TSTP Solution File: SET597+3 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET597+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n013.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 03:00:53 EDT 2024

% Result   : Theorem 2.93s 1.19s
% Output   : CNFRefutation 2.93s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   71 (  18 unt;   0 def)
%            Number of atoms       :  257 (  57 equ)
%            Maximal formula atoms :   24 (   3 avg)
%            Number of connectives :  306 ( 120   ~; 126   |;  50   &)
%                                         (   3 <=>;   5  =>;   0  <=;   2 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   96 (   2 sgn  47   !;  24   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1] : subset(X0,union(X0,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_of_union) ).

fof(f2,axiom,
    ! [X0,X1,X2] :
      ( ( subset(X2,X1)
        & subset(X0,X1) )
     => subset(union(X0,X2),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_subset) ).

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

fof(f6,axiom,
    ! [X0,X1] : union(X0,X1) = union(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).

fof(f7,axiom,
    ! [X0] : subset(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).

fof(f9,conjecture,
    ! [X0,X1,X2] :
      ( union(X1,X2) = X0
    <=> ( ! [X3] :
            ( ( subset(X2,X3)
              & subset(X1,X3) )
           => subset(X0,X3) )
        & subset(X2,X0)
        & subset(X1,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th56) ).

fof(f10,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( union(X1,X2) = X0
      <=> ( ! [X3] :
              ( ( subset(X2,X3)
                & subset(X1,X3) )
             => subset(X0,X3) )
          & subset(X2,X0)
          & subset(X1,X0) ) ),
    inference(negated_conjecture,[],[f9]) ).

fof(f11,plain,
    ! [X0,X1,X2] :
      ( subset(union(X0,X2),X1)
      | ~ subset(X2,X1)
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f2]) ).

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

fof(f14,plain,
    ? [X0,X1,X2] :
      ( union(X1,X2) = X0
    <~> ( ! [X3] :
            ( subset(X0,X3)
            | ~ subset(X2,X3)
            | ~ subset(X1,X3) )
        & subset(X2,X0)
        & subset(X1,X0) ) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f15,plain,
    ? [X0,X1,X2] :
      ( union(X1,X2) = X0
    <~> ( ! [X3] :
            ( subset(X0,X3)
            | ~ subset(X2,X3)
            | ~ subset(X1,X3) )
        & subset(X2,X0)
        & subset(X1,X0) ) ),
    inference(flattening,[],[f14]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f5]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(flattening,[],[f22]) ).

fof(f28,plain,
    ? [X0,X1,X2] :
      ( ( ? [X3] :
            ( ~ subset(X0,X3)
            & subset(X2,X3)
            & subset(X1,X3) )
        | ~ subset(X2,X0)
        | ~ subset(X1,X0)
        | union(X1,X2) != X0 )
      & ( ( ! [X3] :
              ( subset(X0,X3)
              | ~ subset(X2,X3)
              | ~ subset(X1,X3) )
          & subset(X2,X0)
          & subset(X1,X0) )
        | union(X1,X2) = X0 ) ),
    inference(nnf_transformation,[],[f15]) ).

fof(f29,plain,
    ? [X0,X1,X2] :
      ( ( ? [X3] :
            ( ~ subset(X0,X3)
            & subset(X2,X3)
            & subset(X1,X3) )
        | ~ subset(X2,X0)
        | ~ subset(X1,X0)
        | union(X1,X2) != X0 )
      & ( ( ! [X3] :
              ( subset(X0,X3)
              | ~ subset(X2,X3)
              | ~ subset(X1,X3) )
          & subset(X2,X0)
          & subset(X1,X0) )
        | union(X1,X2) = X0 ) ),
    inference(flattening,[],[f28]) ).

fof(f30,plain,
    ? [X0,X1,X2] :
      ( ( ? [X3] :
            ( ~ subset(X0,X3)
            & subset(X2,X3)
            & subset(X1,X3) )
        | ~ subset(X2,X0)
        | ~ subset(X1,X0)
        | union(X1,X2) != X0 )
      & ( ( ! [X4] :
              ( subset(X0,X4)
              | ~ subset(X2,X4)
              | ~ subset(X1,X4) )
          & subset(X2,X0)
          & subset(X1,X0) )
        | union(X1,X2) = X0 ) ),
    inference(rectify,[],[f29]) ).

fof(f31,plain,
    ( ? [X0,X1,X2] :
        ( ( ? [X3] :
              ( ~ subset(X0,X3)
              & subset(X2,X3)
              & subset(X1,X3) )
          | ~ subset(X2,X0)
          | ~ subset(X1,X0)
          | union(X1,X2) != X0 )
        & ( ( ! [X4] :
                ( subset(X0,X4)
                | ~ subset(X2,X4)
                | ~ subset(X1,X4) )
            & subset(X2,X0)
            & subset(X1,X0) )
          | union(X1,X2) = X0 ) )
   => ( ( ? [X3] :
            ( ~ subset(sK2,X3)
            & subset(sK4,X3)
            & subset(sK3,X3) )
        | ~ subset(sK4,sK2)
        | ~ subset(sK3,sK2)
        | sK2 != union(sK3,sK4) )
      & ( ( ! [X4] :
              ( subset(sK2,X4)
              | ~ subset(sK4,X4)
              | ~ subset(sK3,X4) )
          & subset(sK4,sK2)
          & subset(sK3,sK2) )
        | sK2 = union(sK3,sK4) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f32,plain,
    ( ? [X3] :
        ( ~ subset(sK2,X3)
        & subset(sK4,X3)
        & subset(sK3,X3) )
   => ( ~ subset(sK2,sK5)
      & subset(sK4,sK5)
      & subset(sK3,sK5) ) ),
    introduced(choice_axiom,[]) ).

fof(f33,plain,
    ( ( ( ~ subset(sK2,sK5)
        & subset(sK4,sK5)
        & subset(sK3,sK5) )
      | ~ subset(sK4,sK2)
      | ~ subset(sK3,sK2)
      | sK2 != union(sK3,sK4) )
    & ( ( ! [X4] :
            ( subset(sK2,X4)
            | ~ subset(sK4,X4)
            | ~ subset(sK3,X4) )
        & subset(sK4,sK2)
        & subset(sK3,sK2) )
      | sK2 = union(sK3,sK4) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f30,f32,f31]) ).

fof(f34,plain,
    ! [X0,X1] : subset(X0,union(X0,X1)),
    inference(cnf_transformation,[],[f1]) ).

fof(f35,plain,
    ! [X2,X0,X1] :
      ( subset(union(X0,X2),X1)
      | ~ subset(X2,X1)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f12]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f45,plain,
    ! [X0,X1] : union(X0,X1) = union(X1,X0),
    inference(cnf_transformation,[],[f6]) ).

fof(f46,plain,
    ! [X0] : subset(X0,X0),
    inference(cnf_transformation,[],[f7]) ).

fof(f51,plain,
    ( subset(sK3,sK2)
    | sK2 = union(sK3,sK4) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f52,plain,
    ( subset(sK4,sK2)
    | sK2 = union(sK3,sK4) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f53,plain,
    ! [X4] :
      ( subset(sK2,X4)
      | ~ subset(sK4,X4)
      | ~ subset(sK3,X4)
      | sK2 = union(sK3,sK4) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f54,plain,
    ( subset(sK3,sK5)
    | ~ subset(sK4,sK2)
    | ~ subset(sK3,sK2)
    | sK2 != union(sK3,sK4) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f55,plain,
    ( subset(sK4,sK5)
    | ~ subset(sK4,sK2)
    | ~ subset(sK3,sK2)
    | sK2 != union(sK3,sK4) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f56,plain,
    ( ~ subset(sK2,sK5)
    | ~ subset(sK4,sK2)
    | ~ subset(sK3,sK2)
    | sK2 != union(sK3,sK4) ),
    inference(cnf_transformation,[],[f33]) ).

cnf(c_49,plain,
    subset(X0,union(X0,X1)),
    inference(cnf_transformation,[],[f34]) ).

cnf(c_50,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X2,X1)
    | subset(union(X0,X2),X1) ),
    inference(cnf_transformation,[],[f35]) ).

cnf(c_57,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X1,X0)
    | X0 = X1 ),
    inference(cnf_transformation,[],[f44]) ).

cnf(c_60,plain,
    union(X0,X1) = union(X1,X0),
    inference(cnf_transformation,[],[f45]) ).

cnf(c_61,plain,
    subset(X0,X0),
    inference(cnf_transformation,[],[f46]) ).

cnf(c_64,negated_conjecture,
    ( union(sK3,sK4) != sK2
    | ~ subset(sK2,sK5)
    | ~ subset(sK4,sK2)
    | ~ subset(sK3,sK2) ),
    inference(cnf_transformation,[],[f56]) ).

cnf(c_65,negated_conjecture,
    ( union(sK3,sK4) != sK2
    | ~ subset(sK4,sK2)
    | ~ subset(sK3,sK2)
    | subset(sK4,sK5) ),
    inference(cnf_transformation,[],[f55]) ).

cnf(c_66,negated_conjecture,
    ( union(sK3,sK4) != sK2
    | ~ subset(sK4,sK2)
    | ~ subset(sK3,sK2)
    | subset(sK3,sK5) ),
    inference(cnf_transformation,[],[f54]) ).

cnf(c_67,negated_conjecture,
    ( ~ subset(sK4,X0)
    | ~ subset(sK3,X0)
    | union(sK3,sK4) = sK2
    | subset(sK2,X0) ),
    inference(cnf_transformation,[],[f53]) ).

cnf(c_68,negated_conjecture,
    ( union(sK3,sK4) = sK2
    | subset(sK4,sK2) ),
    inference(cnf_transformation,[],[f52]) ).

cnf(c_69,negated_conjecture,
    ( union(sK3,sK4) = sK2
    | subset(sK3,sK2) ),
    inference(cnf_transformation,[],[f51]) ).

cnf(c_179,plain,
    ( union(sK4,sK3) = sK2
    | subset(sK3,sK2) ),
    inference(demodulation,[status(thm)],[c_69,c_60]) ).

cnf(c_184,plain,
    ( union(sK4,sK3) = sK2
    | subset(sK4,sK2) ),
    inference(demodulation,[status(thm)],[c_68,c_60]) ).

cnf(c_237,plain,
    ( ~ subset(sK4,X0)
    | ~ subset(sK3,X0)
    | union(sK4,sK3) = sK2
    | subset(sK2,X0) ),
    inference(demodulation,[status(thm)],[c_67,c_60]) ).

cnf(c_246,plain,
    ( union(sK4,sK3) != sK2
    | ~ subset(sK4,sK2)
    | ~ subset(sK3,sK2)
    | subset(sK3,sK5) ),
    inference(demodulation,[status(thm)],[c_66,c_60]) ).

cnf(c_255,plain,
    ( union(sK4,sK3) != sK2
    | ~ subset(sK4,sK2)
    | ~ subset(sK3,sK2)
    | subset(sK4,sK5) ),
    inference(demodulation,[status(thm)],[c_65,c_60]) ).

cnf(c_264,plain,
    ( union(sK4,sK3) != sK2
    | ~ subset(sK2,sK5)
    | ~ subset(sK4,sK2)
    | ~ subset(sK3,sK2) ),
    inference(demodulation,[status(thm)],[c_64,c_60]) ).

cnf(c_802,plain,
    subset(X0,union(X1,X0)),
    inference(superposition,[status(thm)],[c_60,c_49]) ).

cnf(c_812,plain,
    ( ~ subset(sK4,union(X0,sK3))
    | union(sK4,sK3) = sK2
    | subset(sK2,union(X0,sK3)) ),
    inference(superposition,[status(thm)],[c_802,c_237]) ).

cnf(c_894,plain,
    ( union(sK4,sK3) = sK2
    | subset(sK2,union(sK4,sK3)) ),
    inference(superposition,[status(thm)],[c_49,c_812]) ).

cnf(c_963,plain,
    ( ~ subset(union(X0,X1),X1)
    | union(X0,X1) = X1 ),
    inference(superposition,[status(thm)],[c_802,c_57]) ).

cnf(c_964,plain,
    ( ~ subset(union(sK4,sK3),sK2)
    | union(sK4,sK3) = sK2 ),
    inference(superposition,[status(thm)],[c_894,c_57]) ).

cnf(c_986,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X2,X1)
    | subset(union(X2,X0),X1) ),
    inference(superposition,[status(thm)],[c_60,c_50]) ).

cnf(c_1207,plain,
    ( ~ subset(X0,X0)
    | ~ subset(X1,X0)
    | union(X1,X0) = X0 ),
    inference(superposition,[status(thm)],[c_986,c_963]) ).

cnf(c_1208,plain,
    ( ~ subset(sK4,sK2)
    | ~ subset(sK3,sK2)
    | union(sK4,sK3) = sK2 ),
    inference(superposition,[status(thm)],[c_986,c_964]) ).

cnf(c_1212,plain,
    ( ~ subset(X0,X1)
    | union(X0,X1) = X1 ),
    inference(forward_subsumption_resolution,[status(thm)],[c_1207,c_61]) ).

cnf(c_1332,plain,
    ( union(sK4,sK2) = sK2
    | union(sK4,sK3) = sK2 ),
    inference(superposition,[status(thm)],[c_184,c_1212]) ).

cnf(c_1360,plain,
    union(sK4,sK3) = sK2,
    inference(global_subsumption_just,[status(thm)],[c_179,c_179,c_184,c_1208]) ).

cnf(c_1439,plain,
    subset(sK4,sK2),
    inference(superposition,[status(thm)],[c_1360,c_49]) ).

cnf(c_1492,plain,
    union(sK4,sK3) = sK2,
    inference(global_subsumption_just,[status(thm)],[c_1332,c_1360]) ).

cnf(c_1505,plain,
    ( sK2 != sK2
    | ~ subset(sK4,sK2)
    | ~ subset(sK3,sK2)
    | subset(sK4,sK5) ),
    inference(demodulation,[status(thm)],[c_255,c_1492]) ).

cnf(c_1506,plain,
    ( sK2 != sK2
    | ~ subset(sK4,sK2)
    | ~ subset(sK3,sK2)
    | subset(sK3,sK5) ),
    inference(demodulation,[status(thm)],[c_246,c_1492]) ).

cnf(c_1508,plain,
    ( ~ subset(sK4,sK2)
    | ~ subset(sK3,sK2)
    | subset(sK3,sK5) ),
    inference(equality_resolution_simp,[status(thm)],[c_1506]) ).

cnf(c_1512,plain,
    ( ~ subset(sK4,sK2)
    | ~ subset(sK3,sK2)
    | subset(sK4,sK5) ),
    inference(equality_resolution_simp,[status(thm)],[c_1505]) ).

cnf(c_1531,plain,
    subset(sK3,sK2),
    inference(superposition,[status(thm)],[c_1492,c_802]) ).

cnf(c_1532,plain,
    ( ~ subset(sK4,X0)
    | ~ subset(sK3,X0)
    | subset(sK2,X0) ),
    inference(superposition,[status(thm)],[c_1492,c_986]) ).

cnf(c_1788,plain,
    subset(sK3,sK5),
    inference(global_subsumption_just,[status(thm)],[c_1508,c_179,c_184,c_246,c_1208,c_1439,c_1531]) ).

cnf(c_2023,plain,
    subset(sK4,sK5),
    inference(global_subsumption_just,[status(thm)],[c_1512,c_255,c_1360,c_1439,c_1531]) ).

cnf(c_2049,plain,
    ( ~ subset(sK3,sK5)
    | subset(sK2,sK5) ),
    inference(superposition,[status(thm)],[c_2023,c_1532]) ).

cnf(c_2053,plain,
    subset(sK2,sK5),
    inference(forward_subsumption_resolution,[status(thm)],[c_2049,c_1788]) ).

cnf(c_2060,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_2053,c_1531,c_1439,c_1360,c_264]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET597+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n013.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 : Thu May  2 20:23:49 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.20/0.47  Running first-order theorem proving
% 0.20/0.47  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
% 2.93/1.19  % SZS status Started for theBenchmark.p
% 2.93/1.19  % SZS status Theorem for theBenchmark.p
% 2.93/1.19  
% 2.93/1.19  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 2.93/1.19  
% 2.93/1.19  ------  iProver source info
% 2.93/1.19  
% 2.93/1.19  git: date: 2024-05-02 19:28:25 +0000
% 2.93/1.19  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 2.93/1.19  git: non_committed_changes: false
% 2.93/1.19  
% 2.93/1.19  ------ Parsing...
% 2.93/1.19  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 2.93/1.19  
% 2.93/1.19  ------ Preprocessing... sup_sim: 6  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 
% 2.93/1.19  
% 2.93/1.19  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 2.93/1.19  
% 2.93/1.19  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.93/1.19  ------ Proving...
% 2.93/1.19  ------ Problem Properties 
% 2.93/1.19  
% 2.93/1.19  
% 2.93/1.19  clauses                                 19
% 2.93/1.19  conjectures                             0
% 2.93/1.19  EPR                                     3
% 2.93/1.19  Horn                                    13
% 2.93/1.19  unary                                   3
% 2.93/1.19  binary                                  6
% 2.93/1.19  lits                                    49
% 2.93/1.19  lits eq                                 10
% 2.93/1.19  fd_pure                                 0
% 2.93/1.19  fd_pseudo                               0
% 2.93/1.19  fd_cond                                 0
% 2.93/1.19  fd_pseudo_cond                          3
% 2.93/1.19  AC symbols                              0
% 2.93/1.19  
% 2.93/1.19  ------ Schedule dynamic 5 is on 
% 2.93/1.19  
% 2.93/1.19  ------ no conjectures: strip conj schedule 
% 2.93/1.19  
% 2.93/1.19  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.93/1.19  
% 2.93/1.19  
% 2.93/1.19  ------ 
% 2.93/1.19  Current options:
% 2.93/1.19  ------ 
% 2.93/1.19  
% 2.93/1.19  
% 2.93/1.19  
% 2.93/1.19  
% 2.93/1.19  ------ Proving...
% 2.93/1.19  
% 2.93/1.19  
% 2.93/1.19  % SZS status Theorem for theBenchmark.p
% 2.93/1.19  
% 2.93/1.19  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.93/1.19  
% 2.93/1.19  
%------------------------------------------------------------------------------