TSTP Solution File: SEU154+2 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SEU154+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n024.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 03:04:44 EDT 2024

% Result   : Theorem 3.70s 1.15s
% Output   : CNFRefutation 3.70s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% Comments : 
%------------------------------------------------------------------------------
fof(f7,axiom,
    ! [X0,X1] :
      ( singleton(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).

fof(f33,conjecture,
    ! [X0,X1] :
      ( ~ in(X0,X1)
     => disjoint(singleton(X0),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).

fof(f34,negated_conjecture,
    ~ ! [X0,X1] :
        ( ~ in(X0,X1)
       => disjoint(singleton(X0),X1) ),
    inference(negated_conjecture,[],[f33]) ).

fof(f60,axiom,
    ! [X0,X1] :
      ( ~ ( disjoint(X0,X1)
          & ? [X2] :
              ( in(X2,X1)
              & in(X2,X0) ) )
      & ~ ( ! [X2] :
              ~ ( in(X2,X1)
                & in(X2,X0) )
          & ~ disjoint(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).

fof(f69,axiom,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).

fof(f83,plain,
    ! [X0,X1] :
      ( ~ ( disjoint(X0,X1)
          & ? [X2] :
              ( in(X2,X1)
              & in(X2,X0) ) )
      & ~ ( ! [X3] :
              ~ ( in(X3,X1)
                & in(X3,X0) )
          & ~ disjoint(X0,X1) ) ),
    inference(rectify,[],[f60]) ).

fof(f95,plain,
    ? [X0,X1] :
      ( ~ disjoint(singleton(X0),X1)
      & ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f109,plain,
    ! [X0,X1] :
      ( ( ~ disjoint(X0,X1)
        | ! [X2] :
            ( ~ in(X2,X1)
            | ~ in(X2,X0) ) )
      & ( ? [X3] :
            ( in(X3,X1)
            & in(X3,X0) )
        | disjoint(X0,X1) ) ),
    inference(ennf_transformation,[],[f83]) ).

fof(f126,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | X0 != X2 )
            & ( X0 = X2
              | ~ in(X2,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(nnf_transformation,[],[f7]) ).

fof(f127,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(rectify,[],[f126]) ).

fof(f128,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( X0 != X2
            | ~ in(X2,X1) )
          & ( X0 = X2
            | in(X2,X1) ) )
     => ( ( sK0(X0,X1) != X0
          | ~ in(sK0(X0,X1),X1) )
        & ( sK0(X0,X1) = X0
          | in(sK0(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f129,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ( ( sK0(X0,X1) != X0
            | ~ in(sK0(X0,X1),X1) )
          & ( sK0(X0,X1) = X0
            | in(sK0(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f127,f128]) ).

fof(f163,plain,
    ( ? [X0,X1] :
        ( ~ disjoint(singleton(X0),X1)
        & ~ in(X0,X1) )
   => ( ~ disjoint(singleton(sK8),sK9)
      & ~ in(sK8,sK9) ) ),
    introduced(choice_axiom,[]) ).

fof(f164,plain,
    ( ~ disjoint(singleton(sK8),sK9)
    & ~ in(sK8,sK9) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f95,f163]) ).

fof(f177,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( in(X3,X1)
          & in(X3,X0) )
     => ( in(sK13(X0,X1),X1)
        & in(sK13(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f178,plain,
    ! [X0,X1] :
      ( ( ~ disjoint(X0,X1)
        | ! [X2] :
            ( ~ in(X2,X1)
            | ~ in(X2,X0) ) )
      & ( ( in(sK13(X0,X1),X1)
          & in(sK13(X0,X1),X0) )
        | disjoint(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f109,f177]) ).

fof(f190,plain,
    ! [X3,X0,X1] :
      ( X0 = X3
      | ~ in(X3,X1)
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f129]) ).

fof(f239,plain,
    ~ in(sK8,sK9),
    inference(cnf_transformation,[],[f164]) ).

fof(f240,plain,
    ~ disjoint(singleton(sK8),sK9),
    inference(cnf_transformation,[],[f164]) ).

fof(f272,plain,
    ! [X0,X1] :
      ( in(sK13(X0,X1),X0)
      | disjoint(X0,X1) ),
    inference(cnf_transformation,[],[f178]) ).

fof(f273,plain,
    ! [X0,X1] :
      ( in(sK13(X0,X1),X1)
      | disjoint(X0,X1) ),
    inference(cnf_transformation,[],[f178]) ).

fof(f284,plain,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    inference(cnf_transformation,[],[f69]) ).

fof(f299,plain,
    ! [X3,X0,X1] :
      ( X0 = X3
      | ~ in(X3,X1)
      | unordered_pair(X0,X0) != X1 ),
    inference(definition_unfolding,[],[f190,f284]) ).

fof(f312,plain,
    ~ disjoint(unordered_pair(sK8,sK8),sK9),
    inference(definition_unfolding,[],[f240,f284]) ).

fof(f334,plain,
    ! [X3,X0] :
      ( X0 = X3
      | ~ in(X3,unordered_pair(X0,X0)) ),
    inference(equality_resolution,[],[f299]) ).

cnf(c_60,plain,
    ( ~ in(X0,unordered_pair(X1,X1))
    | X0 = X1 ),
    inference(cnf_transformation,[],[f334]) ).

cnf(c_106,negated_conjecture,
    ~ disjoint(unordered_pair(sK8,sK8),sK9),
    inference(cnf_transformation,[],[f312]) ).

cnf(c_107,negated_conjecture,
    ~ in(sK8,sK9),
    inference(cnf_transformation,[],[f239]) ).

cnf(c_140,plain,
    ( in(sK13(X0,X1),X1)
    | disjoint(X0,X1) ),
    inference(cnf_transformation,[],[f273]) ).

cnf(c_141,plain,
    ( in(sK13(X0,X1),X0)
    | disjoint(X0,X1) ),
    inference(cnf_transformation,[],[f272]) ).

cnf(c_2443,plain,
    unordered_pair(sK8,sK8) = sP0_iProver_def,
    definition ).

cnf(c_2444,negated_conjecture,
    ~ in(sK8,sK9),
    inference(demodulation,[status(thm)],[c_107]) ).

cnf(c_2445,negated_conjecture,
    ~ disjoint(sP0_iProver_def,sK9),
    inference(demodulation,[status(thm)],[c_106,c_2443]) ).

cnf(c_4520,plain,
    ( ~ in(X0,sP0_iProver_def)
    | X0 = sK8 ),
    inference(superposition,[status(thm)],[c_2443,c_60]) ).

cnf(c_5054,plain,
    ( sK13(sP0_iProver_def,X0) = sK8
    | disjoint(sP0_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_141,c_4520]) ).

cnf(c_9592,plain,
    sK13(sP0_iProver_def,sK9) = sK8,
    inference(superposition,[status(thm)],[c_5054,c_2445]) ).

cnf(c_9631,plain,
    ( in(sK8,sK9)
    | disjoint(sP0_iProver_def,sK9) ),
    inference(superposition,[status(thm)],[c_9592,c_140]) ).

cnf(c_9632,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_9631,c_2445,c_2444]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEU154+2 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.13  % Command  : run_iprover %s %d THM
% 0.14/0.34  % Computer : n024.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu May  2 17:46:51 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.21/0.47  Running first-order theorem proving
% 0.21/0.47  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.70/1.15  % SZS status Started for theBenchmark.p
% 3.70/1.15  % SZS status Theorem for theBenchmark.p
% 3.70/1.15  
% 3.70/1.15  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.70/1.15  
% 3.70/1.15  ------  iProver source info
% 3.70/1.15  
% 3.70/1.15  git: date: 2024-05-02 19:28:25 +0000
% 3.70/1.15  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.70/1.15  git: non_committed_changes: false
% 3.70/1.15  
% 3.70/1.15  ------ Parsing...
% 3.70/1.15  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.70/1.15  
% 3.70/1.15  ------ Preprocessing... sup_sim: 3  sf_s  rm: 1 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 3.70/1.15  
% 3.70/1.15  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.70/1.15  
% 3.70/1.15  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.70/1.15  ------ Proving...
% 3.70/1.15  ------ Problem Properties 
% 3.70/1.15  
% 3.70/1.15  
% 3.70/1.15  clauses                                 101
% 3.70/1.15  conjectures                             2
% 3.70/1.15  EPR                                     23
% 3.70/1.15  Horn                                    79
% 3.70/1.15  unary                                   26
% 3.70/1.15  binary                                  41
% 3.70/1.15  lits                                    214
% 3.70/1.15  lits eq                                 65
% 3.70/1.15  fd_pure                                 0
% 3.70/1.15  fd_pseudo                               0
% 3.70/1.15  fd_cond                                 3
% 3.70/1.15  fd_pseudo_cond                          26
% 3.70/1.15  AC symbols                              0
% 3.70/1.15  
% 3.70/1.15  ------ Schedule dynamic 5 is on 
% 3.70/1.15  
% 3.70/1.15  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.70/1.15  
% 3.70/1.15  
% 3.70/1.15  ------ 
% 3.70/1.15  Current options:
% 3.70/1.15  ------ 
% 3.70/1.15  
% 3.70/1.15  
% 3.70/1.15  
% 3.70/1.15  
% 3.70/1.15  ------ Proving...
% 3.70/1.15  
% 3.70/1.15  
% 3.70/1.15  % SZS status Theorem for theBenchmark.p
% 3.70/1.15  
% 3.70/1.15  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.70/1.15  
% 3.70/1.15  
%------------------------------------------------------------------------------