TSTP Solution File: KRS110+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : KRS110+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n016.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 02:33:39 EDT 2024

% Result   : Unsatisfiable 2.14s 1.18s
% Output   : CNFRefutation 2.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   57 (   4 unt;   0 def)
%            Number of atoms       :  201 (   2 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  236 (  92   ~;  77   |;  50   &)
%                                         (  10 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   1 con; 0-1 aty)
%            Number of variables   :  108 (   4 sgn  59   !;  27   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f25,axiom,
    ! [X3] :
      ( cUnsatisfiable(X3)
    <=> ( ! [X4] :
            ( rs(X3,X4)
           => cpxcomp(X4) )
        & ? [X4] :
            ( ca_Ax2(X4)
            & rs(X3,X4) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).

fof(f26,axiom,
    ! [X3] :
      ( cp(X3)
    <=> ~ ? [X4] : ra_Px1(X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).

fof(f27,axiom,
    ! [X3] :
      ( cpxcomp(X3)
    <=> ? [X5] : ra_Px1(X3,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).

fof(f28,axiom,
    ! [X3] :
      ( ca_Ax2(X3)
    <=> ( ? [X4] :
            ( cp(X4)
            & rinvS(X3,X4) )
        & cp(X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).

fof(f35,axiom,
    cUnsatisfiable(i2003_11_14_17_21_12565),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_12) ).

fof(f40,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( ! [X1] :
            ( rs(X0,X1)
           => cpxcomp(X1) )
        & ? [X2] :
            ( ca_Ax2(X2)
            & rs(X0,X2) ) ) ),
    inference(rectify,[],[f25]) ).

fof(f41,plain,
    ! [X0] :
      ( cp(X0)
    <=> ~ ? [X1] : ra_Px1(X0,X1) ),
    inference(rectify,[],[f26]) ).

fof(f42,plain,
    ! [X0] :
      ( cpxcomp(X0)
    <=> ? [X1] : ra_Px1(X0,X1) ),
    inference(rectify,[],[f27]) ).

fof(f43,plain,
    ! [X0] :
      ( ca_Ax2(X0)
    <=> ( ? [X1] :
            ( cp(X1)
            & rinvS(X0,X1) )
        & cp(X0) ) ),
    inference(rectify,[],[f28]) ).

fof(f96,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( ! [X1] :
            ( cpxcomp(X1)
            | ~ rs(X0,X1) )
        & ? [X2] :
            ( ca_Ax2(X2)
            & rs(X0,X2) ) ) ),
    inference(ennf_transformation,[],[f40]) ).

fof(f97,plain,
    ! [X0] :
      ( cp(X0)
    <=> ! [X1] : ~ ra_Px1(X0,X1) ),
    inference(ennf_transformation,[],[f41]) ).

fof(f107,plain,
    ! [X0] :
      ( ( cUnsatisfiable(X0)
        | ? [X1] :
            ( ~ cpxcomp(X1)
            & rs(X0,X1) )
        | ! [X2] :
            ( ~ ca_Ax2(X2)
            | ~ rs(X0,X2) ) )
      & ( ( ! [X1] :
              ( cpxcomp(X1)
              | ~ rs(X0,X1) )
          & ? [X2] :
              ( ca_Ax2(X2)
              & rs(X0,X2) ) )
        | ~ cUnsatisfiable(X0) ) ),
    inference(nnf_transformation,[],[f96]) ).

fof(f108,plain,
    ! [X0] :
      ( ( cUnsatisfiable(X0)
        | ? [X1] :
            ( ~ cpxcomp(X1)
            & rs(X0,X1) )
        | ! [X2] :
            ( ~ ca_Ax2(X2)
            | ~ rs(X0,X2) ) )
      & ( ( ! [X1] :
              ( cpxcomp(X1)
              | ~ rs(X0,X1) )
          & ? [X2] :
              ( ca_Ax2(X2)
              & rs(X0,X2) ) )
        | ~ cUnsatisfiable(X0) ) ),
    inference(flattening,[],[f107]) ).

fof(f109,plain,
    ! [X0] :
      ( ( cUnsatisfiable(X0)
        | ? [X1] :
            ( ~ cpxcomp(X1)
            & rs(X0,X1) )
        | ! [X2] :
            ( ~ ca_Ax2(X2)
            | ~ rs(X0,X2) ) )
      & ( ( ! [X3] :
              ( cpxcomp(X3)
              | ~ rs(X0,X3) )
          & ? [X4] :
              ( ca_Ax2(X4)
              & rs(X0,X4) ) )
        | ~ cUnsatisfiable(X0) ) ),
    inference(rectify,[],[f108]) ).

fof(f110,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ cpxcomp(X1)
          & rs(X0,X1) )
     => ( ~ cpxcomp(sK0(X0))
        & rs(X0,sK0(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f111,plain,
    ! [X0] :
      ( ? [X4] :
          ( ca_Ax2(X4)
          & rs(X0,X4) )
     => ( ca_Ax2(sK1(X0))
        & rs(X0,sK1(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f112,plain,
    ! [X0] :
      ( ( cUnsatisfiable(X0)
        | ( ~ cpxcomp(sK0(X0))
          & rs(X0,sK0(X0)) )
        | ! [X2] :
            ( ~ ca_Ax2(X2)
            | ~ rs(X0,X2) ) )
      & ( ( ! [X3] :
              ( cpxcomp(X3)
              | ~ rs(X0,X3) )
          & ca_Ax2(sK1(X0))
          & rs(X0,sK1(X0)) )
        | ~ cUnsatisfiable(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f109,f111,f110]) ).

fof(f113,plain,
    ! [X0] :
      ( ( cp(X0)
        | ? [X1] : ra_Px1(X0,X1) )
      & ( ! [X1] : ~ ra_Px1(X0,X1)
        | ~ cp(X0) ) ),
    inference(nnf_transformation,[],[f97]) ).

fof(f114,plain,
    ! [X0] :
      ( ( cp(X0)
        | ? [X1] : ra_Px1(X0,X1) )
      & ( ! [X2] : ~ ra_Px1(X0,X2)
        | ~ cp(X0) ) ),
    inference(rectify,[],[f113]) ).

fof(f115,plain,
    ! [X0] :
      ( ? [X1] : ra_Px1(X0,X1)
     => ra_Px1(X0,sK2(X0)) ),
    introduced(choice_axiom,[]) ).

fof(f116,plain,
    ! [X0] :
      ( ( cp(X0)
        | ra_Px1(X0,sK2(X0)) )
      & ( ! [X2] : ~ ra_Px1(X0,X2)
        | ~ cp(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f114,f115]) ).

fof(f117,plain,
    ! [X0] :
      ( ( cpxcomp(X0)
        | ! [X1] : ~ ra_Px1(X0,X1) )
      & ( ? [X1] : ra_Px1(X0,X1)
        | ~ cpxcomp(X0) ) ),
    inference(nnf_transformation,[],[f42]) ).

fof(f118,plain,
    ! [X0] :
      ( ( cpxcomp(X0)
        | ! [X1] : ~ ra_Px1(X0,X1) )
      & ( ? [X2] : ra_Px1(X0,X2)
        | ~ cpxcomp(X0) ) ),
    inference(rectify,[],[f117]) ).

fof(f119,plain,
    ! [X0] :
      ( ? [X2] : ra_Px1(X0,X2)
     => ra_Px1(X0,sK3(X0)) ),
    introduced(choice_axiom,[]) ).

fof(f120,plain,
    ! [X0] :
      ( ( cpxcomp(X0)
        | ! [X1] : ~ ra_Px1(X0,X1) )
      & ( ra_Px1(X0,sK3(X0))
        | ~ cpxcomp(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f118,f119]) ).

fof(f121,plain,
    ! [X0] :
      ( ( ca_Ax2(X0)
        | ! [X1] :
            ( ~ cp(X1)
            | ~ rinvS(X0,X1) )
        | ~ cp(X0) )
      & ( ( ? [X1] :
              ( cp(X1)
              & rinvS(X0,X1) )
          & cp(X0) )
        | ~ ca_Ax2(X0) ) ),
    inference(nnf_transformation,[],[f43]) ).

fof(f122,plain,
    ! [X0] :
      ( ( ca_Ax2(X0)
        | ! [X1] :
            ( ~ cp(X1)
            | ~ rinvS(X0,X1) )
        | ~ cp(X0) )
      & ( ( ? [X1] :
              ( cp(X1)
              & rinvS(X0,X1) )
          & cp(X0) )
        | ~ ca_Ax2(X0) ) ),
    inference(flattening,[],[f121]) ).

fof(f123,plain,
    ! [X0] :
      ( ( ca_Ax2(X0)
        | ! [X1] :
            ( ~ cp(X1)
            | ~ rinvS(X0,X1) )
        | ~ cp(X0) )
      & ( ( ? [X2] :
              ( cp(X2)
              & rinvS(X0,X2) )
          & cp(X0) )
        | ~ ca_Ax2(X0) ) ),
    inference(rectify,[],[f122]) ).

fof(f124,plain,
    ! [X0] :
      ( ? [X2] :
          ( cp(X2)
          & rinvS(X0,X2) )
     => ( cp(sK4(X0))
        & rinvS(X0,sK4(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f125,plain,
    ! [X0] :
      ( ( ca_Ax2(X0)
        | ! [X1] :
            ( ~ cp(X1)
            | ~ rinvS(X0,X1) )
        | ~ cp(X0) )
      & ( ( cp(sK4(X0))
          & rinvS(X0,sK4(X0))
          & cp(X0) )
        | ~ ca_Ax2(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f123,f124]) ).

fof(f155,plain,
    ! [X0] :
      ( rs(X0,sK1(X0))
      | ~ cUnsatisfiable(X0) ),
    inference(cnf_transformation,[],[f112]) ).

fof(f156,plain,
    ! [X0] :
      ( ca_Ax2(sK1(X0))
      | ~ cUnsatisfiable(X0) ),
    inference(cnf_transformation,[],[f112]) ).

fof(f157,plain,
    ! [X3,X0] :
      ( cpxcomp(X3)
      | ~ rs(X0,X3)
      | ~ cUnsatisfiable(X0) ),
    inference(cnf_transformation,[],[f112]) ).

fof(f160,plain,
    ! [X2,X0] :
      ( ~ ra_Px1(X0,X2)
      | ~ cp(X0) ),
    inference(cnf_transformation,[],[f116]) ).

fof(f162,plain,
    ! [X0] :
      ( ra_Px1(X0,sK3(X0))
      | ~ cpxcomp(X0) ),
    inference(cnf_transformation,[],[f120]) ).

fof(f164,plain,
    ! [X0] :
      ( cp(X0)
      | ~ ca_Ax2(X0) ),
    inference(cnf_transformation,[],[f125]) ).

fof(f177,plain,
    cUnsatisfiable(i2003_11_14_17_21_12565),
    inference(cnf_transformation,[],[f35]) ).

cnf(c_55,plain,
    ( ~ rs(X0,X1)
    | ~ cUnsatisfiable(X0)
    | cpxcomp(X1) ),
    inference(cnf_transformation,[],[f157]) ).

cnf(c_56,plain,
    ( ~ cUnsatisfiable(X0)
    | ca_Ax2(sK1(X0)) ),
    inference(cnf_transformation,[],[f156]) ).

cnf(c_57,plain,
    ( ~ cUnsatisfiable(X0)
    | rs(X0,sK1(X0)) ),
    inference(cnf_transformation,[],[f155]) ).

cnf(c_59,plain,
    ( ~ ra_Px1(X0,X1)
    | ~ cp(X0) ),
    inference(cnf_transformation,[],[f160]) ).

cnf(c_61,plain,
    ( ~ cpxcomp(X0)
    | ra_Px1(X0,sK3(X0)) ),
    inference(cnf_transformation,[],[f162]) ).

cnf(c_65,plain,
    ( ~ ca_Ax2(X0)
    | cp(X0) ),
    inference(cnf_transformation,[],[f164]) ).

cnf(c_75,plain,
    cUnsatisfiable(i2003_11_14_17_21_12565),
    inference(cnf_transformation,[],[f177]) ).

cnf(c_118,plain,
    ( ~ cp(X0)
    | ~ ra_Px1(X0,X1) ),
    inference(prop_impl_just,[status(thm)],[c_59]) ).

cnf(c_119,plain,
    ( ~ ra_Px1(X0,X1)
    | ~ cp(X0) ),
    inference(renaming,[status(thm)],[c_118]) ).

cnf(c_128,plain,
    ( ~ cpxcomp(X0)
    | ra_Px1(X0,sK3(X0)) ),
    inference(prop_impl_just,[status(thm)],[c_61]) ).

cnf(c_502,plain,
    ( sK3(X1) != X2
    | X0 != X1
    | ~ cpxcomp(X1)
    | ~ cp(X0) ),
    inference(resolution_lifted,[status(thm)],[c_119,c_128]) ).

cnf(c_503,plain,
    ( ~ cpxcomp(X0)
    | ~ cp(X0) ),
    inference(unflattening,[status(thm)],[c_502]) ).

cnf(c_912,plain,
    ( ~ cp(X0)
    | ~ cpxcomp(X0) ),
    inference(prop_impl_just,[status(thm)],[c_503]) ).

cnf(c_913,plain,
    ( ~ cpxcomp(X0)
    | ~ cp(X0) ),
    inference(renaming,[status(thm)],[c_912]) ).

cnf(c_1917,plain,
    ( ~ cUnsatisfiable(X0)
    | cp(sK1(X0)) ),
    inference(superposition,[status(thm)],[c_56,c_65]) ).

cnf(c_1936,plain,
    ( ~ cpxcomp(sK1(X0))
    | ~ cUnsatisfiable(X0) ),
    inference(superposition,[status(thm)],[c_1917,c_913]) ).

cnf(c_1939,plain,
    ( ~ cpxcomp(sK1(i2003_11_14_17_21_12565))
    | ~ cUnsatisfiable(i2003_11_14_17_21_12565) ),
    inference(instantiation,[status(thm)],[c_1936]) ).

cnf(c_1983,plain,
    ( ~ cUnsatisfiable(X0)
    | cpxcomp(sK1(X0)) ),
    inference(superposition,[status(thm)],[c_57,c_55]) ).

cnf(c_1990,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_21_12565)
    | cpxcomp(sK1(i2003_11_14_17_21_12565)) ),
    inference(instantiation,[status(thm)],[c_1983]) ).

cnf(c_1991,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_1990,c_1939,c_75]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : KRS110+1 : TPTP v8.1.2. Released v3.1.0.
% 0.07/0.14  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n016.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 23:13:30 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  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
% 2.14/1.18  % SZS status Started for theBenchmark.p
% 2.14/1.18  % SZS status Unsatisfiable for theBenchmark.p
% 2.14/1.18  
% 2.14/1.18  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 2.14/1.18  
% 2.14/1.18  ------  iProver source info
% 2.14/1.18  
% 2.14/1.18  git: date: 2024-05-02 19:28:25 +0000
% 2.14/1.18  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 2.14/1.18  git: non_committed_changes: false
% 2.14/1.18  
% 2.14/1.18  ------ Parsing...
% 2.14/1.18  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 2.14/1.18  
% 2.14/1.18  ------ Preprocessing... sup_sim: 0  sf_s  rm: 5 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe_e  sup_sim: 0  sf_s  rm: 3 0s  sf_e  pe_s  pe_e 
% 2.14/1.18  
% 2.14/1.18  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 2.14/1.18  
% 2.14/1.18  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.14/1.18  ------ Proving...
% 2.14/1.18  ------ Problem Properties 
% 2.14/1.18  
% 2.14/1.18  
% 2.14/1.18  clauses                                 17
% 2.14/1.18  conjectures                             0
% 2.14/1.18  EPR                                     11
% 2.14/1.18  Horn                                    15
% 2.14/1.18  unary                                   1
% 2.14/1.18  binary                                  9
% 2.14/1.18  lits                                    43
% 2.14/1.18  lits eq                                 3
% 2.14/1.18  fd_pure                                 0
% 2.14/1.18  fd_pseudo                               0
% 2.14/1.18  fd_cond                                 0
% 2.14/1.18  fd_pseudo_cond                          3
% 2.14/1.18  AC symbols                              0
% 2.14/1.18  
% 2.14/1.18  ------ Schedule dynamic 5 is on 
% 2.14/1.18  
% 2.14/1.18  ------ no conjectures: strip conj schedule 
% 2.14/1.18  
% 2.14/1.18  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.14/1.18  
% 2.14/1.18  
% 2.14/1.18  ------ 
% 2.14/1.18  Current options:
% 2.14/1.18  ------ 
% 2.14/1.18  
% 2.14/1.18  
% 2.14/1.18  
% 2.14/1.18  
% 2.14/1.18  ------ Proving...
% 2.14/1.18  
% 2.14/1.18  
% 2.14/1.18  % SZS status Unsatisfiable for theBenchmark.p
% 2.14/1.18  
% 2.14/1.18  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.14/1.18  
% 2.14/1.18  
%------------------------------------------------------------------------------