TSTP Solution File: PHI010+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : PHI010+1 : TPTP v8.1.2. Released v7.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n029.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 02:53:37 EDT 2024

% Result   : Theorem 0.43s 1.12s
% Output   : CNFRefutation 0.43s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   52 (  10 unt;   0 def)
%            Number of atoms       :  257 (  57 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  306 ( 101   ~;  89   |;  94   &)
%                                         (   6 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :  125 (   2 sgn  81   !;  20   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [X0,X1] :
      ( is_the(X0,X1)
     => ( object(X0)
        & property(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',description_is_property_and_described_is_object) ).

fof(f4,axiom,
    ! [X1,X0,X2] :
      ( ( object(X2)
        & object(X0)
        & property(X1) )
     => ( ( X0 = X2
          & is_the(X0,X1) )
      <=> ? [X3] :
            ( X2 = X3
            & ! [X4] :
                ( object(X4)
               => ( exemplifies_property(X1,X4)
                 => X3 = X4 ) )
            & exemplifies_property(X1,X3)
            & object(X3) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',description_axiom_identity_instance) ).

fof(f5,conjecture,
    ! [X0,X1,X3] :
      ( ( object(X3)
        & property(X1)
        & object(X0) )
     => ( ( X0 = X3
          & is_the(X0,X1) )
       => exemplifies_property(X1,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_1) ).

fof(f6,negated_conjecture,
    ~ ! [X0,X1,X3] :
        ( ( object(X3)
          & property(X1)
          & object(X0) )
       => ( ( X0 = X3
            & is_the(X0,X1) )
         => exemplifies_property(X1,X3) ) ),
    inference(negated_conjecture,[],[f5]) ).

fof(f7,plain,
    ! [X0,X1,X2] :
      ( ( object(X2)
        & object(X1)
        & property(X0) )
     => ( ( X1 = X2
          & is_the(X1,X0) )
      <=> ? [X3] :
            ( X2 = X3
            & ! [X4] :
                ( object(X4)
               => ( exemplifies_property(X0,X4)
                 => X3 = X4 ) )
            & exemplifies_property(X0,X3)
            & object(X3) ) ) ),
    inference(rectify,[],[f4]) ).

fof(f8,plain,
    ~ ! [X0,X1,X2] :
        ( ( object(X2)
          & property(X1)
          & object(X0) )
       => ( ( X0 = X2
            & is_the(X0,X1) )
         => exemplifies_property(X1,X2) ) ),
    inference(rectify,[],[f6]) ).

fof(f11,plain,
    ! [X0,X1] :
      ( ( object(X0)
        & property(X1) )
      | ~ is_the(X0,X1) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f12,plain,
    ! [X0,X1,X2] :
      ( ( ( X1 = X2
          & is_the(X1,X0) )
      <=> ? [X3] :
            ( X2 = X3
            & ! [X4] :
                ( X3 = X4
                | ~ exemplifies_property(X0,X4)
                | ~ object(X4) )
            & exemplifies_property(X0,X3)
            & object(X3) ) )
      | ~ object(X2)
      | ~ object(X1)
      | ~ property(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f13,plain,
    ! [X0,X1,X2] :
      ( ( ( X1 = X2
          & is_the(X1,X0) )
      <=> ? [X3] :
            ( X2 = X3
            & ! [X4] :
                ( X3 = X4
                | ~ exemplifies_property(X0,X4)
                | ~ object(X4) )
            & exemplifies_property(X0,X3)
            & object(X3) ) )
      | ~ object(X2)
      | ~ object(X1)
      | ~ property(X0) ),
    inference(flattening,[],[f12]) ).

fof(f14,plain,
    ? [X0,X1,X2] :
      ( ~ exemplifies_property(X1,X2)
      & X0 = X2
      & is_the(X0,X1)
      & object(X2)
      & property(X1)
      & object(X0) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f15,plain,
    ? [X0,X1,X2] :
      ( ~ exemplifies_property(X1,X2)
      & X0 = X2
      & is_the(X0,X1)
      & object(X2)
      & property(X1)
      & object(X0) ),
    inference(flattening,[],[f14]) ).

fof(f16,plain,
    ! [X2,X0] :
      ( sP0(X2,X0)
    <=> ? [X3] :
          ( X2 = X3
          & ! [X4] :
              ( X3 = X4
              | ~ exemplifies_property(X0,X4)
              | ~ object(X4) )
          & exemplifies_property(X0,X3)
          & object(X3) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f17,plain,
    ! [X0,X2,X1] :
      ( ( ( X1 = X2
          & is_the(X1,X0) )
      <=> sP0(X2,X0) )
      | ~ sP1(X0,X2,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f18,plain,
    ! [X0,X1,X2] :
      ( sP1(X0,X2,X1)
      | ~ object(X2)
      | ~ object(X1)
      | ~ property(X0) ),
    inference(definition_folding,[],[f13,f17,f16]) ).

fof(f19,plain,
    ! [X0,X2,X1] :
      ( ( ( ( X1 = X2
            & is_the(X1,X0) )
          | ~ sP0(X2,X0) )
        & ( sP0(X2,X0)
          | X1 != X2
          | ~ is_the(X1,X0) ) )
      | ~ sP1(X0,X2,X1) ),
    inference(nnf_transformation,[],[f17]) ).

fof(f20,plain,
    ! [X0,X2,X1] :
      ( ( ( ( X1 = X2
            & is_the(X1,X0) )
          | ~ sP0(X2,X0) )
        & ( sP0(X2,X0)
          | X1 != X2
          | ~ is_the(X1,X0) ) )
      | ~ sP1(X0,X2,X1) ),
    inference(flattening,[],[f19]) ).

fof(f21,plain,
    ! [X0,X1,X2] :
      ( ( ( ( X1 = X2
            & is_the(X2,X0) )
          | ~ sP0(X1,X0) )
        & ( sP0(X1,X0)
          | X1 != X2
          | ~ is_the(X2,X0) ) )
      | ~ sP1(X0,X1,X2) ),
    inference(rectify,[],[f20]) ).

fof(f22,plain,
    ! [X2,X0] :
      ( ( sP0(X2,X0)
        | ! [X3] :
            ( X2 != X3
            | ? [X4] :
                ( X3 != X4
                & exemplifies_property(X0,X4)
                & object(X4) )
            | ~ exemplifies_property(X0,X3)
            | ~ object(X3) ) )
      & ( ? [X3] :
            ( X2 = X3
            & ! [X4] :
                ( X3 = X4
                | ~ exemplifies_property(X0,X4)
                | ~ object(X4) )
            & exemplifies_property(X0,X3)
            & object(X3) )
        | ~ sP0(X2,X0) ) ),
    inference(nnf_transformation,[],[f16]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ! [X2] :
            ( X0 != X2
            | ? [X3] :
                ( X2 != X3
                & exemplifies_property(X1,X3)
                & object(X3) )
            | ~ exemplifies_property(X1,X2)
            | ~ object(X2) ) )
      & ( ? [X4] :
            ( X0 = X4
            & ! [X5] :
                ( X4 = X5
                | ~ exemplifies_property(X1,X5)
                | ~ object(X5) )
            & exemplifies_property(X1,X4)
            & object(X4) )
        | ~ sP0(X0,X1) ) ),
    inference(rectify,[],[f22]) ).

fof(f24,plain,
    ! [X1,X2] :
      ( ? [X3] :
          ( X2 != X3
          & exemplifies_property(X1,X3)
          & object(X3) )
     => ( sK2(X1,X2) != X2
        & exemplifies_property(X1,sK2(X1,X2))
        & object(sK2(X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( X0 = X4
          & ! [X5] :
              ( X4 = X5
              | ~ exemplifies_property(X1,X5)
              | ~ object(X5) )
          & exemplifies_property(X1,X4)
          & object(X4) )
     => ( sK3(X0,X1) = X0
        & ! [X5] :
            ( sK3(X0,X1) = X5
            | ~ exemplifies_property(X1,X5)
            | ~ object(X5) )
        & exemplifies_property(X1,sK3(X0,X1))
        & object(sK3(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ! [X2] :
            ( X0 != X2
            | ( sK2(X1,X2) != X2
              & exemplifies_property(X1,sK2(X1,X2))
              & object(sK2(X1,X2)) )
            | ~ exemplifies_property(X1,X2)
            | ~ object(X2) ) )
      & ( ( sK3(X0,X1) = X0
          & ! [X5] :
              ( sK3(X0,X1) = X5
              | ~ exemplifies_property(X1,X5)
              | ~ object(X5) )
          & exemplifies_property(X1,sK3(X0,X1))
          & object(sK3(X0,X1)) )
        | ~ sP0(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f23,f25,f24]) ).

fof(f27,plain,
    ( ? [X0,X1,X2] :
        ( ~ exemplifies_property(X1,X2)
        & X0 = X2
        & is_the(X0,X1)
        & object(X2)
        & property(X1)
        & object(X0) )
   => ( ~ exemplifies_property(sK5,sK6)
      & sK4 = sK6
      & is_the(sK4,sK5)
      & object(sK6)
      & property(sK5)
      & object(sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f28,plain,
    ( ~ exemplifies_property(sK5,sK6)
    & sK4 = sK6
    & is_the(sK4,sK5)
    & object(sK6)
    & property(sK5)
    & object(sK4) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f15,f27]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( property(X1)
      | ~ is_the(X0,X1) ),
    inference(cnf_transformation,[],[f11]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( object(X0)
      | ~ is_the(X0,X1) ),
    inference(cnf_transformation,[],[f11]) ).

fof(f34,plain,
    ! [X2,X0,X1] :
      ( sP0(X1,X0)
      | X1 != X2
      | ~ is_the(X2,X0)
      | ~ sP1(X0,X1,X2) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( exemplifies_property(X1,sK3(X0,X1))
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( sK3(X0,X1) = X0
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f44,plain,
    ! [X2,X0,X1] :
      ( sP1(X0,X2,X1)
      | ~ object(X2)
      | ~ object(X1)
      | ~ property(X0) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f48,plain,
    is_the(sK4,sK5),
    inference(cnf_transformation,[],[f28]) ).

fof(f49,plain,
    sK4 = sK6,
    inference(cnf_transformation,[],[f28]) ).

fof(f50,plain,
    ~ exemplifies_property(sK5,sK6),
    inference(cnf_transformation,[],[f28]) ).

fof(f51,plain,
    is_the(sK6,sK5),
    inference(definition_unfolding,[],[f48,f49]) ).

fof(f53,plain,
    ! [X2,X0] :
      ( sP0(X2,X0)
      | ~ is_the(X2,X0)
      | ~ sP1(X0,X2,X2) ),
    inference(equality_resolution,[],[f34]) ).

cnf(c_52,plain,
    ( ~ is_the(X0,X1)
    | object(X0) ),
    inference(cnf_transformation,[],[f33]) ).

cnf(c_53,plain,
    ( ~ is_the(X0,X1)
    | property(X1) ),
    inference(cnf_transformation,[],[f32]) ).

cnf(c_56,plain,
    ( ~ sP1(X0,X1,X1)
    | ~ is_the(X1,X0)
    | sP0(X1,X0) ),
    inference(cnf_transformation,[],[f53]) ).

cnf(c_60,plain,
    ( ~ sP0(X0,X1)
    | sK3(X0,X1) = X0 ),
    inference(cnf_transformation,[],[f40]) ).

cnf(c_62,plain,
    ( ~ sP0(X0,X1)
    | exemplifies_property(X1,sK3(X0,X1)) ),
    inference(cnf_transformation,[],[f38]) ).

cnf(c_64,plain,
    ( ~ property(X0)
    | ~ object(X1)
    | ~ object(X2)
    | sP1(X0,X2,X1) ),
    inference(cnf_transformation,[],[f44]) ).

cnf(c_65,negated_conjecture,
    ~ exemplifies_property(sK5,sK6),
    inference(cnf_transformation,[],[f50]) ).

cnf(c_66,negated_conjecture,
    is_the(sK6,sK5),
    inference(cnf_transformation,[],[f51]) ).

cnf(c_366,plain,
    ( X0 != X1
    | X2 != X3
    | X2 != X4
    | ~ is_the(X2,X0)
    | ~ property(X1)
    | ~ object(X3)
    | ~ object(X4)
    | sP0(X2,X0) ),
    inference(resolution_lifted,[status(thm)],[c_56,c_64]) ).

cnf(c_367,plain,
    ( ~ is_the(X0,X1)
    | ~ property(X1)
    | ~ object(X0)
    | sP0(X0,X1) ),
    inference(unflattening,[status(thm)],[c_366]) ).

cnf(c_369,plain,
    ( ~ is_the(X0,X1)
    | sP0(X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_367,c_53,c_52,c_367]) ).

cnf(c_390,plain,
    ( X0 != sK6
    | X1 != sK5
    | sP0(X0,X1) ),
    inference(resolution_lifted,[status(thm)],[c_369,c_66]) ).

cnf(c_391,plain,
    sP0(sK6,sK5),
    inference(unflattening,[status(thm)],[c_390]) ).

cnf(c_771,negated_conjecture,
    ~ exemplifies_property(sK5,sK6),
    inference(demodulation,[status(thm)],[c_65]) ).

cnf(c_1041,plain,
    sK3(sK6,sK5) = sK6,
    inference(superposition,[status(thm)],[c_391,c_60]) ).

cnf(c_1058,plain,
    ( ~ sP0(sK6,sK5)
    | exemplifies_property(sK5,sK6) ),
    inference(superposition,[status(thm)],[c_1041,c_62]) ).

cnf(c_1060,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_1058,c_771,c_391]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.10  % Problem  : PHI010+1 : TPTP v8.1.2. Released v7.2.0.
% 0.10/0.11  % Command  : run_iprover %s %d THM
% 0.11/0.31  % Computer : n029.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Thu May  2 22:01:07 EDT 2024
% 0.16/0.31  % CPUTime  : 
% 0.16/0.42  Running first-order theorem proving
% 0.16/0.42  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.43/1.12  % SZS status Started for theBenchmark.p
% 0.43/1.12  % SZS status Theorem for theBenchmark.p
% 0.43/1.12  
% 0.43/1.12  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 0.43/1.12  
% 0.43/1.12  ------  iProver source info
% 0.43/1.12  
% 0.43/1.12  git: date: 2024-05-02 19:28:25 +0000
% 0.43/1.12  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 0.43/1.12  git: non_committed_changes: false
% 0.43/1.12  
% 0.43/1.12  ------ Parsing...
% 0.43/1.12  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 0.43/1.12  
% 0.43/1.12  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e 
% 0.43/1.12  
% 0.43/1.12  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 0.43/1.12  
% 0.43/1.12  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 0.43/1.12  ------ Proving...
% 0.43/1.12  ------ Problem Properties 
% 0.43/1.12  
% 0.43/1.12  
% 0.43/1.12  clauses                                 16
% 0.43/1.12  conjectures                             3
% 0.43/1.12  EPR                                     9
% 0.43/1.12  Horn                                    14
% 0.43/1.12  unary                                   4
% 0.43/1.12  binary                                  6
% 0.43/1.12  lits                                    38
% 0.43/1.12  lits eq                                 4
% 0.43/1.12  fd_pure                                 0
% 0.43/1.12  fd_pseudo                               0
% 0.43/1.12  fd_cond                                 0
% 0.43/1.12  fd_pseudo_cond                          2
% 0.43/1.12  AC symbols                              0
% 0.43/1.12  
% 0.43/1.12  ------ Schedule dynamic 5 is on 
% 0.43/1.12  
% 0.43/1.12  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.43/1.12  
% 0.43/1.12  
% 0.43/1.12  ------ 
% 0.43/1.12  Current options:
% 0.43/1.12  ------ 
% 0.43/1.12  
% 0.43/1.12  
% 0.43/1.12  
% 0.43/1.12  
% 0.43/1.12  ------ Proving...
% 0.43/1.12  
% 0.43/1.12  
% 0.43/1.12  % SZS status Theorem for theBenchmark.p
% 0.43/1.12  
% 0.43/1.12  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.43/1.12  
% 0.43/1.12  
%------------------------------------------------------------------------------