TSTP Solution File: NUN060+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : NUN060+1 : TPTP v8.1.2. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n026.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 02:53:12 EDT 2024

% Result   : Theorem 3.66s 1.20s
% Output   : CNFRefutation 3.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   36 (  12 unt;   0 def)
%            Number of atoms       :  139 (   0 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  154 (  51   ~;  39   |;  58   &)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   0 con; 1-2 aty)
%            Number of variables   :  140 (  14 sgn  43   !;  52   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f5,axiom,
    ! [X13] : id(X13,X13),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).

fof(f12,axiom,
    ! [X37,X38] :
    ? [X39] :
      ( ? [X42] :
          ( r3(X37,X38,X42)
          & r2(X42,X39) )
      & ? [X40] :
          ( ? [X41] :
              ( r3(X37,X41,X40)
              & r2(X38,X41) )
          & id(X40,X39) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1a) ).

fof(f15,axiom,
    ! [X53] :
    ? [X54] :
      ( ? [X55] :
          ( r3(X53,X55,X54)
          & r1(X55) )
      & id(X54,X53) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4a) ).

fof(f19,conjecture,
    ? [X62,X45,X46] :
      ( ? [X39] :
          ( ? [X40] :
              ( ? [X48] :
                  ( ? [X42] :
                      ( ? [X57] :
                          ( r2(X57,X42)
                          & r1(X57) )
                      & r2(X42,X48) )
                  & r2(X48,X40) )
              & r2(X40,X39) )
          & r3(X45,X39,X46) )
      & id(X46,X62) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',greq4id) ).

fof(f20,negated_conjecture,
    ~ ? [X62,X45,X46] :
        ( ? [X39] :
            ( ? [X40] :
                ( ? [X48] :
                    ( ? [X42] :
                        ( ? [X57] :
                            ( r2(X57,X42)
                            & r1(X57) )
                        & r2(X42,X48) )
                    & r2(X48,X40) )
                & r2(X40,X39) )
            & r3(X45,X39,X46) )
        & id(X46,X62) ),
    inference(negated_conjecture,[],[f19]) ).

fof(f24,plain,
    ! [X0] : id(X0,X0),
    inference(rectify,[],[f5]) ).

fof(f31,plain,
    ! [X0,X1] :
    ? [X2] :
      ( ? [X3] :
          ( r3(X0,X1,X3)
          & r2(X3,X2) )
      & ? [X4] :
          ( ? [X5] :
              ( r3(X0,X5,X4)
              & r2(X1,X5) )
          & id(X4,X2) ) ),
    inference(rectify,[],[f12]) ).

fof(f34,plain,
    ! [X0] :
    ? [X1] :
      ( ? [X2] :
          ( r3(X0,X2,X1)
          & r1(X2) )
      & id(X1,X0) ),
    inference(rectify,[],[f15]) ).

fof(f38,plain,
    ~ ? [X0,X1,X2] :
        ( ? [X3] :
            ( ? [X4] :
                ( ? [X5] :
                    ( ? [X6] :
                        ( ? [X7] :
                            ( r2(X7,X6)
                            & r1(X7) )
                        & r2(X6,X5) )
                    & r2(X5,X4) )
                & r2(X4,X3) )
            & r3(X1,X3,X2) )
        & id(X2,X0) ),
    inference(rectify,[],[f20]) ).

fof(f39,plain,
    ! [X0,X1,X2] :
      ( ! [X3] :
          ( ! [X4] :
              ( ! [X5] :
                  ( ! [X6] :
                      ( ! [X7] :
                          ( ~ r2(X7,X6)
                          | ~ r1(X7) )
                      | ~ r2(X6,X5) )
                  | ~ r2(X5,X4) )
              | ~ r2(X4,X3) )
          | ~ r3(X1,X3,X2) )
      | ~ id(X2,X0) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( r3(X0,X1,X3)
              & r2(X3,X2) )
          & ? [X4] :
              ( ? [X5] :
                  ( r3(X0,X5,X4)
                  & r2(X1,X5) )
              & id(X4,X2) ) )
     => ( ? [X3] :
            ( r3(X0,X1,X3)
            & r2(X3,sK4(X0,X1)) )
        & ? [X4] :
            ( ? [X5] :
                ( r3(X0,X5,X4)
                & r2(X1,X5) )
            & id(X4,sK4(X0,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( r3(X0,X1,X3)
          & r2(X3,sK4(X0,X1)) )
     => ( r3(X0,X1,sK5(X0,X1))
        & r2(sK5(X0,X1),sK4(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ? [X5] :
              ( r3(X0,X5,X4)
              & r2(X1,X5) )
          & id(X4,sK4(X0,X1)) )
     => ( ? [X5] :
            ( r3(X0,X5,sK6(X0,X1))
            & r2(X1,X5) )
        & id(sK6(X0,X1),sK4(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( r3(X0,X5,sK6(X0,X1))
          & r2(X1,X5) )
     => ( r3(X0,sK7(X0,X1),sK6(X0,X1))
        & r2(X1,sK7(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( r3(X0,X1,sK5(X0,X1))
      & r2(sK5(X0,X1),sK4(X0,X1))
      & r3(X0,sK7(X0,X1),sK6(X0,X1))
      & r2(X1,sK7(X0,X1))
      & id(sK6(X0,X1),sK4(X0,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f31,f51,f50,f49,f48]) ).

fof(f58,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( r3(X0,X2,X1)
              & r1(X2) )
          & id(X1,X0) )
     => ( ? [X2] :
            ( r3(X0,X2,sK12(X0))
            & r1(X2) )
        & id(sK12(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f59,plain,
    ! [X0] :
      ( ? [X2] :
          ( r3(X0,X2,sK12(X0))
          & r1(X2) )
     => ( r3(X0,sK13(X0),sK12(X0))
        & r1(sK13(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f60,plain,
    ! [X0] :
      ( r3(X0,sK13(X0),sK12(X0))
      & r1(sK13(X0))
      & id(sK12(X0),X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13])],[f34,f59,f58]) ).

fof(f84,plain,
    ! [X0] : id(X0,X0),
    inference(cnf_transformation,[],[f24]) ).

fof(f104,plain,
    ! [X0,X1] : r2(X1,sK7(X0,X1)),
    inference(cnf_transformation,[],[f52]) ).

fof(f107,plain,
    ! [X0,X1] : r3(X0,X1,sK5(X0,X1)),
    inference(cnf_transformation,[],[f52]) ).

fof(f115,plain,
    ! [X0] : r1(sK13(X0)),
    inference(cnf_transformation,[],[f60]) ).

fof(f126,plain,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] :
      ( ~ r2(X7,X6)
      | ~ r1(X7)
      | ~ r2(X6,X5)
      | ~ r2(X5,X4)
      | ~ r2(X4,X3)
      | ~ r3(X1,X3,X2)
      | ~ id(X2,X0) ),
    inference(cnf_transformation,[],[f39]) ).

cnf(c_57,plain,
    id(X0,X0),
    inference(cnf_transformation,[],[f84]) ).

cnf(c_68,plain,
    r3(X0,X1,sK5(X0,X1)),
    inference(cnf_transformation,[],[f107]) ).

cnf(c_71,plain,
    r2(X0,sK7(X1,X0)),
    inference(cnf_transformation,[],[f104]) ).

cnf(c_80,plain,
    r1(sK13(X0)),
    inference(cnf_transformation,[],[f115]) ).

cnf(c_91,negated_conjecture,
    ( ~ r3(X0,X1,X2)
    | ~ id(X2,X3)
    | ~ r2(X4,X1)
    | ~ r2(X5,X4)
    | ~ r2(X6,X7)
    | ~ r2(X7,X5)
    | ~ r1(X6) ),
    inference(cnf_transformation,[],[f126]) ).

cnf(c_427,negated_conjecture,
    ( ~ r3(X0,X1,X2)
    | ~ id(X2,X3)
    | ~ r2(X4,X1)
    | ~ r2(X5,X4)
    | ~ r2(X6,X7)
    | ~ r2(X7,X5)
    | ~ r1(X6) ),
    inference(demodulation,[status(thm)],[c_91]) ).

cnf(c_885,plain,
    ( ~ id(sK5(X0,X1),X2)
    | ~ r2(X3,X1)
    | ~ r2(X4,X3)
    | ~ r2(X5,X6)
    | ~ r2(X6,X4)
    | ~ r1(X5) ),
    inference(superposition,[status(thm)],[c_68,c_427]) ).

cnf(c_928,plain,
    ( ~ r2(X0,X1)
    | ~ r2(X2,X0)
    | ~ r2(X3,X4)
    | ~ r2(X4,X2)
    | ~ r1(X3) ),
    inference(superposition,[status(thm)],[c_57,c_885]) ).

cnf(c_1024,plain,
    ( ~ r2(X0,X1)
    | ~ r2(X2,X3)
    | ~ r2(X3,X0)
    | ~ r1(X2) ),
    inference(superposition,[status(thm)],[c_71,c_928]) ).

cnf(c_1082,plain,
    ( ~ r2(X0,X1)
    | ~ r2(X1,X2)
    | ~ r1(X0) ),
    inference(superposition,[status(thm)],[c_71,c_1024]) ).

cnf(c_1112,plain,
    ( ~ r2(sK7(X0,X1),X2)
    | ~ r1(X1) ),
    inference(superposition,[status(thm)],[c_71,c_1082]) ).

cnf(c_1136,plain,
    ~ r1(X0),
    inference(superposition,[status(thm)],[c_71,c_1112]) ).

cnf(c_1138,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[c_80,c_1136]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : NUN060+1 : TPTP v8.1.2. Released v7.3.0.
% 0.12/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n026.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 : Thu May  2 22:04:21 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  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
% 3.66/1.20  % SZS status Started for theBenchmark.p
% 3.66/1.20  % SZS status Theorem for theBenchmark.p
% 3.66/1.20  
% 3.66/1.20  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.66/1.20  
% 3.66/1.20  ------  iProver source info
% 3.66/1.20  
% 3.66/1.20  git: date: 2024-05-02 19:28:25 +0000
% 3.66/1.20  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.66/1.20  git: non_committed_changes: false
% 3.66/1.20  
% 3.66/1.20  ------ Parsing...
% 3.66/1.20  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.66/1.20  
% 3.66/1.20  ------ Preprocessing... sf_s  rm: 0 0s  sf_e  pe_s  pe_e 
% 3.66/1.20  
% 3.66/1.20  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.66/1.20  ------ Proving...
% 3.66/1.20  ------ Problem Properties 
% 3.66/1.20  
% 3.66/1.20  
% 3.66/1.20  clauses                                 43
% 3.66/1.20  conjectures                             1
% 3.66/1.20  EPR                                     16
% 3.66/1.20  Horn                                    39
% 3.66/1.20  unary                                   18
% 3.66/1.20  binary                                  13
% 3.66/1.20  lits                                    95
% 3.66/1.20  lits eq                                 0
% 3.66/1.20  fd_pure                                 0
% 3.66/1.20  fd_pseudo                               0
% 3.66/1.20  fd_cond                                 0
% 3.66/1.20  fd_pseudo_cond                          0
% 3.66/1.20  AC symbols                              0
% 3.66/1.20  
% 3.66/1.20  ------ Schedule dynamic 5 is on 
% 3.66/1.20  
% 3.66/1.20  ------ no equalities: superposition off 
% 3.66/1.20  
% 3.66/1.20  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.66/1.20  
% 3.66/1.20  
% 3.66/1.20  ------ 
% 3.66/1.20  Current options:
% 3.66/1.20  ------ 
% 3.66/1.20  
% 3.66/1.20  
% 3.66/1.20  
% 3.66/1.20  
% 3.66/1.20  ------ Proving...
% 3.66/1.20  
% 3.66/1.20  
% 3.66/1.20  % SZS status Theorem for theBenchmark.p
% 3.66/1.20  
% 3.66/1.20  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.66/1.20  
% 3.66/1.20  
%------------------------------------------------------------------------------