TSTP Solution File: SET874+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET874+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n017.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 03:01:53 EDT 2024

% Result   : Theorem 1.91s 1.15s
% Output   : CNFRefutation 1.91s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    ! [X0,X1,X2] :
      ( unordered_pair(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( X1 = X3
            | X0 = X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).

fof(f8,axiom,
    ! [X0,X1] :
      ( in(X0,X1)
     => set_union2(singleton(X0),X1) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l23_zfmisc_1) ).

fof(f11,conjecture,
    ! [X0,X1] : unordered_pair(X0,X1) = set_union2(singleton(X0),unordered_pair(X0,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_zfmisc_1) ).

fof(f12,negated_conjecture,
    ~ ! [X0,X1] : unordered_pair(X0,X1) = set_union2(singleton(X0),unordered_pair(X0,X1)),
    inference(negated_conjecture,[],[f11]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( set_union2(singleton(X0),X1) = X1
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f18,plain,
    ? [X0,X1] : unordered_pair(X0,X1) != set_union2(singleton(X0),unordered_pair(X0,X1)),
    inference(ennf_transformation,[],[f12]) ).

fof(f19,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X0,X1) = X2
        | ? [X3] :
            ( ( ( X1 != X3
                & X0 != X3 )
              | ~ in(X3,X2) )
            & ( X1 = X3
              | X0 = X3
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ( X1 != X3
                & X0 != X3 ) )
            & ( X1 = X3
              | X0 = X3
              | ~ in(X3,X2) ) )
        | unordered_pair(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f4]) ).

fof(f20,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X0,X1) = X2
        | ? [X3] :
            ( ( ( X1 != X3
                & X0 != X3 )
              | ~ in(X3,X2) )
            & ( X1 = X3
              | X0 = X3
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ( X1 != X3
                & X0 != X3 ) )
            & ( X1 = X3
              | X0 = X3
              | ~ in(X3,X2) ) )
        | unordered_pair(X0,X1) != X2 ) ),
    inference(flattening,[],[f19]) ).

fof(f21,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X0,X1) = X2
        | ? [X3] :
            ( ( ( X1 != X3
                & X0 != X3 )
              | ~ in(X3,X2) )
            & ( X1 = X3
              | X0 = X3
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ( X1 != X4
                & X0 != X4 ) )
            & ( X1 = X4
              | X0 = X4
              | ~ in(X4,X2) ) )
        | unordered_pair(X0,X1) != X2 ) ),
    inference(rectify,[],[f20]) ).

fof(f22,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ( X1 != X3
              & X0 != X3 )
            | ~ in(X3,X2) )
          & ( X1 = X3
            | X0 = X3
            | in(X3,X2) ) )
     => ( ( ( sK0(X0,X1,X2) != X1
            & sK0(X0,X1,X2) != X0 )
          | ~ in(sK0(X0,X1,X2),X2) )
        & ( sK0(X0,X1,X2) = X1
          | sK0(X0,X1,X2) = X0
          | in(sK0(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f23,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X0,X1) = X2
        | ( ( ( sK0(X0,X1,X2) != X1
              & sK0(X0,X1,X2) != X0 )
            | ~ in(sK0(X0,X1,X2),X2) )
          & ( sK0(X0,X1,X2) = X1
            | sK0(X0,X1,X2) = X0
            | in(sK0(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ( X1 != X4
                & X0 != X4 ) )
            & ( X1 = X4
              | X0 = X4
              | ~ in(X4,X2) ) )
        | unordered_pair(X0,X1) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f21,f22]) ).

fof(f28,plain,
    ( ? [X0,X1] : unordered_pair(X0,X1) != set_union2(singleton(X0),unordered_pair(X0,X1))
   => unordered_pair(sK3,sK4) != set_union2(singleton(sK3),unordered_pair(sK3,sK4)) ),
    introduced(choice_axiom,[]) ).

fof(f29,plain,
    unordered_pair(sK3,sK4) != set_union2(singleton(sK3),unordered_pair(sK3,sK4)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f18,f28]) ).

fof(f34,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X2)
      | X0 != X4
      | unordered_pair(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f23]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( set_union2(singleton(X0),X1) = X1
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f45,plain,
    unordered_pair(sK3,sK4) != set_union2(singleton(sK3),unordered_pair(sK3,sK4)),
    inference(cnf_transformation,[],[f29]) ).

fof(f48,plain,
    ! [X2,X1,X4] :
      ( in(X4,X2)
      | unordered_pair(X4,X1) != X2 ),
    inference(equality_resolution,[],[f34]) ).

fof(f49,plain,
    ! [X1,X4] : in(X4,unordered_pair(X4,X1)),
    inference(equality_resolution,[],[f48]) ).

cnf(c_56,plain,
    in(X0,unordered_pair(X0,X1)),
    inference(cnf_transformation,[],[f49]) ).

cnf(c_61,plain,
    ( ~ in(X0,X1)
    | set_union2(singleton(X0),X1) = X1 ),
    inference(cnf_transformation,[],[f42]) ).

cnf(c_64,negated_conjecture,
    set_union2(singleton(sK3),unordered_pair(sK3,sK4)) != unordered_pair(sK3,sK4),
    inference(cnf_transformation,[],[f45]) ).

cnf(c_180,plain,
    singleton(sK3) = sP0_iProver_def,
    definition ).

cnf(c_181,plain,
    unordered_pair(sK3,sK4) = sP1_iProver_def,
    definition ).

cnf(c_182,plain,
    set_union2(sP0_iProver_def,sP1_iProver_def) = sP2_iProver_def,
    definition ).

cnf(c_183,negated_conjecture,
    sP2_iProver_def != sP1_iProver_def,
    inference(demodulation,[status(thm)],[c_64,c_181,c_180,c_182]) ).

cnf(c_402,plain,
    in(sK3,sP1_iProver_def),
    inference(superposition,[status(thm)],[c_181,c_56]) ).

cnf(c_455,plain,
    set_union2(singleton(sK3),sP1_iProver_def) = sP1_iProver_def,
    inference(superposition,[status(thm)],[c_402,c_61]) ).

cnf(c_456,plain,
    sP1_iProver_def = sP2_iProver_def,
    inference(light_normalisation,[status(thm)],[c_455,c_180,c_182]) ).

cnf(c_460,plain,
    sP1_iProver_def != sP1_iProver_def,
    inference(demodulation,[status(thm)],[c_183,c_456]) ).

cnf(c_461,plain,
    $false,
    inference(equality_resolution_simp,[status(thm)],[c_460]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET874+1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.12  % Command  : run_iprover %s %d THM
% 0.13/0.33  % Computer : n017.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 20:10:06 EDT 2024
% 0.13/0.33  % CPUTime  : 
% 0.19/0.45  Running first-order theorem proving
% 0.19/0.45  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
% 1.91/1.15  % SZS status Started for theBenchmark.p
% 1.91/1.15  % SZS status Theorem for theBenchmark.p
% 1.91/1.15  
% 1.91/1.15  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 1.91/1.15  
% 1.91/1.15  ------  iProver source info
% 1.91/1.15  
% 1.91/1.15  git: date: 2024-05-02 19:28:25 +0000
% 1.91/1.15  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 1.91/1.15  git: non_committed_changes: false
% 1.91/1.15  
% 1.91/1.15  ------ Parsing...
% 1.91/1.15  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 1.91/1.15  
% 1.91/1.15  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 1.91/1.15  
% 1.91/1.15  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 1.91/1.15  
% 1.91/1.15  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 1.91/1.15  ------ Proving...
% 1.91/1.15  ------ Problem Properties 
% 1.91/1.15  
% 1.91/1.15  
% 1.91/1.15  clauses                                 19
% 1.91/1.15  conjectures                             1
% 1.91/1.15  EPR                                     4
% 1.91/1.15  Horn                                    17
% 1.91/1.15  unary                                   11
% 1.91/1.15  binary                                  4
% 1.91/1.15  lits                                    32
% 1.91/1.15  lits eq                                 17
% 1.91/1.15  fd_pure                                 0
% 1.91/1.15  fd_pseudo                               0
% 1.91/1.15  fd_cond                                 0
% 1.91/1.15  fd_pseudo_cond                          3
% 1.91/1.15  AC symbols                              0
% 1.91/1.15  
% 1.91/1.15  ------ Schedule dynamic 5 is on 
% 1.91/1.15  
% 1.91/1.15  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.91/1.15  
% 1.91/1.15  
% 1.91/1.15  ------ 
% 1.91/1.15  Current options:
% 1.91/1.15  ------ 
% 1.91/1.15  
% 1.91/1.15  
% 1.91/1.15  
% 1.91/1.15  
% 1.91/1.15  ------ Proving...
% 1.91/1.15  
% 1.91/1.15  
% 1.91/1.15  % SZS status Theorem for theBenchmark.p
% 1.91/1.15  
% 1.91/1.15  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.91/1.15  
% 1.91/1.15  
%------------------------------------------------------------------------------