TSTP Solution File: KRS097+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : KRS097+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 02:33:36 EDT 2024

% Result   : Unsatisfiable 0.44s 1.12s
% Output   : CNFRefutation 0.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   49 (   4 unt;   0 def)
%            Number of atoms       :  205 (  23 equ)
%            Maximal formula atoms :   18 (   4 avg)
%            Number of connectives :  252 (  96   ~;  80   |;  67   &)
%                                         (   5 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   1 con; 0-1 aty)
%            Number of variables   :  112 (   0 sgn  50   !;  36   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f28,axiom,
    ! [X3] :
      ( cUnsatisfiable(X3)
    <=> ( ? [X5] :
            ( cc(X5)
            & rr(X3,X5) )
        & ~ ? [X4,X6] :
              ( X4 != X6
              & rr(X3,X6)
              & rr(X3,X4) )
        & ? [X5] :
            ( cd(X5)
            & rr(X3,X5) )
        & ? [X4] : rr(X3,X4) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).

fof(f30,axiom,
    cUnsatisfiable(i2003_11_14_17_20_21603),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).

fof(f32,axiom,
    ! [X3] :
      ~ ( cc(X3)
        & cd(X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).

fof(f42,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( ? [X1] :
            ( cc(X1)
            & rr(X0,X1) )
        & ~ ? [X2,X3] :
              ( X2 != X3
              & rr(X0,X3)
              & rr(X0,X2) )
        & ? [X4] :
            ( cd(X4)
            & rr(X0,X4) )
        & ? [X5] : rr(X0,X5) ) ),
    inference(rectify,[],[f28]) ).

fof(f45,plain,
    ! [X0] :
      ~ ( cc(X0)
        & cd(X0) ),
    inference(rectify,[],[f32]) ).

fof(f103,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( ? [X1] :
            ( cc(X1)
            & rr(X0,X1) )
        & ! [X2,X3] :
            ( X2 = X3
            | ~ rr(X0,X3)
            | ~ rr(X0,X2) )
        & ? [X4] :
            ( cd(X4)
            & rr(X0,X4) )
        & ? [X5] : rr(X0,X5) ) ),
    inference(ennf_transformation,[],[f42]) ).

fof(f105,plain,
    ! [X0] :
      ( ~ cc(X0)
      | ~ cd(X0) ),
    inference(ennf_transformation,[],[f45]) ).

fof(f113,plain,
    ! [X0] :
      ( sP0(X0)
    <=> ( ? [X1] :
            ( cc(X1)
            & rr(X0,X1) )
        & ! [X2,X3] :
            ( X2 = X3
            | ~ rr(X0,X3)
            | ~ rr(X0,X2) )
        & ? [X4] :
            ( cd(X4)
            & rr(X0,X4) )
        & ? [X5] : rr(X0,X5) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f114,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> sP0(X0) ),
    inference(definition_folding,[],[f103,f113]) ).

fof(f116,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ! [X1] :
            ( ~ cc(X1)
            | ~ rr(X0,X1) )
        | ? [X2,X3] :
            ( X2 != X3
            & rr(X0,X3)
            & rr(X0,X2) )
        | ! [X4] :
            ( ~ cd(X4)
            | ~ rr(X0,X4) )
        | ! [X5] : ~ rr(X0,X5) )
      & ( ( ? [X1] :
              ( cc(X1)
              & rr(X0,X1) )
          & ! [X2,X3] :
              ( X2 = X3
              | ~ rr(X0,X3)
              | ~ rr(X0,X2) )
          & ? [X4] :
              ( cd(X4)
              & rr(X0,X4) )
          & ? [X5] : rr(X0,X5) )
        | ~ sP0(X0) ) ),
    inference(nnf_transformation,[],[f113]) ).

fof(f117,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ! [X1] :
            ( ~ cc(X1)
            | ~ rr(X0,X1) )
        | ? [X2,X3] :
            ( X2 != X3
            & rr(X0,X3)
            & rr(X0,X2) )
        | ! [X4] :
            ( ~ cd(X4)
            | ~ rr(X0,X4) )
        | ! [X5] : ~ rr(X0,X5) )
      & ( ( ? [X1] :
              ( cc(X1)
              & rr(X0,X1) )
          & ! [X2,X3] :
              ( X2 = X3
              | ~ rr(X0,X3)
              | ~ rr(X0,X2) )
          & ? [X4] :
              ( cd(X4)
              & rr(X0,X4) )
          & ? [X5] : rr(X0,X5) )
        | ~ sP0(X0) ) ),
    inference(flattening,[],[f116]) ).

fof(f118,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ! [X1] :
            ( ~ cc(X1)
            | ~ rr(X0,X1) )
        | ? [X2,X3] :
            ( X2 != X3
            & rr(X0,X3)
            & rr(X0,X2) )
        | ! [X4] :
            ( ~ cd(X4)
            | ~ rr(X0,X4) )
        | ! [X5] : ~ rr(X0,X5) )
      & ( ( ? [X6] :
              ( cc(X6)
              & rr(X0,X6) )
          & ! [X7,X8] :
              ( X7 = X8
              | ~ rr(X0,X8)
              | ~ rr(X0,X7) )
          & ? [X9] :
              ( cd(X9)
              & rr(X0,X9) )
          & ? [X10] : rr(X0,X10) )
        | ~ sP0(X0) ) ),
    inference(rectify,[],[f117]) ).

fof(f119,plain,
    ! [X0] :
      ( ? [X2,X3] :
          ( X2 != X3
          & rr(X0,X3)
          & rr(X0,X2) )
     => ( sK1(X0) != sK2(X0)
        & rr(X0,sK2(X0))
        & rr(X0,sK1(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f120,plain,
    ! [X0] :
      ( ? [X6] :
          ( cc(X6)
          & rr(X0,X6) )
     => ( cc(sK3(X0))
        & rr(X0,sK3(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f121,plain,
    ! [X0] :
      ( ? [X9] :
          ( cd(X9)
          & rr(X0,X9) )
     => ( cd(sK4(X0))
        & rr(X0,sK4(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f122,plain,
    ! [X0] :
      ( ? [X10] : rr(X0,X10)
     => rr(X0,sK5(X0)) ),
    introduced(choice_axiom,[]) ).

fof(f123,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ! [X1] :
            ( ~ cc(X1)
            | ~ rr(X0,X1) )
        | ( sK1(X0) != sK2(X0)
          & rr(X0,sK2(X0))
          & rr(X0,sK1(X0)) )
        | ! [X4] :
            ( ~ cd(X4)
            | ~ rr(X0,X4) )
        | ! [X5] : ~ rr(X0,X5) )
      & ( ( cc(sK3(X0))
          & rr(X0,sK3(X0))
          & ! [X7,X8] :
              ( X7 = X8
              | ~ rr(X0,X8)
              | ~ rr(X0,X7) )
          & cd(sK4(X0))
          & rr(X0,sK4(X0))
          & rr(X0,sK5(X0)) )
        | ~ sP0(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5])],[f118,f122,f121,f120,f119]) ).

fof(f124,plain,
    ! [X0] :
      ( ( cUnsatisfiable(X0)
        | ~ sP0(X0) )
      & ( sP0(X0)
        | ~ cUnsatisfiable(X0) ) ),
    inference(nnf_transformation,[],[f114]) ).

fof(f157,plain,
    ! [X0] :
      ( rr(X0,sK4(X0))
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f123]) ).

fof(f158,plain,
    ! [X0] :
      ( cd(sK4(X0))
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f123]) ).

fof(f159,plain,
    ! [X0,X8,X7] :
      ( X7 = X8
      | ~ rr(X0,X8)
      | ~ rr(X0,X7)
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f123]) ).

fof(f160,plain,
    ! [X0] :
      ( rr(X0,sK3(X0))
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f123]) ).

fof(f161,plain,
    ! [X0] :
      ( cc(sK3(X0))
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f123]) ).

fof(f165,plain,
    ! [X0] :
      ( sP0(X0)
      | ~ cUnsatisfiable(X0) ),
    inference(cnf_transformation,[],[f124]) ).

fof(f170,plain,
    cUnsatisfiable(i2003_11_14_17_20_21603),
    inference(cnf_transformation,[],[f30]) ).

fof(f172,plain,
    ! [X0] :
      ( ~ cc(X0)
      | ~ cd(X0) ),
    inference(cnf_transformation,[],[f105]) ).

cnf(c_56,plain,
    ( ~ sP0(X0)
    | cc(sK3(X0)) ),
    inference(cnf_transformation,[],[f161]) ).

cnf(c_57,plain,
    ( ~ sP0(X0)
    | rr(X0,sK3(X0)) ),
    inference(cnf_transformation,[],[f160]) ).

cnf(c_58,plain,
    ( ~ rr(X0,X1)
    | ~ rr(X0,X2)
    | ~ sP0(X0)
    | X1 = X2 ),
    inference(cnf_transformation,[],[f159]) ).

cnf(c_59,plain,
    ( ~ sP0(X0)
    | cd(sK4(X0)) ),
    inference(cnf_transformation,[],[f158]) ).

cnf(c_60,plain,
    ( ~ sP0(X0)
    | rr(X0,sK4(X0)) ),
    inference(cnf_transformation,[],[f157]) ).

cnf(c_63,plain,
    ( ~ cUnsatisfiable(X0)
    | sP0(X0) ),
    inference(cnf_transformation,[],[f165]) ).

cnf(c_67,plain,
    cUnsatisfiable(i2003_11_14_17_20_21603),
    inference(cnf_transformation,[],[f170]) ).

cnf(c_69,plain,
    ( ~ cc(X0)
    | ~ cd(X0) ),
    inference(cnf_transformation,[],[f172]) ).

cnf(c_106,plain,
    ( ~ cUnsatisfiable(X0)
    | sP0(X0) ),
    inference(prop_impl_just,[status(thm)],[c_63]) ).

cnf(c_114,plain,
    ( ~ cUnsatisfiable(X0)
    | cc(sK3(X0)) ),
    inference(prop_impl_just,[status(thm)],[c_63,c_56]) ).

cnf(c_116,plain,
    ( ~ cUnsatisfiable(X0)
    | rr(X0,sK3(X0)) ),
    inference(prop_impl_just,[status(thm)],[c_63,c_57]) ).

cnf(c_118,plain,
    ( ~ cUnsatisfiable(X0)
    | cd(sK4(X0)) ),
    inference(prop_impl_just,[status(thm)],[c_63,c_59]) ).

cnf(c_120,plain,
    ( ~ cUnsatisfiable(X0)
    | rr(X0,sK4(X0)) ),
    inference(prop_impl_just,[status(thm)],[c_63,c_60]) ).

cnf(c_126,plain,
    ( ~ cc(X0)
    | ~ cd(X0) ),
    inference(prop_impl_just,[status(thm)],[c_69]) ).

cnf(c_219,plain,
    ( ~ rr(X0,X1)
    | ~ rr(X0,X2)
    | ~ cUnsatisfiable(X0)
    | X1 = X2 ),
    inference(bin_hyper_res,[status(thm)],[c_58,c_106]) ).

cnf(c_584,plain,
    ( sK3(X0) != X1
    | ~ cd(X1)
    | ~ cUnsatisfiable(X0) ),
    inference(resolution_lifted,[status(thm)],[c_114,c_126]) ).

cnf(c_585,plain,
    ( ~ cd(sK3(X0))
    | ~ cUnsatisfiable(X0) ),
    inference(unflattening,[status(thm)],[c_584]) ).

cnf(c_685,plain,
    ( sK3(X0) != sK4(X1)
    | ~ cUnsatisfiable(X0)
    | ~ cUnsatisfiable(X1) ),
    inference(resolution_lifted,[status(thm)],[c_118,c_585]) ).

cnf(c_686,plain,
    ( sK3(i2003_11_14_17_20_21603) != sK4(i2003_11_14_17_20_21603)
    | ~ cUnsatisfiable(i2003_11_14_17_20_21603) ),
    inference(instantiation,[status(thm)],[c_685]) ).

cnf(c_1201,plain,
    ( ~ rr(X0,X1)
    | ~ cUnsatisfiable(X0)
    | sK3(X0) = X1 ),
    inference(superposition,[status(thm)],[c_116,c_219]) ).

cnf(c_1223,plain,
    ( ~ cUnsatisfiable(X0)
    | sK3(X0) = sK4(X0) ),
    inference(superposition,[status(thm)],[c_120,c_1201]) ).

cnf(c_1230,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_20_21603)
    | sK3(i2003_11_14_17_20_21603) = sK4(i2003_11_14_17_20_21603) ),
    inference(instantiation,[status(thm)],[c_1223]) ).

cnf(c_1231,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_1230,c_686,c_67]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : KRS097+1 : TPTP v8.1.2. Released v3.1.0.
% 0.11/0.12  % Command  : run_iprover %s %d THM
% 0.11/0.32  % Computer : n014.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Thu May  2 22:35:02 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.16/0.43  Running first-order theorem proving
% 0.16/0.43  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
% 0.44/1.12  % SZS status Started for theBenchmark.p
% 0.44/1.12  % SZS status Unsatisfiable for theBenchmark.p
% 0.44/1.12  
% 0.44/1.12  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 0.44/1.12  
% 0.44/1.12  ------  iProver source info
% 0.44/1.12  
% 0.44/1.12  git: date: 2024-05-02 19:28:25 +0000
% 0.44/1.12  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 0.44/1.12  git: non_committed_changes: false
% 0.44/1.12  
% 0.44/1.12  ------ Parsing...
% 0.44/1.12  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 0.44/1.12  
% 0.44/1.12  ------ Preprocessing... sup_sim: 0  sf_s  rm: 13 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 
% 0.44/1.12  
% 0.44/1.12  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 0.44/1.12  
% 0.44/1.12  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 0.44/1.12  ------ Proving...
% 0.44/1.12  ------ Problem Properties 
% 0.44/1.12  
% 0.44/1.12  
% 0.44/1.12  clauses                                 10
% 0.44/1.12  conjectures                             0
% 0.44/1.12  EPR                                     2
% 0.44/1.12  Horn                                    8
% 0.44/1.12  unary                                   1
% 0.44/1.12  binary                                  5
% 0.44/1.12  lits                                    36
% 0.44/1.12  lits eq                                 2
% 0.44/1.12  fd_pure                                 0
% 0.44/1.12  fd_pseudo                               0
% 0.44/1.12  fd_cond                                 0
% 0.44/1.12  fd_pseudo_cond                          1
% 0.44/1.12  AC symbols                              0
% 0.44/1.12  
% 0.44/1.12  ------ Schedule dynamic 5 is on 
% 0.44/1.12  
% 0.44/1.12  ------ no conjectures: strip conj schedule 
% 0.44/1.12  
% 0.44/1.12  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 0.44/1.12  
% 0.44/1.12  
% 0.44/1.12  ------ 
% 0.44/1.12  Current options:
% 0.44/1.12  ------ 
% 0.44/1.12  
% 0.44/1.12  
% 0.44/1.12  
% 0.44/1.12  
% 0.44/1.12  ------ Proving...
% 0.44/1.12  
% 0.44/1.12  
% 0.44/1.12  % SZS status Unsatisfiable for theBenchmark.p
% 0.44/1.12  
% 0.44/1.12  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.44/1.12  
% 0.44/1.12  
%------------------------------------------------------------------------------