TSTP Solution File: KRS127+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : KRS127+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n012.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 02:33:42 EDT 2024

% Result   : Unsatisfiable 1.92s 1.16s
% Output   : CNFRefutation 1.92s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   64 (   4 unt;   0 def)
%            Number of atoms       :  234 (  25 equ)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives :  279 ( 109   ~;  92   |;  60   &)
%                                         (   9 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   1 con; 0-1 aty)
%            Number of variables   :  137 (   4 sgn  69   !;  34   ?)

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

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

fof(f17,axiom,
    ! [X3] :
      ( cd(X3)
    <=> ~ ? [X4] : ra_Px1(X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).

fof(f18,axiom,
    ! [X3] :
      ( cdxcomp(X3)
    <=> ? [X5] : ra_Px1(X3,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).

fof(f19,axiom,
    cUnsatisfiable(i2003_11_14_17_22_27794),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).

fof(f22,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( ! [X1,X2] :
            ( ( rr(X0,X2)
              & rr(X0,X1) )
           => X1 = X2 )
        & ? [X3] :
            ( cd(X3)
            & rr(X0,X3) )
        & ? [X4] :
            ( cc(X4)
            & rr(X0,X4) ) ) ),
    inference(rectify,[],[f15]) ).

fof(f23,plain,
    ! [X0] :
      ( cc(X0)
     => cdxcomp(X0) ),
    inference(rectify,[],[f16]) ).

fof(f24,plain,
    ! [X0] :
      ( cd(X0)
    <=> ~ ? [X1] : ra_Px1(X0,X1) ),
    inference(rectify,[],[f17]) ).

fof(f25,plain,
    ! [X0] :
      ( cdxcomp(X0)
    <=> ? [X1] : ra_Px1(X0,X1) ),
    inference(rectify,[],[f18]) ).

fof(f50,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( ! [X1,X2] :
            ( X1 = X2
            | ~ rr(X0,X2)
            | ~ rr(X0,X1) )
        & ? [X3] :
            ( cd(X3)
            & rr(X0,X3) )
        & ? [X4] :
            ( cc(X4)
            & rr(X0,X4) ) ) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f51,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( ! [X1,X2] :
            ( X1 = X2
            | ~ rr(X0,X2)
            | ~ rr(X0,X1) )
        & ? [X3] :
            ( cd(X3)
            & rr(X0,X3) )
        & ? [X4] :
            ( cc(X4)
            & rr(X0,X4) ) ) ),
    inference(flattening,[],[f50]) ).

fof(f52,plain,
    ! [X0] :
      ( cdxcomp(X0)
      | ~ cc(X0) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f53,plain,
    ! [X0] :
      ( cd(X0)
    <=> ! [X1] : ~ ra_Px1(X0,X1) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f55,plain,
    ! [X0] :
      ( ( cUnsatisfiable(X0)
        | ? [X1,X2] :
            ( X1 != X2
            & rr(X0,X2)
            & rr(X0,X1) )
        | ! [X3] :
            ( ~ cd(X3)
            | ~ rr(X0,X3) )
        | ! [X4] :
            ( ~ cc(X4)
            | ~ rr(X0,X4) ) )
      & ( ( ! [X1,X2] :
              ( X1 = X2
              | ~ rr(X0,X2)
              | ~ rr(X0,X1) )
          & ? [X3] :
              ( cd(X3)
              & rr(X0,X3) )
          & ? [X4] :
              ( cc(X4)
              & rr(X0,X4) ) )
        | ~ cUnsatisfiable(X0) ) ),
    inference(nnf_transformation,[],[f51]) ).

fof(f56,plain,
    ! [X0] :
      ( ( cUnsatisfiable(X0)
        | ? [X1,X2] :
            ( X1 != X2
            & rr(X0,X2)
            & rr(X0,X1) )
        | ! [X3] :
            ( ~ cd(X3)
            | ~ rr(X0,X3) )
        | ! [X4] :
            ( ~ cc(X4)
            | ~ rr(X0,X4) ) )
      & ( ( ! [X1,X2] :
              ( X1 = X2
              | ~ rr(X0,X2)
              | ~ rr(X0,X1) )
          & ? [X3] :
              ( cd(X3)
              & rr(X0,X3) )
          & ? [X4] :
              ( cc(X4)
              & rr(X0,X4) ) )
        | ~ cUnsatisfiable(X0) ) ),
    inference(flattening,[],[f55]) ).

fof(f57,plain,
    ! [X0] :
      ( ( cUnsatisfiable(X0)
        | ? [X1,X2] :
            ( X1 != X2
            & rr(X0,X2)
            & rr(X0,X1) )
        | ! [X3] :
            ( ~ cd(X3)
            | ~ rr(X0,X3) )
        | ! [X4] :
            ( ~ cc(X4)
            | ~ rr(X0,X4) ) )
      & ( ( ! [X5,X6] :
              ( X5 = X6
              | ~ rr(X0,X6)
              | ~ rr(X0,X5) )
          & ? [X7] :
              ( cd(X7)
              & rr(X0,X7) )
          & ? [X8] :
              ( cc(X8)
              & rr(X0,X8) ) )
        | ~ cUnsatisfiable(X0) ) ),
    inference(rectify,[],[f56]) ).

fof(f58,plain,
    ! [X0] :
      ( ? [X1,X2] :
          ( X1 != X2
          & rr(X0,X2)
          & rr(X0,X1) )
     => ( sK0(X0) != sK1(X0)
        & rr(X0,sK1(X0))
        & rr(X0,sK0(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f59,plain,
    ! [X0] :
      ( ? [X7] :
          ( cd(X7)
          & rr(X0,X7) )
     => ( cd(sK2(X0))
        & rr(X0,sK2(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f60,plain,
    ! [X0] :
      ( ? [X8] :
          ( cc(X8)
          & rr(X0,X8) )
     => ( cc(sK3(X0))
        & rr(X0,sK3(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f61,plain,
    ! [X0] :
      ( ( cUnsatisfiable(X0)
        | ( sK0(X0) != sK1(X0)
          & rr(X0,sK1(X0))
          & rr(X0,sK0(X0)) )
        | ! [X3] :
            ( ~ cd(X3)
            | ~ rr(X0,X3) )
        | ! [X4] :
            ( ~ cc(X4)
            | ~ rr(X0,X4) ) )
      & ( ( ! [X5,X6] :
              ( X5 = X6
              | ~ rr(X0,X6)
              | ~ rr(X0,X5) )
          & cd(sK2(X0))
          & rr(X0,sK2(X0))
          & cc(sK3(X0))
          & rr(X0,sK3(X0)) )
        | ~ cUnsatisfiable(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f57,f60,f59,f58]) ).

fof(f62,plain,
    ! [X0] :
      ( ( cd(X0)
        | ? [X1] : ra_Px1(X0,X1) )
      & ( ! [X1] : ~ ra_Px1(X0,X1)
        | ~ cd(X0) ) ),
    inference(nnf_transformation,[],[f53]) ).

fof(f63,plain,
    ! [X0] :
      ( ( cd(X0)
        | ? [X1] : ra_Px1(X0,X1) )
      & ( ! [X2] : ~ ra_Px1(X0,X2)
        | ~ cd(X0) ) ),
    inference(rectify,[],[f62]) ).

fof(f64,plain,
    ! [X0] :
      ( ? [X1] : ra_Px1(X0,X1)
     => ra_Px1(X0,sK4(X0)) ),
    introduced(choice_axiom,[]) ).

fof(f65,plain,
    ! [X0] :
      ( ( cd(X0)
        | ra_Px1(X0,sK4(X0)) )
      & ( ! [X2] : ~ ra_Px1(X0,X2)
        | ~ cd(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f63,f64]) ).

fof(f66,plain,
    ! [X0] :
      ( ( cdxcomp(X0)
        | ! [X1] : ~ ra_Px1(X0,X1) )
      & ( ? [X1] : ra_Px1(X0,X1)
        | ~ cdxcomp(X0) ) ),
    inference(nnf_transformation,[],[f25]) ).

fof(f67,plain,
    ! [X0] :
      ( ( cdxcomp(X0)
        | ! [X1] : ~ ra_Px1(X0,X1) )
      & ( ? [X2] : ra_Px1(X0,X2)
        | ~ cdxcomp(X0) ) ),
    inference(rectify,[],[f66]) ).

fof(f68,plain,
    ! [X0] :
      ( ? [X2] : ra_Px1(X0,X2)
     => ra_Px1(X0,sK5(X0)) ),
    introduced(choice_axiom,[]) ).

fof(f69,plain,
    ! [X0] :
      ( ( cdxcomp(X0)
        | ! [X1] : ~ ra_Px1(X0,X1) )
      & ( ra_Px1(X0,sK5(X0))
        | ~ cdxcomp(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f67,f68]) ).

fof(f86,plain,
    ! [X0] :
      ( rr(X0,sK3(X0))
      | ~ cUnsatisfiable(X0) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f87,plain,
    ! [X0] :
      ( cc(sK3(X0))
      | ~ cUnsatisfiable(X0) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f88,plain,
    ! [X0] :
      ( rr(X0,sK2(X0))
      | ~ cUnsatisfiable(X0) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f89,plain,
    ! [X0] :
      ( cd(sK2(X0))
      | ~ cUnsatisfiable(X0) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f90,plain,
    ! [X0,X6,X5] :
      ( X5 = X6
      | ~ rr(X0,X6)
      | ~ rr(X0,X5)
      | ~ cUnsatisfiable(X0) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f94,plain,
    ! [X0] :
      ( cdxcomp(X0)
      | ~ cc(X0) ),
    inference(cnf_transformation,[],[f52]) ).

fof(f95,plain,
    ! [X2,X0] :
      ( ~ ra_Px1(X0,X2)
      | ~ cd(X0) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f97,plain,
    ! [X0] :
      ( ra_Px1(X0,sK5(X0))
      | ~ cdxcomp(X0) ),
    inference(cnf_transformation,[],[f69]) ).

fof(f99,plain,
    cUnsatisfiable(i2003_11_14_17_22_27794),
    inference(cnf_transformation,[],[f19]) ).

cnf(c_56,plain,
    ( ~ rr(X0,X1)
    | ~ rr(X0,X2)
    | ~ cUnsatisfiable(X0)
    | X1 = X2 ),
    inference(cnf_transformation,[],[f90]) ).

cnf(c_57,plain,
    ( ~ cUnsatisfiable(X0)
    | cd(sK2(X0)) ),
    inference(cnf_transformation,[],[f89]) ).

cnf(c_58,plain,
    ( ~ cUnsatisfiable(X0)
    | rr(X0,sK2(X0)) ),
    inference(cnf_transformation,[],[f88]) ).

cnf(c_59,plain,
    ( ~ cUnsatisfiable(X0)
    | cc(sK3(X0)) ),
    inference(cnf_transformation,[],[f87]) ).

cnf(c_60,plain,
    ( ~ cUnsatisfiable(X0)
    | rr(X0,sK3(X0)) ),
    inference(cnf_transformation,[],[f86]) ).

cnf(c_61,plain,
    ( ~ cc(X0)
    | cdxcomp(X0) ),
    inference(cnf_transformation,[],[f94]) ).

cnf(c_63,plain,
    ( ~ ra_Px1(X0,X1)
    | ~ cd(X0) ),
    inference(cnf_transformation,[],[f95]) ).

cnf(c_65,plain,
    ( ~ cdxcomp(X0)
    | ra_Px1(X0,sK5(X0)) ),
    inference(cnf_transformation,[],[f97]) ).

cnf(c_66,plain,
    cUnsatisfiable(i2003_11_14_17_22_27794),
    inference(cnf_transformation,[],[f99]) ).

cnf(c_85,plain,
    ( ~ cUnsatisfiable(X0)
    | cd(sK2(X0)) ),
    inference(prop_impl_just,[status(thm)],[c_57]) ).

cnf(c_89,plain,
    ( ~ cUnsatisfiable(X0)
    | cc(sK3(X0)) ),
    inference(prop_impl_just,[status(thm)],[c_59]) ).

cnf(c_93,plain,
    ( ~ cdxcomp(X0)
    | ra_Px1(X0,sK5(X0)) ),
    inference(prop_impl_just,[status(thm)],[c_65]) ).

cnf(c_95,plain,
    ( ~ cc(X0)
    | cdxcomp(X0) ),
    inference(prop_impl_just,[status(thm)],[c_61]) ).

cnf(c_97,plain,
    ( ~ cd(X0)
    | ~ ra_Px1(X0,X1) ),
    inference(prop_impl_just,[status(thm)],[c_63]) ).

cnf(c_98,plain,
    ( ~ ra_Px1(X0,X1)
    | ~ cd(X0) ),
    inference(renaming,[status(thm)],[c_97]) ).

cnf(c_375,plain,
    ( sK5(X1) != X2
    | X0 != X1
    | ~ cd(X0)
    | ~ cdxcomp(X1) ),
    inference(resolution_lifted,[status(thm)],[c_98,c_93]) ).

cnf(c_376,plain,
    ( ~ cd(X0)
    | ~ cdxcomp(X0) ),
    inference(unflattening,[status(thm)],[c_375]) ).

cnf(c_390,plain,
    ( X0 != X1
    | ~ cd(X1)
    | ~ cc(X0) ),
    inference(resolution_lifted,[status(thm)],[c_95,c_376]) ).

cnf(c_391,plain,
    ( ~ cd(X0)
    | ~ cc(X0) ),
    inference(unflattening,[status(thm)],[c_390]) ).

cnf(c_461,plain,
    ( sK2(X0) != X1
    | ~ cUnsatisfiable(X0)
    | ~ cc(X1) ),
    inference(resolution_lifted,[status(thm)],[c_85,c_391]) ).

cnf(c_462,plain,
    ( ~ cc(sK2(X0))
    | ~ cUnsatisfiable(X0) ),
    inference(unflattening,[status(thm)],[c_461]) ).

cnf(c_550,plain,
    ( sK2(X0) != sK3(X1)
    | ~ cUnsatisfiable(X0)
    | ~ cUnsatisfiable(X1) ),
    inference(resolution_lifted,[status(thm)],[c_89,c_462]) ).

cnf(c_551,plain,
    ( sK2(i2003_11_14_17_22_27794) != sK3(i2003_11_14_17_22_27794)
    | ~ cUnsatisfiable(i2003_11_14_17_22_27794) ),
    inference(instantiation,[status(thm)],[c_550]) ).

cnf(c_1007,plain,
    ( ~ rr(X0,X1)
    | ~ cUnsatisfiable(X0)
    | sK2(X0) = X1 ),
    inference(superposition,[status(thm)],[c_58,c_56]) ).

cnf(c_1024,plain,
    ( ~ cUnsatisfiable(X0)
    | sK2(X0) = sK3(X0) ),
    inference(superposition,[status(thm)],[c_60,c_1007]) ).

cnf(c_1027,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_22_27794)
    | sK2(i2003_11_14_17_22_27794) = sK3(i2003_11_14_17_22_27794) ),
    inference(instantiation,[status(thm)],[c_1024]) ).

cnf(c_1028,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_1027,c_551,c_66]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : KRS127+1 : TPTP v8.1.2. Released v3.1.0.
% 0.03/0.13  % Command  : run_iprover %s %d THM
% 0.12/0.33  % Computer : n012.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu May  2 22:30:11 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 0.18/0.46  Running first-order theorem proving
% 0.18/0.46  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
% 1.92/1.16  % SZS status Started for theBenchmark.p
% 1.92/1.16  % SZS status Unsatisfiable for theBenchmark.p
% 1.92/1.16  
% 1.92/1.16  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 1.92/1.16  
% 1.92/1.16  ------  iProver source info
% 1.92/1.16  
% 1.92/1.16  git: date: 2024-05-02 19:28:25 +0000
% 1.92/1.16  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 1.92/1.16  git: non_committed_changes: false
% 1.92/1.16  
% 1.92/1.16  ------ Parsing...
% 1.92/1.16  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 1.92/1.16  
% 1.92/1.16  ------ 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: 3 0s  sf_e  pe_s  pe_e 
% 1.92/1.16  
% 1.92/1.16  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 1.92/1.16  
% 1.92/1.16  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 1.92/1.16  ------ Proving...
% 1.92/1.16  ------ Problem Properties 
% 1.92/1.16  
% 1.92/1.16  
% 1.92/1.16  clauses                                 9
% 1.92/1.16  conjectures                             0
% 1.92/1.16  EPR                                     2
% 1.92/1.16  Horn                                    7
% 1.92/1.16  unary                                   1
% 1.92/1.16  binary                                  4
% 1.92/1.16  lits                                    31
% 1.92/1.16  lits eq                                 2
% 1.92/1.16  fd_pure                                 0
% 1.92/1.16  fd_pseudo                               0
% 1.92/1.16  fd_cond                                 0
% 1.92/1.16  fd_pseudo_cond                          1
% 1.92/1.16  AC symbols                              0
% 1.92/1.16  
% 1.92/1.16  ------ Schedule dynamic 5 is on 
% 1.92/1.16  
% 1.92/1.16  ------ no conjectures: strip conj schedule 
% 1.92/1.16  
% 1.92/1.16  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 1.92/1.16  
% 1.92/1.16  
% 1.92/1.16  ------ 
% 1.92/1.16  Current options:
% 1.92/1.16  ------ 
% 1.92/1.16  
% 1.92/1.16  
% 1.92/1.16  
% 1.92/1.16  
% 1.92/1.16  ------ Proving...
% 1.92/1.16  
% 1.92/1.16  
% 1.92/1.16  % SZS status Unsatisfiable for theBenchmark.p
% 1.92/1.16  
% 1.92/1.16  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.92/1.16  
% 1.92/1.16  
%------------------------------------------------------------------------------