TSTP Solution File: SET595+4 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET595+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n015.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 03:00:52 EDT 2024

% Result   : Theorem 61.71s 9.27s
% Output   : CNFRefutation 61.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   63 (   5 unt;   0 def)
%            Number of atoms       :  179 (   2 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  194 (  78   ~;  78   |;  24   &)
%                                         (   7 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :  124 (   3 sgn  79   !;   7   ?)

% 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(f7,axiom,
    ! [X1,X0,X3] :
      ( member(X1,difference(X3,X0))
    <=> ( ~ member(X1,X0)
        & member(X1,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference) ).

fof(f12,conjecture,
    ! [X0,X3] :
      ( subset(X0,X3)
     => equal_set(union(difference(X3,X0),X0),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI27) ).

fof(f13,negated_conjecture,
    ~ ! [X0,X3] :
        ( subset(X0,X3)
       => equal_set(union(difference(X3,X0),X0),X3) ),
    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(f18,plain,
    ! [X0,X1,X2] :
      ( member(X0,difference(X2,X1))
    <=> ( ~ member(X0,X1)
        & member(X0,X2) ) ),
    inference(rectify,[],[f7]) ).

fof(f23,plain,
    ~ ! [X0,X1] :
        ( subset(X0,X1)
       => equal_set(union(difference(X1,X0),X0),X1) ),
    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] :
      ( ~ equal_set(union(difference(X1,X0),X0),X1)
      & subset(X0,X1) ),
    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(f39,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,difference(X2,X1))
        | member(X0,X1)
        | ~ member(X0,X2) )
      & ( ( ~ member(X0,X1)
          & member(X0,X2) )
        | ~ member(X0,difference(X2,X1)) ) ),
    inference(nnf_transformation,[],[f18]) ).

fof(f40,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,difference(X2,X1))
        | member(X0,X1)
        | ~ member(X0,X2) )
      & ( ( ~ member(X0,X1)
          & member(X0,X2) )
        | ~ member(X0,difference(X2,X1)) ) ),
    inference(flattening,[],[f39]) ).

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

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

fof(f54,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f33]) ).

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(f67,plain,
    ! [X2,X0,X1] :
      ( member(X0,X2)
      | ~ member(X0,difference(X2,X1)) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f69,plain,
    ! [X2,X0,X1] :
      ( member(X0,difference(X2,X1))
      | member(X0,X1)
      | ~ member(X0,X2) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f81,plain,
    subset(sK3,sK4),
    inference(cnf_transformation,[],[f53]) ).

fof(f82,plain,
    ~ equal_set(union(difference(sK4,sK3),sK3),sK4),
    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_51,plain,
    ( ~ subset(X0,X1)
    | ~ member(X2,X0)
    | member(X2,X1) ),
    inference(cnf_transformation,[],[f54]) ).

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_62,plain,
    ( ~ member(X0,X1)
    | member(X0,difference(X1,X2))
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f69]) ).

cnf(c_64,plain,
    ( ~ member(X0,difference(X1,X2))
    | member(X0,X1) ),
    inference(cnf_transformation,[],[f67]) ).

cnf(c_76,negated_conjecture,
    ~ equal_set(union(difference(sK4,sK3),sK3),sK4),
    inference(cnf_transformation,[],[f82]) ).

cnf(c_77,negated_conjecture,
    subset(sK3,sK4),
    inference(cnf_transformation,[],[f81]) ).

cnf(c_432,plain,
    ( union(difference(sK4,sK3),sK3) != X0
    | X1 != sK4
    | ~ subset(X0,X1)
    | ~ subset(X1,X0) ),
    inference(resolution_lifted,[status(thm)],[c_52,c_76]) ).

cnf(c_433,plain,
    ( ~ subset(union(difference(sK4,sK3),sK3),sK4)
    | ~ subset(sK4,union(difference(sK4,sK3),sK3)) ),
    inference(unflattening,[status(thm)],[c_432]) ).

cnf(c_1530,plain,
    ( ~ member(sK0(union(difference(sK4,sK3),sK3),sK4),sK4)
    | subset(union(difference(sK4,sK3),sK3),sK4) ),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_1531,plain,
    ( member(sK0(union(difference(sK4,sK3),sK3),sK4),union(difference(sK4,sK3),sK3))
    | subset(union(difference(sK4,sK3),sK3),sK4) ),
    inference(instantiation,[status(thm)],[c_50]) ).

cnf(c_1925,plain,
    ( ~ member(X0,union(difference(X1,X2),X3))
    | member(X0,difference(X1,X2))
    | member(X0,X3) ),
    inference(instantiation,[status(thm)],[c_60]) ).

cnf(c_1984,plain,
    ( ~ member(sK0(X0,union(X1,X2)),X2)
    | subset(X0,union(X1,X2)) ),
    inference(superposition,[status(thm)],[c_58,c_49]) ).

cnf(c_2017,plain,
    ( ~ member(sK0(X0,union(X1,X2)),X1)
    | subset(X0,union(X1,X2)) ),
    inference(superposition,[status(thm)],[c_59,c_49]) ).

cnf(c_2064,plain,
    ( member(sK0(sK4,union(difference(sK4,sK3),sK3)),sK4)
    | subset(sK4,union(difference(sK4,sK3),sK3)) ),
    inference(instantiation,[status(thm)],[c_50]) ).

cnf(c_8485,plain,
    ( ~ member(sK0(union(difference(sK4,sK3),sK3),sK4),union(difference(sK4,sK3),sK3))
    | member(sK0(union(difference(sK4,sK3),sK3),sK4),difference(sK4,sK3))
    | member(sK0(union(difference(sK4,sK3),sK3),sK4),sK3) ),
    inference(instantiation,[status(thm)],[c_1925]) ).

cnf(c_21023,plain,
    ( ~ member(sK0(sK4,union(difference(sK4,sK3),sK3)),sK4)
    | member(sK0(sK4,union(difference(sK4,sK3),sK3)),difference(sK4,X0))
    | member(sK0(sK4,union(difference(sK4,sK3),sK3)),X0) ),
    inference(instantiation,[status(thm)],[c_62]) ).

cnf(c_21029,plain,
    ( ~ member(sK0(sK4,union(difference(sK4,sK3),sK3)),sK4)
    | member(sK0(sK4,union(difference(sK4,sK3),sK3)),difference(sK4,sK3))
    | member(sK0(sK4,union(difference(sK4,sK3),sK3)),sK3) ),
    inference(instantiation,[status(thm)],[c_21023]) ).

cnf(c_22965,plain,
    ( ~ member(sK0(union(difference(sK4,sK3),sK3),sK4),X0)
    | ~ subset(X0,sK4)
    | member(sK0(union(difference(sK4,sK3),sK3),sK4),sK4) ),
    inference(instantiation,[status(thm)],[c_51]) ).

cnf(c_22966,plain,
    ( ~ member(sK0(union(difference(sK4,sK3),sK3),sK4),sK3)
    | ~ subset(sK3,sK4)
    | member(sK0(union(difference(sK4,sK3),sK3),sK4),sK4) ),
    inference(instantiation,[status(thm)],[c_22965]) ).

cnf(c_35788,plain,
    ( ~ member(sK0(union(difference(sK4,sK3),sK3),sK4),difference(sK4,sK3))
    | member(sK0(union(difference(sK4,sK3),sK3),sK4),sK4) ),
    inference(instantiation,[status(thm)],[c_64]) ).

cnf(c_305486,plain,
    ( ~ member(sK0(sK4,union(difference(sK4,sK3),sK3)),sK3)
    | subset(sK4,union(difference(sK4,sK3),sK3)) ),
    inference(instantiation,[status(thm)],[c_1984]) ).

cnf(c_305614,plain,
    ( ~ member(sK0(sK4,union(difference(sK4,sK3),sK3)),difference(sK4,sK3))
    | subset(sK4,union(difference(sK4,sK3),sK3)) ),
    inference(instantiation,[status(thm)],[c_2017]) ).

cnf(c_307102,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_305614,c_305486,c_35788,c_22966,c_21029,c_8485,c_2064,c_1531,c_1530,c_433,c_77]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : SET595+4 : TPTP v8.1.2. Released v2.2.0.
% 0.04/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n015.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 : Thu May  2 20:46:06 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 61.71/9.27  % SZS status Started for theBenchmark.p
% 61.71/9.27  % SZS status Theorem for theBenchmark.p
% 61.71/9.27  
% 61.71/9.27  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 61.71/9.27  
% 61.71/9.27  ------  iProver source info
% 61.71/9.27  
% 61.71/9.27  git: date: 2024-05-02 19:28:25 +0000
% 61.71/9.27  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 61.71/9.27  git: non_committed_changes: false
% 61.71/9.27  
% 61.71/9.27  ------ Parsing...
% 61.71/9.27  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 61.71/9.27  
% 61.71/9.27  ------ 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 
% 61.71/9.27  
% 61.71/9.27  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 61.71/9.27  
% 61.71/9.27  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 61.71/9.27  ------ Proving...
% 61.71/9.27  ------ Problem Properties 
% 61.71/9.27  
% 61.71/9.27  
% 61.71/9.27  clauses                                 28
% 61.71/9.27  conjectures                             1
% 61.71/9.27  EPR                                     3
% 61.71/9.27  Horn                                    23
% 61.71/9.27  unary                                   5
% 61.71/9.27  binary                                  16
% 61.71/9.27  lits                                    58
% 61.71/9.27  lits eq                                 3
% 61.71/9.27  fd_pure                                 0
% 61.71/9.27  fd_pseudo                               0
% 61.71/9.27  fd_cond                                 0
% 61.71/9.27  fd_pseudo_cond                          2
% 61.71/9.27  AC symbols                              0
% 61.71/9.27  
% 61.71/9.27  ------ Schedule dynamic 5 is on 
% 61.71/9.27  
% 61.71/9.27  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 61.71/9.27  
% 61.71/9.27  
% 61.71/9.27  ------ 
% 61.71/9.27  Current options:
% 61.71/9.27  ------ 
% 61.71/9.27  
% 61.71/9.27  
% 61.71/9.27  
% 61.71/9.27  
% 61.71/9.27  ------ Proving...
% 61.71/9.27  
% 61.71/9.27  
% 61.71/9.27  % SZS status Theorem for theBenchmark.p
% 61.71/9.27  
% 61.71/9.27  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 61.71/9.27  
% 61.71/9.28  
%------------------------------------------------------------------------------