TSTP Solution File: LCL686+1.001 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : LCL686+1.001 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n010.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 : Thu Aug 31 07:52:00 EDT 2023

% Result   : Theorem 0.80s 1.20s
% Output   : CNFRefutation 0.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   34 (   5 unt;   0 def)
%            Number of atoms       :  285 (   0 equ)
%            Maximal formula atoms :   38 (   8 avg)
%            Number of connectives :  436 ( 185   ~; 146   |;  98   &)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   8 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-1 aty)
%            Number of variables   :  115 (   0 sgn;  64   !;  39   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0] : r1(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).

fof(f3,conjecture,
    ~ ? [X0] :
        ~ ( ! [X1] :
              ( ~ ! [X0] :
                    ( ~ ( ! [X1] :
                            ( ( p1(X1)
                              & p2(X1) )
                            | ( ~ p2(X1)
                              & ~ p1(X1) )
                            | ~ r1(X0,X1) )
                        | ! [X1] :
                            ( p3(X1)
                            | ~ r1(X0,X1) )
                        | ~ ! [X1] :
                              ( ~ ( ( p1(X1)
                                    & ~ p2(X1) )
                                  | ( ~ p1(X1)
                                    & p2(X1) ) )
                              | ~ r1(X0,X1) )
                        | ! [X1] :
                            ( $false
                            | ~ r1(X0,X1) ) )
                    | ~ r1(X1,X0) )
              | ~ r1(X0,X1) )
          | ! [X1] :
              ( ! [X0] :
                  ( ~ p1(X0)
                  | ~ r1(X1,X0) )
              | ~ p3(X1)
              | ~ r1(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',main) ).

fof(f4,negated_conjecture,
    ~ ~ ? [X0] :
          ~ ( ! [X1] :
                ( ~ ! [X0] :
                      ( ~ ( ! [X1] :
                              ( ( p1(X1)
                                & p2(X1) )
                              | ( ~ p2(X1)
                                & ~ p1(X1) )
                              | ~ r1(X0,X1) )
                          | ! [X1] :
                              ( p3(X1)
                              | ~ r1(X0,X1) )
                          | ~ ! [X1] :
                                ( ~ ( ( p1(X1)
                                      & ~ p2(X1) )
                                    | ( ~ p1(X1)
                                      & p2(X1) ) )
                                | ~ r1(X0,X1) )
                          | ! [X1] :
                              ( $false
                              | ~ r1(X0,X1) ) )
                      | ~ r1(X1,X0) )
                | ~ r1(X0,X1) )
            | ! [X1] :
                ( ! [X0] :
                    ( ~ p1(X0)
                    | ~ r1(X1,X0) )
                | ~ p3(X1)
                | ~ r1(X0,X1) ) ),
    inference(negated_conjecture,[],[f3]) ).

fof(f5,plain,
    ~ ~ ? [X0] :
          ~ ( ! [X1] :
                ( ~ ! [X2] :
                      ( ~ ( ! [X3] :
                              ( ( p1(X3)
                                & p2(X3) )
                              | ( ~ p2(X3)
                                & ~ p1(X3) )
                              | ~ r1(X2,X3) )
                          | ! [X4] :
                              ( p3(X4)
                              | ~ r1(X2,X4) )
                          | ~ ! [X5] :
                                ( ~ ( ( p1(X5)
                                      & ~ p2(X5) )
                                    | ( ~ p1(X5)
                                      & p2(X5) ) )
                                | ~ r1(X2,X5) )
                          | ! [X6] :
                              ( $false
                              | ~ r1(X2,X6) ) )
                      | ~ r1(X1,X2) )
                | ~ r1(X0,X1) )
            | ! [X7] :
                ( ! [X8] :
                    ( ~ p1(X8)
                    | ~ r1(X7,X8) )
                | ~ p3(X7)
                | ~ r1(X0,X7) ) ),
    inference(rectify,[],[f4]) ).

fof(f6,plain,
    ~ ~ ? [X0] :
          ~ ( ! [X1] :
                ( ~ ! [X2] :
                      ( ~ ( ! [X3] :
                              ( ( p1(X3)
                                & p2(X3) )
                              | ( ~ p2(X3)
                                & ~ p1(X3) )
                              | ~ r1(X2,X3) )
                          | ! [X4] :
                              ( p3(X4)
                              | ~ r1(X2,X4) )
                          | ~ ! [X5] :
                                ( ~ ( ( p1(X5)
                                      & ~ p2(X5) )
                                    | ( ~ p1(X5)
                                      & p2(X5) ) )
                                | ~ r1(X2,X5) )
                          | ! [X6] : ~ r1(X2,X6) )
                      | ~ r1(X1,X2) )
                | ~ r1(X0,X1) )
            | ! [X7] :
                ( ! [X8] :
                    ( ~ p1(X8)
                    | ~ r1(X7,X8) )
                | ~ p3(X7)
                | ~ r1(X0,X7) ) ),
    inference(true_and_false_elimination,[],[f5]) ).

fof(f7,plain,
    ? [X0] :
      ~ ( ! [X1] :
            ( ~ ! [X2] :
                  ( ~ ( ! [X3] :
                          ( ( p1(X3)
                            & p2(X3) )
                          | ( ~ p2(X3)
                            & ~ p1(X3) )
                          | ~ r1(X2,X3) )
                      | ! [X4] :
                          ( p3(X4)
                          | ~ r1(X2,X4) )
                      | ~ ! [X5] :
                            ( ~ ( ( p1(X5)
                                  & ~ p2(X5) )
                                | ( ~ p1(X5)
                                  & p2(X5) ) )
                            | ~ r1(X2,X5) )
                      | ! [X6] : ~ r1(X2,X6) )
                  | ~ r1(X1,X2) )
            | ~ r1(X0,X1) )
        | ! [X7] :
            ( ! [X8] :
                ( ~ p1(X8)
                | ~ r1(X7,X8) )
            | ~ p3(X7)
            | ~ r1(X0,X7) ) ),
    inference(flattening,[],[f6]) ).

fof(f10,plain,
    ? [X0] :
      ( ? [X1] :
          ( ! [X2] :
              ( ( ? [X3] :
                    ( ( ~ p1(X3)
                      | ~ p2(X3) )
                    & ( p2(X3)
                      | p1(X3) )
                    & r1(X2,X3) )
                & ? [X4] :
                    ( ~ p3(X4)
                    & r1(X2,X4) )
                & ! [X5] :
                    ( ( ( ~ p1(X5)
                        | p2(X5) )
                      & ( p1(X5)
                        | ~ p2(X5) ) )
                    | ~ r1(X2,X5) )
                & ? [X6] : r1(X2,X6) )
              | ~ r1(X1,X2) )
          & r1(X0,X1) )
      & ? [X7] :
          ( ? [X8] :
              ( p1(X8)
              & r1(X7,X8) )
          & p3(X7)
          & r1(X0,X7) ) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f11,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ! [X2] :
                ( ( ? [X3] :
                      ( ( ~ p1(X3)
                        | ~ p2(X3) )
                      & ( p2(X3)
                        | p1(X3) )
                      & r1(X2,X3) )
                  & ? [X4] :
                      ( ~ p3(X4)
                      & r1(X2,X4) )
                  & ! [X5] :
                      ( ( ( ~ p1(X5)
                          | p2(X5) )
                        & ( p1(X5)
                          | ~ p2(X5) ) )
                      | ~ r1(X2,X5) )
                  & ? [X6] : r1(X2,X6) )
                | ~ r1(X1,X2) )
            & r1(X0,X1) )
        & ? [X7] :
            ( ? [X8] :
                ( p1(X8)
                & r1(X7,X8) )
            & p3(X7)
            & r1(X0,X7) ) )
   => ( ? [X1] :
          ( ! [X2] :
              ( ( ? [X3] :
                    ( ( ~ p1(X3)
                      | ~ p2(X3) )
                    & ( p2(X3)
                      | p1(X3) )
                    & r1(X2,X3) )
                & ? [X4] :
                    ( ~ p3(X4)
                    & r1(X2,X4) )
                & ! [X5] :
                    ( ( ( ~ p1(X5)
                        | p2(X5) )
                      & ( p1(X5)
                        | ~ p2(X5) ) )
                    | ~ r1(X2,X5) )
                & ? [X6] : r1(X2,X6) )
              | ~ r1(X1,X2) )
          & r1(sK0,X1) )
      & ? [X7] :
          ( ? [X8] :
              ( p1(X8)
              & r1(X7,X8) )
          & p3(X7)
          & r1(sK0,X7) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f12,plain,
    ( ? [X1] :
        ( ! [X2] :
            ( ( ? [X3] :
                  ( ( ~ p1(X3)
                    | ~ p2(X3) )
                  & ( p2(X3)
                    | p1(X3) )
                  & r1(X2,X3) )
              & ? [X4] :
                  ( ~ p3(X4)
                  & r1(X2,X4) )
              & ! [X5] :
                  ( ( ( ~ p1(X5)
                      | p2(X5) )
                    & ( p1(X5)
                      | ~ p2(X5) ) )
                  | ~ r1(X2,X5) )
              & ? [X6] : r1(X2,X6) )
            | ~ r1(X1,X2) )
        & r1(sK0,X1) )
   => ( ! [X2] :
          ( ( ? [X3] :
                ( ( ~ p1(X3)
                  | ~ p2(X3) )
                & ( p2(X3)
                  | p1(X3) )
                & r1(X2,X3) )
            & ? [X4] :
                ( ~ p3(X4)
                & r1(X2,X4) )
            & ! [X5] :
                ( ( ( ~ p1(X5)
                    | p2(X5) )
                  & ( p1(X5)
                    | ~ p2(X5) ) )
                | ~ r1(X2,X5) )
            & ? [X6] : r1(X2,X6) )
          | ~ r1(sK1,X2) )
      & r1(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f13,plain,
    ! [X2] :
      ( ? [X3] :
          ( ( ~ p1(X3)
            | ~ p2(X3) )
          & ( p2(X3)
            | p1(X3) )
          & r1(X2,X3) )
     => ( ( ~ p1(sK2(X2))
          | ~ p2(sK2(X2)) )
        & ( p2(sK2(X2))
          | p1(sK2(X2)) )
        & r1(X2,sK2(X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f14,plain,
    ! [X2] :
      ( ? [X4] :
          ( ~ p3(X4)
          & r1(X2,X4) )
     => ( ~ p3(sK3(X2))
        & r1(X2,sK3(X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f15,plain,
    ! [X2] :
      ( ? [X6] : r1(X2,X6)
     => r1(X2,sK4(X2)) ),
    introduced(choice_axiom,[]) ).

fof(f16,plain,
    ( ? [X7] :
        ( ? [X8] :
            ( p1(X8)
            & r1(X7,X8) )
        & p3(X7)
        & r1(sK0,X7) )
   => ( ? [X8] :
          ( p1(X8)
          & r1(sK5,X8) )
      & p3(sK5)
      & r1(sK0,sK5) ) ),
    introduced(choice_axiom,[]) ).

fof(f17,plain,
    ( ? [X8] :
        ( p1(X8)
        & r1(sK5,X8) )
   => ( p1(sK6)
      & r1(sK5,sK6) ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ( ! [X2] :
        ( ( ( ~ p1(sK2(X2))
            | ~ p2(sK2(X2)) )
          & ( p2(sK2(X2))
            | p1(sK2(X2)) )
          & r1(X2,sK2(X2))
          & ~ p3(sK3(X2))
          & r1(X2,sK3(X2))
          & ! [X5] :
              ( ( ( ~ p1(X5)
                  | p2(X5) )
                & ( p1(X5)
                  | ~ p2(X5) ) )
              | ~ r1(X2,X5) )
          & r1(X2,sK4(X2)) )
        | ~ r1(sK1,X2) )
    & r1(sK0,sK1)
    & p1(sK6)
    & r1(sK5,sK6)
    & p3(sK5)
    & r1(sK0,sK5) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6])],[f10,f17,f16,f15,f14,f13,f12,f11]) ).

fof(f19,plain,
    ! [X0] : r1(X0,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f27,plain,
    ! [X2,X5] :
      ( p1(X5)
      | ~ p2(X5)
      | ~ r1(X2,X5)
      | ~ r1(sK1,X2) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f28,plain,
    ! [X2,X5] :
      ( ~ p1(X5)
      | p2(X5)
      | ~ r1(X2,X5)
      | ~ r1(sK1,X2) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f31,plain,
    ! [X2] :
      ( r1(X2,sK2(X2))
      | ~ r1(sK1,X2) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f32,plain,
    ! [X2] :
      ( p2(sK2(X2))
      | p1(sK2(X2))
      | ~ r1(sK1,X2) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f33,plain,
    ! [X2] :
      ( ~ p1(sK2(X2))
      | ~ p2(sK2(X2))
      | ~ r1(sK1,X2) ),
    inference(cnf_transformation,[],[f18]) ).

cnf(c_49,plain,
    r1(X0,X0),
    inference(cnf_transformation,[],[f19]) ).

cnf(c_51,negated_conjecture,
    ( ~ r1(sK1,X0)
    | ~ p1(sK2(X0))
    | ~ p2(sK2(X0)) ),
    inference(cnf_transformation,[],[f33]) ).

cnf(c_52,negated_conjecture,
    ( ~ r1(sK1,X0)
    | p1(sK2(X0))
    | p2(sK2(X0)) ),
    inference(cnf_transformation,[],[f32]) ).

cnf(c_53,negated_conjecture,
    ( ~ r1(sK1,X0)
    | r1(X0,sK2(X0)) ),
    inference(cnf_transformation,[],[f31]) ).

cnf(c_56,negated_conjecture,
    ( ~ r1(X0,X1)
    | ~ r1(sK1,X0)
    | ~ p1(X1)
    | p2(X1) ),
    inference(cnf_transformation,[],[f28]) ).

cnf(c_57,negated_conjecture,
    ( ~ r1(X0,X1)
    | ~ r1(sK1,X0)
    | ~ p2(X1)
    | p1(X1) ),
    inference(cnf_transformation,[],[f27]) ).

cnf(c_64,plain,
    r1(sK1,sK1),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_68,plain,
    ( ~ r1(sK1,sK1)
    | r1(sK1,sK2(sK1)) ),
    inference(instantiation,[status(thm)],[c_53]) ).

cnf(c_137,plain,
    ( ~ r1(X0,sK2(X1))
    | ~ r1(sK1,X0)
    | ~ r1(sK1,X1)
    | p1(sK2(X1)) ),
    inference(resolution,[status(thm)],[c_52,c_57]) ).

cnf(c_138,plain,
    ( ~ r1(sK1,sK2(sK1))
    | ~ r1(sK1,sK1)
    | p1(sK2(sK1)) ),
    inference(instantiation,[status(thm)],[c_137]) ).

cnf(c_151,plain,
    ( ~ r1(X0,sK2(X1))
    | ~ r1(sK1,X0)
    | ~ r1(sK1,X1)
    | ~ p1(sK2(X1)) ),
    inference(resolution,[status(thm)],[c_51,c_56]) ).

cnf(c_152,plain,
    ( ~ r1(sK1,sK2(sK1))
    | ~ r1(sK1,sK1)
    | ~ p1(sK2(sK1)) ),
    inference(instantiation,[status(thm)],[c_151]) ).

cnf(c_153,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_152,c_138,c_68,c_64]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem  : LCL686+1.001 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n010.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Fri Aug 25 07:12:20 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.49  Running first-order theorem proving
% 0.20/0.49  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.80/1.20  % SZS status Started for theBenchmark.p
% 0.80/1.20  % SZS status Theorem for theBenchmark.p
% 0.80/1.20  
% 0.80/1.20  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.80/1.20  
% 0.80/1.20  ------  iProver source info
% 0.80/1.20  
% 0.80/1.20  git: date: 2023-05-31 18:12:56 +0000
% 0.80/1.20  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.80/1.20  git: non_committed_changes: false
% 0.80/1.20  git: last_make_outside_of_git: false
% 0.80/1.20  
% 0.80/1.20  ------ Parsing...
% 0.80/1.20  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 0.80/1.20  
% 0.80/1.20  ------ Preprocessing... sf_s  rm: 2 0s  sf_e  pe_s 
% 0.80/1.20  
% 0.80/1.20  % SZS status Theorem for theBenchmark.p
% 0.80/1.20  
% 0.80/1.20  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.80/1.20  
% 0.80/1.20  
%------------------------------------------------------------------------------