TSTP Solution File: SET700+4 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET700+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n012.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 03:01:17 EDT 2024

% Result   : Theorem 20.79s 3.65s
% Output   : CNFRefutation 20.79s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).

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

fof(f7,axiom,
    ! [X1,X0,X3] :
      ( member(X1,difference(X3,X0))
    <=> ( ~ member(X1,X0)
        & member(X1,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference) ).

fof(f12,conjecture,
    ! [X0,X1,X3] :
      ( ( subset(X1,X3)
        & subset(X0,X3) )
     => ( subset(X0,X1)
      <=> subset(intersection(X0,difference(X3,X1)),X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI34) ).

fof(f13,negated_conjecture,
    ~ ! [X0,X1,X3] :
        ( ( subset(X1,X3)
          & subset(X0,X3) )
       => ( subset(X0,X1)
        <=> subset(intersection(X0,difference(X3,X1)),X1) ) ),
    inference(negated_conjecture,[],[f12]) ).

fof(f15,plain,
    ! [X0,X1,X2] :
      ( member(X0,intersection(X1,X2))
    <=> ( member(X0,X2)
        & member(X0,X1) ) ),
    inference(rectify,[],[f4]) ).

fof(f18,plain,
    ! [X0,X1,X2] :
      ( member(X0,difference(X2,X1))
    <=> ( ~ member(X0,X1)
        & member(X0,X2) ) ),
    inference(rectify,[],[f7]) ).

fof(f23,plain,
    ~ ! [X0,X1,X2] :
        ( ( subset(X1,X2)
          & subset(X0,X2) )
       => ( subset(X0,X1)
        <=> subset(intersection(X0,difference(X2,X1)),X1) ) ),
    inference(rectify,[],[f13]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f26,plain,
    ? [X0,X1,X2] :
      ( ( subset(X0,X1)
      <~> subset(intersection(X0,difference(X2,X1)),X1) )
      & subset(X1,X2)
      & subset(X0,X2) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f27,plain,
    ? [X0,X1,X2] :
      ( ( subset(X0,X1)
      <~> subset(intersection(X0,difference(X2,X1)),X1) )
      & subset(X1,X2)
      & subset(X0,X2) ),
    inference(flattening,[],[f26]) ).

fof(f28,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,[],[f24]) ).

fof(f29,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,[],[f28]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK0(X0,X1),X1)
        & member(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ member(sK0(X0,X1),X1)
          & member(sK0(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f29,f30]) ).

fof(f33,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,intersection(X1,X2))
        | ~ member(X0,X2)
        | ~ member(X0,X1) )
      & ( ( member(X0,X2)
          & member(X0,X1) )
        | ~ member(X0,intersection(X1,X2)) ) ),
    inference(nnf_transformation,[],[f15]) ).

fof(f34,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,intersection(X1,X2))
        | ~ member(X0,X2)
        | ~ member(X0,X1) )
      & ( ( member(X0,X2)
          & member(X0,X1) )
        | ~ member(X0,intersection(X1,X2)) ) ),
    inference(flattening,[],[f33]) ).

fof(f37,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,difference(X2,X1))
        | member(X0,X1)
        | ~ member(X0,X2) )
      & ( ( ~ member(X0,X1)
          & member(X0,X2) )
        | ~ member(X0,difference(X2,X1)) ) ),
    inference(nnf_transformation,[],[f18]) ).

fof(f38,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,difference(X2,X1))
        | member(X0,X1)
        | ~ member(X0,X2) )
      & ( ( ~ member(X0,X1)
          & member(X0,X2) )
        | ~ member(X0,difference(X2,X1)) ) ),
    inference(flattening,[],[f37]) ).

fof(f50,plain,
    ? [X0,X1,X2] :
      ( ( ~ subset(intersection(X0,difference(X2,X1)),X1)
        | ~ subset(X0,X1) )
      & ( subset(intersection(X0,difference(X2,X1)),X1)
        | subset(X0,X1) )
      & subset(X1,X2)
      & subset(X0,X2) ),
    inference(nnf_transformation,[],[f27]) ).

fof(f51,plain,
    ? [X0,X1,X2] :
      ( ( ~ subset(intersection(X0,difference(X2,X1)),X1)
        | ~ subset(X0,X1) )
      & ( subset(intersection(X0,difference(X2,X1)),X1)
        | subset(X0,X1) )
      & subset(X1,X2)
      & subset(X0,X2) ),
    inference(flattening,[],[f50]) ).

fof(f52,plain,
    ( ? [X0,X1,X2] :
        ( ( ~ subset(intersection(X0,difference(X2,X1)),X1)
          | ~ subset(X0,X1) )
        & ( subset(intersection(X0,difference(X2,X1)),X1)
          | subset(X0,X1) )
        & subset(X1,X2)
        & subset(X0,X2) )
   => ( ( ~ subset(intersection(sK3,difference(sK5,sK4)),sK4)
        | ~ subset(sK3,sK4) )
      & ( subset(intersection(sK3,difference(sK5,sK4)),sK4)
        | subset(sK3,sK4) )
      & subset(sK4,sK5)
      & subset(sK3,sK5) ) ),
    introduced(choice_axiom,[]) ).

fof(f53,plain,
    ( ( ~ subset(intersection(sK3,difference(sK5,sK4)),sK4)
      | ~ subset(sK3,sK4) )
    & ( subset(intersection(sK3,difference(sK5,sK4)),sK4)
      | subset(sK3,sK4) )
    & subset(sK4,sK5)
    & subset(sK3,sK5) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f51,f52]) ).

fof(f54,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK0(X0,X1),X0) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f59,plain,
    ! [X2,X0,X1] :
      ( member(X0,X1)
      | ~ member(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f60,plain,
    ! [X2,X0,X1] :
      ( member(X0,X2)
      | ~ member(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f61,plain,
    ! [X2,X0,X1] :
      ( member(X0,intersection(X1,X2))
      | ~ member(X0,X2)
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f67,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,X1)
      | ~ member(X0,difference(X2,X1)) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f68,plain,
    ! [X2,X0,X1] :
      ( member(X0,difference(X2,X1))
      | member(X0,X1)
      | ~ member(X0,X2) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f80,plain,
    subset(sK3,sK5),
    inference(cnf_transformation,[],[f53]) ).

fof(f82,plain,
    ( subset(intersection(sK3,difference(sK5,sK4)),sK4)
    | subset(sK3,sK4) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f83,plain,
    ( ~ subset(intersection(sK3,difference(sK5,sK4)),sK4)
    | ~ subset(sK3,sK4) ),
    inference(cnf_transformation,[],[f53]) ).

cnf(c_49,plain,
    ( ~ member(sK0(X0,X1),X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f56]) ).

cnf(c_50,plain,
    ( member(sK0(X0,X1),X0)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f55]) ).

cnf(c_51,plain,
    ( ~ subset(X0,X1)
    | ~ member(X2,X0)
    | member(X2,X1) ),
    inference(cnf_transformation,[],[f54]) ).

cnf(c_54,plain,
    ( ~ member(X0,X1)
    | ~ member(X0,X2)
    | member(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[],[f61]) ).

cnf(c_55,plain,
    ( ~ member(X0,intersection(X1,X2))
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f60]) ).

cnf(c_56,plain,
    ( ~ member(X0,intersection(X1,X2))
    | member(X0,X1) ),
    inference(cnf_transformation,[],[f59]) ).

cnf(c_61,plain,
    ( ~ member(X0,X1)
    | member(X0,difference(X1,X2))
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f68]) ).

cnf(c_62,plain,
    ( ~ member(X0,difference(X1,X2))
    | ~ member(X0,X2) ),
    inference(cnf_transformation,[],[f67]) ).

cnf(c_75,negated_conjecture,
    ( ~ subset(intersection(sK3,difference(sK5,sK4)),sK4)
    | ~ subset(sK3,sK4) ),
    inference(cnf_transformation,[],[f83]) ).

cnf(c_76,negated_conjecture,
    ( subset(intersection(sK3,difference(sK5,sK4)),sK4)
    | subset(sK3,sK4) ),
    inference(cnf_transformation,[],[f82]) ).

cnf(c_78,negated_conjecture,
    subset(sK3,sK5),
    inference(cnf_transformation,[],[f80]) ).

cnf(c_443,plain,
    difference(sK5,sK4) = sP0_iProver_def,
    definition ).

cnf(c_444,plain,
    intersection(sK3,sP0_iProver_def) = sP1_iProver_def,
    definition ).

cnf(c_447,negated_conjecture,
    ( subset(sK3,sK4)
    | subset(sP1_iProver_def,sK4) ),
    inference(demodulation,[status(thm)],[c_76,c_443,c_444]) ).

cnf(c_448,negated_conjecture,
    ( ~ subset(sK3,sK4)
    | ~ subset(sP1_iProver_def,sK4) ),
    inference(demodulation,[status(thm)],[c_75]) ).

cnf(c_1066,plain,
    ( ~ member(X0,sP1_iProver_def)
    | member(X0,sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_444,c_55]) ).

cnf(c_1077,plain,
    ( member(sK0(sP1_iProver_def,X0),sP0_iProver_def)
    | subset(sP1_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_50,c_1066]) ).

cnf(c_1091,plain,
    ( ~ member(X0,sP1_iProver_def)
    | member(X0,sK3) ),
    inference(superposition,[status(thm)],[c_444,c_56]) ).

cnf(c_1101,plain,
    ( member(sK0(sP1_iProver_def,X0),sK3)
    | subset(sP1_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_50,c_1091]) ).

cnf(c_1237,plain,
    ( ~ member(X0,sK4)
    | ~ member(X0,sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_443,c_62]) ).

cnf(c_1248,plain,
    ( ~ member(sK0(sK3,sK4),sK4)
    | subset(sK3,sK4) ),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_1260,plain,
    ( member(sK0(sK3,sK4),sK3)
    | subset(sK3,sK4) ),
    inference(instantiation,[status(thm)],[c_50]) ).

cnf(c_1341,plain,
    ( ~ subset(sK3,X0)
    | member(sK0(sP1_iProver_def,X1),X0)
    | subset(sP1_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_1101,c_51]) ).

cnf(c_1407,plain,
    ( ~ subset(sK3,sK4)
    | member(sK0(sP1_iProver_def,sK4),sK4)
    | subset(sP1_iProver_def,sK4) ),
    inference(instantiation,[status(thm)],[c_1341]) ).

cnf(c_1794,plain,
    ( ~ member(sK0(sP1_iProver_def,X0),sK4)
    | subset(sP1_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_1077,c_1237]) ).

cnf(c_1806,plain,
    ( ~ member(sK0(sP1_iProver_def,sK4),sK4)
    | subset(sP1_iProver_def,sK4) ),
    inference(instantiation,[status(thm)],[c_1794]) ).

cnf(c_2314,plain,
    ( ~ member(sK0(sK3,sK4),sK3)
    | ~ subset(sK3,X0)
    | member(sK0(sK3,sK4),X0) ),
    inference(instantiation,[status(thm)],[c_51]) ).

cnf(c_2319,plain,
    ( ~ member(sK0(sK3,sK4),X0)
    | ~ member(sK0(sK3,sK4),sK3)
    | member(sK0(sK3,sK4),intersection(sK3,X0)) ),
    inference(instantiation,[status(thm)],[c_54]) ).

cnf(c_13092,plain,
    ( ~ member(sK0(sK3,sK4),sK3)
    | ~ subset(sK3,sK5)
    | member(sK0(sK3,sK4),sK5) ),
    inference(instantiation,[status(thm)],[c_2314]) ).

cnf(c_14383,negated_conjecture,
    subset(sP1_iProver_def,sK4),
    inference(global_subsumption_just,[status(thm)],[c_447,c_447,c_1407,c_1806]) ).

cnf(c_20470,plain,
    ( ~ member(sK0(sK3,sK4),X0)
    | ~ subset(X0,sK4)
    | member(sK0(sK3,sK4),sK4) ),
    inference(instantiation,[status(thm)],[c_51]) ).

cnf(c_23569,plain,
    ( ~ member(sK0(sK3,sK4),X0)
    | member(sK0(sK3,sK4),difference(X0,sK4))
    | member(sK0(sK3,sK4),sK4) ),
    inference(instantiation,[status(thm)],[c_61]) ).

cnf(c_32963,plain,
    ( ~ member(sK0(sK3,sK4),sK5)
    | member(sK0(sK3,sK4),difference(sK5,sK4))
    | member(sK0(sK3,sK4),sK4) ),
    inference(instantiation,[status(thm)],[c_23569]) ).

cnf(c_61722,plain,
    ( ~ member(sK0(sK3,sK4),difference(sK5,sK4))
    | ~ member(sK0(sK3,sK4),sK3)
    | member(sK0(sK3,sK4),intersection(sK3,difference(sK5,sK4))) ),
    inference(instantiation,[status(thm)],[c_2319]) ).

cnf(c_87590,plain,
    ( ~ member(sK0(sK3,sK4),intersection(sK3,difference(sK5,sK4)))
    | ~ subset(intersection(sK3,difference(sK5,sK4)),sK4)
    | member(sK0(sK3,sK4),sK4) ),
    inference(instantiation,[status(thm)],[c_20470]) ).

cnf(c_87592,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_87590,c_61722,c_32963,c_14383,c_13092,c_1260,c_1248,c_448,c_76,c_78]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SET700+4 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.12  % Command  : run_iprover %s %d THM
% 0.12/0.32  % Computer : n012.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 300
% 0.12/0.32  % DateTime : Thu May  2 20:12:55 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.17/0.44  Running first-order theorem proving
% 0.17/0.44  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
% 20.79/3.65  % SZS status Started for theBenchmark.p
% 20.79/3.65  % SZS status Theorem for theBenchmark.p
% 20.79/3.65  
% 20.79/3.65  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 20.79/3.65  
% 20.79/3.65  ------  iProver source info
% 20.79/3.65  
% 20.79/3.65  git: date: 2024-05-02 19:28:25 +0000
% 20.79/3.65  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 20.79/3.65  git: non_committed_changes: false
% 20.79/3.65  
% 20.79/3.65  ------ Parsing...
% 20.79/3.65  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 20.79/3.65  
% 20.79/3.65  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 20.79/3.65  
% 20.79/3.65  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 20.79/3.65  
% 20.79/3.65  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 20.79/3.65  ------ Proving...
% 20.79/3.65  ------ Problem Properties 
% 20.79/3.65  
% 20.79/3.65  
% 20.79/3.65  clauses                                 32
% 20.79/3.65  conjectures                             4
% 20.79/3.65  EPR                                     6
% 20.79/3.65  Horn                                    26
% 20.79/3.65  unary                                   8
% 20.79/3.65  binary                                  17
% 20.79/3.65  lits                                    63
% 20.79/3.65  lits eq                                 5
% 20.79/3.65  fd_pure                                 0
% 20.79/3.65  fd_pseudo                               0
% 20.79/3.65  fd_cond                                 0
% 20.79/3.65  fd_pseudo_cond                          2
% 20.79/3.65  AC symbols                              0
% 20.79/3.65  
% 20.79/3.65  ------ Schedule dynamic 5 is on 
% 20.79/3.65  
% 20.79/3.65  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 20.79/3.65  
% 20.79/3.65  
% 20.79/3.65  ------ 
% 20.79/3.65  Current options:
% 20.79/3.65  ------ 
% 20.79/3.65  
% 20.79/3.65  
% 20.79/3.65  
% 20.79/3.65  
% 20.79/3.65  ------ Proving...
% 20.79/3.65  
% 20.79/3.65  
% 20.79/3.65  % SZS status Theorem for theBenchmark.p
% 20.79/3.65  
% 20.79/3.65  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 20.79/3.65  
% 20.79/3.66  
%------------------------------------------------------------------------------