TSTP Solution File: SET587+3 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET587+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n005.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 03:00:51 EDT 2024

% Result   : Theorem 0.46s 1.17s
% Output   : CNFRefutation 0.46s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [X0,X1,X2] :
      ( member(X2,difference(X0,X1))
    <=> ( ~ member(X2,X1)
        & member(X2,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).

fof(f3,axiom,
    ! [X0] : ~ member(X0,empty_set),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).

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

fof(f9,conjecture,
    ! [X0,X1] :
      ( difference(X0,X1) = empty_set
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_difference_empty_set) ).

fof(f10,negated_conjecture,
    ~ ! [X0,X1] :
        ( difference(X0,X1) = empty_set
      <=> subset(X0,X1) ),
    inference(negated_conjecture,[],[f9]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f13,plain,
    ? [X0,X1] :
      ( difference(X0,X1) = empty_set
    <~> subset(X0,X1) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f17,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,difference(X0,X1))
        | member(X2,X1)
        | ~ member(X2,X0) )
      & ( ( ~ member(X2,X1)
          & member(X2,X0) )
        | ~ member(X2,difference(X0,X1)) ) ),
    inference(nnf_transformation,[],[f2]) ).

fof(f18,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,difference(X0,X1))
        | member(X2,X1)
        | ~ member(X2,X0) )
      & ( ( ~ member(X2,X1)
          & member(X2,X0) )
        | ~ member(X2,difference(X0,X1)) ) ),
    inference(flattening,[],[f17]) ).

fof(f19,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,[],[f12]) ).

fof(f20,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,[],[f19]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK1(X0,X1),X1)
        & member(sK1(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ member(sK1(X0,X1),X1)
          & member(sK1(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f20,f21]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f5]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(flattening,[],[f23]) ).

fof(f29,plain,
    ? [X0,X1] :
      ( ( ~ subset(X0,X1)
        | difference(X0,X1) != empty_set )
      & ( subset(X0,X1)
        | difference(X0,X1) = empty_set ) ),
    inference(nnf_transformation,[],[f13]) ).

fof(f30,plain,
    ( ? [X0,X1] :
        ( ( ~ subset(X0,X1)
          | difference(X0,X1) != empty_set )
        & ( subset(X0,X1)
          | difference(X0,X1) = empty_set ) )
   => ( ( ~ subset(sK3,sK4)
        | empty_set != difference(sK3,sK4) )
      & ( subset(sK3,sK4)
        | empty_set = difference(sK3,sK4) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f31,plain,
    ( ( ~ subset(sK3,sK4)
      | empty_set != difference(sK3,sK4) )
    & ( subset(sK3,sK4)
      | empty_set = difference(sK3,sK4) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f29,f30]) ).

fof(f34,plain,
    ! [X2,X0,X1] :
      ( member(X2,X0)
      | ~ member(X2,difference(X0,X1)) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f35,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,X1)
      | ~ member(X2,difference(X0,X1)) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f36,plain,
    ! [X2,X0,X1] :
      ( member(X2,difference(X0,X1))
      | member(X2,X1)
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f37,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(cnf_transformation,[],[f3]) ).

fof(f38,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK1(X0,X1),X0) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sK1(X0,X1),X1) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f49,plain,
    ( subset(sK3,sK4)
    | empty_set = difference(sK3,sK4) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f50,plain,
    ( ~ subset(sK3,sK4)
    | empty_set != difference(sK3,sK4) ),
    inference(cnf_transformation,[],[f31]) ).

cnf(c_51,plain,
    ( ~ member(X0,X1)
    | member(X0,difference(X1,X2))
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f36]) ).

cnf(c_52,plain,
    ( ~ member(X0,difference(X1,X2))
    | ~ member(X0,X2) ),
    inference(cnf_transformation,[],[f35]) ).

cnf(c_53,plain,
    ( ~ member(X0,difference(X1,X2))
    | member(X0,X1) ),
    inference(cnf_transformation,[],[f34]) ).

cnf(c_54,plain,
    ~ member(X0,empty_set),
    inference(cnf_transformation,[],[f37]) ).

cnf(c_55,plain,
    ( ~ member(sK1(X0,X1),X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f40]) ).

cnf(c_56,plain,
    ( member(sK1(X0,X1),X0)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f39]) ).

cnf(c_57,plain,
    ( ~ member(X0,X1)
    | ~ subset(X1,X2)
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f38]) ).

cnf(c_58,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X1,X0)
    | X0 = X1 ),
    inference(cnf_transformation,[],[f43]) ).

cnf(c_64,negated_conjecture,
    ( difference(sK3,sK4) != empty_set
    | ~ subset(sK3,sK4) ),
    inference(cnf_transformation,[],[f50]) ).

cnf(c_65,negated_conjecture,
    ( difference(sK3,sK4) = empty_set
    | subset(sK3,sK4) ),
    inference(cnf_transformation,[],[f49]) ).

cnf(c_453,plain,
    difference(sK3,sK4) = sP0_iProver_def,
    definition ).

cnf(c_454,negated_conjecture,
    ( sP0_iProver_def = empty_set
    | subset(sK3,sK4) ),
    inference(demodulation,[status(thm)],[c_65,c_453]) ).

cnf(c_455,negated_conjecture,
    ( sP0_iProver_def != empty_set
    | ~ subset(sK3,sK4) ),
    inference(demodulation,[status(thm)],[c_64]) ).

cnf(c_800,plain,
    subset(empty_set,X0),
    inference(superposition,[status(thm)],[c_56,c_54]) ).

cnf(c_807,plain,
    ( ~ member(X0,sP0_iProver_def)
    | member(X0,sK3) ),
    inference(superposition,[status(thm)],[c_453,c_53]) ).

cnf(c_820,plain,
    ( ~ member(X0,sK3)
    | member(X0,sK4)
    | member(X0,sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_453,c_51]) ).

cnf(c_841,plain,
    ( ~ member(X0,sK4)
    | ~ member(X0,sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_453,c_52]) ).

cnf(c_871,plain,
    ( ~ subset(X0,empty_set)
    | X0 = empty_set ),
    inference(superposition,[status(thm)],[c_800,c_58]) ).

cnf(c_882,plain,
    ( member(sK1(sP0_iProver_def,X0),sK3)
    | subset(sP0_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_56,c_807]) ).

cnf(c_890,plain,
    ( ~ member(sK1(sP0_iProver_def,X0),sK4)
    | subset(sP0_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_56,c_841]) ).

cnf(c_904,plain,
    ( ~ subset(sK3,X0)
    | member(sK1(sP0_iProver_def,X1),X0)
    | subset(sP0_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_882,c_57]) ).

cnf(c_932,plain,
    ( member(sK1(sK3,X0),sK4)
    | member(sK1(sK3,X0),sP0_iProver_def)
    | subset(sK3,X0) ),
    inference(superposition,[status(thm)],[c_56,c_820]) ).

cnf(c_1600,plain,
    ( ~ subset(sK3,sK4)
    | subset(sP0_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_904,c_890]) ).

cnf(c_1675,plain,
    ( empty_set = sP0_iProver_def
    | subset(sP0_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_454,c_1600]) ).

cnf(c_1710,plain,
    empty_set = sP0_iProver_def,
    inference(superposition,[status(thm)],[c_1675,c_871]) ).

cnf(c_1721,plain,
    ~ member(X0,sP0_iProver_def),
    inference(demodulation,[status(thm)],[c_54,c_1710]) ).

cnf(c_1722,plain,
    ( sP0_iProver_def != sP0_iProver_def
    | ~ subset(sK3,sK4) ),
    inference(demodulation,[status(thm)],[c_455,c_1710]) ).

cnf(c_1724,plain,
    ~ subset(sK3,sK4),
    inference(equality_resolution_simp,[status(thm)],[c_1722]) ).

cnf(c_1794,plain,
    ( member(sK1(sK3,X0),sK4)
    | subset(sK3,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_932,c_1721]) ).

cnf(c_1800,plain,
    subset(sK3,sK4),
    inference(superposition,[status(thm)],[c_1794,c_55]) ).

cnf(c_1801,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_1800,c_1724]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET587+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13  % Command  : run_iprover %s %d THM
% 0.12/0.34  % Computer : n005.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu May  2 20:13:26 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 0.18/0.46  Running first-order theorem proving
% 0.18/0.46  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
% 0.46/1.17  % SZS status Started for theBenchmark.p
% 0.46/1.17  % SZS status Theorem for theBenchmark.p
% 0.46/1.17  
% 0.46/1.17  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 0.46/1.17  
% 0.46/1.17  ------  iProver source info
% 0.46/1.17  
% 0.46/1.17  git: date: 2024-05-02 19:28:25 +0000
% 0.46/1.17  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 0.46/1.17  git: non_committed_changes: false
% 0.46/1.17  
% 0.46/1.17  ------ Parsing...
% 0.46/1.17  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 0.46/1.17  
% 0.46/1.17  ------ Preprocessing... sup_sim: 0  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 
% 0.46/1.17  
% 0.46/1.17  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 0.46/1.17  
% 0.46/1.17  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 0.46/1.17  ------ Proving...
% 0.46/1.17  ------ Problem Properties 
% 0.46/1.17  
% 0.46/1.17  
% 0.46/1.17  clauses                                 16
% 0.46/1.17  conjectures                             2
% 0.46/1.17  EPR                                     6
% 0.46/1.17  Horn                                    11
% 0.46/1.17  unary                                   3
% 0.46/1.17  binary                                  6
% 0.46/1.17  lits                                    36
% 0.46/1.17  lits eq                                 8
% 0.46/1.17  fd_pure                                 0
% 0.46/1.17  fd_pseudo                               0
% 0.46/1.17  fd_cond                                 0
% 0.46/1.17  fd_pseudo_cond                          5
% 0.46/1.17  AC symbols                              0
% 0.46/1.17  
% 0.46/1.17  ------ Schedule dynamic 5 is on 
% 0.46/1.17  
% 0.46/1.17  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.46/1.17  
% 0.46/1.17  
% 0.46/1.17  ------ 
% 0.46/1.17  Current options:
% 0.46/1.17  ------ 
% 0.46/1.17  
% 0.46/1.17  
% 0.46/1.17  
% 0.46/1.17  
% 0.46/1.17  ------ Proving...
% 0.46/1.17  
% 0.46/1.17  
% 0.46/1.17  % SZS status Theorem for theBenchmark.p
% 0.46/1.17  
% 0.46/1.17  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.46/1.17  
% 0.46/1.17  
%------------------------------------------------------------------------------