TSTP Solution File: SET947+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET947+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n018.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 03:02:05 EDT 2024

% Result   : Theorem 2.43s 1.17s
% Output   : CNFRefutation 2.43s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [X0,X1] :
      ( powerset(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> subset(X2,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( in(X0,X1)
     => subset(X0,union(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l50_zfmisc_1) ).

fof(f8,conjecture,
    ! [X0] : subset(X0,powerset(union(X0))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_zfmisc_1) ).

fof(f9,negated_conjecture,
    ~ ! [X0] : subset(X0,powerset(union(X0))),
    inference(negated_conjecture,[],[f8]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f13,plain,
    ! [X0,X1] :
      ( subset(X0,union(X1))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f14,plain,
    ? [X0] : ~ subset(X0,powerset(union(X0))),
    inference(ennf_transformation,[],[f9]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( ( powerset(X0) = X1
        | ? [X2] :
            ( ( ~ subset(X2,X0)
              | ~ in(X2,X1) )
            & ( subset(X2,X0)
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | ~ subset(X2,X0) )
            & ( subset(X2,X0)
              | ~ in(X2,X1) ) )
        | powerset(X0) != X1 ) ),
    inference(nnf_transformation,[],[f2]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( ( powerset(X0) = X1
        | ? [X2] :
            ( ( ~ subset(X2,X0)
              | ~ in(X2,X1) )
            & ( subset(X2,X0)
              | in(X2,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | ~ subset(X3,X0) )
            & ( subset(X3,X0)
              | ~ in(X3,X1) ) )
        | powerset(X0) != X1 ) ),
    inference(rectify,[],[f15]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ subset(X2,X0)
            | ~ in(X2,X1) )
          & ( subset(X2,X0)
            | in(X2,X1) ) )
     => ( ( ~ subset(sK0(X0,X1),X0)
          | ~ in(sK0(X0,X1),X1) )
        & ( subset(sK0(X0,X1),X0)
          | in(sK0(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ( powerset(X0) = X1
        | ( ( ~ subset(sK0(X0,X1),X0)
            | ~ in(sK0(X0,X1),X1) )
          & ( subset(sK0(X0,X1),X0)
            | in(sK0(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | ~ subset(X3,X0) )
            & ( subset(X3,X0)
              | ~ in(X3,X1) ) )
        | powerset(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f16,f17]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f12]) ).

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

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

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

fof(f27,plain,
    ( ? [X0] : ~ subset(X0,powerset(union(X0)))
   => ~ subset(sK4,powerset(union(sK4))) ),
    introduced(choice_axiom,[]) ).

fof(f28,plain,
    ~ subset(sK4,powerset(union(sK4))),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f14,f27]) ).

fof(f31,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | ~ subset(X3,X0)
      | powerset(X0) != X1 ),
    inference(cnf_transformation,[],[f18]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sK1(X0,X1),X0) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ in(sK1(X0,X1),X1) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( subset(X0,union(X1))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f41,plain,
    ~ subset(sK4,powerset(union(sK4))),
    inference(cnf_transformation,[],[f28]) ).

fof(f42,plain,
    ! [X3,X0] :
      ( in(X3,powerset(X0))
      | ~ subset(X3,X0) ),
    inference(equality_resolution,[],[f31]) ).

cnf(c_52,plain,
    ( ~ subset(X0,X1)
    | in(X0,powerset(X1)) ),
    inference(cnf_transformation,[],[f42]) ).

cnf(c_54,plain,
    ( ~ in(sK1(X0,X1),X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f36]) ).

cnf(c_55,plain,
    ( in(sK1(X0,X1),X0)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f35]) ).

cnf(c_57,plain,
    ( ~ in(X0,X1)
    | subset(X0,union(X1)) ),
    inference(cnf_transformation,[],[f37]) ).

cnf(c_61,negated_conjecture,
    ~ subset(sK4,powerset(union(sK4))),
    inference(cnf_transformation,[],[f41]) ).

cnf(c_896,plain,
    union(sK4) = sP0_iProver_def,
    definition ).

cnf(c_897,plain,
    powerset(sP0_iProver_def) = sP1_iProver_def,
    definition ).

cnf(c_898,negated_conjecture,
    ~ subset(sK4,sP1_iProver_def),
    inference(demodulation,[status(thm)],[c_61,c_896,c_897]) ).

cnf(c_1209,plain,
    ( ~ subset(X0,sP0_iProver_def)
    | in(X0,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_897,c_52]) ).

cnf(c_1257,plain,
    ( ~ in(X0,sK4)
    | subset(X0,sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_896,c_57]) ).

cnf(c_1283,plain,
    ( subset(sK1(sK4,X0),sP0_iProver_def)
    | subset(sK4,X0) ),
    inference(superposition,[status(thm)],[c_55,c_1257]) ).

cnf(c_1298,plain,
    ( in(sK1(sK4,X0),sP1_iProver_def)
    | subset(sK4,X0) ),
    inference(superposition,[status(thm)],[c_1283,c_1209]) ).

cnf(c_1306,plain,
    subset(sK4,sP1_iProver_def),
    inference(superposition,[status(thm)],[c_1298,c_54]) ).

cnf(c_1308,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_1306,c_898]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET947+1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.13  % Command  : run_iprover %s %d THM
% 0.12/0.34  % Computer : n018.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 20:49:01 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 0.19/0.47  Running first-order theorem proving
% 0.19/0.47  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
% 2.43/1.17  % SZS status Started for theBenchmark.p
% 2.43/1.17  % SZS status Theorem for theBenchmark.p
% 2.43/1.17  
% 2.43/1.17  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 2.43/1.17  
% 2.43/1.17  ------  iProver source info
% 2.43/1.17  
% 2.43/1.17  git: date: 2024-05-02 19:28:25 +0000
% 2.43/1.17  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 2.43/1.17  git: non_committed_changes: false
% 2.43/1.17  
% 2.43/1.17  ------ Parsing...
% 2.43/1.17  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 2.43/1.17  
% 2.43/1.17  ------ 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 
% 2.43/1.17  
% 2.43/1.17  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 2.43/1.17  
% 2.43/1.17  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.43/1.17  ------ Proving...
% 2.43/1.17  ------ Problem Properties 
% 2.43/1.17  
% 2.43/1.17  
% 2.43/1.17  clauses                                 14
% 2.43/1.17  conjectures                             1
% 2.43/1.17  EPR                                     5
% 2.43/1.17  Horn                                    12
% 2.43/1.17  unary                                   5
% 2.43/1.17  binary                                  6
% 2.43/1.17  lits                                    26
% 2.43/1.17  lits eq                                 5
% 2.43/1.17  fd_pure                                 0
% 2.43/1.17  fd_pseudo                               0
% 2.43/1.17  fd_cond                                 0
% 2.43/1.17  fd_pseudo_cond                          2
% 2.43/1.17  AC symbols                              0
% 2.43/1.17  
% 2.43/1.17  ------ Schedule dynamic 5 is on 
% 2.43/1.17  
% 2.43/1.17  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.43/1.17  
% 2.43/1.17  
% 2.43/1.17  ------ 
% 2.43/1.17  Current options:
% 2.43/1.17  ------ 
% 2.43/1.17  
% 2.43/1.17  
% 2.43/1.17  
% 2.43/1.17  
% 2.43/1.17  ------ Proving...
% 2.43/1.17  
% 2.43/1.17  
% 2.43/1.17  % SZS status Theorem for theBenchmark.p
% 2.43/1.17  
% 2.43/1.17  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.43/1.17  
% 2.43/1.17  
%------------------------------------------------------------------------------