TSTP Solution File: SEU104+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SEU104+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n025.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 : Thu Aug 31 17:03:44 EDT 2023

% Result   : Theorem 0.61s 1.18s
% Output   : CNFRefutation 0.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   66 (  22 unt;   0 def)
%            Number of atoms       :  194 (  14 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  214 (  86   ~;  76   |;  37   &)
%                                         (   3 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   2 con; 0-2 aty)
%            Number of variables   :   97 (   1 sgn;  66   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f6,axiom,
    ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

fof(f17,axiom,
    ! [X0,X1] : set_union2(X0,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).

fof(f28,axiom,
    ! [X0] :
      ( preboolean(X0)
    <=> ! [X1,X2] :
          ( ( in(X2,X0)
            & in(X1,X0) )
         => ( in(set_difference(X1,X2),X0)
            & in(set_union2(X1,X2),X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_finsub_1) ).

fof(f29,conjecture,
    ! [X0] :
      ( ~ empty(X0)
     => ( ! [X1] :
            ( element(X1,X0)
           => ! [X2] :
                ( element(X2,X0)
               => ( in(set_difference(X1,X2),X0)
                  & in(symmetric_difference(X1,X2),X0) ) ) )
       => preboolean(X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_finsub_1) ).

fof(f30,negated_conjecture,
    ~ ! [X0] :
        ( ~ empty(X0)
       => ( ! [X1] :
              ( element(X1,X0)
             => ! [X2] :
                  ( element(X2,X0)
                 => ( in(set_difference(X1,X2),X0)
                    & in(symmetric_difference(X1,X2),X0) ) ) )
         => preboolean(X0) ) ),
    inference(negated_conjecture,[],[f29]) ).

fof(f32,axiom,
    ! [X0,X1] :
      ( in(X0,X1)
     => element(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).

fof(f34,axiom,
    ! [X0] : set_difference(X0,empty_set) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).

fof(f43,axiom,
    ! [X0,X1] : set_union2(X0,X1) = symmetric_difference(X0,set_difference(X1,X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t98_xboole_1) ).

fof(f44,plain,
    ! [X0] : set_union2(X0,X0) = X0,
    inference(rectify,[],[f17]) ).

fof(f71,plain,
    ! [X0] :
      ( preboolean(X0)
    <=> ! [X1,X2] :
          ( ( in(set_difference(X1,X2),X0)
            & in(set_union2(X1,X2),X0) )
          | ~ in(X2,X0)
          | ~ in(X1,X0) ) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f72,plain,
    ! [X0] :
      ( preboolean(X0)
    <=> ! [X1,X2] :
          ( ( in(set_difference(X1,X2),X0)
            & in(set_union2(X1,X2),X0) )
          | ~ in(X2,X0)
          | ~ in(X1,X0) ) ),
    inference(flattening,[],[f71]) ).

fof(f73,plain,
    ? [X0] :
      ( ~ preboolean(X0)
      & ! [X1] :
          ( ! [X2] :
              ( ( in(set_difference(X1,X2),X0)
                & in(symmetric_difference(X1,X2),X0) )
              | ~ element(X2,X0) )
          | ~ element(X1,X0) )
      & ~ empty(X0) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f74,plain,
    ? [X0] :
      ( ~ preboolean(X0)
      & ! [X1] :
          ( ! [X2] :
              ( ( in(set_difference(X1,X2),X0)
                & in(symmetric_difference(X1,X2),X0) )
              | ~ element(X2,X0) )
          | ~ element(X1,X0) )
      & ~ empty(X0) ),
    inference(flattening,[],[f73]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( element(X0,X1)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f105,plain,
    ! [X0] :
      ( ( preboolean(X0)
        | ? [X1,X2] :
            ( ( ~ in(set_difference(X1,X2),X0)
              | ~ in(set_union2(X1,X2),X0) )
            & in(X2,X0)
            & in(X1,X0) ) )
      & ( ! [X1,X2] :
            ( ( in(set_difference(X1,X2),X0)
              & in(set_union2(X1,X2),X0) )
            | ~ in(X2,X0)
            | ~ in(X1,X0) )
        | ~ preboolean(X0) ) ),
    inference(nnf_transformation,[],[f72]) ).

fof(f106,plain,
    ! [X0] :
      ( ( preboolean(X0)
        | ? [X1,X2] :
            ( ( ~ in(set_difference(X1,X2),X0)
              | ~ in(set_union2(X1,X2),X0) )
            & in(X2,X0)
            & in(X1,X0) ) )
      & ( ! [X3,X4] :
            ( ( in(set_difference(X3,X4),X0)
              & in(set_union2(X3,X4),X0) )
            | ~ in(X4,X0)
            | ~ in(X3,X0) )
        | ~ preboolean(X0) ) ),
    inference(rectify,[],[f105]) ).

fof(f107,plain,
    ! [X0] :
      ( ? [X1,X2] :
          ( ( ~ in(set_difference(X1,X2),X0)
            | ~ in(set_union2(X1,X2),X0) )
          & in(X2,X0)
          & in(X1,X0) )
     => ( ( ~ in(set_difference(sK10(X0),sK11(X0)),X0)
          | ~ in(set_union2(sK10(X0),sK11(X0)),X0) )
        & in(sK11(X0),X0)
        & in(sK10(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f108,plain,
    ! [X0] :
      ( ( preboolean(X0)
        | ( ( ~ in(set_difference(sK10(X0),sK11(X0)),X0)
            | ~ in(set_union2(sK10(X0),sK11(X0)),X0) )
          & in(sK11(X0),X0)
          & in(sK10(X0),X0) ) )
      & ( ! [X3,X4] :
            ( ( in(set_difference(X3,X4),X0)
              & in(set_union2(X3,X4),X0) )
            | ~ in(X4,X0)
            | ~ in(X3,X0) )
        | ~ preboolean(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11])],[f106,f107]) ).

fof(f109,plain,
    ( ? [X0] :
        ( ~ preboolean(X0)
        & ! [X1] :
            ( ! [X2] :
                ( ( in(set_difference(X1,X2),X0)
                  & in(symmetric_difference(X1,X2),X0) )
                | ~ element(X2,X0) )
            | ~ element(X1,X0) )
        & ~ empty(X0) )
   => ( ~ preboolean(sK12)
      & ! [X1] :
          ( ! [X2] :
              ( ( in(set_difference(X1,X2),sK12)
                & in(symmetric_difference(X1,X2),sK12) )
              | ~ element(X2,sK12) )
          | ~ element(X1,sK12) )
      & ~ empty(sK12) ) ),
    introduced(choice_axiom,[]) ).

fof(f110,plain,
    ( ~ preboolean(sK12)
    & ! [X1] :
        ( ! [X2] :
            ( ( in(set_difference(X1,X2),sK12)
              & in(symmetric_difference(X1,X2),sK12) )
            | ~ element(X2,sK12) )
        | ~ element(X1,sK12) )
    & ~ empty(sK12) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f74,f109]) ).

fof(f117,plain,
    ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
    inference(cnf_transformation,[],[f6]) ).

fof(f128,plain,
    ! [X0] : set_union2(X0,X0) = X0,
    inference(cnf_transformation,[],[f44]) ).

fof(f153,plain,
    ! [X0] :
      ( preboolean(X0)
      | in(sK10(X0),X0) ),
    inference(cnf_transformation,[],[f108]) ).

fof(f154,plain,
    ! [X0] :
      ( preboolean(X0)
      | in(sK11(X0),X0) ),
    inference(cnf_transformation,[],[f108]) ).

fof(f155,plain,
    ! [X0] :
      ( preboolean(X0)
      | ~ in(set_difference(sK10(X0),sK11(X0)),X0)
      | ~ in(set_union2(sK10(X0),sK11(X0)),X0) ),
    inference(cnf_transformation,[],[f108]) ).

fof(f157,plain,
    ! [X2,X1] :
      ( in(symmetric_difference(X1,X2),sK12)
      | ~ element(X2,sK12)
      | ~ element(X1,sK12) ),
    inference(cnf_transformation,[],[f110]) ).

fof(f158,plain,
    ! [X2,X1] :
      ( in(set_difference(X1,X2),sK12)
      | ~ element(X2,sK12)
      | ~ element(X1,sK12) ),
    inference(cnf_transformation,[],[f110]) ).

fof(f159,plain,
    ~ preboolean(sK12),
    inference(cnf_transformation,[],[f110]) ).

fof(f161,plain,
    ! [X0,X1] :
      ( element(X0,X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f163,plain,
    ! [X0] : set_difference(X0,empty_set) = X0,
    inference(cnf_transformation,[],[f34]) ).

fof(f172,plain,
    ! [X0,X1] : set_union2(X0,X1) = symmetric_difference(X0,set_difference(X1,X0)),
    inference(cnf_transformation,[],[f43]) ).

fof(f174,plain,
    ! [X0,X1] : symmetric_difference(X0,set_difference(X1,X0)) = symmetric_difference(X1,set_difference(X0,X1)),
    inference(definition_unfolding,[],[f117,f172,f172]) ).

fof(f178,plain,
    ! [X0] : symmetric_difference(X0,set_difference(X0,X0)) = X0,
    inference(definition_unfolding,[],[f128,f172]) ).

fof(f179,plain,
    ! [X0] :
      ( preboolean(X0)
      | ~ in(set_difference(sK10(X0),sK11(X0)),X0)
      | ~ in(symmetric_difference(sK10(X0),set_difference(sK11(X0),sK10(X0))),X0) ),
    inference(definition_unfolding,[],[f155,f172]) ).

cnf(c_56,plain,
    symmetric_difference(X0,set_difference(X1,X0)) = symmetric_difference(X1,set_difference(X0,X1)),
    inference(cnf_transformation,[],[f174]) ).

cnf(c_66,plain,
    symmetric_difference(X0,set_difference(X0,X0)) = X0,
    inference(cnf_transformation,[],[f178]) ).

cnf(c_89,plain,
    ( ~ in(symmetric_difference(sK10(X0),set_difference(sK11(X0),sK10(X0))),X0)
    | ~ in(set_difference(sK10(X0),sK11(X0)),X0)
    | preboolean(X0) ),
    inference(cnf_transformation,[],[f179]) ).

cnf(c_90,plain,
    ( in(sK11(X0),X0)
    | preboolean(X0) ),
    inference(cnf_transformation,[],[f154]) ).

cnf(c_91,plain,
    ( in(sK10(X0),X0)
    | preboolean(X0) ),
    inference(cnf_transformation,[],[f153]) ).

cnf(c_94,negated_conjecture,
    ~ preboolean(sK12),
    inference(cnf_transformation,[],[f159]) ).

cnf(c_95,negated_conjecture,
    ( ~ element(X0,sK12)
    | ~ element(X1,sK12)
    | in(set_difference(X0,X1),sK12) ),
    inference(cnf_transformation,[],[f158]) ).

cnf(c_96,negated_conjecture,
    ( ~ element(X0,sK12)
    | ~ element(X1,sK12)
    | in(symmetric_difference(X0,X1),sK12) ),
    inference(cnf_transformation,[],[f157]) ).

cnf(c_99,plain,
    ( ~ in(X0,X1)
    | element(X0,X1) ),
    inference(cnf_transformation,[],[f161]) ).

cnf(c_101,plain,
    set_difference(X0,empty_set) = X0,
    inference(cnf_transformation,[],[f163]) ).

cnf(c_123,plain,
    ( in(sK10(sK12),sK12)
    | preboolean(sK12) ),
    inference(instantiation,[status(thm)],[c_91]) ).

cnf(c_124,plain,
    ( in(sK11(sK12),sK12)
    | preboolean(sK12) ),
    inference(instantiation,[status(thm)],[c_90]) ).

cnf(c_1634,plain,
    ( ~ element(X0,sK12)
    | ~ element(empty_set,sK12)
    | in(X0,sK12) ),
    inference(superposition,[status(thm)],[c_101,c_95]) ).

cnf(c_1689,plain,
    ( element(sK11(X0),X0)
    | preboolean(X0) ),
    inference(superposition,[status(thm)],[c_90,c_99]) ).

cnf(c_1690,plain,
    ( element(sK10(X0),X0)
    | preboolean(X0) ),
    inference(superposition,[status(thm)],[c_91,c_99]) ).

cnf(c_1691,plain,
    ( ~ element(X0,sK12)
    | ~ element(X1,sK12)
    | element(set_difference(X0,X1),sK12) ),
    inference(superposition,[status(thm)],[c_95,c_99]) ).

cnf(c_1712,plain,
    ( ~ element(empty_set,sK12)
    | in(sK11(sK12),sK12)
    | preboolean(sK12) ),
    inference(superposition,[status(thm)],[c_1689,c_1634]) ).

cnf(c_1713,plain,
    ( ~ element(empty_set,sK12)
    | in(sK11(sK12),sK12) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_1712,c_94]) ).

cnf(c_1720,plain,
    ( ~ element(empty_set,sK12)
    | in(sK10(sK12),sK12)
    | preboolean(sK12) ),
    inference(superposition,[status(thm)],[c_1690,c_1634]) ).

cnf(c_1721,plain,
    ( ~ element(empty_set,sK12)
    | in(sK10(sK12),sK12) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_1720,c_94]) ).

cnf(c_1724,plain,
    in(sK11(sK12),sK12),
    inference(global_subsumption_just,[status(thm)],[c_1713,c_94,c_124]) ).

cnf(c_1726,plain,
    element(sK11(sK12),sK12),
    inference(superposition,[status(thm)],[c_1724,c_99]) ).

cnf(c_1727,plain,
    in(sK10(sK12),sK12),
    inference(global_subsumption_just,[status(thm)],[c_1721,c_94,c_123]) ).

cnf(c_1729,plain,
    element(sK10(sK12),sK12),
    inference(superposition,[status(thm)],[c_1727,c_99]) ).

cnf(c_1937,plain,
    ( ~ element(set_difference(X0,X0),sK12)
    | ~ element(X0,sK12)
    | in(X0,sK12) ),
    inference(superposition,[status(thm)],[c_66,c_96]) ).

cnf(c_2037,plain,
    ( ~ element(X0,sK12)
    | in(X0,sK12) ),
    inference(superposition,[status(thm)],[c_1691,c_1937]) ).

cnf(c_2145,plain,
    ( ~ element(set_difference(X0,X1),sK12)
    | ~ element(X1,sK12)
    | in(symmetric_difference(X0,set_difference(X1,X0)),sK12) ),
    inference(superposition,[status(thm)],[c_56,c_96]) ).

cnf(c_2440,plain,
    ( ~ in(set_difference(sK10(sK12),sK11(sK12)),sK12)
    | ~ element(set_difference(sK10(sK12),sK11(sK12)),sK12)
    | ~ element(sK11(sK12),sK12)
    | preboolean(sK12) ),
    inference(superposition,[status(thm)],[c_2145,c_89]) ).

cnf(c_2441,plain,
    ( ~ in(set_difference(sK10(sK12),sK11(sK12)),sK12)
    | ~ element(set_difference(sK10(sK12),sK11(sK12)),sK12) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_2440,c_94,c_1726]) ).

cnf(c_2523,plain,
    ~ element(set_difference(sK10(sK12),sK11(sK12)),sK12),
    inference(forward_subsumption_resolution,[status(thm)],[c_2441,c_2037]) ).

cnf(c_2524,plain,
    ( ~ element(sK10(sK12),sK12)
    | ~ element(sK11(sK12),sK12) ),
    inference(superposition,[status(thm)],[c_1691,c_2523]) ).

cnf(c_2525,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_2524,c_1726,c_1729]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU104+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n025.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Wed Aug 23 15:46:06 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.47  Running first-order theorem proving
% 0.20/0.47  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.61/1.18  % SZS status Started for theBenchmark.p
% 0.61/1.18  % SZS status Theorem for theBenchmark.p
% 0.61/1.18  
% 0.61/1.18  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.61/1.18  
% 0.61/1.18  ------  iProver source info
% 0.61/1.18  
% 0.61/1.18  git: date: 2023-05-31 18:12:56 +0000
% 0.61/1.18  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.61/1.18  git: non_committed_changes: false
% 0.61/1.18  git: last_make_outside_of_git: false
% 0.61/1.18  
% 0.61/1.18  ------ Parsing...
% 0.61/1.18  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 0.61/1.18  
% 0.61/1.18  ------ Preprocessing... sup_sim: 1  sf_s  rm: 11 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 
% 0.61/1.18  
% 0.61/1.18  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 0.61/1.18  
% 0.61/1.18  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 0.61/1.18  ------ Proving...
% 0.61/1.18  ------ Problem Properties 
% 0.61/1.18  
% 0.61/1.18  
% 0.61/1.18  clauses                                 45
% 0.61/1.18  conjectures                             4
% 0.61/1.18  EPR                                     14
% 0.61/1.18  Horn                                    39
% 0.61/1.18  unary                                   22
% 0.61/1.18  binary                                  14
% 0.61/1.18  lits                                    79
% 0.61/1.18  lits eq                                 9
% 0.61/1.18  fd_pure                                 0
% 0.61/1.18  fd_pseudo                               0
% 0.61/1.18  fd_cond                                 1
% 0.61/1.18  fd_pseudo_cond                          1
% 0.61/1.18  AC symbols                              0
% 0.61/1.18  
% 0.61/1.18  ------ Schedule dynamic 5 is on 
% 0.61/1.18  
% 0.61/1.18  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.61/1.18  
% 0.61/1.18  
% 0.61/1.18  ------ 
% 0.61/1.18  Current options:
% 0.61/1.18  ------ 
% 0.61/1.18  
% 0.61/1.18  
% 0.61/1.18  
% 0.61/1.18  
% 0.61/1.18  ------ Proving...
% 0.61/1.18  
% 0.61/1.18  
% 0.61/1.18  % SZS status Theorem for theBenchmark.p
% 0.61/1.18  
% 0.61/1.18  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.61/1.18  
% 0.61/1.18  
%------------------------------------------------------------------------------