TSTP Solution File: GRP012+5 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : GRP012+5 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n003.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 02:19:46 EDT 2024

% Result   : Theorem 3.69s 1.15s
% Output   : CNFRefutation 3.69s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   41 (  18 unt;   0 def)
%            Number of atoms       :  208 (   0 equ)
%            Maximal formula atoms :   32 (   5 avg)
%            Number of connectives :  243 (  76   ~;  61   |;  91   &)
%                                         (   0 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :  270 (   0 sgn 195   !;  37   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,conjecture,
    ! [X0] :
      ( ( ! [X1] : product(inverse(X1),X1,X0)
        & ! [X1] : product(X1,inverse(X1),X0)
        & ! [X1] : product(X0,X1,X1)
        & ! [X1] : product(X1,X0,X1)
        & ! [X1,X2,X3,X4,X5,X6] :
            ( ( product(X1,X5,X6)
              & product(X2,X3,X5)
              & product(X1,X2,X4) )
           => product(X4,X3,X6) )
        & ! [X1,X2,X3,X4,X5,X6] :
            ( ( product(X4,X3,X6)
              & product(X2,X3,X5)
              & product(X1,X2,X4) )
           => product(X1,X5,X6) )
        & ! [X1,X2] :
          ? [X3] : product(X1,X2,X3) )
     => ! [X4,X5,X6,X1] :
          ( ( product(X5,X4,X1)
            & product(inverse(X4),inverse(X5),X6) )
         => product(inverse(X6),inverse(X1),X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distribution) ).

fof(f2,negated_conjecture,
    ~ ! [X0] :
        ( ( ! [X1] : product(inverse(X1),X1,X0)
          & ! [X1] : product(X1,inverse(X1),X0)
          & ! [X1] : product(X0,X1,X1)
          & ! [X1] : product(X1,X0,X1)
          & ! [X1,X2,X3,X4,X5,X6] :
              ( ( product(X1,X5,X6)
                & product(X2,X3,X5)
                & product(X1,X2,X4) )
             => product(X4,X3,X6) )
          & ! [X1,X2,X3,X4,X5,X6] :
              ( ( product(X4,X3,X6)
                & product(X2,X3,X5)
                & product(X1,X2,X4) )
             => product(X1,X5,X6) )
          & ! [X1,X2] :
            ? [X3] : product(X1,X2,X3) )
       => ! [X4,X5,X6,X1] :
            ( ( product(X5,X4,X1)
              & product(inverse(X4),inverse(X5),X6) )
           => product(inverse(X6),inverse(X1),X0) ) ),
    inference(negated_conjecture,[],[f1]) ).

fof(f3,plain,
    ~ ! [X0] :
        ( ( ! [X1] : product(inverse(X1),X1,X0)
          & ! [X2] : product(X2,inverse(X2),X0)
          & ! [X3] : product(X0,X3,X3)
          & ! [X4] : product(X4,X0,X4)
          & ! [X5,X6,X7,X8,X9,X10] :
              ( ( product(X5,X9,X10)
                & product(X6,X7,X9)
                & product(X5,X6,X8) )
             => product(X8,X7,X10) )
          & ! [X11,X12,X13,X14,X15,X16] :
              ( ( product(X14,X13,X16)
                & product(X12,X13,X15)
                & product(X11,X12,X14) )
             => product(X11,X15,X16) )
          & ! [X17,X18] :
            ? [X19] : product(X17,X18,X19) )
       => ! [X20,X21,X22,X23] :
            ( ( product(X21,X20,X23)
              & product(inverse(X20),inverse(X21),X22) )
           => product(inverse(X22),inverse(X23),X0) ) ),
    inference(rectify,[],[f2]) ).

fof(f4,plain,
    ? [X0] :
      ( ? [X20,X21,X22,X23] :
          ( ~ product(inverse(X22),inverse(X23),X0)
          & product(X21,X20,X23)
          & product(inverse(X20),inverse(X21),X22) )
      & ! [X1] : product(inverse(X1),X1,X0)
      & ! [X2] : product(X2,inverse(X2),X0)
      & ! [X3] : product(X0,X3,X3)
      & ! [X4] : product(X4,X0,X4)
      & ! [X5,X6,X7,X8,X9,X10] :
          ( product(X8,X7,X10)
          | ~ product(X5,X9,X10)
          | ~ product(X6,X7,X9)
          | ~ product(X5,X6,X8) )
      & ! [X11,X12,X13,X14,X15,X16] :
          ( product(X11,X15,X16)
          | ~ product(X14,X13,X16)
          | ~ product(X12,X13,X15)
          | ~ product(X11,X12,X14) )
      & ! [X17,X18] :
        ? [X19] : product(X17,X18,X19) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f5,plain,
    ? [X0] :
      ( ? [X20,X21,X22,X23] :
          ( ~ product(inverse(X22),inverse(X23),X0)
          & product(X21,X20,X23)
          & product(inverse(X20),inverse(X21),X22) )
      & ! [X1] : product(inverse(X1),X1,X0)
      & ! [X2] : product(X2,inverse(X2),X0)
      & ! [X3] : product(X0,X3,X3)
      & ! [X4] : product(X4,X0,X4)
      & ! [X5,X6,X7,X8,X9,X10] :
          ( product(X8,X7,X10)
          | ~ product(X5,X9,X10)
          | ~ product(X6,X7,X9)
          | ~ product(X5,X6,X8) )
      & ! [X11,X12,X13,X14,X15,X16] :
          ( product(X11,X15,X16)
          | ~ product(X14,X13,X16)
          | ~ product(X12,X13,X15)
          | ~ product(X11,X12,X14) )
      & ! [X17,X18] :
        ? [X19] : product(X17,X18,X19) ),
    inference(flattening,[],[f4]) ).

fof(f6,plain,
    ? [X0] :
      ( ? [X1,X2,X3,X4] :
          ( ~ product(inverse(X3),inverse(X4),X0)
          & product(X2,X1,X4)
          & product(inverse(X1),inverse(X2),X3) )
      & ! [X5] : product(inverse(X5),X5,X0)
      & ! [X6] : product(X6,inverse(X6),X0)
      & ! [X7] : product(X0,X7,X7)
      & ! [X8] : product(X8,X0,X8)
      & ! [X9,X10,X11,X12,X13,X14] :
          ( product(X12,X11,X14)
          | ~ product(X9,X13,X14)
          | ~ product(X10,X11,X13)
          | ~ product(X9,X10,X12) )
      & ! [X15,X16,X17,X18,X19,X20] :
          ( product(X15,X19,X20)
          | ~ product(X18,X17,X20)
          | ~ product(X16,X17,X19)
          | ~ product(X15,X16,X18) )
      & ! [X21,X22] :
        ? [X23] : product(X21,X22,X23) ),
    inference(rectify,[],[f5]) ).

fof(f7,plain,
    ( ? [X0] :
        ( ? [X1,X2,X3,X4] :
            ( ~ product(inverse(X3),inverse(X4),X0)
            & product(X2,X1,X4)
            & product(inverse(X1),inverse(X2),X3) )
        & ! [X5] : product(inverse(X5),X5,X0)
        & ! [X6] : product(X6,inverse(X6),X0)
        & ! [X7] : product(X0,X7,X7)
        & ! [X8] : product(X8,X0,X8)
        & ! [X9,X10,X11,X12,X13,X14] :
            ( product(X12,X11,X14)
            | ~ product(X9,X13,X14)
            | ~ product(X10,X11,X13)
            | ~ product(X9,X10,X12) )
        & ! [X15,X16,X17,X18,X19,X20] :
            ( product(X15,X19,X20)
            | ~ product(X18,X17,X20)
            | ~ product(X16,X17,X19)
            | ~ product(X15,X16,X18) )
        & ! [X21,X22] :
          ? [X23] : product(X21,X22,X23) )
   => ( ? [X4,X3,X2,X1] :
          ( ~ product(inverse(X3),inverse(X4),sK0)
          & product(X2,X1,X4)
          & product(inverse(X1),inverse(X2),X3) )
      & ! [X5] : product(inverse(X5),X5,sK0)
      & ! [X6] : product(X6,inverse(X6),sK0)
      & ! [X7] : product(sK0,X7,X7)
      & ! [X8] : product(X8,sK0,X8)
      & ! [X9,X10,X11,X12,X13,X14] :
          ( product(X12,X11,X14)
          | ~ product(X9,X13,X14)
          | ~ product(X10,X11,X13)
          | ~ product(X9,X10,X12) )
      & ! [X15,X16,X17,X18,X19,X20] :
          ( product(X15,X19,X20)
          | ~ product(X18,X17,X20)
          | ~ product(X16,X17,X19)
          | ~ product(X15,X16,X18) )
      & ! [X21,X22] :
        ? [X23] : product(X21,X22,X23) ) ),
    introduced(choice_axiom,[]) ).

fof(f8,plain,
    ( ? [X4,X3,X2,X1] :
        ( ~ product(inverse(X3),inverse(X4),sK0)
        & product(X2,X1,X4)
        & product(inverse(X1),inverse(X2),X3) )
   => ( ~ product(inverse(sK3),inverse(sK4),sK0)
      & product(sK2,sK1,sK4)
      & product(inverse(sK1),inverse(sK2),sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f9,plain,
    ! [X21,X22] :
      ( ? [X23] : product(X21,X22,X23)
     => product(X21,X22,sK5(X21,X22)) ),
    introduced(choice_axiom,[]) ).

fof(f10,plain,
    ( ~ product(inverse(sK3),inverse(sK4),sK0)
    & product(sK2,sK1,sK4)
    & product(inverse(sK1),inverse(sK2),sK3)
    & ! [X5] : product(inverse(X5),X5,sK0)
    & ! [X6] : product(X6,inverse(X6),sK0)
    & ! [X7] : product(sK0,X7,X7)
    & ! [X8] : product(X8,sK0,X8)
    & ! [X9,X10,X11,X12,X13,X14] :
        ( product(X12,X11,X14)
        | ~ product(X9,X13,X14)
        | ~ product(X10,X11,X13)
        | ~ product(X9,X10,X12) )
    & ! [X15,X16,X17,X18,X19,X20] :
        ( product(X15,X19,X20)
        | ~ product(X18,X17,X20)
        | ~ product(X16,X17,X19)
        | ~ product(X15,X16,X18) )
    & ! [X21,X22] : product(X21,X22,sK5(X21,X22)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f6,f9,f8,f7]) ).

fof(f12,plain,
    ! [X18,X19,X16,X17,X15,X20] :
      ( product(X15,X19,X20)
      | ~ product(X18,X17,X20)
      | ~ product(X16,X17,X19)
      | ~ product(X15,X16,X18) ),
    inference(cnf_transformation,[],[f10]) ).

fof(f13,plain,
    ! [X10,X11,X9,X14,X12,X13] :
      ( product(X12,X11,X14)
      | ~ product(X9,X13,X14)
      | ~ product(X10,X11,X13)
      | ~ product(X9,X10,X12) ),
    inference(cnf_transformation,[],[f10]) ).

fof(f14,plain,
    ! [X8] : product(X8,sK0,X8),
    inference(cnf_transformation,[],[f10]) ).

fof(f15,plain,
    ! [X7] : product(sK0,X7,X7),
    inference(cnf_transformation,[],[f10]) ).

fof(f16,plain,
    ! [X6] : product(X6,inverse(X6),sK0),
    inference(cnf_transformation,[],[f10]) ).

fof(f17,plain,
    ! [X5] : product(inverse(X5),X5,sK0),
    inference(cnf_transformation,[],[f10]) ).

fof(f18,plain,
    product(inverse(sK1),inverse(sK2),sK3),
    inference(cnf_transformation,[],[f10]) ).

fof(f19,plain,
    product(sK2,sK1,sK4),
    inference(cnf_transformation,[],[f10]) ).

fof(f20,plain,
    ~ product(inverse(sK3),inverse(sK4),sK0),
    inference(cnf_transformation,[],[f10]) ).

cnf(c_49,negated_conjecture,
    ~ product(inverse(sK3),inverse(sK4),sK0),
    inference(cnf_transformation,[],[f20]) ).

cnf(c_50,negated_conjecture,
    product(sK2,sK1,sK4),
    inference(cnf_transformation,[],[f19]) ).

cnf(c_51,negated_conjecture,
    product(inverse(sK1),inverse(sK2),sK3),
    inference(cnf_transformation,[],[f18]) ).

cnf(c_52,negated_conjecture,
    product(inverse(X0),X0,sK0),
    inference(cnf_transformation,[],[f17]) ).

cnf(c_53,negated_conjecture,
    product(X0,inverse(X0),sK0),
    inference(cnf_transformation,[],[f16]) ).

cnf(c_54,negated_conjecture,
    product(sK0,X0,X0),
    inference(cnf_transformation,[],[f15]) ).

cnf(c_55,negated_conjecture,
    product(X0,sK0,X0),
    inference(cnf_transformation,[],[f14]) ).

cnf(c_56,negated_conjecture,
    ( ~ product(X0,X1,X2)
    | ~ product(X0,X3,X4)
    | ~ product(X3,X5,X1)
    | product(X4,X5,X2) ),
    inference(cnf_transformation,[],[f13]) ).

cnf(c_57,negated_conjecture,
    ( ~ product(X0,X1,X2)
    | ~ product(X1,X3,X5)
    | ~ product(X2,X3,X4)
    | product(X0,X5,X4) ),
    inference(cnf_transformation,[],[f12]) ).

cnf(c_315,plain,
    ( ~ product(inverse(X0),X1,X2)
    | ~ product(X1,X3,X0)
    | product(X2,X3,sK0) ),
    inference(superposition,[status(thm)],[c_52,c_56]) ).

cnf(c_317,plain,
    ( ~ product(X0,X1,X2)
    | ~ product(sK0,X0,X3)
    | product(X3,X1,X2) ),
    inference(superposition,[status(thm)],[c_54,c_56]) ).

cnf(c_318,plain,
    ( ~ product(X0,X1,X2)
    | ~ product(X1,X3,sK0)
    | product(X2,X3,X0) ),
    inference(superposition,[status(thm)],[c_55,c_56]) ).

cnf(c_508,plain,
    ( ~ product(X0,X1,X2)
    | ~ product(sK0,X1,X3)
    | product(inverse(X0),X2,X3) ),
    inference(superposition,[status(thm)],[c_52,c_57]) ).

cnf(c_1011,plain,
    ( ~ product(inverse(sK2),X0,sK1)
    | product(sK3,X0,sK0) ),
    inference(superposition,[status(thm)],[c_51,c_315]) ).

cnf(c_1373,plain,
    ( ~ product(sK0,X0,X1)
    | product(X1,inverse(X0),sK0) ),
    inference(superposition,[status(thm)],[c_53,c_317]) ).

cnf(c_1623,plain,
    ( ~ product(X0,X1,sK0)
    | product(sK0,X1,inverse(X0)) ),
    inference(superposition,[status(thm)],[c_52,c_318]) ).

cnf(c_2080,plain,
    ( ~ product(sK0,sK1,X0)
    | product(inverse(sK2),sK4,X0) ),
    inference(superposition,[status(thm)],[c_50,c_508]) ).

cnf(c_3120,plain,
    ~ product(sK0,sK4,inverse(sK3)),
    inference(superposition,[status(thm)],[c_1373,c_49]) ).

cnf(c_3703,plain,
    ~ product(sK3,sK4,sK0),
    inference(superposition,[status(thm)],[c_1623,c_3120]) ).

cnf(c_4574,plain,
    ( ~ product(sK0,sK1,sK1)
    | product(sK3,sK4,sK0) ),
    inference(superposition,[status(thm)],[c_2080,c_1011]) ).

cnf(c_4579,plain,
    ~ product(sK0,sK1,sK1),
    inference(global_subsumption_just,[status(thm)],[c_4574,c_3703,c_4574]) ).

cnf(c_4731,plain,
    $false,
    inference(superposition,[status(thm)],[c_54,c_4579]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : GRP012+5 : TPTP v8.1.2. Released v3.1.0.
% 0.13/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n003.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Fri May  3 00:10:05 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.20/0.47  Running first-order theorem proving
% 0.20/0.47  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
% 3.69/1.15  % SZS status Started for theBenchmark.p
% 3.69/1.15  % SZS status Theorem for theBenchmark.p
% 3.69/1.15  
% 3.69/1.15  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.69/1.15  
% 3.69/1.15  ------  iProver source info
% 3.69/1.15  
% 3.69/1.15  git: date: 2024-05-02 19:28:25 +0000
% 3.69/1.15  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.69/1.15  git: non_committed_changes: false
% 3.69/1.15  
% 3.69/1.15  ------ Parsing...
% 3.69/1.15  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.69/1.15  
% 3.69/1.15  ------ Preprocessing... sf_s  rm: 0 0s  sf_e  pe_s  pe_e 
% 3.69/1.15  
% 3.69/1.15  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.69/1.15  ------ Proving...
% 3.69/1.15  ------ Problem Properties 
% 3.69/1.15  
% 3.69/1.15  
% 3.69/1.15  clauses                                 10
% 3.69/1.15  conjectures                             10
% 3.69/1.15  EPR                                     5
% 3.69/1.15  Horn                                    10
% 3.69/1.15  unary                                   8
% 3.69/1.15  binary                                  0
% 3.69/1.15  lits                                    16
% 3.69/1.15  lits eq                                 0
% 3.69/1.15  fd_pure                                 0
% 3.69/1.15  fd_pseudo                               0
% 3.69/1.15  fd_cond                                 0
% 3.69/1.15  fd_pseudo_cond                          0
% 3.69/1.15  AC symbols                              0
% 3.69/1.15  
% 3.69/1.15  ------ Input Options Time Limit: Unbounded
% 3.69/1.15  
% 3.69/1.15  
% 3.69/1.15  ------ 
% 3.69/1.15  Current options:
% 3.69/1.15  ------ 
% 3.69/1.15  
% 3.69/1.15  
% 3.69/1.15  
% 3.69/1.15  
% 3.69/1.15  ------ Proving...
% 3.69/1.15  
% 3.69/1.15  
% 3.69/1.15  % SZS status Theorem for theBenchmark.p
% 3.69/1.15  
% 3.69/1.15  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.69/1.15  
% 3.69/1.16  
%------------------------------------------------------------------------------