TSTP Solution File: SET159+4 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SET159+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n014.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 15:06:53 EDT 2023

% Result   : Theorem 17.33s 3.24s
% Output   : CNFRefutation 17.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   56 (   9 unt;   0 def)
%            Number of atoms       :  144 (   2 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  154 (  66   ~;  65   |;  14   &)
%                                         (   5 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   88 (   2 sgn;  61   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( equal_set(X0,X1)
    <=> ( subset(X1,X0)
        & subset(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).

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

fof(f12,conjecture,
    ! [X0,X1,X5] : equal_set(union(union(X0,X1),X5),union(X0,union(X1,X5))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI09) ).

fof(f13,negated_conjecture,
    ~ ! [X0,X1,X5] : equal_set(union(union(X0,X1),X5),union(X0,union(X1,X5))),
    inference(negated_conjecture,[],[f12]) ).

fof(f16,plain,
    ! [X0,X1,X2] :
      ( member(X0,union(X1,X2))
    <=> ( member(X0,X2)
        | member(X0,X1) ) ),
    inference(rectify,[],[f5]) ).

fof(f23,plain,
    ~ ! [X0,X1,X2] : equal_set(union(union(X0,X1),X2),union(X0,union(X1,X2))),
    inference(rectify,[],[f13]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ( subset(X1,X0)
        & subset(X0,X1) )
     => equal_set(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f2]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(flattening,[],[f26]) ).

fof(f29,plain,
    ? [X0,X1,X2] : ~ equal_set(union(union(X0,X1),X2),union(X0,union(X1,X2))),
    inference(ennf_transformation,[],[f23]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X2] :
            ( member(X2,X1)
            | ~ member(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f25]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f30]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK0(X0,X1),X1)
        & member(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ member(sK0(X0,X1),X1)
          & member(sK0(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f31,f32]) ).

fof(f37,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,union(X1,X2))
        | ( ~ member(X0,X2)
          & ~ member(X0,X1) ) )
      & ( member(X0,X2)
        | member(X0,X1)
        | ~ member(X0,union(X1,X2)) ) ),
    inference(nnf_transformation,[],[f16]) ).

fof(f38,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,union(X1,X2))
        | ( ~ member(X0,X2)
          & ~ member(X0,X1) ) )
      & ( member(X0,X2)
        | member(X0,X1)
        | ~ member(X0,union(X1,X2)) ) ),
    inference(flattening,[],[f37]) ).

fof(f52,plain,
    ( ? [X0,X1,X2] : ~ equal_set(union(union(X0,X1),X2),union(X0,union(X1,X2)))
   => ~ equal_set(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))) ),
    introduced(choice_axiom,[]) ).

fof(f53,plain,
    ~ equal_set(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f29,f52]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK0(X0,X1),X0) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f63,plain,
    ! [X2,X0,X1] :
      ( member(X0,X2)
      | member(X0,X1)
      | ~ member(X0,union(X1,X2)) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f64,plain,
    ! [X2,X0,X1] :
      ( member(X0,union(X1,X2))
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f65,plain,
    ! [X2,X0,X1] :
      ( member(X0,union(X1,X2))
      | ~ member(X0,X2) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f81,plain,
    ~ equal_set(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),
    inference(cnf_transformation,[],[f53]) ).

cnf(c_49,plain,
    ( ~ member(sK0(X0,X1),X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f56]) ).

cnf(c_50,plain,
    ( member(sK0(X0,X1),X0)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f55]) ).

cnf(c_52,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X1,X0)
    | equal_set(X0,X1) ),
    inference(cnf_transformation,[],[f57]) ).

cnf(c_58,plain,
    ( ~ member(X0,X1)
    | member(X0,union(X2,X1)) ),
    inference(cnf_transformation,[],[f65]) ).

cnf(c_59,plain,
    ( ~ member(X0,X1)
    | member(X0,union(X1,X2)) ),
    inference(cnf_transformation,[],[f64]) ).

cnf(c_60,plain,
    ( ~ member(X0,union(X1,X2))
    | member(X0,X1)
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f63]) ).

cnf(c_76,negated_conjecture,
    ~ equal_set(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),
    inference(cnf_transformation,[],[f81]) ).

cnf(c_372,plain,
    ( union(union(sK3,sK4),sK5) != X0
    | union(sK3,union(sK4,sK5)) != X1
    | ~ subset(X0,X1)
    | ~ subset(X1,X0) ),
    inference(resolution_lifted,[status(thm)],[c_52,c_76]) ).

cnf(c_373,plain,
    ( ~ subset(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5)))
    | ~ subset(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)) ),
    inference(unflattening,[status(thm)],[c_372]) ).

cnf(c_438,plain,
    ( ~ subset(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5)))
    | ~ subset(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)) ),
    inference(prop_impl_just,[status(thm)],[c_373]) ).

cnf(c_1363,plain,
    ( ~ member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),union(union(sK3,sK4),sK5))
    | subset(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)) ),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_1378,plain,
    ( member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),union(sK3,union(sK4,sK5)))
    | subset(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)) ),
    inference(instantiation,[status(thm)],[c_50]) ).

cnf(c_1615,plain,
    ( member(sK0(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),union(union(sK3,sK4),sK5))
    | subset(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))) ),
    inference(instantiation,[status(thm)],[c_50]) ).

cnf(c_1616,plain,
    ( ~ member(sK0(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),union(sK3,union(sK4,sK5)))
    | subset(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))) ),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_1688,plain,
    ( ~ member(sK0(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),union(union(sK3,sK4),sK5))
    | member(sK0(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),union(sK3,sK4))
    | member(sK0(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),sK5) ),
    inference(instantiation,[status(thm)],[c_60]) ).

cnf(c_1826,plain,
    ( ~ member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),union(sK3,union(sK4,sK5)))
    | member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),union(sK4,sK5))
    | member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),sK3) ),
    inference(instantiation,[status(thm)],[c_60]) ).

cnf(c_3681,plain,
    ( ~ member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),sK5)
    | member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),union(union(sK3,sK4),sK5)) ),
    inference(instantiation,[status(thm)],[c_58]) ).

cnf(c_3682,plain,
    ( ~ member(sK0(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),union(sK4,sK5))
    | member(sK0(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),union(sK3,union(sK4,sK5))) ),
    inference(instantiation,[status(thm)],[c_58]) ).

cnf(c_3683,plain,
    ( ~ member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),union(sK3,sK4))
    | member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),union(union(sK3,sK4),sK5)) ),
    inference(instantiation,[status(thm)],[c_59]) ).

cnf(c_3684,plain,
    ( ~ member(sK0(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),sK3)
    | member(sK0(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),union(sK3,union(sK4,sK5))) ),
    inference(instantiation,[status(thm)],[c_59]) ).

cnf(c_5518,plain,
    ( ~ member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),union(X0,sK5))
    | member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),X0)
    | member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),sK5) ),
    inference(instantiation,[status(thm)],[c_60]) ).

cnf(c_5547,plain,
    ( ~ member(sK0(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),sK5)
    | member(sK0(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),union(sK4,sK5)) ),
    inference(instantiation,[status(thm)],[c_58]) ).

cnf(c_5548,plain,
    ( ~ member(sK0(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),sK4)
    | member(sK0(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),union(sK4,sK5)) ),
    inference(instantiation,[status(thm)],[c_59]) ).

cnf(c_5569,plain,
    ( ~ member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),sK4)
    | member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),union(sK3,sK4)) ),
    inference(instantiation,[status(thm)],[c_58]) ).

cnf(c_5570,plain,
    ( ~ member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),sK3)
    | member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),union(sK3,sK4)) ),
    inference(instantiation,[status(thm)],[c_59]) ).

cnf(c_8382,plain,
    ( ~ member(sK0(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),union(sK3,sK4))
    | member(sK0(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),sK3)
    | member(sK0(union(union(sK3,sK4),sK5),union(sK3,union(sK4,sK5))),sK4) ),
    inference(instantiation,[status(thm)],[c_60]) ).

cnf(c_8430,plain,
    ~ subset(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),
    inference(global_subsumption_just,[status(thm)],[c_438,c_373,c_1616,c_1615,c_1688,c_3682,c_3684,c_5547,c_5548,c_8382]) ).

cnf(c_15849,plain,
    ( ~ member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),union(sK4,sK5))
    | member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),sK4)
    | member(sK0(union(sK3,union(sK4,sK5)),union(union(sK3,sK4),sK5)),sK5) ),
    inference(instantiation,[status(thm)],[c_5518]) ).

cnf(c_15850,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_15849,c_8430,c_5570,c_5569,c_3683,c_3681,c_1826,c_1378,c_1363]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.17  % Problem  : SET159+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.18  % Command  : run_iprover %s %d THM
% 0.16/0.38  % Computer : n014.cluster.edu
% 0.16/0.38  % Model    : x86_64 x86_64
% 0.16/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38  % Memory   : 8042.1875MB
% 0.16/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38  % CPULimit : 300
% 0.16/0.38  % WCLimit  : 300
% 0.16/0.38  % DateTime : Sat Aug 26 15:27:02 EDT 2023
% 0.16/0.38  % CPUTime  : 
% 0.22/0.52  Running first-order theorem proving
% 0.22/0.52  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 17.33/3.24  % SZS status Started for theBenchmark.p
% 17.33/3.24  % SZS status Theorem for theBenchmark.p
% 17.33/3.24  
% 17.33/3.24  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 17.33/3.24  
% 17.33/3.24  ------  iProver source info
% 17.33/3.24  
% 17.33/3.24  git: date: 2023-05-31 18:12:56 +0000
% 17.33/3.24  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 17.33/3.24  git: non_committed_changes: false
% 17.33/3.24  git: last_make_outside_of_git: false
% 17.33/3.24  
% 17.33/3.24  ------ Parsing...
% 17.33/3.24  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 17.33/3.24  
% 17.33/3.24  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e 
% 17.33/3.24  
% 17.33/3.24  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 17.33/3.24  
% 17.33/3.24  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 17.33/3.24  ------ Proving...
% 17.33/3.24  ------ Problem Properties 
% 17.33/3.24  
% 17.33/3.24  
% 17.33/3.24  clauses                                 27
% 17.33/3.24  conjectures                             0
% 17.33/3.24  EPR                                     2
% 17.33/3.24  Horn                                    22
% 17.33/3.24  unary                                   4
% 17.33/3.24  binary                                  16
% 17.33/3.24  lits                                    57
% 17.33/3.24  lits eq                                 3
% 17.33/3.24  fd_pure                                 0
% 17.33/3.24  fd_pseudo                               0
% 17.33/3.24  fd_cond                                 0
% 17.33/3.24  fd_pseudo_cond                          2
% 17.33/3.24  AC symbols                              0
% 17.33/3.24  
% 17.33/3.24  ------ Input Options Time Limit: Unbounded
% 17.33/3.24  
% 17.33/3.24  
% 17.33/3.24  ------ 
% 17.33/3.24  Current options:
% 17.33/3.24  ------ 
% 17.33/3.24  
% 17.33/3.24  
% 17.33/3.24  
% 17.33/3.24  
% 17.33/3.24  ------ Proving...
% 17.33/3.24  
% 17.33/3.24  
% 17.33/3.24  % SZS status Theorem for theBenchmark.p
% 17.33/3.24  
% 17.33/3.24  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.33/3.24  
% 17.33/3.25  
%------------------------------------------------------------------------------