TSTP Solution File: KRS099+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : KRS099+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n018.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 02:33:37 EDT 2024

% Result   : Unsatisfiable 2.23s 1.15s
% Output   : CNFRefutation 2.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   48 (   4 unt;   0 def)
%            Number of atoms       :  297 (  75 equ)
%            Maximal formula atoms :   16 (   6 avg)
%            Number of connectives :  390 ( 141   ~; 111   |; 120   &)
%                                         (   8 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   1 con; 0-1 aty)
%            Number of variables   :  138 (   0 sgn  84   !;  42   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f13,axiom,
    ! [X3] :
      ( cUnsatisfiable(X3)
    <=> ( ! [X4,X5] :
            ( ( rtt(X3,X5)
              & rtt(X3,X4) )
           => X4 = X5 )
        & ! [X4,X5] :
            ( ( rtt(X3,X5)
              & rtt(X3,X4) )
           => X4 = X5 )
        & ! [X7] :
            ( rtt(X3,X7)
           => ca(X7) )
        & ? [X4,X5,X6] :
            ( X5 != X6
            & X4 != X6
            & X4 != X5
            & rtt(X3,X6)
            & rtt(X3,X5)
            & rtt(X3,X4) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).

fof(f16,axiom,
    cUnsatisfiable(i2003_11_14_17_20_29215),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).

fof(f19,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( ! [X1,X2] :
            ( ( rtt(X0,X2)
              & rtt(X0,X1) )
           => X1 = X2 )
        & ! [X3,X4] :
            ( ( rtt(X0,X4)
              & rtt(X0,X3) )
           => X3 = X4 )
        & ! [X5] :
            ( rtt(X0,X5)
           => ca(X5) )
        & ? [X6,X7,X8] :
            ( X7 != X8
            & X6 != X8
            & X6 != X7
            & rtt(X0,X8)
            & rtt(X0,X7)
            & rtt(X0,X6) ) ) ),
    inference(rectify,[],[f13]) ).

fof(f42,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( ! [X1,X2] :
            ( X1 = X2
            | ~ rtt(X0,X2)
            | ~ rtt(X0,X1) )
        & ! [X3,X4] :
            ( X3 = X4
            | ~ rtt(X0,X4)
            | ~ rtt(X0,X3) )
        & ! [X5] :
            ( ca(X5)
            | ~ rtt(X0,X5) )
        & ? [X6,X7,X8] :
            ( X7 != X8
            & X6 != X8
            & X6 != X7
            & rtt(X0,X8)
            & rtt(X0,X7)
            & rtt(X0,X6) ) ) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f43,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( ! [X1,X2] :
            ( X1 = X2
            | ~ rtt(X0,X2)
            | ~ rtt(X0,X1) )
        & ! [X3,X4] :
            ( X3 = X4
            | ~ rtt(X0,X4)
            | ~ rtt(X0,X3) )
        & ! [X5] :
            ( ca(X5)
            | ~ rtt(X0,X5) )
        & ? [X6,X7,X8] :
            ( X7 != X8
            & X6 != X8
            & X6 != X7
            & rtt(X0,X8)
            & rtt(X0,X7)
            & rtt(X0,X6) ) ) ),
    inference(flattening,[],[f42]) ).

fof(f47,plain,
    ! [X0] :
      ( sP0(X0)
    <=> ! [X3,X4] :
          ( X3 = X4
          | ~ rtt(X0,X4)
          | ~ rtt(X0,X3) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f48,plain,
    ! [X0] :
      ( sP1(X0)
    <=> ? [X6,X7,X8] :
          ( X7 != X8
          & X6 != X8
          & X6 != X7
          & rtt(X0,X8)
          & rtt(X0,X7)
          & rtt(X0,X6) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f49,plain,
    ! [X0] :
      ( sP2(X0)
    <=> ( ! [X1,X2] :
            ( X1 = X2
            | ~ rtt(X0,X2)
            | ~ rtt(X0,X1) )
        & sP0(X0)
        & ! [X5] :
            ( ca(X5)
            | ~ rtt(X0,X5) )
        & sP1(X0) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f50,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> sP2(X0) ),
    inference(definition_folding,[],[f43,f49,f48,f47]) ).

fof(f52,plain,
    ! [X0] :
      ( ( sP2(X0)
        | ? [X1,X2] :
            ( X1 != X2
            & rtt(X0,X2)
            & rtt(X0,X1) )
        | ~ sP0(X0)
        | ? [X5] :
            ( ~ ca(X5)
            & rtt(X0,X5) )
        | ~ sP1(X0) )
      & ( ( ! [X1,X2] :
              ( X1 = X2
              | ~ rtt(X0,X2)
              | ~ rtt(X0,X1) )
          & sP0(X0)
          & ! [X5] :
              ( ca(X5)
              | ~ rtt(X0,X5) )
          & sP1(X0) )
        | ~ sP2(X0) ) ),
    inference(nnf_transformation,[],[f49]) ).

fof(f53,plain,
    ! [X0] :
      ( ( sP2(X0)
        | ? [X1,X2] :
            ( X1 != X2
            & rtt(X0,X2)
            & rtt(X0,X1) )
        | ~ sP0(X0)
        | ? [X5] :
            ( ~ ca(X5)
            & rtt(X0,X5) )
        | ~ sP1(X0) )
      & ( ( ! [X1,X2] :
              ( X1 = X2
              | ~ rtt(X0,X2)
              | ~ rtt(X0,X1) )
          & sP0(X0)
          & ! [X5] :
              ( ca(X5)
              | ~ rtt(X0,X5) )
          & sP1(X0) )
        | ~ sP2(X0) ) ),
    inference(flattening,[],[f52]) ).

fof(f54,plain,
    ! [X0] :
      ( ( sP2(X0)
        | ? [X1,X2] :
            ( X1 != X2
            & rtt(X0,X2)
            & rtt(X0,X1) )
        | ~ sP0(X0)
        | ? [X3] :
            ( ~ ca(X3)
            & rtt(X0,X3) )
        | ~ sP1(X0) )
      & ( ( ! [X4,X5] :
              ( X4 = X5
              | ~ rtt(X0,X5)
              | ~ rtt(X0,X4) )
          & sP0(X0)
          & ! [X6] :
              ( ca(X6)
              | ~ rtt(X0,X6) )
          & sP1(X0) )
        | ~ sP2(X0) ) ),
    inference(rectify,[],[f53]) ).

fof(f55,plain,
    ! [X0] :
      ( ? [X1,X2] :
          ( X1 != X2
          & rtt(X0,X2)
          & rtt(X0,X1) )
     => ( sK3(X0) != sK4(X0)
        & rtt(X0,sK4(X0))
        & rtt(X0,sK3(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f56,plain,
    ! [X0] :
      ( ? [X3] :
          ( ~ ca(X3)
          & rtt(X0,X3) )
     => ( ~ ca(sK5(X0))
        & rtt(X0,sK5(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f57,plain,
    ! [X0] :
      ( ( sP2(X0)
        | ( sK3(X0) != sK4(X0)
          & rtt(X0,sK4(X0))
          & rtt(X0,sK3(X0)) )
        | ~ sP0(X0)
        | ( ~ ca(sK5(X0))
          & rtt(X0,sK5(X0)) )
        | ~ sP1(X0) )
      & ( ( ! [X4,X5] :
              ( X4 = X5
              | ~ rtt(X0,X5)
              | ~ rtt(X0,X4) )
          & sP0(X0)
          & ! [X6] :
              ( ca(X6)
              | ~ rtt(X0,X6) )
          & sP1(X0) )
        | ~ sP2(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f54,f56,f55]) ).

fof(f58,plain,
    ! [X0] :
      ( ( sP1(X0)
        | ! [X6,X7,X8] :
            ( X7 = X8
            | X6 = X8
            | X6 = X7
            | ~ rtt(X0,X8)
            | ~ rtt(X0,X7)
            | ~ rtt(X0,X6) ) )
      & ( ? [X6,X7,X8] :
            ( X7 != X8
            & X6 != X8
            & X6 != X7
            & rtt(X0,X8)
            & rtt(X0,X7)
            & rtt(X0,X6) )
        | ~ sP1(X0) ) ),
    inference(nnf_transformation,[],[f48]) ).

fof(f59,plain,
    ! [X0] :
      ( ( sP1(X0)
        | ! [X1,X2,X3] :
            ( X2 = X3
            | X1 = X3
            | X1 = X2
            | ~ rtt(X0,X3)
            | ~ rtt(X0,X2)
            | ~ rtt(X0,X1) ) )
      & ( ? [X4,X5,X6] :
            ( X5 != X6
            & X4 != X6
            & X4 != X5
            & rtt(X0,X6)
            & rtt(X0,X5)
            & rtt(X0,X4) )
        | ~ sP1(X0) ) ),
    inference(rectify,[],[f58]) ).

fof(f60,plain,
    ! [X0] :
      ( ? [X4,X5,X6] :
          ( X5 != X6
          & X4 != X6
          & X4 != X5
          & rtt(X0,X6)
          & rtt(X0,X5)
          & rtt(X0,X4) )
     => ( sK7(X0) != sK8(X0)
        & sK6(X0) != sK8(X0)
        & sK6(X0) != sK7(X0)
        & rtt(X0,sK8(X0))
        & rtt(X0,sK7(X0))
        & rtt(X0,sK6(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f61,plain,
    ! [X0] :
      ( ( sP1(X0)
        | ! [X1,X2,X3] :
            ( X2 = X3
            | X1 = X3
            | X1 = X2
            | ~ rtt(X0,X3)
            | ~ rtt(X0,X2)
            | ~ rtt(X0,X1) ) )
      & ( ( sK7(X0) != sK8(X0)
          & sK6(X0) != sK8(X0)
          & sK6(X0) != sK7(X0)
          & rtt(X0,sK8(X0))
          & rtt(X0,sK7(X0))
          & rtt(X0,sK6(X0)) )
        | ~ sP1(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f59,f60]) ).

fof(f62,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ? [X3,X4] :
            ( X3 != X4
            & rtt(X0,X4)
            & rtt(X0,X3) ) )
      & ( ! [X3,X4] :
            ( X3 = X4
            | ~ rtt(X0,X4)
            | ~ rtt(X0,X3) )
        | ~ sP0(X0) ) ),
    inference(nnf_transformation,[],[f47]) ).

fof(f63,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ? [X1,X2] :
            ( X1 != X2
            & rtt(X0,X2)
            & rtt(X0,X1) ) )
      & ( ! [X3,X4] :
            ( X3 = X4
            | ~ rtt(X0,X4)
            | ~ rtt(X0,X3) )
        | ~ sP0(X0) ) ),
    inference(rectify,[],[f62]) ).

fof(f64,plain,
    ! [X0] :
      ( ? [X1,X2] :
          ( X1 != X2
          & rtt(X0,X2)
          & rtt(X0,X1) )
     => ( sK9(X0) != sK10(X0)
        & rtt(X0,sK10(X0))
        & rtt(X0,sK9(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f65,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ( sK9(X0) != sK10(X0)
          & rtt(X0,sK10(X0))
          & rtt(X0,sK9(X0)) ) )
      & ( ! [X3,X4] :
            ( X3 = X4
            | ~ rtt(X0,X4)
            | ~ rtt(X0,X3) )
        | ~ sP0(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f63,f64]) ).

fof(f66,plain,
    ! [X0] :
      ( ( cUnsatisfiable(X0)
        | ~ sP2(X0) )
      & ( sP2(X0)
        | ~ cUnsatisfiable(X0) ) ),
    inference(nnf_transformation,[],[f50]) ).

fof(f81,plain,
    ! [X0] :
      ( sP1(X0)
      | ~ sP2(X0) ),
    inference(cnf_transformation,[],[f57]) ).

fof(f83,plain,
    ! [X0] :
      ( sP0(X0)
      | ~ sP2(X0) ),
    inference(cnf_transformation,[],[f57]) ).

fof(f91,plain,
    ! [X0] :
      ( rtt(X0,sK6(X0))
      | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f93,plain,
    ! [X0] :
      ( rtt(X0,sK8(X0))
      | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f95,plain,
    ! [X0] :
      ( sK6(X0) != sK8(X0)
      | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f98,plain,
    ! [X3,X0,X4] :
      ( X3 = X4
      | ~ rtt(X0,X4)
      | ~ rtt(X0,X3)
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f102,plain,
    ! [X0] :
      ( sP2(X0)
      | ~ cUnsatisfiable(X0) ),
    inference(cnf_transformation,[],[f66]) ).

fof(f106,plain,
    cUnsatisfiable(i2003_11_14_17_20_29215),
    inference(cnf_transformation,[],[f16]) ).

cnf(c_60,plain,
    ( ~ sP2(X0)
    | sP0(X0) ),
    inference(cnf_transformation,[],[f83]) ).

cnf(c_62,plain,
    ( ~ sP2(X0)
    | sP1(X0) ),
    inference(cnf_transformation,[],[f81]) ).

cnf(c_65,plain,
    ( sK8(X0) != sK6(X0)
    | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f95]) ).

cnf(c_67,plain,
    ( ~ sP1(X0)
    | rtt(X0,sK8(X0)) ),
    inference(cnf_transformation,[],[f93]) ).

cnf(c_69,plain,
    ( ~ sP1(X0)
    | rtt(X0,sK6(X0)) ),
    inference(cnf_transformation,[],[f91]) ).

cnf(c_73,plain,
    ( ~ rtt(X0,X1)
    | ~ rtt(X0,X2)
    | ~ sP0(X0)
    | X1 = X2 ),
    inference(cnf_transformation,[],[f98]) ).

cnf(c_75,plain,
    ( ~ cUnsatisfiable(X0)
    | sP2(X0) ),
    inference(cnf_transformation,[],[f102]) ).

cnf(c_78,plain,
    cUnsatisfiable(i2003_11_14_17_20_29215),
    inference(cnf_transformation,[],[f106]) ).

cnf(c_82,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_20_29215)
    | sP2(i2003_11_14_17_20_29215) ),
    inference(instantiation,[status(thm)],[c_75]) ).

cnf(c_83,plain,
    ( ~ sP2(i2003_11_14_17_20_29215)
    | sP1(i2003_11_14_17_20_29215) ),
    inference(instantiation,[status(thm)],[c_62]) ).

cnf(c_84,plain,
    ( ~ sP2(i2003_11_14_17_20_29215)
    | sP0(i2003_11_14_17_20_29215) ),
    inference(instantiation,[status(thm)],[c_60]) ).

cnf(c_96,plain,
    ( sK8(i2003_11_14_17_20_29215) != sK6(i2003_11_14_17_20_29215)
    | ~ sP1(i2003_11_14_17_20_29215) ),
    inference(instantiation,[status(thm)],[c_65]) ).

cnf(c_3441,plain,
    ( ~ rtt(X0,X1)
    | ~ sP0(X0)
    | ~ sP1(X0)
    | sK8(X0) = X1 ),
    inference(superposition,[status(thm)],[c_67,c_73]) ).

cnf(c_3511,plain,
    ( ~ sP0(X0)
    | ~ sP1(X0)
    | sK8(X0) = sK6(X0) ),
    inference(superposition,[status(thm)],[c_69,c_3441]) ).

cnf(c_3520,plain,
    ( ~ sP0(i2003_11_14_17_20_29215)
    | ~ sP1(i2003_11_14_17_20_29215)
    | sK8(i2003_11_14_17_20_29215) = sK6(i2003_11_14_17_20_29215) ),
    inference(instantiation,[status(thm)],[c_3511]) ).

cnf(c_3521,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_3520,c_96,c_84,c_83,c_82,c_78]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : KRS099+1 : TPTP v8.1.2. Released v3.1.0.
% 0.14/0.13  % Command  : run_iprover %s %d THM
% 0.14/0.34  % Computer : n018.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 22:51:01 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.21/0.47  Running first-order theorem proving
% 0.21/0.47  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
% 2.23/1.15  % SZS status Started for theBenchmark.p
% 2.23/1.15  % SZS status Unsatisfiable for theBenchmark.p
% 2.23/1.15  
% 2.23/1.15  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 2.23/1.15  
% 2.23/1.15  ------  iProver source info
% 2.23/1.15  
% 2.23/1.15  git: date: 2024-05-02 19:28:25 +0000
% 2.23/1.15  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 2.23/1.15  git: non_committed_changes: false
% 2.23/1.15  
% 2.23/1.15  ------ Parsing...
% 2.23/1.15  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 2.23/1.15  
% 2.23/1.15  ------ Preprocessing... sup_sim: 0  sf_s  rm: 7 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 2.23/1.15  
% 2.23/1.15  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 2.23/1.15  
% 2.23/1.15  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.23/1.15  ------ Proving...
% 2.23/1.15  ------ Problem Properties 
% 2.23/1.15  
% 2.23/1.15  
% 2.23/1.15  clauses                                 22
% 2.23/1.15  conjectures                             0
% 2.23/1.15  EPR                                     7
% 2.23/1.15  Horn                                    14
% 2.23/1.15  unary                                   1
% 2.23/1.15  binary                                  11
% 2.23/1.15  lits                                    71
% 2.23/1.15  lits eq                                 11
% 2.23/1.15  fd_pure                                 0
% 2.23/1.15  fd_pseudo                               0
% 2.23/1.15  fd_cond                                 0
% 2.23/1.15  fd_pseudo_cond                          3
% 2.23/1.15  AC symbols                              0
% 2.23/1.15  
% 2.23/1.15  ------ Schedule dynamic 5 is on 
% 2.23/1.15  
% 2.23/1.15  ------ no conjectures: strip conj schedule 
% 2.23/1.15  
% 2.23/1.15  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.23/1.15  
% 2.23/1.15  
% 2.23/1.15  ------ 
% 2.23/1.15  Current options:
% 2.23/1.15  ------ 
% 2.23/1.15  
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% 2.23/1.15  
% 2.23/1.15  ------ Proving...
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% 2.23/1.15  % SZS status Unsatisfiable for theBenchmark.p
% 2.23/1.15  
% 2.23/1.15  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.23/1.15  
% 2.23/1.15  
%------------------------------------------------------------------------------