TSTP Solution File: SEU126+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SEU126+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n018.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 17:03:52 EDT 2023

% Result   : Theorem 2.41s 1.16s
% Output   : CNFRefutation 2.41s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   36 (   9 unt;   0 def)
%            Number of atoms       :  152 (  27 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  183 (  67   ~;  70   |;  36   &)
%                                         (   4 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-3 aty)
%            Number of variables   :   80 (   0 sgn;  57   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

fof(f4,axiom,
    ! [X0,X1,X2] :
      ( set_union2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            | in(X3,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

fof(f15,conjecture,
    ! [X0,X1] :
      ( subset(X0,X1)
     => set_union2(X0,X1) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).

fof(f16,negated_conjecture,
    ~ ! [X0,X1] :
        ( subset(X0,X1)
       => set_union2(X0,X1) = X1 ),
    inference(negated_conjecture,[],[f15]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f27,plain,
    ? [X0,X1] :
      ( set_union2(X0,X1) != X1
      & subset(X0,X1) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f33,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ? [X3] :
            ( ( ( ~ in(X3,X1)
                & ~ in(X3,X0) )
              | ~ in(X3,X2) )
            & ( in(X3,X1)
              | in(X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ( ~ in(X3,X1)
                & ~ in(X3,X0) ) )
            & ( in(X3,X1)
              | in(X3,X0)
              | ~ in(X3,X2) ) )
        | set_union2(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f4]) ).

fof(f34,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ? [X3] :
            ( ( ( ~ in(X3,X1)
                & ~ in(X3,X0) )
              | ~ in(X3,X2) )
            & ( in(X3,X1)
              | in(X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ( ~ in(X3,X1)
                & ~ in(X3,X0) ) )
            & ( in(X3,X1)
              | in(X3,X0)
              | ~ in(X3,X2) ) )
        | set_union2(X0,X1) != X2 ) ),
    inference(flattening,[],[f33]) ).

fof(f35,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ? [X3] :
            ( ( ( ~ in(X3,X1)
                & ~ in(X3,X0) )
              | ~ in(X3,X2) )
            & ( in(X3,X1)
              | in(X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ( ~ in(X4,X1)
                & ~ in(X4,X0) ) )
            & ( in(X4,X1)
              | in(X4,X0)
              | ~ in(X4,X2) ) )
        | set_union2(X0,X1) != X2 ) ),
    inference(rectify,[],[f34]) ).

fof(f36,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ( ~ in(X3,X1)
              & ~ in(X3,X0) )
            | ~ in(X3,X2) )
          & ( in(X3,X1)
            | in(X3,X0)
            | in(X3,X2) ) )
     => ( ( ( ~ in(sK0(X0,X1,X2),X1)
            & ~ in(sK0(X0,X1,X2),X0) )
          | ~ in(sK0(X0,X1,X2),X2) )
        & ( in(sK0(X0,X1,X2),X1)
          | in(sK0(X0,X1,X2),X0)
          | in(sK0(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f37,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ( ( ( ~ in(sK0(X0,X1,X2),X1)
              & ~ in(sK0(X0,X1,X2),X0) )
            | ~ in(sK0(X0,X1,X2),X2) )
          & ( in(sK0(X0,X1,X2),X1)
            | in(sK0(X0,X1,X2),X0)
            | in(sK0(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ( ~ in(X4,X1)
                & ~ in(X4,X0) ) )
            & ( in(X4,X1)
              | in(X4,X0)
              | ~ in(X4,X2) ) )
        | set_union2(X0,X1) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f35,f36]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f24]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f38]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK1(X0,X1),X1)
        & in(sK1(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK1(X0,X1),X1)
          & in(sK1(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f39,f40]) ).

fof(f46,plain,
    ( ? [X0,X1] :
        ( set_union2(X0,X1) != X1
        & subset(X0,X1) )
   => ( sK5 != set_union2(sK4,sK5)
      & subset(sK4,sK5) ) ),
    introduced(choice_axiom,[]) ).

fof(f47,plain,
    ( sK5 != set_union2(sK4,sK5)
    & subset(sK4,sK5) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f27,f46]) ).

fof(f49,plain,
    ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
    inference(cnf_transformation,[],[f2]) ).

fof(f56,plain,
    ! [X2,X0,X1] :
      ( set_union2(X0,X1) = X2
      | in(sK0(X0,X1,X2),X1)
      | in(sK0(X0,X1,X2),X0)
      | in(sK0(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f57,plain,
    ! [X2,X0,X1] :
      ( set_union2(X0,X1) = X2
      | ~ in(sK0(X0,X1,X2),X0)
      | ~ in(sK0(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f59,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | ~ in(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f41]) ).

fof(f69,plain,
    subset(sK4,sK5),
    inference(cnf_transformation,[],[f47]) ).

fof(f70,plain,
    sK5 != set_union2(sK4,sK5),
    inference(cnf_transformation,[],[f47]) ).

cnf(c_50,plain,
    set_union2(X0,X1) = set_union2(X1,X0),
    inference(cnf_transformation,[],[f49]) ).

cnf(c_55,plain,
    ( ~ in(sK0(X0,X1,X2),X0)
    | ~ in(sK0(X0,X1,X2),X2)
    | set_union2(X0,X1) = X2 ),
    inference(cnf_transformation,[],[f57]) ).

cnf(c_56,plain,
    ( set_union2(X0,X1) = X2
    | in(sK0(X0,X1,X2),X0)
    | in(sK0(X0,X1,X2),X1)
    | in(sK0(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f56]) ).

cnf(c_62,plain,
    ( ~ in(X0,X1)
    | ~ subset(X1,X2)
    | in(X0,X2) ),
    inference(cnf_transformation,[],[f59]) ).

cnf(c_70,negated_conjecture,
    set_union2(sK4,sK5) != sK5,
    inference(cnf_transformation,[],[f70]) ).

cnf(c_71,negated_conjecture,
    subset(sK4,sK5),
    inference(cnf_transformation,[],[f69]) ).

cnf(c_200,plain,
    set_union2(sK5,sK4) != sK5,
    inference(demodulation,[status(thm)],[c_70,c_50]) ).

cnf(c_1205,plain,
    ( ~ in(sK0(sK5,sK4,sK5),sK5)
    | set_union2(sK5,sK4) = sK5 ),
    inference(instantiation,[status(thm)],[c_55]) ).

cnf(c_1206,plain,
    ( set_union2(sK5,sK4) = sK5
    | in(sK0(sK5,sK4,sK5),sK5)
    | in(sK0(sK5,sK4,sK5),sK4) ),
    inference(instantiation,[status(thm)],[c_56]) ).

cnf(c_1225,plain,
    ( ~ in(sK0(sK5,sK4,sK5),sK4)
    | ~ subset(sK4,X0)
    | in(sK0(sK5,sK4,sK5),X0) ),
    inference(instantiation,[status(thm)],[c_62]) ).

cnf(c_2070,plain,
    ( ~ in(sK0(sK5,sK4,sK5),sK4)
    | ~ subset(sK4,sK5)
    | in(sK0(sK5,sK4,sK5),sK5) ),
    inference(instantiation,[status(thm)],[c_1225]) ).

cnf(c_2071,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_2070,c_1206,c_1205,c_200,c_71]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU126+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.12/0.33  % Computer : n018.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Wed Aug 23 19:21:42 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.18/0.46  Running first-order theorem proving
% 0.18/0.46  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.41/1.16  % SZS status Started for theBenchmark.p
% 2.41/1.16  % SZS status Theorem for theBenchmark.p
% 2.41/1.16  
% 2.41/1.16  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.41/1.16  
% 2.41/1.16  ------  iProver source info
% 2.41/1.16  
% 2.41/1.16  git: date: 2023-05-31 18:12:56 +0000
% 2.41/1.16  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.41/1.16  git: non_committed_changes: false
% 2.41/1.16  git: last_make_outside_of_git: false
% 2.41/1.16  
% 2.41/1.16  ------ Parsing...
% 2.41/1.16  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 2.41/1.16  
% 2.41/1.16  ------ Preprocessing... sup_sim: 1  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 
% 2.41/1.16  
% 2.41/1.16  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 2.41/1.16  
% 2.41/1.16  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.41/1.16  ------ Proving...
% 2.41/1.16  ------ Problem Properties 
% 2.41/1.16  
% 2.41/1.16  
% 2.41/1.16  clauses                                 25
% 2.41/1.16  conjectures                             1
% 2.41/1.16  EPR                                     11
% 2.41/1.16  Horn                                    22
% 2.41/1.16  unary                                   9
% 2.41/1.16  binary                                  9
% 2.41/1.16  lits                                    49
% 2.41/1.16  lits eq                                 10
% 2.41/1.16  fd_pure                                 0
% 2.41/1.16  fd_pseudo                               0
% 2.41/1.16  fd_cond                                 1
% 2.41/1.16  fd_pseudo_cond                          5
% 2.41/1.16  AC symbols                              0
% 2.41/1.16  
% 2.41/1.16  ------ Schedule dynamic 5 is on 
% 2.41/1.16  
% 2.41/1.16  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.41/1.16  
% 2.41/1.16  
% 2.41/1.16  ------ 
% 2.41/1.16  Current options:
% 2.41/1.16  ------ 
% 2.41/1.16  
% 2.41/1.16  
% 2.41/1.16  
% 2.41/1.16  
% 2.41/1.16  ------ Proving...
% 2.41/1.16  
% 2.41/1.16  
% 2.41/1.16  % SZS status Theorem for theBenchmark.p
% 2.41/1.16  
% 2.41/1.16  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.41/1.16  
% 2.41/1.16  
%------------------------------------------------------------------------------