TSTP Solution File: SEU321+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SEU321+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n028.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 03:05:28 EDT 2024

% Result   : Theorem 2.78s 1.12s
% Output   : CNFRefutation 2.78s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% Comments : 
%------------------------------------------------------------------------------
fof(f33,axiom,
    ! [X0] :
      ( ( one_sorted_str(X0)
        & ~ empty_carrier(X0) )
     => ~ empty(the_carrier(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).

fof(f34,axiom,
    ( v5_membered(empty_set)
    & v4_membered(empty_set)
    & v3_membered(empty_set)
    & v2_membered(empty_set)
    & v1_membered(empty_set)
    & empty(empty_set) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_membered) ).

fof(f40,conjecture,
    ! [X0] :
      ( ( one_sorted_str(X0)
        & ~ empty_carrier(X0) )
     => ! [X1] :
          ( element(X1,powerset(the_carrier(X0)))
         => ! [X2] :
              ( element(X2,the_carrier(X0))
             => ( in(X2,subset_complement(the_carrier(X0),X1))
              <=> ~ in(X2,X1) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l40_tops_1) ).

fof(f41,negated_conjecture,
    ~ ! [X0] :
        ( ( one_sorted_str(X0)
          & ~ empty_carrier(X0) )
       => ! [X1] :
            ( element(X1,powerset(the_carrier(X0)))
           => ! [X2] :
                ( element(X2,the_carrier(X0))
               => ( in(X2,subset_complement(the_carrier(X0),X1))
                <=> ~ in(X2,X1) ) ) ) ),
    inference(negated_conjecture,[],[f40]) ).

fof(f42,axiom,
    ! [X0] :
      ( empty_set != X0
     => ! [X1] :
          ( element(X1,powerset(X0))
         => ! [X2] :
              ( element(X2,X0)
             => ( ~ in(X2,X1)
               => in(X2,subset_complement(X0,X1)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_subset_1) ).

fof(f43,axiom,
    ! [X0,X1,X2] :
      ( element(X2,powerset(X0))
     => ~ ( in(X1,X2)
          & in(X1,subset_complement(X0,X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_subset_1) ).

fof(f80,plain,
    ! [X0] :
      ( ~ empty(the_carrier(X0))
      | ~ one_sorted_str(X0)
      | empty_carrier(X0) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f81,plain,
    ! [X0] :
      ( ~ empty(the_carrier(X0))
      | ~ one_sorted_str(X0)
      | empty_carrier(X0) ),
    inference(flattening,[],[f80]) ).

fof(f88,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ( in(X2,subset_complement(the_carrier(X0),X1))
              <~> ~ in(X2,X1) )
              & element(X2,the_carrier(X0)) )
          & element(X1,powerset(the_carrier(X0))) )
      & one_sorted_str(X0)
      & ~ empty_carrier(X0) ),
    inference(ennf_transformation,[],[f41]) ).

fof(f89,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ( in(X2,subset_complement(the_carrier(X0),X1))
              <~> ~ in(X2,X1) )
              & element(X2,the_carrier(X0)) )
          & element(X1,powerset(the_carrier(X0))) )
      & one_sorted_str(X0)
      & ~ empty_carrier(X0) ),
    inference(flattening,[],[f88]) ).

fof(f90,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( in(X2,subset_complement(X0,X1))
              | in(X2,X1)
              | ~ element(X2,X0) )
          | ~ element(X1,powerset(X0)) )
      | empty_set = X0 ),
    inference(ennf_transformation,[],[f42]) ).

fof(f91,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( in(X2,subset_complement(X0,X1))
              | in(X2,X1)
              | ~ element(X2,X0) )
          | ~ element(X1,powerset(X0)) )
      | empty_set = X0 ),
    inference(flattening,[],[f90]) ).

fof(f92,plain,
    ! [X0,X1,X2] :
      ( ~ in(X1,X2)
      | ~ in(X1,subset_complement(X0,X2))
      | ~ element(X2,powerset(X0)) ),
    inference(ennf_transformation,[],[f43]) ).

fof(f93,plain,
    ! [X0,X1,X2] :
      ( ~ in(X1,X2)
      | ~ in(X1,subset_complement(X0,X2))
      | ~ element(X2,powerset(X0)) ),
    inference(flattening,[],[f92]) ).

fof(f104,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ( in(X2,X1)
                | ~ in(X2,subset_complement(the_carrier(X0),X1)) )
              & ( ~ in(X2,X1)
                | in(X2,subset_complement(the_carrier(X0),X1)) )
              & element(X2,the_carrier(X0)) )
          & element(X1,powerset(the_carrier(X0))) )
      & one_sorted_str(X0)
      & ~ empty_carrier(X0) ),
    inference(nnf_transformation,[],[f89]) ).

fof(f105,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ( in(X2,X1)
                | ~ in(X2,subset_complement(the_carrier(X0),X1)) )
              & ( ~ in(X2,X1)
                | in(X2,subset_complement(the_carrier(X0),X1)) )
              & element(X2,the_carrier(X0)) )
          & element(X1,powerset(the_carrier(X0))) )
      & one_sorted_str(X0)
      & ~ empty_carrier(X0) ),
    inference(flattening,[],[f104]) ).

fof(f106,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ( in(X2,X1)
                  | ~ in(X2,subset_complement(the_carrier(X0),X1)) )
                & ( ~ in(X2,X1)
                  | in(X2,subset_complement(the_carrier(X0),X1)) )
                & element(X2,the_carrier(X0)) )
            & element(X1,powerset(the_carrier(X0))) )
        & one_sorted_str(X0)
        & ~ empty_carrier(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ( in(X2,X1)
                | ~ in(X2,subset_complement(the_carrier(sK5),X1)) )
              & ( ~ in(X2,X1)
                | in(X2,subset_complement(the_carrier(sK5),X1)) )
              & element(X2,the_carrier(sK5)) )
          & element(X1,powerset(the_carrier(sK5))) )
      & one_sorted_str(sK5)
      & ~ empty_carrier(sK5) ) ),
    introduced(choice_axiom,[]) ).

fof(f107,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ( in(X2,X1)
              | ~ in(X2,subset_complement(the_carrier(sK5),X1)) )
            & ( ~ in(X2,X1)
              | in(X2,subset_complement(the_carrier(sK5),X1)) )
            & element(X2,the_carrier(sK5)) )
        & element(X1,powerset(the_carrier(sK5))) )
   => ( ? [X2] :
          ( ( in(X2,sK6)
            | ~ in(X2,subset_complement(the_carrier(sK5),sK6)) )
          & ( ~ in(X2,sK6)
            | in(X2,subset_complement(the_carrier(sK5),sK6)) )
          & element(X2,the_carrier(sK5)) )
      & element(sK6,powerset(the_carrier(sK5))) ) ),
    introduced(choice_axiom,[]) ).

fof(f108,plain,
    ( ? [X2] :
        ( ( in(X2,sK6)
          | ~ in(X2,subset_complement(the_carrier(sK5),sK6)) )
        & ( ~ in(X2,sK6)
          | in(X2,subset_complement(the_carrier(sK5),sK6)) )
        & element(X2,the_carrier(sK5)) )
   => ( ( in(sK7,sK6)
        | ~ in(sK7,subset_complement(the_carrier(sK5),sK6)) )
      & ( ~ in(sK7,sK6)
        | in(sK7,subset_complement(the_carrier(sK5),sK6)) )
      & element(sK7,the_carrier(sK5)) ) ),
    introduced(choice_axiom,[]) ).

fof(f109,plain,
    ( ( in(sK7,sK6)
      | ~ in(sK7,subset_complement(the_carrier(sK5),sK6)) )
    & ( ~ in(sK7,sK6)
      | in(sK7,subset_complement(the_carrier(sK5),sK6)) )
    & element(sK7,the_carrier(sK5))
    & element(sK6,powerset(the_carrier(sK5)))
    & one_sorted_str(sK5)
    & ~ empty_carrier(sK5) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f105,f108,f107,f106]) ).

fof(f153,plain,
    ! [X0] :
      ( ~ empty(the_carrier(X0))
      | ~ one_sorted_str(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f81]) ).

fof(f154,plain,
    empty(empty_set),
    inference(cnf_transformation,[],[f34]) ).

fof(f165,plain,
    ~ empty_carrier(sK5),
    inference(cnf_transformation,[],[f109]) ).

fof(f166,plain,
    one_sorted_str(sK5),
    inference(cnf_transformation,[],[f109]) ).

fof(f167,plain,
    element(sK6,powerset(the_carrier(sK5))),
    inference(cnf_transformation,[],[f109]) ).

fof(f168,plain,
    element(sK7,the_carrier(sK5)),
    inference(cnf_transformation,[],[f109]) ).

fof(f169,plain,
    ( ~ in(sK7,sK6)
    | in(sK7,subset_complement(the_carrier(sK5),sK6)) ),
    inference(cnf_transformation,[],[f109]) ).

fof(f170,plain,
    ( in(sK7,sK6)
    | ~ in(sK7,subset_complement(the_carrier(sK5),sK6)) ),
    inference(cnf_transformation,[],[f109]) ).

fof(f171,plain,
    ! [X2,X0,X1] :
      ( in(X2,subset_complement(X0,X1))
      | in(X2,X1)
      | ~ element(X2,X0)
      | ~ element(X1,powerset(X0))
      | empty_set = X0 ),
    inference(cnf_transformation,[],[f91]) ).

fof(f172,plain,
    ! [X2,X0,X1] :
      ( ~ in(X1,X2)
      | ~ in(X1,subset_complement(X0,X2))
      | ~ element(X2,powerset(X0)) ),
    inference(cnf_transformation,[],[f93]) ).

cnf(c_92,plain,
    ( ~ empty(the_carrier(X0))
    | ~ one_sorted_str(X0)
    | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f153]) ).

cnf(c_98,plain,
    empty(empty_set),
    inference(cnf_transformation,[],[f154]) ).

cnf(c_104,negated_conjecture,
    ( ~ in(sK7,subset_complement(the_carrier(sK5),sK6))
    | in(sK7,sK6) ),
    inference(cnf_transformation,[],[f170]) ).

cnf(c_105,negated_conjecture,
    ( ~ in(sK7,sK6)
    | in(sK7,subset_complement(the_carrier(sK5),sK6)) ),
    inference(cnf_transformation,[],[f169]) ).

cnf(c_106,negated_conjecture,
    element(sK7,the_carrier(sK5)),
    inference(cnf_transformation,[],[f168]) ).

cnf(c_107,negated_conjecture,
    element(sK6,powerset(the_carrier(sK5))),
    inference(cnf_transformation,[],[f167]) ).

cnf(c_108,negated_conjecture,
    one_sorted_str(sK5),
    inference(cnf_transformation,[],[f166]) ).

cnf(c_109,negated_conjecture,
    ~ empty_carrier(sK5),
    inference(cnf_transformation,[],[f165]) ).

cnf(c_110,plain,
    ( ~ element(X0,powerset(X1))
    | ~ element(X2,X1)
    | X1 = empty_set
    | in(X2,subset_complement(X1,X0))
    | in(X2,X0) ),
    inference(cnf_transformation,[],[f171]) ).

cnf(c_111,plain,
    ( ~ in(X0,subset_complement(X1,X2))
    | ~ element(X2,powerset(X1))
    | ~ in(X0,X2) ),
    inference(cnf_transformation,[],[f172]) ).

cnf(c_787,plain,
    ( X0 != sK5
    | ~ empty(the_carrier(X0))
    | ~ one_sorted_str(X0) ),
    inference(resolution_lifted,[status(thm)],[c_92,c_109]) ).

cnf(c_788,plain,
    ( ~ empty(the_carrier(sK5))
    | ~ one_sorted_str(sK5) ),
    inference(unflattening,[status(thm)],[c_787]) ).

cnf(c_789,plain,
    ~ empty(the_carrier(sK5)),
    inference(global_subsumption_just,[status(thm)],[c_788,c_108,c_788]) ).

cnf(c_1058,plain,
    the_carrier(sK5) = sP0_iProver_def,
    definition ).

cnf(c_1059,plain,
    powerset(sP0_iProver_def) = sP1_iProver_def,
    definition ).

cnf(c_1060,plain,
    subset_complement(sP0_iProver_def,sK6) = sP2_iProver_def,
    definition ).

cnf(c_1061,negated_conjecture,
    element(sK6,sP1_iProver_def),
    inference(demodulation,[status(thm)],[c_107,c_1058,c_1059]) ).

cnf(c_1062,negated_conjecture,
    element(sK7,sP0_iProver_def),
    inference(demodulation,[status(thm)],[c_106]) ).

cnf(c_1063,negated_conjecture,
    ( ~ in(sK7,sK6)
    | in(sK7,sP2_iProver_def) ),
    inference(demodulation,[status(thm)],[c_105,c_1060]) ).

cnf(c_1064,negated_conjecture,
    ( ~ in(sK7,sP2_iProver_def)
    | in(sK7,sK6) ),
    inference(demodulation,[status(thm)],[c_104]) ).

cnf(c_1584,plain,
    ~ empty(sP0_iProver_def),
    inference(light_normalisation,[status(thm)],[c_789,c_1058]) ).

cnf(c_1820,plain,
    ( ~ element(sK6,powerset(sP0_iProver_def))
    | ~ in(X0,sK6)
    | ~ in(X0,sP2_iProver_def) ),
    inference(superposition,[status(thm)],[c_1060,c_111]) ).

cnf(c_1821,plain,
    ( ~ in(X0,sK6)
    | ~ in(X0,sP2_iProver_def)
    | ~ element(sK6,sP1_iProver_def) ),
    inference(light_normalisation,[status(thm)],[c_1820,c_1059]) ).

cnf(c_1822,plain,
    ( ~ in(X0,sK6)
    | ~ in(X0,sP2_iProver_def) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_1821,c_1061]) ).

cnf(c_1840,plain,
    ( ~ element(sK6,powerset(sP0_iProver_def))
    | ~ element(X0,sP0_iProver_def)
    | empty_set = sP0_iProver_def
    | in(X0,sK6)
    | in(X0,sP2_iProver_def) ),
    inference(superposition,[status(thm)],[c_1060,c_110]) ).

cnf(c_1846,plain,
    ( ~ element(X0,sP0_iProver_def)
    | ~ element(sK6,sP1_iProver_def)
    | empty_set = sP0_iProver_def
    | in(X0,sK6)
    | in(X0,sP2_iProver_def) ),
    inference(light_normalisation,[status(thm)],[c_1840,c_1059]) ).

cnf(c_1847,plain,
    ( ~ element(X0,sP0_iProver_def)
    | empty_set = sP0_iProver_def
    | in(X0,sK6)
    | in(X0,sP2_iProver_def) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_1846,c_1061]) ).

cnf(c_1911,plain,
    ~ in(sK7,sP2_iProver_def),
    inference(backward_subsumption_resolution,[status(thm)],[c_1064,c_1822]) ).

cnf(c_1912,plain,
    ~ in(sK7,sK6),
    inference(backward_subsumption_resolution,[status(thm)],[c_1063,c_1822]) ).

cnf(c_1929,plain,
    ( empty_set = sP0_iProver_def
    | in(sK7,sK6)
    | in(sK7,sP2_iProver_def) ),
    inference(superposition,[status(thm)],[c_1062,c_1847]) ).

cnf(c_1930,plain,
    empty_set = sP0_iProver_def,
    inference(forward_subsumption_resolution,[status(thm)],[c_1929,c_1911,c_1912]) ).

cnf(c_1933,plain,
    empty(sP0_iProver_def),
    inference(demodulation,[status(thm)],[c_98,c_1930]) ).

cnf(c_1934,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_1933,c_1584]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SEU321+1 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.11  % Command  : run_iprover %s %d THM
% 0.11/0.32  % Computer : n028.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Thu May  2 18:10:32 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.17/0.43  Running first-order theorem proving
% 0.17/0.43  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
% 2.78/1.12  % SZS status Started for theBenchmark.p
% 2.78/1.12  % SZS status Theorem for theBenchmark.p
% 2.78/1.12  
% 2.78/1.12  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 2.78/1.12  
% 2.78/1.12  ------  iProver source info
% 2.78/1.12  
% 2.78/1.12  git: date: 2024-05-02 19:28:25 +0000
% 2.78/1.12  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 2.78/1.12  git: non_committed_changes: false
% 2.78/1.12  
% 2.78/1.12  ------ Parsing...
% 2.78/1.12  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 2.78/1.12  
% 2.78/1.12  ------ Preprocessing... sup_sim: 0  sf_s  rm: 40 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe_e  sup_sim: 0  sf_s  rm: 8 0s  sf_e  pe_s  pe_e 
% 2.78/1.12  
% 2.78/1.12  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 2.78/1.12  
% 2.78/1.12  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.78/1.12  ------ Proving...
% 2.78/1.12  ------ Problem Properties 
% 2.78/1.12  
% 2.78/1.12  
% 2.78/1.12  clauses                                 29
% 2.78/1.12  conjectures                             4
% 2.78/1.12  EPR                                     12
% 2.78/1.12  Horn                                    27
% 2.78/1.12  unary                                   15
% 2.78/1.12  binary                                  8
% 2.78/1.12  lits                                    51
% 2.78/1.12  lits eq                                 7
% 2.78/1.12  fd_pure                                 0
% 2.78/1.12  fd_pseudo                               0
% 2.78/1.12  fd_cond                                 2
% 2.78/1.12  fd_pseudo_cond                          1
% 2.78/1.12  AC symbols                              0
% 2.78/1.12  
% 2.78/1.12  ------ Schedule dynamic 5 is on 
% 2.78/1.12  
% 2.78/1.12  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.78/1.12  
% 2.78/1.12  
% 2.78/1.12  ------ 
% 2.78/1.12  Current options:
% 2.78/1.12  ------ 
% 2.78/1.12  
% 2.78/1.12  
% 2.78/1.12  
% 2.78/1.12  
% 2.78/1.12  ------ Proving...
% 2.78/1.12  
% 2.78/1.12  
% 2.78/1.12  % SZS status Theorem for theBenchmark.p
% 2.78/1.12  
% 2.78/1.12  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.78/1.12  
% 2.78/1.13  
%------------------------------------------------------------------------------