TSTP Solution File: SET592+3 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET592+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n027.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 03:00:52 EDT 2024

% Result   : Theorem 2.08s 1.20s
% Output   : CNFRefutation 2.08s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0] :
      ( subset(X0,empty_set)
     => empty_set = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_of_empty_set_is_empty_set) ).

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

fof(f7,axiom,
    ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).

fof(f11,conjecture,
    ! [X0,X1,X2] :
      ( ( empty_set = intersection(X1,X2)
        & subset(X0,X2)
        & subset(X0,X1) )
     => empty_set = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th51) ).

fof(f12,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ( empty_set = intersection(X1,X2)
          & subset(X0,X2)
          & subset(X0,X1) )
       => empty_set = X0 ),
    inference(negated_conjecture,[],[f11]) ).

fof(f13,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ subset(X0,empty_set) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f14,plain,
    ! [X0,X1,X2] :
      ( subset(X0,intersection(X1,X2))
      | ~ subset(X0,X2)
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f15,plain,
    ! [X0,X1,X2] :
      ( subset(X0,intersection(X1,X2))
      | ~ subset(X0,X2)
      | ~ subset(X0,X1) ),
    inference(flattening,[],[f14]) ).

fof(f17,plain,
    ? [X0,X1,X2] :
      ( empty_set != X0
      & empty_set = intersection(X1,X2)
      & subset(X0,X2)
      & subset(X0,X1) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f18,plain,
    ? [X0,X1,X2] :
      ( empty_set != X0
      & empty_set = intersection(X1,X2)
      & subset(X0,X2)
      & subset(X0,X1) ),
    inference(flattening,[],[f17]) ).

fof(f31,plain,
    ( ? [X0,X1,X2] :
        ( empty_set != X0
        & empty_set = intersection(X1,X2)
        & subset(X0,X2)
        & subset(X0,X1) )
   => ( empty_set != sK2
      & empty_set = intersection(sK3,sK4)
      & subset(sK2,sK4)
      & subset(sK2,sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f32,plain,
    ( empty_set != sK2
    & empty_set = intersection(sK3,sK4)
    & subset(sK2,sK4)
    & subset(sK2,sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f18,f31]) ).

fof(f33,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ subset(X0,empty_set) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f34,plain,
    ! [X2,X0,X1] :
      ( subset(X0,intersection(X1,X2))
      | ~ subset(X0,X2)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f45,plain,
    ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
    inference(cnf_transformation,[],[f7]) ).

fof(f51,plain,
    subset(sK2,sK3),
    inference(cnf_transformation,[],[f32]) ).

fof(f52,plain,
    subset(sK2,sK4),
    inference(cnf_transformation,[],[f32]) ).

fof(f53,plain,
    empty_set = intersection(sK3,sK4),
    inference(cnf_transformation,[],[f32]) ).

fof(f54,plain,
    empty_set != sK2,
    inference(cnf_transformation,[],[f32]) ).

cnf(c_49,plain,
    ( ~ subset(X0,empty_set)
    | X0 = empty_set ),
    inference(cnf_transformation,[],[f33]) ).

cnf(c_50,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X0,X2)
    | subset(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[],[f34]) ).

cnf(c_61,plain,
    intersection(X0,X1) = intersection(X1,X0),
    inference(cnf_transformation,[],[f45]) ).

cnf(c_65,negated_conjecture,
    empty_set != sK2,
    inference(cnf_transformation,[],[f54]) ).

cnf(c_66,negated_conjecture,
    intersection(sK3,sK4) = empty_set,
    inference(cnf_transformation,[],[f53]) ).

cnf(c_67,negated_conjecture,
    subset(sK2,sK4),
    inference(cnf_transformation,[],[f52]) ).

cnf(c_68,negated_conjecture,
    subset(sK2,sK3),
    inference(cnf_transformation,[],[f51]) ).

cnf(c_337,plain,
    intersection(sK3,sK4) = sP0_iProver_def,
    definition ).

cnf(c_338,negated_conjecture,
    subset(sK2,sK3),
    inference(demodulation,[status(thm)],[c_68]) ).

cnf(c_339,negated_conjecture,
    subset(sK2,sK4),
    inference(demodulation,[status(thm)],[c_67]) ).

cnf(c_340,negated_conjecture,
    sP0_iProver_def = empty_set,
    inference(demodulation,[status(thm)],[c_66,c_337]) ).

cnf(c_341,negated_conjecture,
    empty_set != sK2,
    inference(demodulation,[status(thm)],[c_65]) ).

cnf(c_556,plain,
    sK2 != sP0_iProver_def,
    inference(light_normalisation,[status(thm)],[c_341,c_340]) ).

cnf(c_558,plain,
    ( ~ subset(X0,sP0_iProver_def)
    | X0 = sP0_iProver_def ),
    inference(light_normalisation,[status(thm)],[c_49,c_340]) ).

cnf(c_727,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X0,X2)
    | subset(X0,intersection(X2,X1)) ),
    inference(superposition,[status(thm)],[c_61,c_50]) ).

cnf(c_1450,plain,
    ( ~ subset(X0,sK3)
    | ~ subset(X0,sK4)
    | subset(X0,sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_337,c_727]) ).

cnf(c_1523,plain,
    ( ~ subset(sK2,sK4)
    | subset(sK2,sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_338,c_1450]) ).

cnf(c_1529,plain,
    subset(sK2,sP0_iProver_def),
    inference(forward_subsumption_resolution,[status(thm)],[c_1523,c_339]) ).

cnf(c_1549,plain,
    sK2 = sP0_iProver_def,
    inference(superposition,[status(thm)],[c_1529,c_558]) ).

cnf(c_1550,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_1549,c_556]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SET592+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.13  % Command  : run_iprover %s %d THM
% 0.15/0.34  % Computer : n027.cluster.edu
% 0.15/0.34  % Model    : x86_64 x86_64
% 0.15/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34  % Memory   : 8042.1875MB
% 0.15/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34  % CPULimit : 300
% 0.15/0.34  % WCLimit  : 300
% 0.15/0.34  % DateTime : Thu May  2 20:53:20 EDT 2024
% 0.15/0.35  % CPUTime  : 
% 0.21/0.48  Running first-order theorem proving
% 0.21/0.48  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
% 2.08/1.20  % SZS status Started for theBenchmark.p
% 2.08/1.20  % SZS status Theorem for theBenchmark.p
% 2.08/1.20  
% 2.08/1.20  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 2.08/1.20  
% 2.08/1.20  ------  iProver source info
% 2.08/1.20  
% 2.08/1.20  git: date: 2024-05-02 19:28:25 +0000
% 2.08/1.20  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 2.08/1.20  git: non_committed_changes: false
% 2.08/1.20  
% 2.08/1.20  ------ Parsing...
% 2.08/1.20  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 2.08/1.20  
% 2.08/1.20  ------ 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 
% 2.08/1.20  
% 2.08/1.20  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 2.08/1.20  
% 2.08/1.20  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.08/1.20  ------ Proving...
% 2.08/1.20  ------ Problem Properties 
% 2.08/1.20  
% 2.08/1.20  
% 2.08/1.20  clauses                                 19
% 2.08/1.20  conjectures                             4
% 2.08/1.20  EPR                                     9
% 2.08/1.20  Horn                                    17
% 2.08/1.20  unary                                   8
% 2.08/1.20  binary                                  5
% 2.08/1.20  lits                                    36
% 2.08/1.20  lits eq                                 8
% 2.08/1.20  fd_pure                                 0
% 2.08/1.20  fd_pseudo                               0
% 2.08/1.20  fd_cond                                 1
% 2.08/1.20  fd_pseudo_cond                          3
% 2.08/1.20  AC symbols                              0
% 2.08/1.20  
% 2.08/1.20  ------ Schedule dynamic 5 is on 
% 2.08/1.20  
% 2.08/1.20  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.08/1.20  
% 2.08/1.20  
% 2.08/1.20  ------ 
% 2.08/1.20  Current options:
% 2.08/1.20  ------ 
% 2.08/1.20  
% 2.08/1.20  
% 2.08/1.20  
% 2.08/1.20  
% 2.08/1.20  ------ Proving...
% 2.08/1.20  
% 2.08/1.20  
% 2.08/1.20  % SZS status Theorem for theBenchmark.p
% 2.08/1.20  
% 2.08/1.20  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.08/1.20  
% 2.08/1.20  
%------------------------------------------------------------------------------