TSTP Solution File: SET185+3 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SET185+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n020.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 15:07:02 EDT 2023

% Result   : Theorem 0.52s 1.20s
% Output   : CNFRefutation 0.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   53 (   9 unt;   0 def)
%            Number of atoms       :  170 (  25 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  190 (  73   ~;  79   |;  27   &)
%                                         (   5 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   97 (   2 sgn;  65   !;  10   ?)

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

fof(f2,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).

fof(f4,axiom,
    ! [X0,X1] : union(X0,X1) = union(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( X0 = X1
    <=> ! [X2] :
          ( member(X2,X0)
        <=> member(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).

fof(f7,conjecture,
    ! [X0,X1] :
      ( subset(X0,X1)
     => union(X0,X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_subset_union) ).

fof(f8,negated_conjecture,
    ~ ! [X0,X1] :
        ( subset(X0,X1)
       => union(X0,X1) = X1 ),
    inference(negated_conjecture,[],[f7]) ).

fof(f9,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f10,plain,
    ? [X0,X1] :
      ( union(X0,X1) != X1
      & subset(X0,X1) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f11,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,union(X0,X1))
        | ( ~ member(X2,X1)
          & ~ member(X2,X0) ) )
      & ( member(X2,X1)
        | member(X2,X0)
        | ~ member(X2,union(X0,X1)) ) ),
    inference(nnf_transformation,[],[f1]) ).

fof(f12,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,union(X0,X1))
        | ( ~ member(X2,X1)
          & ~ member(X2,X0) ) )
      & ( member(X2,X1)
        | member(X2,X0)
        | ~ member(X2,union(X0,X1)) ) ),
    inference(flattening,[],[f11]) ).

fof(f13,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,[],[f9]) ).

fof(f14,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,[],[f13]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK0(X0,X1),X1)
        & member(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f16,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])],[f14,f15]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ? [X2] :
            ( ( ~ member(X2,X1)
              | ~ member(X2,X0) )
            & ( member(X2,X1)
              | member(X2,X0) ) ) )
      & ( ! [X2] :
            ( ( member(X2,X0)
              | ~ member(X2,X1) )
            & ( member(X2,X1)
              | ~ member(X2,X0) ) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f6]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ? [X2] :
            ( ( ~ member(X2,X1)
              | ~ member(X2,X0) )
            & ( member(X2,X1)
              | member(X2,X0) ) ) )
      & ( ! [X3] :
            ( ( member(X3,X0)
              | ~ member(X3,X1) )
            & ( member(X3,X1)
              | ~ member(X3,X0) ) )
        | X0 != X1 ) ),
    inference(rectify,[],[f19]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ member(X2,X1)
            | ~ member(X2,X0) )
          & ( member(X2,X1)
            | member(X2,X0) ) )
     => ( ( ~ member(sK1(X0,X1),X1)
          | ~ member(sK1(X0,X1),X0) )
        & ( member(sK1(X0,X1),X1)
          | member(sK1(X0,X1),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ( ( ~ member(sK1(X0,X1),X1)
            | ~ member(sK1(X0,X1),X0) )
          & ( member(sK1(X0,X1),X1)
            | member(sK1(X0,X1),X0) ) ) )
      & ( ! [X3] :
            ( ( member(X3,X0)
              | ~ member(X3,X1) )
            & ( member(X3,X1)
              | ~ member(X3,X0) ) )
        | X0 != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f20,f21]) ).

fof(f23,plain,
    ( ? [X0,X1] :
        ( union(X0,X1) != X1
        & subset(X0,X1) )
   => ( sK3 != union(sK2,sK3)
      & subset(sK2,sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f24,plain,
    ( sK3 != union(sK2,sK3)
    & subset(sK2,sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f10,f23]) ).

fof(f25,plain,
    ! [X2,X0,X1] :
      ( member(X2,X1)
      | member(X2,X0)
      | ~ member(X2,union(X0,X1)) ),
    inference(cnf_transformation,[],[f12]) ).

fof(f26,plain,
    ! [X2,X0,X1] :
      ( member(X2,union(X0,X1))
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f12]) ).

fof(f28,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK0(X0,X1),X0) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f34,plain,
    ! [X0,X1] : union(X0,X1) = union(X1,X0),
    inference(cnf_transformation,[],[f4]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( X0 = X1
      | member(sK1(X0,X1),X1)
      | member(sK1(X0,X1),X0) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ member(sK1(X0,X1),X1)
      | ~ member(sK1(X0,X1),X0) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f40,plain,
    subset(sK2,sK3),
    inference(cnf_transformation,[],[f24]) ).

fof(f41,plain,
    sK3 != union(sK2,sK3),
    inference(cnf_transformation,[],[f24]) ).

cnf(c_50,plain,
    ( ~ member(X0,X1)
    | member(X0,union(X1,X2)) ),
    inference(cnf_transformation,[],[f26]) ).

cnf(c_51,plain,
    ( ~ member(X0,union(X1,X2))
    | member(X0,X1)
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f25]) ).

cnf(c_52,plain,
    ( ~ member(sK0(X0,X1),X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f30]) ).

cnf(c_53,plain,
    ( member(sK0(X0,X1),X0)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f29]) ).

cnf(c_54,plain,
    ( ~ member(X0,X1)
    | ~ subset(X1,X2)
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f28]) ).

cnf(c_58,plain,
    union(X0,X1) = union(X1,X0),
    inference(cnf_transformation,[],[f34]) ).

cnf(c_60,plain,
    ( ~ member(sK1(X0,X1),X0)
    | ~ member(sK1(X0,X1),X1)
    | X0 = X1 ),
    inference(cnf_transformation,[],[f39]) ).

cnf(c_61,plain,
    ( X0 = X1
    | member(sK1(X0,X1),X0)
    | member(sK1(X0,X1),X1) ),
    inference(cnf_transformation,[],[f38]) ).

cnf(c_62,negated_conjecture,
    union(sK2,sK3) != sK3,
    inference(cnf_transformation,[],[f41]) ).

cnf(c_63,negated_conjecture,
    subset(sK2,sK3),
    inference(cnf_transformation,[],[f40]) ).

cnf(c_125,plain,
    union(sK3,sK2) != sK3,
    inference(demodulation,[status(thm)],[c_62,c_58]) ).

cnf(c_623,plain,
    ( ~ member(sK1(union(sK3,sK2),sK3),union(sK3,sK2))
    | ~ member(sK1(union(sK3,sK2),sK3),sK3)
    | union(sK3,sK2) = sK3 ),
    inference(instantiation,[status(thm)],[c_60]) ).

cnf(c_624,plain,
    ( union(sK3,sK2) = sK3
    | member(sK1(union(sK3,sK2),sK3),union(sK3,sK2))
    | member(sK1(union(sK3,sK2),sK3),sK3) ),
    inference(instantiation,[status(thm)],[c_61]) ).

cnf(c_642,plain,
    ( member(sK0(union(sK3,sK2),sK3),union(sK3,sK2))
    | subset(union(sK3,sK2),sK3) ),
    inference(instantiation,[status(thm)],[c_53]) ).

cnf(c_643,plain,
    ( ~ member(sK0(union(sK3,sK2),sK3),sK3)
    | subset(union(sK3,sK2),sK3) ),
    inference(instantiation,[status(thm)],[c_52]) ).

cnf(c_670,plain,
    ( ~ member(sK1(union(sK3,sK2),sK3),union(sK3,sK2))
    | ~ subset(union(sK3,sK2),X0)
    | member(sK1(union(sK3,sK2),sK3),X0) ),
    inference(instantiation,[status(thm)],[c_54]) ).

cnf(c_675,plain,
    ( ~ member(sK1(union(sK3,sK2),sK3),union(sK3,sK2))
    | ~ subset(union(sK3,sK2),sK3)
    | member(sK1(union(sK3,sK2),sK3),sK3) ),
    inference(instantiation,[status(thm)],[c_670]) ).

cnf(c_947,plain,
    ( ~ member(sK1(union(sK3,sK2),sK3),sK3)
    | member(sK1(union(sK3,sK2),sK3),union(sK3,X0)) ),
    inference(instantiation,[status(thm)],[c_50]) ).

cnf(c_1466,plain,
    ( ~ member(sK0(union(sK3,sK2),sK3),union(sK3,sK2))
    | member(sK0(union(sK3,sK2),sK3),sK3)
    | member(sK0(union(sK3,sK2),sK3),sK2) ),
    inference(instantiation,[status(thm)],[c_51]) ).

cnf(c_2616,plain,
    ( ~ member(sK0(union(sK3,sK2),sK3),sK2)
    | ~ subset(sK2,X0)
    | member(sK0(union(sK3,sK2),sK3),X0) ),
    inference(instantiation,[status(thm)],[c_54]) ).

cnf(c_2621,plain,
    ( ~ member(sK0(union(sK3,sK2),sK3),sK2)
    | ~ subset(sK2,sK3)
    | member(sK0(union(sK3,sK2),sK3),sK3) ),
    inference(instantiation,[status(thm)],[c_2616]) ).

cnf(c_2940,plain,
    ( ~ member(sK1(union(sK3,sK2),sK3),sK3)
    | member(sK1(union(sK3,sK2),sK3),union(sK3,sK2)) ),
    inference(instantiation,[status(thm)],[c_947]) ).

cnf(c_5385,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_2940,c_2621,c_1466,c_675,c_642,c_643,c_624,c_623,c_125,c_63]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET185+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n020.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sat Aug 26 11:54:14 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.46  Running first-order theorem proving
% 0.19/0.46  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.52/1.20  % SZS status Started for theBenchmark.p
% 0.52/1.20  % SZS status Theorem for theBenchmark.p
% 0.52/1.20  
% 0.52/1.20  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.52/1.20  
% 0.52/1.20  ------  iProver source info
% 0.52/1.20  
% 0.52/1.20  git: date: 2023-05-31 18:12:56 +0000
% 0.52/1.20  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.52/1.20  git: non_committed_changes: false
% 0.52/1.20  git: last_make_outside_of_git: false
% 0.52/1.20  
% 0.52/1.20  ------ Parsing...
% 0.52/1.20  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 0.52/1.20  
% 0.52/1.20  ------ 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 
% 0.52/1.20  
% 0.52/1.20  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 0.52/1.20  
% 0.52/1.20  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 0.52/1.20  ------ Proving...
% 0.52/1.20  ------ Problem Properties 
% 0.52/1.20  
% 0.52/1.20  
% 0.52/1.20  clauses                                 13
% 0.52/1.20  conjectures                             1
% 0.52/1.20  EPR                                     4
% 0.52/1.20  Horn                                    10
% 0.52/1.20  unary                                   4
% 0.52/1.20  binary                                  4
% 0.52/1.20  lits                                    27
% 0.52/1.20  lits eq                                 5
% 0.52/1.20  fd_pure                                 0
% 0.52/1.20  fd_pseudo                               0
% 0.52/1.20  fd_cond                                 0
% 0.52/1.20  fd_pseudo_cond                          3
% 0.52/1.20  AC symbols                              0
% 0.52/1.20  
% 0.52/1.20  ------ Schedule dynamic 5 is on 
% 0.52/1.20  
% 0.52/1.20  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.52/1.20  
% 0.52/1.20  
% 0.52/1.20  ------ 
% 0.52/1.20  Current options:
% 0.52/1.20  ------ 
% 0.52/1.20  
% 0.52/1.20  
% 0.52/1.20  
% 0.52/1.20  
% 0.52/1.20  ------ Proving...
% 0.52/1.20  
% 0.52/1.20  
% 0.52/1.20  % SZS status Theorem for theBenchmark.p
% 0.52/1.20  
% 0.52/1.20  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.52/1.20  
% 0.52/1.20  
%------------------------------------------------------------------------------