TSTP Solution File: SYN078+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SYN078+1 : TPTP v8.1.2. Released v2.0.0.
% 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 03:29:10 EDT 2024

% Result   : Theorem 2.02s 1.17s
% Output   : CNFRefutation 2.02s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,conjecture,
    ( ! [X0] :
        ( ? [X1] :
            ( f(X1) = X0
            & big_p(X1) )
       => big_p(X0) )
  <=> ! [X2] :
        ( big_p(X2)
       => big_p(f(X2)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel56) ).

fof(f2,negated_conjecture,
    ~ ( ! [X0] :
          ( ? [X1] :
              ( f(X1) = X0
              & big_p(X1) )
         => big_p(X0) )
    <=> ! [X2] :
          ( big_p(X2)
         => big_p(f(X2)) ) ),
    inference(negated_conjecture,[],[f1]) ).

fof(f3,plain,
    ( ! [X0] :
        ( big_p(X0)
        | ! [X1] :
            ( f(X1) != X0
            | ~ big_p(X1) ) )
  <~> ! [X2] :
        ( big_p(f(X2))
        | ~ big_p(X2) ) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f4,plain,
    ( ( ? [X2] :
          ( ~ big_p(f(X2))
          & big_p(X2) )
      | ? [X0] :
          ( ~ big_p(X0)
          & ? [X1] :
              ( f(X1) = X0
              & big_p(X1) ) ) )
    & ( ! [X2] :
          ( big_p(f(X2))
          | ~ big_p(X2) )
      | ! [X0] :
          ( big_p(X0)
          | ! [X1] :
              ( f(X1) != X0
              | ~ big_p(X1) ) ) ) ),
    inference(nnf_transformation,[],[f3]) ).

fof(f5,plain,
    ( ( ? [X0] :
          ( ~ big_p(f(X0))
          & big_p(X0) )
      | ? [X1] :
          ( ~ big_p(X1)
          & ? [X2] :
              ( f(X2) = X1
              & big_p(X2) ) ) )
    & ( ! [X3] :
          ( big_p(f(X3))
          | ~ big_p(X3) )
      | ! [X4] :
          ( big_p(X4)
          | ! [X5] :
              ( f(X5) != X4
              | ~ big_p(X5) ) ) ) ),
    inference(rectify,[],[f4]) ).

fof(f6,plain,
    ( ? [X0] :
        ( ~ big_p(f(X0))
        & big_p(X0) )
   => ( ~ big_p(f(sK0))
      & big_p(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f7,plain,
    ( ? [X1] :
        ( ~ big_p(X1)
        & ? [X2] :
            ( f(X2) = X1
            & big_p(X2) ) )
   => ( ~ big_p(sK1)
      & ? [X2] :
          ( f(X2) = sK1
          & big_p(X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f8,plain,
    ( ? [X2] :
        ( f(X2) = sK1
        & big_p(X2) )
   => ( sK1 = f(sK2)
      & big_p(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f9,plain,
    ( ( ( ~ big_p(f(sK0))
        & big_p(sK0) )
      | ( ~ big_p(sK1)
        & sK1 = f(sK2)
        & big_p(sK2) ) )
    & ( ! [X3] :
          ( big_p(f(X3))
          | ~ big_p(X3) )
      | ! [X4] :
          ( big_p(X4)
          | ! [X5] :
              ( f(X5) != X4
              | ~ big_p(X5) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f5,f8,f7,f6]) ).

fof(f10,plain,
    ! [X3,X4,X5] :
      ( big_p(f(X3))
      | ~ big_p(X3)
      | big_p(X4)
      | f(X5) != X4
      | ~ big_p(X5) ),
    inference(cnf_transformation,[],[f9]) ).

fof(f11,plain,
    ( big_p(sK0)
    | big_p(sK2) ),
    inference(cnf_transformation,[],[f9]) ).

fof(f12,plain,
    ( big_p(sK0)
    | sK1 = f(sK2) ),
    inference(cnf_transformation,[],[f9]) ).

fof(f13,plain,
    ( big_p(sK0)
    | ~ big_p(sK1) ),
    inference(cnf_transformation,[],[f9]) ).

fof(f14,plain,
    ( ~ big_p(f(sK0))
    | big_p(sK2) ),
    inference(cnf_transformation,[],[f9]) ).

fof(f15,plain,
    ( ~ big_p(f(sK0))
    | sK1 = f(sK2) ),
    inference(cnf_transformation,[],[f9]) ).

fof(f16,plain,
    ( ~ big_p(f(sK0))
    | ~ big_p(sK1) ),
    inference(cnf_transformation,[],[f9]) ).

fof(f17,plain,
    ! [X3,X5] :
      ( big_p(f(X3))
      | ~ big_p(X3)
      | big_p(f(X5))
      | ~ big_p(X5) ),
    inference(equality_resolution,[],[f10]) ).

cnf(c_49,negated_conjecture,
    ( ~ big_p(f(sK0))
    | ~ big_p(sK1) ),
    inference(cnf_transformation,[],[f16]) ).

cnf(c_50,negated_conjecture,
    ( ~ big_p(f(sK0))
    | f(sK2) = sK1 ),
    inference(cnf_transformation,[],[f15]) ).

cnf(c_51,negated_conjecture,
    ( ~ big_p(f(sK0))
    | big_p(sK2) ),
    inference(cnf_transformation,[],[f14]) ).

cnf(c_52,negated_conjecture,
    ( ~ big_p(sK1)
    | big_p(sK0) ),
    inference(cnf_transformation,[],[f13]) ).

cnf(c_53,negated_conjecture,
    ( f(sK2) = sK1
    | big_p(sK0) ),
    inference(cnf_transformation,[],[f12]) ).

cnf(c_54,negated_conjecture,
    ( big_p(sK0)
    | big_p(sK2) ),
    inference(cnf_transformation,[],[f11]) ).

cnf(c_55,negated_conjecture,
    ( ~ big_p(X0)
    | ~ big_p(X1)
    | big_p(f(X0))
    | big_p(f(X1)) ),
    inference(cnf_transformation,[],[f17]) ).

cnf(c_56,plain,
    ( ~ big_p(sK0)
    | big_p(f(sK0)) ),
    inference(instantiation,[status(thm)],[c_55]) ).

cnf(c_57,negated_conjecture,
    big_p(sK2),
    inference(global_subsumption_just,[status(thm)],[c_54,c_54,c_51,c_56]) ).

cnf(c_59,negated_conjecture,
    ~ big_p(sK1),
    inference(global_subsumption_just,[status(thm)],[c_52,c_52,c_49,c_56]) ).

cnf(c_61,negated_conjecture,
    big_p(sK2),
    inference(global_subsumption_just,[status(thm)],[c_51,c_57]) ).

cnf(c_63,negated_conjecture,
    f(sK2) = sK1,
    inference(global_subsumption_just,[status(thm)],[c_53,c_53,c_50,c_56]) ).

cnf(c_65,negated_conjecture,
    ~ big_p(sK1),
    inference(global_subsumption_just,[status(thm)],[c_49,c_59]) ).

cnf(c_67,negated_conjecture,
    f(sK2) = sK1,
    inference(global_subsumption_just,[status(thm)],[c_50,c_63]) ).

cnf(c_115,negated_conjecture,
    ( ~ big_p(X0)
    | big_p(f(X0))
    | ~ sP0_iProver_def ),
    inference(splitting,[splitting(split),new_symbols(definition,[sP0_iProver_def])],[c_55]) ).

cnf(c_116,negated_conjecture,
    sP0_iProver_def,
    inference(splitting,[splitting(split),new_symbols(definition,[])],[c_55]) ).

cnf(c_117,plain,
    f(sK2) = sP1_iProver_def,
    definition ).

cnf(c_118,negated_conjecture,
    sP1_iProver_def = sK1,
    inference(demodulation,[status(thm)],[c_67,c_117]) ).

cnf(c_119,negated_conjecture,
    ~ big_p(sK1),
    inference(demodulation,[status(thm)],[c_65]) ).

cnf(c_120,negated_conjecture,
    big_p(sK2),
    inference(demodulation,[status(thm)],[c_61]) ).

cnf(c_121,negated_conjecture,
    sP0_iProver_def,
    inference(demodulation,[status(thm)],[c_116]) ).

cnf(c_122,negated_conjecture,
    ( ~ big_p(X0)
    | ~ sP0_iProver_def
    | big_p(f(X0)) ),
    inference(demodulation,[status(thm)],[c_115]) ).

cnf(c_198,plain,
    ~ big_p(sP1_iProver_def),
    inference(light_normalisation,[status(thm)],[c_119,c_118]) ).

cnf(c_199,negated_conjecture,
    ( ~ big_p(X0)
    | big_p(f(X0)) ),
    inference(global_subsumption_just,[status(thm)],[c_122,c_121,c_122]) ).

cnf(c_203,plain,
    ( ~ big_p(sK2)
    | big_p(sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_117,c_199]) ).

cnf(c_204,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_203,c_198,c_120]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SYN078+1 : TPTP v8.1.2. Released v2.0.0.
% 0.12/0.13  % Command  : run_iprover %s %d THM
% 0.14/0.34  % Computer : n014.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 20:34:32 EDT 2024
% 0.14/0.34  % 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
% 2.02/1.17  % SZS status Started for theBenchmark.p
% 2.02/1.17  % SZS status Theorem for theBenchmark.p
% 2.02/1.17  
% 2.02/1.17  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 2.02/1.17  
% 2.02/1.17  ------  iProver source info
% 2.02/1.17  
% 2.02/1.17  git: date: 2024-05-02 19:28:25 +0000
% 2.02/1.17  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 2.02/1.17  git: non_committed_changes: false
% 2.02/1.17  
% 2.02/1.17  ------ Parsing...
% 2.02/1.17  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 2.02/1.17  
% 2.02/1.17  ------ Preprocessing... sup_sim: 0  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 
% 2.02/1.17  
% 2.02/1.17  ------ Preprocessing... gs_s  sp: 2 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 2.02/1.17  
% 2.02/1.17  ------ Preprocessing... sf_s  rm: 2 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.02/1.17  ------ Proving...
% 2.02/1.17  ------ Problem Properties 
% 2.02/1.17  
% 2.02/1.17  
% 2.02/1.17  clauses                                 6
% 2.02/1.17  conjectures                             5
% 2.02/1.17  EPR                                     4
% 2.02/1.17  Horn                                    6
% 2.02/1.17  unary                                   5
% 2.02/1.17  binary                                  0
% 2.02/1.17  lits                                    8
% 2.02/1.17  lits eq                                 2
% 2.02/1.17  fd_pure                                 0
% 2.02/1.17  fd_pseudo                               0
% 2.02/1.17  fd_cond                                 0
% 2.02/1.17  fd_pseudo_cond                          0
% 2.02/1.17  AC symbols                              0
% 2.02/1.17  
% 2.02/1.17  ------ Schedule dynamic 5 is on 
% 2.02/1.17  
% 2.02/1.17  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.02/1.17  
% 2.02/1.17  
% 2.02/1.17  ------ 
% 2.02/1.17  Current options:
% 2.02/1.17  ------ 
% 2.02/1.17  
% 2.02/1.17  
% 2.02/1.17  
% 2.02/1.17  
% 2.02/1.17  ------ Proving...
% 2.02/1.17  
% 2.02/1.17  
% 2.02/1.17  % SZS status Theorem for theBenchmark.p
% 2.02/1.17  
% 2.02/1.17  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.02/1.17  
% 2.02/1.17  
%------------------------------------------------------------------------------