TSTP Solution File: SET803+4 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET803+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n016.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 03:01:35 EDT 2024

% Result   : Theorem 1.83s 1.13s
% Output   : CNFRefutation 1.83s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   52 (  14 unt;   0 def)
%            Number of atoms       :  172 (  45 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  193 (  73   ~;  55   |;  44   &)
%                                         (   4 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :  127 (   5 sgn  62   !;  26   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f5,axiom,
    ! [X0,X1,X5] :
      ( greatest(X5,X0,X1)
    <=> ( ! [X2] :
            ( member(X2,X1)
           => apply(X0,X2,X5) )
        & member(X5,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',greatest) ).

fof(f7,axiom,
    ! [X0,X1,X5] :
      ( max(X5,X0,X1)
    <=> ( ! [X2] :
            ( ( apply(X0,X5,X2)
              & member(X2,X1) )
           => X2 = X5 )
        & member(X5,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',max) ).

fof(f11,conjecture,
    ! [X0,X1] :
      ( order(X0,X1)
     => ! [X7,X8] :
          ( ( X7 != X8
            & max(X8,X0,X1)
            & max(X7,X0,X1) )
         => ~ ? [X5] : greatest(X5,X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV15) ).

fof(f12,negated_conjecture,
    ~ ! [X0,X1] :
        ( order(X0,X1)
       => ! [X7,X8] :
            ( ( X7 != X8
              & max(X8,X0,X1)
              & max(X7,X0,X1) )
           => ~ ? [X5] : greatest(X5,X0,X1) ) ),
    inference(negated_conjecture,[],[f11]) ).

fof(f16,plain,
    ! [X0,X1,X2] :
      ( greatest(X2,X0,X1)
    <=> ( ! [X3] :
            ( member(X3,X1)
           => apply(X0,X3,X2) )
        & member(X2,X1) ) ),
    inference(rectify,[],[f5]) ).

fof(f18,plain,
    ! [X0,X1,X2] :
      ( max(X2,X0,X1)
    <=> ( ! [X3] :
            ( ( apply(X0,X2,X3)
              & member(X3,X1) )
           => X2 = X3 )
        & member(X2,X1) ) ),
    inference(rectify,[],[f7]) ).

fof(f22,plain,
    ~ ! [X0,X1] :
        ( order(X0,X1)
       => ! [X2,X3] :
            ( ( X2 != X3
              & max(X3,X0,X1)
              & max(X2,X0,X1) )
           => ~ ? [X4] : greatest(X4,X0,X1) ) ),
    inference(rectify,[],[f12]) ).

fof(f23,plain,
    ! [X0,X1,X2] :
      ( max(X2,X0,X1)
     => ( ! [X3] :
            ( ( apply(X0,X2,X3)
              & member(X3,X1) )
           => X2 = X3 )
        & member(X2,X1) ) ),
    inference(unused_predicate_definition_removal,[],[f18]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( greatest(X2,X0,X1)
     => ( ! [X3] :
            ( member(X3,X1)
           => apply(X0,X3,X2) )
        & member(X2,X1) ) ),
    inference(unused_predicate_definition_removal,[],[f16]) ).

fof(f28,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( apply(X0,X3,X2)
            | ~ member(X3,X1) )
        & member(X2,X1) )
      | ~ greatest(X2,X0,X1) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( X2 = X3
            | ~ apply(X0,X2,X3)
            | ~ member(X3,X1) )
        & member(X2,X1) )
      | ~ max(X2,X0,X1) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f30,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( X2 = X3
            | ~ apply(X0,X2,X3)
            | ~ member(X3,X1) )
        & member(X2,X1) )
      | ~ max(X2,X0,X1) ),
    inference(flattening,[],[f29]) ).

fof(f31,plain,
    ? [X0,X1] :
      ( ? [X2,X3] :
          ( ? [X4] : greatest(X4,X0,X1)
          & X2 != X3
          & max(X3,X0,X1)
          & max(X2,X0,X1) )
      & order(X0,X1) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f32,plain,
    ? [X0,X1] :
      ( ? [X2,X3] :
          ( ? [X4] : greatest(X4,X0,X1)
          & X2 != X3
          & max(X3,X0,X1)
          & max(X2,X0,X1) )
      & order(X0,X1) ),
    inference(flattening,[],[f31]) ).

fof(f33,plain,
    ( ? [X0,X1] :
        ( ? [X2,X3] :
            ( ? [X4] : greatest(X4,X0,X1)
            & X2 != X3
            & max(X3,X0,X1)
            & max(X2,X0,X1) )
        & order(X0,X1) )
   => ( ? [X3,X2] :
          ( ? [X4] : greatest(X4,sK0,sK1)
          & X2 != X3
          & max(X3,sK0,sK1)
          & max(X2,sK0,sK1) )
      & order(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f34,plain,
    ( ? [X3,X2] :
        ( ? [X4] : greatest(X4,sK0,sK1)
        & X2 != X3
        & max(X3,sK0,sK1)
        & max(X2,sK0,sK1) )
   => ( ? [X4] : greatest(X4,sK0,sK1)
      & sK2 != sK3
      & max(sK3,sK0,sK1)
      & max(sK2,sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f35,plain,
    ( ? [X4] : greatest(X4,sK0,sK1)
   => greatest(sK4,sK0,sK1) ),
    introduced(choice_axiom,[]) ).

fof(f36,plain,
    ( greatest(sK4,sK0,sK1)
    & sK2 != sK3
    & max(sK3,sK0,sK1)
    & max(sK2,sK0,sK1)
    & order(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f32,f35,f34,f33]) ).

fof(f40,plain,
    ! [X2,X0,X1] :
      ( member(X2,X1)
      | ~ greatest(X2,X0,X1) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f41,plain,
    ! [X2,X3,X0,X1] :
      ( apply(X0,X3,X2)
      | ~ member(X3,X1)
      | ~ greatest(X2,X0,X1) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f42,plain,
    ! [X2,X0,X1] :
      ( member(X2,X1)
      | ~ max(X2,X0,X1) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f43,plain,
    ! [X2,X3,X0,X1] :
      ( X2 = X3
      | ~ apply(X0,X2,X3)
      | ~ member(X3,X1)
      | ~ max(X2,X0,X1) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f45,plain,
    max(sK2,sK0,sK1),
    inference(cnf_transformation,[],[f36]) ).

fof(f46,plain,
    max(sK3,sK0,sK1),
    inference(cnf_transformation,[],[f36]) ).

fof(f47,plain,
    sK2 != sK3,
    inference(cnf_transformation,[],[f36]) ).

fof(f48,plain,
    greatest(sK4,sK0,sK1),
    inference(cnf_transformation,[],[f36]) ).

cnf(c_52,plain,
    ( ~ greatest(X0,X1,X2)
    | ~ member(X3,X2)
    | apply(X1,X3,X0) ),
    inference(cnf_transformation,[],[f41]) ).

cnf(c_53,plain,
    ( ~ greatest(X0,X1,X2)
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f40]) ).

cnf(c_54,plain,
    ( ~ apply(X0,X1,X2)
    | ~ max(X1,X0,X3)
    | ~ member(X2,X3)
    | X1 = X2 ),
    inference(cnf_transformation,[],[f43]) ).

cnf(c_55,plain,
    ( ~ max(X0,X1,X2)
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f42]) ).

cnf(c_56,negated_conjecture,
    greatest(sK4,sK0,sK1),
    inference(cnf_transformation,[],[f48]) ).

cnf(c_57,negated_conjecture,
    sK2 != sK3,
    inference(cnf_transformation,[],[f47]) ).

cnf(c_58,negated_conjecture,
    max(sK3,sK0,sK1),
    inference(cnf_transformation,[],[f46]) ).

cnf(c_59,negated_conjecture,
    max(sK2,sK0,sK1),
    inference(cnf_transformation,[],[f45]) ).

cnf(c_189,plain,
    ( X0 != sK4
    | X1 != sK0
    | X2 != sK1
    | member(X0,X2) ),
    inference(resolution_lifted,[status(thm)],[c_53,c_56]) ).

cnf(c_190,plain,
    member(sK4,sK1),
    inference(unflattening,[status(thm)],[c_189]) ).

cnf(c_194,plain,
    ( X0 != sK4
    | X1 != sK0
    | X2 != sK1
    | ~ member(X3,X2)
    | apply(X1,X3,X0) ),
    inference(resolution_lifted,[status(thm)],[c_52,c_56]) ).

cnf(c_195,plain,
    ( ~ member(X0,sK1)
    | apply(sK0,X0,sK4) ),
    inference(unflattening,[status(thm)],[c_194]) ).

cnf(c_206,plain,
    ( X0 != sK0
    | X1 != sK3
    | X2 != sK1
    | ~ apply(X0,X1,X3)
    | ~ member(X3,X2)
    | X1 = X3 ),
    inference(resolution_lifted,[status(thm)],[c_54,c_58]) ).

cnf(c_207,plain,
    ( ~ apply(sK0,sK3,X0)
    | ~ member(X0,sK1)
    | sK3 = X0 ),
    inference(unflattening,[status(thm)],[c_206]) ).

cnf(c_218,plain,
    ( X0 != sK0
    | X1 != sK2
    | X2 != sK1
    | ~ apply(X0,X1,X3)
    | ~ member(X3,X2)
    | X1 = X3 ),
    inference(resolution_lifted,[status(thm)],[c_54,c_59]) ).

cnf(c_219,plain,
    ( ~ apply(sK0,sK2,X0)
    | ~ member(X0,sK1)
    | sK2 = X0 ),
    inference(unflattening,[status(thm)],[c_218]) ).

cnf(c_230,plain,
    ( X0 != sK3
    | X1 != sK0
    | X2 != sK1
    | member(X0,X2) ),
    inference(resolution_lifted,[status(thm)],[c_55,c_58]) ).

cnf(c_231,plain,
    member(sK3,sK1),
    inference(unflattening,[status(thm)],[c_230]) ).

cnf(c_235,plain,
    ( X0 != sK2
    | X1 != sK0
    | X2 != sK1
    | member(X0,X2) ),
    inference(resolution_lifted,[status(thm)],[c_55,c_59]) ).

cnf(c_236,plain,
    member(sK2,sK1),
    inference(unflattening,[status(thm)],[c_235]) ).

cnf(c_403,negated_conjecture,
    sK2 != sK3,
    inference(demodulation,[status(thm)],[c_57]) ).

cnf(c_577,plain,
    ( ~ member(sK4,sK1)
    | ~ member(sK3,sK1)
    | sK4 = sK3 ),
    inference(superposition,[status(thm)],[c_195,c_207]) ).

cnf(c_579,plain,
    sK4 = sK3,
    inference(forward_subsumption_resolution,[status(thm)],[c_577,c_231,c_190]) ).

cnf(c_580,plain,
    ( ~ member(X0,sK1)
    | apply(sK0,X0,sK3) ),
    inference(demodulation,[status(thm)],[c_195,c_579]) ).

cnf(c_621,plain,
    ( ~ member(sK2,sK1)
    | ~ member(sK3,sK1)
    | sK2 = sK3 ),
    inference(superposition,[status(thm)],[c_580,c_219]) ).

cnf(c_624,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_621,c_403,c_231,c_236]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11  % Problem  : SET803+4 : TPTP v8.1.2. Released v3.2.0.
% 0.05/0.12  % Command  : run_iprover %s %d THM
% 0.11/0.33  % Computer : n016.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Thu May  2 21:13:15 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 0.17/0.45  Running first-order theorem proving
% 0.17/0.45  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
% 1.83/1.13  % SZS status Started for theBenchmark.p
% 1.83/1.13  % SZS status Theorem for theBenchmark.p
% 1.83/1.13  
% 1.83/1.13  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 1.83/1.13  
% 1.83/1.13  ------  iProver source info
% 1.83/1.13  
% 1.83/1.13  git: date: 2024-05-02 19:28:25 +0000
% 1.83/1.13  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 1.83/1.13  git: non_committed_changes: false
% 1.83/1.13  
% 1.83/1.13  ------ Parsing...
% 1.83/1.13  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 1.83/1.13  
% 1.83/1.13  ------ 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: 4 0s  sf_e  pe_s  pe_e 
% 1.83/1.13  
% 1.83/1.13  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 1.83/1.13  
% 1.83/1.13  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 1.83/1.13  ------ Proving...
% 1.83/1.13  ------ Problem Properties 
% 1.83/1.13  
% 1.83/1.13  
% 1.83/1.13  clauses                                 10
% 1.83/1.13  conjectures                             1
% 1.83/1.13  EPR                                     10
% 1.83/1.13  Horn                                    10
% 1.83/1.13  unary                                   4
% 1.83/1.13  binary                                  2
% 1.83/1.13  lits                                    25
% 1.83/1.13  lits eq                                 4
% 1.83/1.13  fd_pure                                 0
% 1.83/1.13  fd_pseudo                               0
% 1.83/1.13  fd_cond                                 2
% 1.83/1.13  fd_pseudo_cond                          1
% 1.83/1.13  AC symbols                              0
% 1.83/1.13  
% 1.83/1.13  ------ Schedule dynamic 5 is on 
% 1.83/1.13  
% 1.83/1.13  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.83/1.13  
% 1.83/1.13  
% 1.83/1.13  ------ 
% 1.83/1.13  Current options:
% 1.83/1.13  ------ 
% 1.83/1.13  
% 1.83/1.13  
% 1.83/1.13  
% 1.83/1.13  
% 1.83/1.13  ------ Proving...
% 1.83/1.13  
% 1.83/1.13  
% 1.83/1.13  % SZS status Theorem for theBenchmark.p
% 1.83/1.13  
% 1.83/1.13  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.83/1.13  
% 1.83/1.13  
%------------------------------------------------------------------------------