TSTP Solution File: SET877+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET877+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n016.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 03:01:54 EDT 2024

% Result   : Theorem 2.33s 1.20s
% Output   : CNFRefutation 2.33s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( singleton(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( singleton(X1) = set_intersection2(X0,singleton(X1))
     => in(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l30_zfmisc_1) ).

fof(f8,conjecture,
    ! [X0,X1] :
      ( singleton(X0) = set_intersection2(singleton(X0),singleton(X1))
     => X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_zfmisc_1) ).

fof(f9,negated_conjecture,
    ~ ! [X0,X1] :
        ( singleton(X0) = set_intersection2(singleton(X0),singleton(X1))
       => X0 = X1 ),
    inference(negated_conjecture,[],[f8]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( in(X1,X0)
      | singleton(X1) != set_intersection2(X0,singleton(X1)) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f13,plain,
    ? [X0,X1] :
      ( X0 != X1
      & singleton(X0) = set_intersection2(singleton(X0),singleton(X1)) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f14,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,[],[f3]) ).

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

fof(f16,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(f17,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])],[f15,f16]) ).

fof(f22,plain,
    ( ? [X0,X1] :
        ( X0 != X1
        & singleton(X0) = set_intersection2(singleton(X0),singleton(X1)) )
   => ( sK3 != sK4
      & singleton(sK3) = set_intersection2(singleton(sK3),singleton(sK4)) ) ),
    introduced(choice_axiom,[]) ).

fof(f23,plain,
    ( sK3 != sK4
    & singleton(sK3) = set_intersection2(singleton(sK3),singleton(sK4)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f13,f22]) ).

fof(f25,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[],[f2]) ).

fof(f26,plain,
    ! [X3,X0,X1] :
      ( X0 = X3
      | ~ in(X3,X1)
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f17]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( in(X1,X0)
      | singleton(X1) != set_intersection2(X0,singleton(X1)) ),
    inference(cnf_transformation,[],[f12]) ).

fof(f34,plain,
    singleton(sK3) = set_intersection2(singleton(sK3),singleton(sK4)),
    inference(cnf_transformation,[],[f23]) ).

fof(f35,plain,
    sK3 != sK4,
    inference(cnf_transformation,[],[f23]) ).

fof(f38,plain,
    ! [X3,X0] :
      ( X0 = X3
      | ~ in(X3,singleton(X0)) ),
    inference(equality_resolution,[],[f26]) ).

cnf(c_50,plain,
    set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[],[f25]) ).

cnf(c_54,plain,
    ( ~ in(X0,singleton(X1))
    | X0 = X1 ),
    inference(cnf_transformation,[],[f38]) ).

cnf(c_56,plain,
    ( set_intersection2(X0,singleton(X1)) != singleton(X1)
    | in(X1,X0) ),
    inference(cnf_transformation,[],[f31]) ).

cnf(c_59,negated_conjecture,
    sK3 != sK4,
    inference(cnf_transformation,[],[f35]) ).

cnf(c_60,negated_conjecture,
    set_intersection2(singleton(sK3),singleton(sK4)) = singleton(sK3),
    inference(cnf_transformation,[],[f34]) ).

cnf(c_205,plain,
    singleton(sK3) = sP0_iProver_def,
    definition ).

cnf(c_206,plain,
    singleton(sK4) = sP1_iProver_def,
    definition ).

cnf(c_207,plain,
    set_intersection2(sP0_iProver_def,sP1_iProver_def) = sP2_iProver_def,
    definition ).

cnf(c_208,negated_conjecture,
    sP2_iProver_def = sP0_iProver_def,
    inference(demodulation,[status(thm)],[c_60,c_206,c_205,c_207]) ).

cnf(c_359,plain,
    set_intersection2(sP0_iProver_def,sP1_iProver_def) = sP0_iProver_def,
    inference(light_normalisation,[status(thm)],[c_207,c_208]) ).

cnf(c_372,plain,
    ( ~ in(X0,sP1_iProver_def)
    | X0 = sK4 ),
    inference(superposition,[status(thm)],[c_206,c_54]) ).

cnf(c_377,plain,
    ( ~ in(sK3,sP1_iProver_def)
    | sK3 = sK4 ),
    inference(instantiation,[status(thm)],[c_372]) ).

cnf(c_397,plain,
    ( set_intersection2(X0,sP0_iProver_def) != sP0_iProver_def
    | in(sK3,X0) ),
    inference(superposition,[status(thm)],[c_205,c_56]) ).

cnf(c_412,plain,
    ( set_intersection2(sP0_iProver_def,X0) != sP0_iProver_def
    | in(sK3,X0) ),
    inference(superposition,[status(thm)],[c_50,c_397]) ).

cnf(c_442,plain,
    in(sK3,sP1_iProver_def),
    inference(superposition,[status(thm)],[c_359,c_412]) ).

cnf(c_443,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_442,c_377,c_59]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SET877+1 : TPTP v8.1.2. Released v3.2.0.
% 0.08/0.14  % Command  : run_iprover %s %d THM
% 0.15/0.35  % Computer : n016.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Thu May  2 21:08:15 EDT 2024
% 0.15/0.35  % CPUTime  : 
% 0.21/0.48  Running first-order theorem proving
% 0.21/0.48  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
% 2.33/1.20  % SZS status Started for theBenchmark.p
% 2.33/1.20  % SZS status Theorem for theBenchmark.p
% 2.33/1.20  
% 2.33/1.20  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 2.33/1.20  
% 2.33/1.20  ------  iProver source info
% 2.33/1.20  
% 2.33/1.20  git: date: 2024-05-02 19:28:25 +0000
% 2.33/1.20  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 2.33/1.20  git: non_committed_changes: false
% 2.33/1.20  
% 2.33/1.20  ------ Parsing...
% 2.33/1.20  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 2.33/1.20  
% 2.33/1.20  ------ 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 
% 2.33/1.20  
% 2.33/1.20  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 2.33/1.20  
% 2.33/1.20  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.33/1.20  ------ Proving...
% 2.33/1.20  ------ Problem Properties 
% 2.33/1.20  
% 2.33/1.20  
% 2.33/1.20  clauses                                 14
% 2.33/1.20  conjectures                             2
% 2.33/1.20  EPR                                     4
% 2.33/1.20  Horn                                    13
% 2.33/1.20  unary                                   9
% 2.33/1.20  binary                                  3
% 2.33/1.20  lits                                    21
% 2.33/1.20  lits eq                                 14
% 2.33/1.20  fd_pure                                 0
% 2.33/1.20  fd_pseudo                               0
% 2.33/1.20  fd_cond                                 0
% 2.33/1.20  fd_pseudo_cond                          2
% 2.33/1.20  AC symbols                              0
% 2.33/1.20  
% 2.33/1.20  ------ Schedule dynamic 5 is on 
% 2.33/1.20  
% 2.33/1.20  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.33/1.20  
% 2.33/1.20  
% 2.33/1.20  ------ 
% 2.33/1.20  Current options:
% 2.33/1.20  ------ 
% 2.33/1.20  
% 2.33/1.20  
% 2.33/1.20  
% 2.33/1.20  
% 2.33/1.20  ------ Proving...
% 2.33/1.20  
% 2.33/1.20  
% 2.33/1.20  % SZS status Theorem for theBenchmark.p
% 2.33/1.20  
% 2.33/1.20  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.33/1.20  
% 2.33/1.20  
%------------------------------------------------------------------------------