TSTP Solution File: KRS077+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : KRS077+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n014.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 02:33:32 EDT 2024

% Result   : Unsatisfiable 2.15s 1.21s
% Output   : CNFRefutation 2.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   61 (   5 unt;   0 def)
%            Number of atoms       :  260 (  25 equ)
%            Maximal formula atoms :   20 (   4 avg)
%            Number of connectives :  317 ( 118   ~; 106   |;  75   &)
%                                         (   8 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   1 con; 0-1 aty)
%            Number of variables   :  145 (   0 sgn  77   !;  30   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f15,axiom,
    ! [X3] :
      ( cUnsatisfiable(X3)
    <=> ( ? [X6] :
            ( cp(X6)
            & rs(X3,X6) )
        & ~ cp(X3)
        & ? [X6] :
            ( ! [X7] :
                ( rinvS(X6,X7)
               => cp(X7) )
            & rr(X3,X6) )
        & ! [X4,X5] :
            ( ( rr(X3,X5)
              & rr(X3,X4) )
           => X4 = X5 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).

fof(f16,axiom,
    ! [X3,X6] :
      ( rinvS(X3,X6)
    <=> rs(X6,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).

fof(f17,axiom,
    cUnsatisfiable(i2003_11_14_17_19_09372),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).

fof(f18,axiom,
    ! [X3,X6] :
      ( rs(X3,X6)
     => rr(X3,X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).

fof(f21,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( ? [X1] :
            ( cp(X1)
            & rs(X0,X1) )
        & ~ cp(X0)
        & ? [X2] :
            ( ! [X3] :
                ( rinvS(X2,X3)
               => cp(X3) )
            & rr(X0,X2) )
        & ! [X4,X5] :
            ( ( rr(X0,X5)
              & rr(X0,X4) )
           => X4 = X5 ) ) ),
    inference(rectify,[],[f15]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( rinvS(X0,X1)
    <=> rs(X1,X0) ),
    inference(rectify,[],[f16]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( rs(X0,X1)
     => rr(X0,X1) ),
    inference(rectify,[],[f18]) ).

fof(f48,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( ? [X1] :
            ( cp(X1)
            & rs(X0,X1) )
        & ~ cp(X0)
        & ? [X2] :
            ( ! [X3] :
                ( cp(X3)
                | ~ rinvS(X2,X3) )
            & rr(X0,X2) )
        & ! [X4,X5] :
            ( X4 = X5
            | ~ rr(X0,X5)
            | ~ rr(X0,X4) ) ) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f49,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( ? [X1] :
            ( cp(X1)
            & rs(X0,X1) )
        & ~ cp(X0)
        & ? [X2] :
            ( ! [X3] :
                ( cp(X3)
                | ~ rinvS(X2,X3) )
            & rr(X0,X2) )
        & ! [X4,X5] :
            ( X4 = X5
            | ~ rr(X0,X5)
            | ~ rr(X0,X4) ) ) ),
    inference(flattening,[],[f48]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( rr(X0,X1)
      | ~ rs(X0,X1) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f51,plain,
    ! [X0] :
      ( sP0(X0)
    <=> ( ? [X1] :
            ( cp(X1)
            & rs(X0,X1) )
        & ~ cp(X0)
        & ? [X2] :
            ( ! [X3] :
                ( cp(X3)
                | ~ rinvS(X2,X3) )
            & rr(X0,X2) )
        & ! [X4,X5] :
            ( X4 = X5
            | ~ rr(X0,X5)
            | ~ rr(X0,X4) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f52,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> sP0(X0) ),
    inference(definition_folding,[],[f49,f51]) ).

fof(f54,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ! [X1] :
            ( ~ cp(X1)
            | ~ rs(X0,X1) )
        | cp(X0)
        | ! [X2] :
            ( ? [X3] :
                ( ~ cp(X3)
                & rinvS(X2,X3) )
            | ~ rr(X0,X2) )
        | ? [X4,X5] :
            ( X4 != X5
            & rr(X0,X5)
            & rr(X0,X4) ) )
      & ( ( ? [X1] :
              ( cp(X1)
              & rs(X0,X1) )
          & ~ cp(X0)
          & ? [X2] :
              ( ! [X3] :
                  ( cp(X3)
                  | ~ rinvS(X2,X3) )
              & rr(X0,X2) )
          & ! [X4,X5] :
              ( X4 = X5
              | ~ rr(X0,X5)
              | ~ rr(X0,X4) ) )
        | ~ sP0(X0) ) ),
    inference(nnf_transformation,[],[f51]) ).

fof(f55,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ! [X1] :
            ( ~ cp(X1)
            | ~ rs(X0,X1) )
        | cp(X0)
        | ! [X2] :
            ( ? [X3] :
                ( ~ cp(X3)
                & rinvS(X2,X3) )
            | ~ rr(X0,X2) )
        | ? [X4,X5] :
            ( X4 != X5
            & rr(X0,X5)
            & rr(X0,X4) ) )
      & ( ( ? [X1] :
              ( cp(X1)
              & rs(X0,X1) )
          & ~ cp(X0)
          & ? [X2] :
              ( ! [X3] :
                  ( cp(X3)
                  | ~ rinvS(X2,X3) )
              & rr(X0,X2) )
          & ! [X4,X5] :
              ( X4 = X5
              | ~ rr(X0,X5)
              | ~ rr(X0,X4) ) )
        | ~ sP0(X0) ) ),
    inference(flattening,[],[f54]) ).

fof(f56,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ! [X1] :
            ( ~ cp(X1)
            | ~ rs(X0,X1) )
        | cp(X0)
        | ! [X2] :
            ( ? [X3] :
                ( ~ cp(X3)
                & rinvS(X2,X3) )
            | ~ rr(X0,X2) )
        | ? [X4,X5] :
            ( X4 != X5
            & rr(X0,X5)
            & rr(X0,X4) ) )
      & ( ( ? [X6] :
              ( cp(X6)
              & rs(X0,X6) )
          & ~ cp(X0)
          & ? [X7] :
              ( ! [X8] :
                  ( cp(X8)
                  | ~ rinvS(X7,X8) )
              & rr(X0,X7) )
          & ! [X9,X10] :
              ( X9 = X10
              | ~ rr(X0,X10)
              | ~ rr(X0,X9) ) )
        | ~ sP0(X0) ) ),
    inference(rectify,[],[f55]) ).

fof(f57,plain,
    ! [X2] :
      ( ? [X3] :
          ( ~ cp(X3)
          & rinvS(X2,X3) )
     => ( ~ cp(sK1(X2))
        & rinvS(X2,sK1(X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f58,plain,
    ! [X0] :
      ( ? [X4,X5] :
          ( X4 != X5
          & rr(X0,X5)
          & rr(X0,X4) )
     => ( sK2(X0) != sK3(X0)
        & rr(X0,sK3(X0))
        & rr(X0,sK2(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f59,plain,
    ! [X0] :
      ( ? [X6] :
          ( cp(X6)
          & rs(X0,X6) )
     => ( cp(sK4(X0))
        & rs(X0,sK4(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f60,plain,
    ! [X0] :
      ( ? [X7] :
          ( ! [X8] :
              ( cp(X8)
              | ~ rinvS(X7,X8) )
          & rr(X0,X7) )
     => ( ! [X8] :
            ( cp(X8)
            | ~ rinvS(sK5(X0),X8) )
        & rr(X0,sK5(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f61,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ! [X1] :
            ( ~ cp(X1)
            | ~ rs(X0,X1) )
        | cp(X0)
        | ! [X2] :
            ( ( ~ cp(sK1(X2))
              & rinvS(X2,sK1(X2)) )
            | ~ rr(X0,X2) )
        | ( sK2(X0) != sK3(X0)
          & rr(X0,sK3(X0))
          & rr(X0,sK2(X0)) ) )
      & ( ( cp(sK4(X0))
          & rs(X0,sK4(X0))
          & ~ cp(X0)
          & ! [X8] :
              ( cp(X8)
              | ~ rinvS(sK5(X0),X8) )
          & rr(X0,sK5(X0))
          & ! [X9,X10] :
              ( X9 = X10
              | ~ rr(X0,X10)
              | ~ rr(X0,X9) ) )
        | ~ sP0(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5])],[f56,f60,f59,f58,f57]) ).

fof(f62,plain,
    ! [X0] :
      ( ( cUnsatisfiable(X0)
        | ~ sP0(X0) )
      & ( sP0(X0)
        | ~ cUnsatisfiable(X0) ) ),
    inference(nnf_transformation,[],[f52]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( ( rinvS(X0,X1)
        | ~ rs(X1,X0) )
      & ( rs(X1,X0)
        | ~ rinvS(X0,X1) ) ),
    inference(nnf_transformation,[],[f22]) ).

fof(f80,plain,
    ! [X10,X0,X9] :
      ( X9 = X10
      | ~ rr(X0,X10)
      | ~ rr(X0,X9)
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f81,plain,
    ! [X0] :
      ( rr(X0,sK5(X0))
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f82,plain,
    ! [X0,X8] :
      ( cp(X8)
      | ~ rinvS(sK5(X0),X8)
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f83,plain,
    ! [X0] :
      ( ~ cp(X0)
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f84,plain,
    ! [X0] :
      ( rs(X0,sK4(X0))
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f92,plain,
    ! [X0] :
      ( sP0(X0)
      | ~ cUnsatisfiable(X0) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f95,plain,
    ! [X0,X1] :
      ( rinvS(X0,X1)
      | ~ rs(X1,X0) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f96,plain,
    cUnsatisfiable(i2003_11_14_17_19_09372),
    inference(cnf_transformation,[],[f17]) ).

fof(f97,plain,
    ! [X0,X1] :
      ( rr(X0,X1)
      | ~ rs(X0,X1) ),
    inference(cnf_transformation,[],[f50]) ).

cnf(c_60,plain,
    ( ~ sP0(X0)
    | rs(X0,sK4(X0)) ),
    inference(cnf_transformation,[],[f84]) ).

cnf(c_61,plain,
    ( ~ sP0(X0)
    | ~ cp(X0) ),
    inference(cnf_transformation,[],[f83]) ).

cnf(c_62,plain,
    ( ~ rinvS(sK5(X0),X1)
    | ~ sP0(X0)
    | cp(X1) ),
    inference(cnf_transformation,[],[f82]) ).

cnf(c_63,plain,
    ( ~ sP0(X0)
    | rr(X0,sK5(X0)) ),
    inference(cnf_transformation,[],[f81]) ).

cnf(c_64,plain,
    ( ~ rr(X0,X1)
    | ~ rr(X0,X2)
    | ~ sP0(X0)
    | X1 = X2 ),
    inference(cnf_transformation,[],[f80]) ).

cnf(c_66,plain,
    ( ~ cUnsatisfiable(X0)
    | sP0(X0) ),
    inference(cnf_transformation,[],[f92]) ).

cnf(c_67,plain,
    ( ~ rs(X0,X1)
    | rinvS(X1,X0) ),
    inference(cnf_transformation,[],[f95]) ).

cnf(c_69,plain,
    cUnsatisfiable(i2003_11_14_17_19_09372),
    inference(cnf_transformation,[],[f96]) ).

cnf(c_70,plain,
    ( ~ rs(X0,X1)
    | rr(X0,X1) ),
    inference(cnf_transformation,[],[f97]) ).

cnf(c_74,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
    | sP0(i2003_11_14_17_19_09372) ),
    inference(instantiation,[status(thm)],[c_66]) ).

cnf(c_75,plain,
    ( ~ sP0(i2003_11_14_17_19_09372)
    | ~ cp(i2003_11_14_17_19_09372) ),
    inference(instantiation,[status(thm)],[c_61]) ).

cnf(c_91,plain,
    ( ~ cUnsatisfiable(X0)
    | sP0(X0) ),
    inference(prop_impl_just,[status(thm)],[c_66]) ).

cnf(c_93,plain,
    ( ~ rs(X0,X1)
    | rr(X0,X1) ),
    inference(prop_impl_just,[status(thm)],[c_70]) ).

cnf(c_95,plain,
    ( ~ rs(X0,X1)
    | rinvS(X1,X0) ),
    inference(prop_impl_just,[status(thm)],[c_67]) ).

cnf(c_103,plain,
    ( ~ cUnsatisfiable(X0)
    | rs(X0,sK4(X0)) ),
    inference(prop_impl_just,[status(thm)],[c_66,c_60]) ).

cnf(c_107,plain,
    ( ~ cUnsatisfiable(X0)
    | rr(X0,sK5(X0)) ),
    inference(prop_impl_just,[status(thm)],[c_66,c_63]) ).

cnf(c_163,plain,
    ( ~ rinvS(sK5(X0),X1)
    | ~ cUnsatisfiable(X0)
    | cp(X1) ),
    inference(bin_hyper_res,[status(thm)],[c_62,c_91]) ).

cnf(c_164,plain,
    ( ~ rr(X0,X1)
    | ~ rr(X0,X2)
    | ~ cUnsatisfiable(X0)
    | X1 = X2 ),
    inference(bin_hyper_res,[status(thm)],[c_64,c_91]) ).

cnf(c_687,plain,
    ( sK4(X1) != X2
    | X0 != X1
    | ~ cUnsatisfiable(X1)
    | rr(X0,X2) ),
    inference(resolution_lifted,[status(thm)],[c_93,c_103]) ).

cnf(c_688,plain,
    ( ~ cUnsatisfiable(X0)
    | rr(X0,sK4(X0)) ),
    inference(unflattening,[status(thm)],[c_687]) ).

cnf(c_696,plain,
    ( sK4(X1) != X2
    | X0 != X1
    | ~ cUnsatisfiable(X1)
    | rinvS(X2,X0) ),
    inference(resolution_lifted,[status(thm)],[c_95,c_103]) ).

cnf(c_697,plain,
    ( ~ cUnsatisfiable(X0)
    | rinvS(sK4(X0),X0) ),
    inference(unflattening,[status(thm)],[c_696]) ).

cnf(c_698,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
    | rinvS(sK4(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372) ),
    inference(instantiation,[status(thm)],[c_697]) ).

cnf(c_3963,plain,
    ( ~ rr(X0,X1)
    | ~ cUnsatisfiable(X0)
    | sK5(X0) = X1 ),
    inference(superposition,[status(thm)],[c_107,c_164]) ).

cnf(c_3980,plain,
    ( ~ cUnsatisfiable(X0)
    | sK4(X0) = sK5(X0) ),
    inference(superposition,[status(thm)],[c_688,c_3963]) ).

cnf(c_4020,plain,
    sK4(i2003_11_14_17_19_09372) = sK5(i2003_11_14_17_19_09372),
    inference(superposition,[status(thm)],[c_69,c_3980]) ).

cnf(c_4021,plain,
    ( ~ rinvS(sK4(i2003_11_14_17_19_09372),X0)
    | ~ cUnsatisfiable(i2003_11_14_17_19_09372)
    | cp(X0) ),
    inference(superposition,[status(thm)],[c_4020,c_163]) ).

cnf(c_4024,plain,
    ( ~ rinvS(sK4(i2003_11_14_17_19_09372),X0)
    | cp(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_4021,c_69]) ).

cnf(c_4027,plain,
    ( ~ rinvS(sK4(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372)
    | cp(i2003_11_14_17_19_09372) ),
    inference(instantiation,[status(thm)],[c_4024]) ).

cnf(c_4028,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_4027,c_698,c_75,c_74,c_69]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : KRS077+1 : TPTP v8.1.2. Released v3.1.0.
% 0.07/0.13  % Command  : run_iprover %s %d THM
% 0.14/0.34  % Computer : n014.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu May  2 22:31:17 EDT 2024
% 0.14/0.34  % CPUTime  : 
% 0.20/0.47  Running first-order theorem proving
% 0.20/0.47  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
% 2.15/1.21  % SZS status Started for theBenchmark.p
% 2.15/1.21  % SZS status Unsatisfiable for theBenchmark.p
% 2.15/1.21  
% 2.15/1.21  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 2.15/1.21  
% 2.15/1.21  ------  iProver source info
% 2.15/1.21  
% 2.15/1.21  git: date: 2024-05-02 19:28:25 +0000
% 2.15/1.21  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 2.15/1.21  git: non_committed_changes: false
% 2.15/1.21  
% 2.15/1.21  ------ Parsing...
% 2.15/1.21  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 2.15/1.21  
% 2.15/1.21  ------ Preprocessing... sup_sim: 0  sf_s  rm: 5 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e 
% 2.15/1.21  
% 2.15/1.21  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 2.15/1.21  
% 2.15/1.21  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.15/1.21  ------ Proving...
% 2.15/1.21  ------ Problem Properties 
% 2.15/1.21  
% 2.15/1.21  
% 2.15/1.21  clauses                                 15
% 2.15/1.21  conjectures                             0
% 2.15/1.21  EPR                                     4
% 2.15/1.21  Horn                                    9
% 2.15/1.21  unary                                   1
% 2.15/1.21  binary                                  6
% 2.15/1.21  lits                                    62
% 2.15/1.21  lits eq                                 3
% 2.15/1.21  fd_pure                                 0
% 2.15/1.21  fd_pseudo                               0
% 2.15/1.21  fd_cond                                 0
% 2.15/1.21  fd_pseudo_cond                          1
% 2.15/1.21  AC symbols                              0
% 2.15/1.21  
% 2.15/1.21  ------ Schedule dynamic 5 is on 
% 2.15/1.21  
% 2.15/1.21  ------ no conjectures: strip conj schedule 
% 2.15/1.21  
% 2.15/1.21  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.15/1.21  
% 2.15/1.21  
% 2.15/1.21  ------ 
% 2.15/1.21  Current options:
% 2.15/1.21  ------ 
% 2.15/1.21  
% 2.15/1.21  
% 2.15/1.21  
% 2.15/1.21  
% 2.15/1.21  ------ Proving...
% 2.15/1.21  
% 2.15/1.21  
% 2.15/1.21  % SZS status Unsatisfiable for theBenchmark.p
% 2.15/1.21  
% 2.15/1.21  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.15/1.21  
% 2.15/1.21  
%------------------------------------------------------------------------------