TSTP Solution File: SET063+4 by iProver---3.9

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%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET063+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n027.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 02:59:38 EDT 2024

% Result   : Theorem 3.48s 1.11s
% Output   : CNFRefutation 3.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   41 (  12 unt;   0 def)
%            Number of atoms       :  104 (   2 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  113 (  50   ~;  38   |;  16   &)
%                                         (   5 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   68 (   2 sgn  51   !;   5   ?)

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

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

fof(f4,axiom,
    ! [X2,X0,X1] :
      ( member(X2,intersection(X0,X1))
    <=> ( member(X2,X1)
        & member(X2,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).

fof(f6,axiom,
    ! [X2] : ~ member(X2,empty_set),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).

fof(f12,conjecture,
    ! [X0] : equal_set(intersection(X0,empty_set),empty_set),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI17) ).

fof(f13,negated_conjecture,
    ~ ! [X0] : equal_set(intersection(X0,empty_set),empty_set),
    inference(negated_conjecture,[],[f12]) ).

fof(f15,plain,
    ! [X0,X1,X2] :
      ( member(X0,intersection(X1,X2))
    <=> ( member(X0,X2)
        & member(X0,X1) ) ),
    inference(rectify,[],[f4]) ).

fof(f17,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(rectify,[],[f6]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ( subset(X1,X0)
        & subset(X0,X1) )
     => equal_set(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f2]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(flattening,[],[f25]) ).

fof(f28,plain,
    ? [X0] : ~ equal_set(intersection(X0,empty_set),empty_set),
    inference(ennf_transformation,[],[f13]) ).

fof(f29,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,[],[f24]) ).

fof(f30,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,[],[f29]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK0(X0,X1),X1)
        & member(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f32,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])],[f30,f31]) ).

fof(f34,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,intersection(X1,X2))
        | ~ member(X0,X2)
        | ~ member(X0,X1) )
      & ( ( member(X0,X2)
          & member(X0,X1) )
        | ~ member(X0,intersection(X1,X2)) ) ),
    inference(nnf_transformation,[],[f15]) ).

fof(f35,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,intersection(X1,X2))
        | ~ member(X0,X2)
        | ~ member(X0,X1) )
      & ( ( member(X0,X2)
          & member(X0,X1) )
        | ~ member(X0,intersection(X1,X2)) ) ),
    inference(flattening,[],[f34]) ).

fof(f51,plain,
    ( ? [X0] : ~ equal_set(intersection(X0,empty_set),empty_set)
   => ~ equal_set(intersection(sK3,empty_set),empty_set) ),
    introduced(choice_axiom,[]) ).

fof(f52,plain,
    ~ equal_set(intersection(sK3,empty_set),empty_set),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f28,f51]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK0(X0,X1),X0) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f60,plain,
    ! [X2,X0,X1] :
      ( member(X0,X2)
      | ~ member(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f65,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(cnf_transformation,[],[f17]) ).

fof(f80,plain,
    ~ equal_set(intersection(sK3,empty_set),empty_set),
    inference(cnf_transformation,[],[f52]) ).

cnf(c_49,plain,
    ( ~ member(sK0(X0,X1),X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f55]) ).

cnf(c_50,plain,
    ( member(sK0(X0,X1),X0)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f54]) ).

cnf(c_52,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X1,X0)
    | equal_set(X0,X1) ),
    inference(cnf_transformation,[],[f56]) ).

cnf(c_56,plain,
    ( ~ member(X0,intersection(X1,X2))
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f60]) ).

cnf(c_61,plain,
    ~ member(X0,empty_set),
    inference(cnf_transformation,[],[f65]) ).

cnf(c_76,negated_conjecture,
    ~ equal_set(intersection(sK3,empty_set),empty_set),
    inference(cnf_transformation,[],[f80]) ).

cnf(c_422,plain,
    ( intersection(sK3,empty_set) != X0
    | X1 != empty_set
    | ~ subset(X0,X1)
    | ~ subset(X1,X0) ),
    inference(resolution_lifted,[status(thm)],[c_52,c_76]) ).

cnf(c_423,plain,
    ( ~ subset(intersection(sK3,empty_set),empty_set)
    | ~ subset(empty_set,intersection(sK3,empty_set)) ),
    inference(unflattening,[status(thm)],[c_422]) ).

cnf(c_1434,plain,
    ( ~ member(sK0(intersection(sK3,empty_set),empty_set),empty_set)
    | subset(intersection(sK3,empty_set),empty_set) ),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_1489,plain,
    ( member(sK0(intersection(sK3,empty_set),empty_set),intersection(sK3,empty_set))
    | subset(intersection(sK3,empty_set),empty_set) ),
    inference(instantiation,[status(thm)],[c_50]) ).

cnf(c_1852,plain,
    ( member(sK0(empty_set,intersection(sK3,empty_set)),empty_set)
    | subset(empty_set,intersection(sK3,empty_set)) ),
    inference(instantiation,[status(thm)],[c_50]) ).

cnf(c_1952,plain,
    ~ member(sK0(empty_set,intersection(sK3,empty_set)),empty_set),
    inference(instantiation,[status(thm)],[c_61]) ).

cnf(c_2012,plain,
    ( ~ member(sK0(intersection(sK3,empty_set),empty_set),intersection(sK3,empty_set))
    | member(sK0(intersection(sK3,empty_set),empty_set),empty_set) ),
    inference(instantiation,[status(thm)],[c_56]) ).

cnf(c_2013,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_2012,c_1952,c_1852,c_1489,c_1434,c_423]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem  : SET063+4 : TPTP v8.1.2. Released v2.2.0.
% 0.05/0.11  % Command  : run_iprover %s %d THM
% 0.10/0.31  % Computer : n027.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Thu May  2 20:52:50 EDT 2024
% 0.10/0.31  % CPUTime  : 
% 0.16/0.41  Running first-order theorem proving
% 0.16/0.41  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
% 3.48/1.11  % SZS status Started for theBenchmark.p
% 3.48/1.11  % SZS status Theorem for theBenchmark.p
% 3.48/1.11  
% 3.48/1.11  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.48/1.11  
% 3.48/1.11  ------  iProver source info
% 3.48/1.11  
% 3.48/1.11  git: date: 2024-05-02 19:28:25 +0000
% 3.48/1.11  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.48/1.11  git: non_committed_changes: false
% 3.48/1.11  
% 3.48/1.11  ------ Parsing...
% 3.48/1.11  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.48/1.11  
% 3.48/1.11  ------ 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 
% 3.48/1.11  
% 3.48/1.11  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.48/1.11  
% 3.48/1.11  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.48/1.11  ------ Proving...
% 3.48/1.11  ------ Problem Properties 
% 3.48/1.11  
% 3.48/1.11  
% 3.48/1.11  clauses                                 27
% 3.48/1.11  conjectures                             0
% 3.48/1.11  EPR                                     2
% 3.48/1.11  Horn                                    22
% 3.48/1.11  unary                                   4
% 3.48/1.11  binary                                  16
% 3.48/1.11  lits                                    57
% 3.48/1.11  lits eq                                 3
% 3.48/1.11  fd_pure                                 0
% 3.48/1.11  fd_pseudo                               0
% 3.48/1.11  fd_cond                                 0
% 3.48/1.11  fd_pseudo_cond                          2
% 3.48/1.11  AC symbols                              0
% 3.48/1.11  
% 3.48/1.11  ------ Schedule dynamic 5 is on 
% 3.48/1.11  
% 3.48/1.11  ------ no conjectures: strip conj schedule 
% 3.48/1.11  
% 3.48/1.11  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.48/1.11  
% 3.48/1.11  
% 3.48/1.11  ------ 
% 3.48/1.11  Current options:
% 3.48/1.11  ------ 
% 3.48/1.11  
% 3.48/1.11  
% 3.48/1.11  
% 3.48/1.11  
% 3.48/1.11  ------ Proving...
% 3.48/1.11  
% 3.48/1.11  
% 3.48/1.11  % SZS status Theorem for theBenchmark.p
% 3.48/1.11  
% 3.48/1.11  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.48/1.11  
% 3.48/1.11  
%------------------------------------------------------------------------------