
        & ( ! [X2] :
              ( ~ member(X2,X0)
              | ~ ilf_type(X2,set_type) )
          | ~ empty(X0) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(rectify,[],[f62]) ).

fof(f64,plain,
    ! [X0] :
      ( ? [X1] :
          ( member(X1,X0)
          & ilf_type(X1,set_type) )
     => ( member(sK1(X0),X0)
        & ilf_type(sK1(X0),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f65,plain,
    ! [X0] :
      ( ( ( empty(X0)
          | ( member(sK1(X0),X0)
            & ilf_type(sK1(X0),set_type) ) )
        & ( ! [X2] :
              ( ~ member(X2,X0)
              | ~ ilf_type(X2,set_type) )
          | ~ empty(X0) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f63,f64]) ).

fof(f86,plain,
    ( ? [X0] :
        ( ~ not_equal(identity_relation_of(X0),empty_set)
        & ilf_type(X0,set_type)
        & ~ empty(X0) )
   => ( ~ not_equal(identity_relation_of(sK9),empty_set)
      & ilf_type(sK9,set_type)
      & ~ empty(sK9) ) ),
    introduced(choice_axiom,[]) ).

fof(f87,plain,
    ( ~ not_equal(identity_relation_of(sK9),empty_set)
    & ilf_type(sK9,set_type)
    & ~ empty(sK9) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f52,f86]) ).

fof(f88,plain,
    ! [X0,X1] :
      ( member(ordered_pair(X1,X1),identity_relation_of(X0))
      | ~ member(X1,X0)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f90,plain,
    ! [X0] :
      ( ~ member(X0,empty_set)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f102,plain,
    ! [X0,X1] :
      ( not_equal(X0,X1)
      | X0 = X1
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f105,plain,
    ! [X0] :
      ( empty(X0)
      | member(sK1(X0),X0)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f132,plain,
    ! [X0] : ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f23]) ).

fof(f133,plain,
    ~ empty(sK9),
    inference(cnf_transformation,[],[f87]) ).

fof(f135,plain,
    ~ not_equal(identity_relation_of(sK9),empty_set),
    inference(cnf_transformation,[],[f87]) ).

cnf(c_50,plain,
    ( ~ member(X0,X1)
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | member(ordered_pair(X0,X0),identity_relation_of(X1)) ),
    inference(cnf_transformation,[],[f88]) ).

cnf(c_51,plain,
    ( ~ member(X0,empty_set)
    | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f90]) ).

cnf(c_53,plain,
    ( ~ member(X0,X1)
    | ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | member(ordered_pair(X0,X0),identity_relation_of(X1)) ),
    inference(cnf_transformation,[],[f140]) ).

cnf(c_62,plain,
    ( ~ ilf_type(X0,set_type)
    | ~ ilf_type(X1,set_type)
    | X0 = X1
    | not_equal(X1,X0) ),
    inference(cnf_transformation,[],[f102]) ).

cnf(c_64,plain,
    ( ~ ilf_type(X0,set_type)
    | member(sK1(X0),X0)
    | empty(X0) ),
    inference(cnf_transformation,[],[f105]) ).

cnf(c_92,plain,
    ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f132]) ).

cnf(c_93,negated_conjecture,
    ~ not_equal(identity_relation_of(sK9),empty_set),
    inference(cnf_transformation,[],[f135]) ).

cnf(c_95,negated_conjecture,
    ~ empty(sK9),
    inference(cnf_transformation,[],[f133]) ).

cnf(c_145,plain,
    ~ member(X0,empty_set),
    inference(global_subsumption_just,[status(thm)],[c_51,c_92,c_51]) ).

cnf(c_187,plain,
    ( ~ ilf_type(X1,set_type)
    | X0 = X1
    | not_equal(X1,X0) ),
    inference(global_subsumption_just,[status(thm)],[c_62,c_92,c_62]) ).

cnf(c_188,plain,
    ( ~ ilf_type(X0,set_type)
    | X1 = X0
    | not_equal(X0,X1) ),
    inference(renaming,[status(thm)],[c_187]) ).

cnf(c_189,plain,
    ( X1 = X0
    | not_equal(X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_188,c_92,c_188]) ).

cnf(c_190,plain,
    ( X0 = X1
    | not_equal(X1,X0) ),
    inference(renaming,[status(thm)],[c_189]) ).

cnf(c_218,plain,
    ( ~ member(X0,X1)
    | ~ ilf_type(X1,set_type)
    | member(ordered_pair(X0,X0),identity_relation_of(X1)) ),
    inference(global_subsumption_just,[status(thm)],[c_53,c_92,c_53]) ).

cnf(c_220,plain,
    ( ~ member(X0,X1)
    | ~ ilf_type(X1,set_type)
    | member(ordered_pair(X0,X0),identity_relation_of(X1)) ),
    inference(global_subsumption_just,[status(thm)],[c_50,c_218]) ).

cnf(c_279,plain,
    ( X0 = X1
    | not_equal(X1,X0) ),
    inference(prop_impl_just,[status(thm)],[c_190]) ).

cnf(c_365,plain,
    ( ~ member(X0,X1)
    | member(ordered_pair(X0,X0),identity_relation_of(X1)) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_220,c_92]) ).

cnf(c_652,plain,
    ( identity_relation_of(sK9) != X1
    | X0 != empty_set
    | X0 = X1 ),
    inference(resolution_lifted,[status(thm)],[c_279,c_93]) ).

cnf(c_653,plain,
    empty_set = identity_relation_of(sK9),
    inference(unflattening,[status(thm)],[c_652]) ).

cnf(c_914,plain,
    ( ~ member(X0,X1)
    | member(ordered_pair(X0,X0),identity_relation_of(X1)) ),
    inference(prop_impl_just,[status(thm)],[c_365]) ).

cnf(c_938,plain,
    ( empty(X0)
    | member(sK1(X0),X0) ),
    inference(prop_impl_just,[status(thm)],[c_92,c_64]) ).

cnf(c_939,plain,
    ( member(sK1(X0),X0)
    | empty(X0) ),
    inference(renaming,[status(thm)],[c_938]) ).

cnf(c_2181,plain,
    ( ~ member(X0,sK9)
    | member(ordered_pair(X0,X0),empty_set) ),
    inference(superposition,[status(thm)],[c_653,c_914]) ).

cnf(c_2185,plain,
    ~ member(X0,sK9),
    inference(forward_subsumption_resolution,[status(thm)],[c_2181,c_145]) ).

cnf(c_2194,plain,
    empty(sK9),
    inference(superposition,[status(thm)],[c_939,c_2185]) ).

cnf(c_2197,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_2194,c_95]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET679+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n004.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Sat Aug 26 12:54:53 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.21/0.47  Running first-order theorem proving
% 0.21/0.47  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.94/1.14  % SZS status Started for theBenchmark.p
% 2.94/1.14  % SZS status Theorem for theBenchmark.p
% 2.94/1.14  
% 2.94/1.14  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.94/1.14  
% 2.94/1.14  ------  iProver source info
% 2.94/1.14  
% 2.94/1.14  git: date: 2023-05-31 18:12:56 +0000
% 2.94/1.14  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.94/1.14  git: non_committed_changes: false
% 2.94/1.14  git: last_make_outside_of_git: false
% 2.94/1.14  
% 2.94/1.14  ------ Parsing...
% 2.94/1.14  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 2.94/1.14  
% 2.94/1.14  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e 
% 2.94/1.14  
% 2.94/1.14  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 2.94/1.14  
% 2.94/1.14  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.94/1.14  ------ Proving...
% 2.94/1.14  ------ Problem Properties 
% 2.94/1.14  
% 2.94/1.14  
% 2.94/1.14  clauses                                 31
% 2.94/1.14  conjectures                             1
% 2.94/1.14  EPR                                     9
% 2.94/1.14  Horn                                    25
% 2.94/1.14  unary                                   9
% 2.94/1.14  binary                                  17
% 2.94/1.14  lits                                    58
% 2.94/1.14  lits eq                                 6
% 2.94/1.14  fd_pure                                 0
% 2.94/1.14  fd_pseudo                               0
% 2.94/1.14  fd_cond                                 0
% 2.94/1.14  fd_pseudo_cond                          3
% 2.94/1.14  AC symbols                              0
% 2.94/1.14  
% 2.94/1.14  ------ Schedule dynamic 5 is on 
% 2.94/1.14  
% 2.94/1.14  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.94/1.14  
% 2.94/1.14  
% 2.94/1.14  ------ 
% 2.94/1.14  Current options:
% 2.94/1.14  ------ 
% 2.94/1.14  
% 2.94/1.14  
% 2.94/1.14  
% 2.94/1.14  
% 2.94/1.14  ------ Proving...
% 2.94/1.14  
% 2.94/1.14  
% 2.94/1.14  % SZS status Theorem for theBenchmark.p
% 2.94/1.14  
% 2.94/1.14  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.94/1.14  
% 2.94/1.14  
%------------------------------------------------------------------------------