TSTP Solution File: SET921+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET921+1 : TPTP v8.1.2. Released v3.2.0.
% 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 03:02:00 EDT 2024

% Result   : Theorem 0.46s 1.14s
% Output   : CNFRefutation 0.46s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [X0,X1] :
      ( singleton(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).

fof(f3,axiom,
    ! [X0,X1,X2] :
      ( set_difference(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( ~ in(X3,X1)
            & in(X3,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).

fof(f6,conjecture,
    ! [X0,X1,X2] :
      ( in(X0,set_difference(X1,singleton(X2)))
    <=> ( X0 != X2
        & in(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_zfmisc_1) ).

fof(f7,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( in(X0,set_difference(X1,singleton(X2)))
      <=> ( X0 != X2
          & in(X0,X1) ) ),
    inference(negated_conjecture,[],[f6]) ).

fof(f9,plain,
    ? [X0,X1,X2] :
      ( in(X0,set_difference(X1,singleton(X2)))
    <~> ( X0 != X2
        & in(X0,X1) ) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f10,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | X0 != X2 )
            & ( X0 = X2
              | ~ in(X2,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(nnf_transformation,[],[f2]) ).

fof(f11,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(rectify,[],[f10]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( X0 != X2
            | ~ in(X2,X1) )
          & ( X0 = X2
            | in(X2,X1) ) )
     => ( ( sK0(X0,X1) != X0
          | ~ in(sK0(X0,X1),X1) )
        & ( sK0(X0,X1) = X0
          | in(sK0(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f13,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ( ( sK0(X0,X1) != X0
            | ~ in(sK0(X0,X1),X1) )
          & ( sK0(X0,X1) = X0
            | in(sK0(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f11,f12]) ).

fof(f14,plain,
    ! [X0,X1,X2] :
      ( ( set_difference(X0,X1) = X2
        | ? [X3] :
            ( ( in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( ~ in(X3,X1)
                & in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | in(X3,X1)
              | ~ in(X3,X0) )
            & ( ( ~ in(X3,X1)
                & in(X3,X0) )
              | ~ in(X3,X2) ) )
        | set_difference(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f3]) ).

fof(f15,plain,
    ! [X0,X1,X2] :
      ( ( set_difference(X0,X1) = X2
        | ? [X3] :
            ( ( in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( ~ in(X3,X1)
                & in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | in(X3,X1)
              | ~ in(X3,X0) )
            & ( ( ~ in(X3,X1)
                & in(X3,X0) )
              | ~ in(X3,X2) ) )
        | set_difference(X0,X1) != X2 ) ),
    inference(flattening,[],[f14]) ).

fof(f16,plain,
    ! [X0,X1,X2] :
      ( ( set_difference(X0,X1) = X2
        | ? [X3] :
            ( ( in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( ~ in(X3,X1)
                & in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | in(X4,X1)
              | ~ in(X4,X0) )
            & ( ( ~ in(X4,X1)
                & in(X4,X0) )
              | ~ in(X4,X2) ) )
        | set_difference(X0,X1) != X2 ) ),
    inference(rectify,[],[f15]) ).

fof(f17,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( in(X3,X1)
            | ~ in(X3,X0)
            | ~ in(X3,X2) )
          & ( ( ~ in(X3,X1)
              & in(X3,X0) )
            | in(X3,X2) ) )
     => ( ( in(sK1(X0,X1,X2),X1)
          | ~ in(sK1(X0,X1,X2),X0)
          | ~ in(sK1(X0,X1,X2),X2) )
        & ( ( ~ in(sK1(X0,X1,X2),X1)
            & in(sK1(X0,X1,X2),X0) )
          | in(sK1(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ! [X0,X1,X2] :
      ( ( set_difference(X0,X1) = X2
        | ( ( in(sK1(X0,X1,X2),X1)
            | ~ in(sK1(X0,X1,X2),X0)
            | ~ in(sK1(X0,X1,X2),X2) )
          & ( ( ~ in(sK1(X0,X1,X2),X1)
              & in(sK1(X0,X1,X2),X0) )
            | in(sK1(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | in(X4,X1)
              | ~ in(X4,X0) )
            & ( ( ~ in(X4,X1)
                & in(X4,X0) )
              | ~ in(X4,X2) ) )
        | set_difference(X0,X1) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f16,f17]) ).

fof(f23,plain,
    ? [X0,X1,X2] :
      ( ( X0 = X2
        | ~ in(X0,X1)
        | ~ in(X0,set_difference(X1,singleton(X2))) )
      & ( ( X0 != X2
          & in(X0,X1) )
        | in(X0,set_difference(X1,singleton(X2))) ) ),
    inference(nnf_transformation,[],[f9]) ).

fof(f24,plain,
    ? [X0,X1,X2] :
      ( ( X0 = X2
        | ~ in(X0,X1)
        | ~ in(X0,set_difference(X1,singleton(X2))) )
      & ( ( X0 != X2
          & in(X0,X1) )
        | in(X0,set_difference(X1,singleton(X2))) ) ),
    inference(flattening,[],[f23]) ).

fof(f25,plain,
    ( ? [X0,X1,X2] :
        ( ( X0 = X2
          | ~ in(X0,X1)
          | ~ in(X0,set_difference(X1,singleton(X2))) )
        & ( ( X0 != X2
            & in(X0,X1) )
          | in(X0,set_difference(X1,singleton(X2))) ) )
   => ( ( sK4 = sK6
        | ~ in(sK4,sK5)
        | ~ in(sK4,set_difference(sK5,singleton(sK6))) )
      & ( ( sK4 != sK6
          & in(sK4,sK5) )
        | in(sK4,set_difference(sK5,singleton(sK6))) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f26,plain,
    ( ( sK4 = sK6
      | ~ in(sK4,sK5)
      | ~ in(sK4,set_difference(sK5,singleton(sK6))) )
    & ( ( sK4 != sK6
        & in(sK4,sK5) )
      | in(sK4,set_difference(sK5,singleton(sK6))) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f24,f25]) ).

fof(f28,plain,
    ! [X3,X0,X1] :
      ( X0 = X3
      | ~ in(X3,X1)
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f13]) ).

fof(f29,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | X0 != X3
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f13]) ).

fof(f32,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X0)
      | ~ in(X4,X2)
      | set_difference(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f18]) ).

fof(f33,plain,
    ! [X2,X0,X1,X4] :
      ( ~ in(X4,X1)
      | ~ in(X4,X2)
      | set_difference(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f18]) ).

fof(f34,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X2)
      | in(X4,X1)
      | ~ in(X4,X0)
      | set_difference(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f18]) ).

fof(f40,plain,
    ( in(sK4,sK5)
    | in(sK4,set_difference(sK5,singleton(sK6))) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f41,plain,
    ( sK4 != sK6
    | in(sK4,set_difference(sK5,singleton(sK6))) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f42,plain,
    ( sK4 = sK6
    | ~ in(sK4,sK5)
    | ~ in(sK4,set_difference(sK5,singleton(sK6))) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f43,plain,
    ! [X3,X1] :
      ( in(X3,X1)
      | singleton(X3) != X1 ),
    inference(equality_resolution,[],[f29]) ).

fof(f44,plain,
    ! [X3] : in(X3,singleton(X3)),
    inference(equality_resolution,[],[f43]) ).

fof(f45,plain,
    ! [X3,X0] :
      ( X0 = X3
      | ~ in(X3,singleton(X0)) ),
    inference(equality_resolution,[],[f28]) ).

fof(f46,plain,
    ! [X0,X1,X4] :
      ( in(X4,set_difference(X0,X1))
      | in(X4,X1)
      | ~ in(X4,X0) ),
    inference(equality_resolution,[],[f34]) ).

fof(f47,plain,
    ! [X0,X1,X4] :
      ( ~ in(X4,X1)
      | ~ in(X4,set_difference(X0,X1)) ),
    inference(equality_resolution,[],[f33]) ).

fof(f48,plain,
    ! [X0,X1,X4] :
      ( in(X4,X0)
      | ~ in(X4,set_difference(X0,X1)) ),
    inference(equality_resolution,[],[f32]) ).

cnf(c_52,plain,
    in(X0,singleton(X0)),
    inference(cnf_transformation,[],[f44]) ).

cnf(c_53,plain,
    ( ~ in(X0,singleton(X1))
    | X0 = X1 ),
    inference(cnf_transformation,[],[f45]) ).

cnf(c_57,plain,
    ( ~ in(X0,X1)
    | in(X0,set_difference(X1,X2))
    | in(X0,X2) ),
    inference(cnf_transformation,[],[f46]) ).

cnf(c_58,plain,
    ( ~ in(X0,set_difference(X1,X2))
    | ~ in(X0,X2) ),
    inference(cnf_transformation,[],[f47]) ).

cnf(c_59,plain,
    ( ~ in(X0,set_difference(X1,X2))
    | in(X0,X1) ),
    inference(cnf_transformation,[],[f48]) ).

cnf(c_62,negated_conjecture,
    ( ~ in(sK4,set_difference(sK5,singleton(sK6)))
    | ~ in(sK4,sK5)
    | sK4 = sK6 ),
    inference(cnf_transformation,[],[f42]) ).

cnf(c_63,negated_conjecture,
    ( sK4 != sK6
    | in(sK4,set_difference(sK5,singleton(sK6))) ),
    inference(cnf_transformation,[],[f41]) ).

cnf(c_64,negated_conjecture,
    ( in(sK4,set_difference(sK5,singleton(sK6)))
    | in(sK4,sK5) ),
    inference(cnf_transformation,[],[f40]) ).

cnf(c_89,plain,
    in(sK4,sK5),
    inference(backward_subsumption_resolution,[status(thm)],[c_64,c_59]) ).

cnf(c_218,plain,
    ( ~ in(sK4,set_difference(sK5,singleton(sK6)))
    | sK4 = sK6 ),
    inference(prop_impl_just,[status(thm)],[c_62,c_89]) ).

cnf(c_400,plain,
    singleton(sK6) = sP0_iProver_def,
    definition ).

cnf(c_401,plain,
    set_difference(sK5,sP0_iProver_def) = sP1_iProver_def,
    definition ).

cnf(c_402,negated_conjecture,
    ( sK4 != sK6
    | in(sK4,sP1_iProver_def) ),
    inference(demodulation,[status(thm)],[c_63,c_400,c_401]) ).

cnf(c_613,plain,
    in(sK6,sP0_iProver_def),
    inference(superposition,[status(thm)],[c_400,c_52]) ).

cnf(c_622,plain,
    ( ~ in(sK4,sP1_iProver_def)
    | sK4 = sK6 ),
    inference(light_normalisation,[status(thm)],[c_218,c_400,c_401]) ).

cnf(c_632,plain,
    ( ~ in(X0,sP0_iProver_def)
    | X0 = sK6 ),
    inference(superposition,[status(thm)],[c_400,c_53]) ).

cnf(c_635,plain,
    ( ~ in(sK4,sP0_iProver_def)
    | sK4 = sK6 ),
    inference(instantiation,[status(thm)],[c_632]) ).

cnf(c_647,plain,
    ( ~ in(X0,sP0_iProver_def)
    | ~ in(X0,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_401,c_58]) ).

cnf(c_657,plain,
    ( ~ in(X0,sK5)
    | in(X0,sP0_iProver_def)
    | in(X0,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_401,c_57]) ).

cnf(c_667,plain,
    ( ~ in(sK4,sK5)
    | in(sK4,sP0_iProver_def)
    | in(sK4,sP1_iProver_def) ),
    inference(instantiation,[status(thm)],[c_657]) ).

cnf(c_685,plain,
    ~ in(sK6,sP1_iProver_def),
    inference(superposition,[status(thm)],[c_613,c_647]) ).

cnf(c_692,plain,
    ( in(sK4,sP0_iProver_def)
    | in(sK4,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_89,c_657]) ).

cnf(c_695,plain,
    in(sK4,sP1_iProver_def),
    inference(global_subsumption_just,[status(thm)],[c_692,c_89,c_402,c_635,c_667]) ).

cnf(c_697,plain,
    sK4 = sK6,
    inference(backward_subsumption_resolution,[status(thm)],[c_622,c_695]) ).

cnf(c_698,plain,
    ~ in(sK4,sP1_iProver_def),
    inference(demodulation,[status(thm)],[c_685,c_697]) ).

cnf(c_705,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_698,c_695]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SET921+1 : TPTP v8.1.2. Released v3.2.0.
% 0.10/0.12  % Command  : run_iprover %s %d THM
% 0.13/0.33  % Computer : n015.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Thu May  2 20:53:51 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.19/0.46  Running first-order theorem proving
% 0.19/0.46  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
% 0.46/1.14  % SZS status Started for theBenchmark.p
% 0.46/1.14  % SZS status Theorem for theBenchmark.p
% 0.46/1.14  
% 0.46/1.14  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 0.46/1.14  
% 0.46/1.14  ------  iProver source info
% 0.46/1.14  
% 0.46/1.14  git: date: 2024-05-02 19:28:25 +0000
% 0.46/1.14  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 0.46/1.14  git: non_committed_changes: false
% 0.46/1.14  
% 0.46/1.14  ------ Parsing...
% 0.46/1.14  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 0.46/1.14  
% 0.46/1.14  ------ 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 
% 0.46/1.14  
% 0.46/1.14  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 0.46/1.14  
% 0.46/1.14  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 0.46/1.14  ------ Proving...
% 0.46/1.14  ------ Problem Properties 
% 0.46/1.14  
% 0.46/1.14  
% 0.46/1.14  clauses                                 17
% 0.46/1.14  conjectures                             1
% 0.46/1.14  EPR                                     4
% 0.46/1.14  Horn                                    12
% 0.46/1.14  unary                                   5
% 0.46/1.14  binary                                  6
% 0.46/1.14  lits                                    36
% 0.46/1.14  lits eq                                 13
% 0.46/1.14  fd_pure                                 0
% 0.46/1.14  fd_pseudo                               0
% 0.46/1.14  fd_cond                                 0
% 0.46/1.14  fd_pseudo_cond                          5
% 0.46/1.14  AC symbols                              0
% 0.46/1.14  
% 0.46/1.14  ------ Schedule dynamic 5 is on 
% 0.46/1.14  
% 0.46/1.14  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.46/1.14  
% 0.46/1.14  
% 0.46/1.14  ------ 
% 0.46/1.14  Current options:
% 0.46/1.14  ------ 
% 0.46/1.14  
% 0.46/1.14  
% 0.46/1.14  
% 0.46/1.14  
% 0.46/1.14  ------ Proving...
% 0.46/1.14  
% 0.46/1.14  
% 0.46/1.14  % SZS status Theorem for theBenchmark.p
% 0.46/1.14  
% 0.46/1.14  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.46/1.14  
% 0.46/1.14  
%------------------------------------------------------------------------------