TSTP Solution File: NUN073+2 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : NUN073+2 : TPTP v8.1.2. Released v7.3.0.
% 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 : Thu Aug 31 12:49:18 EDT 2023

% Result   : Theorem 2.34s 1.15s
% Output   : CNFRefutation 2.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   59 (  26 unt;   0 def)
%            Number of atoms       :  167 (  51 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  180 (  72   ~;  51   |;  50   &)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-1 aty)
%            Number of variables   :   94 (   1 sgn;  58   !;  27   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ? [X0] :
    ! [X1] :
      ( ( X0 = X1
        & r1(X1) )
      | ( X0 != X1
        & ~ r1(X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).

fof(f2,axiom,
    ! [X2] :
    ? [X3] :
    ! [X4] :
      ( ( X3 = X4
        & r2(X2,X4) )
      | ( X3 != X4
        & ~ r2(X2,X4) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).

fof(f7,axiom,
    ! [X25,X26] :
      ( X25 = X26
      | ! [X27] :
          ( ~ r2(X26,X27)
          | ! [X28] :
              ( X27 != X28
              | ~ r2(X25,X28) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3a) ).

fof(f11,axiom,
    ! [X40,X41] :
      ( ~ r2(X40,X41)
      | ! [X42] :
          ( X41 != X42
          | ~ r1(X42) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7a) ).

fof(f12,conjecture,
    ! [X38] :
      ( ! [X22] :
          ( ~ r2(X22,X38)
          | ! [X16] :
              ( ~ r2(X16,X22)
              | ~ r1(X16) ) )
      | ! [X21] :
          ( X21 != X38
          | ! [X15] :
              ( ~ r2(X15,X21)
              | ~ r1(X15) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oneuneqtwo) ).

fof(f13,negated_conjecture,
    ~ ! [X38] :
        ( ! [X22] :
            ( ~ r2(X22,X38)
            | ! [X16] :
                ( ~ r2(X16,X22)
                | ~ r1(X16) ) )
        | ! [X21] :
            ( X21 != X38
            | ! [X15] :
                ( ~ r2(X15,X21)
                | ~ r1(X15) ) ) ),
    inference(negated_conjecture,[],[f12]) ).

fof(f14,plain,
    ! [X0] :
    ? [X1] :
    ! [X2] :
      ( ( X1 = X2
        & r2(X0,X2) )
      | ( X1 != X2
        & ~ r2(X0,X2) ) ),
    inference(rectify,[],[f2]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ! [X2] :
          ( ~ r2(X1,X2)
          | ! [X3] :
              ( X2 != X3
              | ~ r2(X0,X3) ) ) ),
    inference(rectify,[],[f7]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ~ r2(X0,X1)
      | ! [X2] :
          ( X1 != X2
          | ~ r1(X2) ) ),
    inference(rectify,[],[f11]) ).

fof(f24,plain,
    ~ ! [X0] :
        ( ! [X1] :
            ( ~ r2(X1,X0)
            | ! [X2] :
                ( ~ r2(X2,X1)
                | ~ r1(X2) ) )
        | ! [X3] :
            ( X0 != X3
            | ! [X4] :
                ( ~ r2(X4,X3)
                | ~ r1(X4) ) ) ),
    inference(rectify,[],[f13]) ).

fof(f25,plain,
    ? [X0] :
      ( ? [X1] :
          ( r2(X1,X0)
          & ? [X2] :
              ( r2(X2,X1)
              & r1(X2) ) )
      & ? [X3] :
          ( X0 = X3
          & ? [X4] :
              ( r2(X4,X3)
              & r1(X4) ) ) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f26,plain,
    ( ? [X0] :
      ! [X1] :
        ( ( X0 = X1
          & r1(X1) )
        | ( X0 != X1
          & ~ r1(X1) ) )
   => ! [X1] :
        ( ( sK0 = X1
          & r1(X1) )
        | ( sK0 != X1
          & ~ r1(X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f27,plain,
    ! [X1] :
      ( ( sK0 = X1
        & r1(X1) )
      | ( sK0 != X1
        & ~ r1(X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f1,f26]) ).

fof(f28,plain,
    ! [X0] :
      ( ? [X1] :
        ! [X2] :
          ( ( X1 = X2
            & r2(X0,X2) )
          | ( X1 != X2
            & ~ r2(X0,X2) ) )
     => ! [X2] :
          ( ( sK1(X0) = X2
            & r2(X0,X2) )
          | ( sK1(X0) != X2
            & ~ r2(X0,X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f29,plain,
    ! [X0,X2] :
      ( ( sK1(X0) = X2
        & r2(X0,X2) )
      | ( sK1(X0) != X2
        & ~ r2(X0,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f14,f28]) ).

fof(f54,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( r2(X1,X0)
            & ? [X2] :
                ( r2(X2,X1)
                & r1(X2) ) )
        & ? [X3] :
            ( X0 = X3
            & ? [X4] :
                ( r2(X4,X3)
                & r1(X4) ) ) )
   => ( ? [X1] :
          ( r2(X1,sK20)
          & ? [X2] :
              ( r2(X2,X1)
              & r1(X2) ) )
      & ? [X3] :
          ( sK20 = X3
          & ? [X4] :
              ( r2(X4,X3)
              & r1(X4) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f55,plain,
    ( ? [X1] :
        ( r2(X1,sK20)
        & ? [X2] :
            ( r2(X2,X1)
            & r1(X2) ) )
   => ( r2(sK21,sK20)
      & ? [X2] :
          ( r2(X2,sK21)
          & r1(X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f56,plain,
    ( ? [X2] :
        ( r2(X2,sK21)
        & r1(X2) )
   => ( r2(sK22,sK21)
      & r1(sK22) ) ),
    introduced(choice_axiom,[]) ).

fof(f57,plain,
    ( ? [X3] :
        ( sK20 = X3
        & ? [X4] :
            ( r2(X4,X3)
            & r1(X4) ) )
   => ( sK20 = sK23
      & ? [X4] :
          ( r2(X4,sK23)
          & r1(X4) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f58,plain,
    ( ? [X4] :
        ( r2(X4,sK23)
        & r1(X4) )
   => ( r2(sK24,sK23)
      & r1(sK24) ) ),
    introduced(choice_axiom,[]) ).

fof(f59,plain,
    ( r2(sK21,sK20)
    & r2(sK22,sK21)
    & r1(sK22)
    & sK20 = sK23
    & r2(sK24,sK23)
    & r1(sK24) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23,sK24])],[f25,f58,f57,f56,f55,f54]) ).

fof(f61,plain,
    ! [X1] :
      ( r1(X1)
      | sK0 != X1 ),
    inference(cnf_transformation,[],[f27]) ).

fof(f62,plain,
    ! [X1] :
      ( sK0 = X1
      | ~ r1(X1) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f66,plain,
    ! [X2,X0] :
      ( sK1(X0) = X2
      | ~ r2(X0,X2) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f86,plain,
    ! [X2,X3,X0,X1] :
      ( X0 = X1
      | ~ r2(X1,X2)
      | X2 != X3
      | ~ r2(X0,X3) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f98,plain,
    ! [X2,X0,X1] :
      ( ~ r2(X0,X1)
      | X1 != X2
      | ~ r1(X2) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f99,plain,
    r1(sK24),
    inference(cnf_transformation,[],[f59]) ).

fof(f100,plain,
    r2(sK24,sK23),
    inference(cnf_transformation,[],[f59]) ).

fof(f101,plain,
    sK20 = sK23,
    inference(cnf_transformation,[],[f59]) ).

fof(f102,plain,
    r1(sK22),
    inference(cnf_transformation,[],[f59]) ).

fof(f103,plain,
    r2(sK22,sK21),
    inference(cnf_transformation,[],[f59]) ).

fof(f104,plain,
    r2(sK21,sK20),
    inference(cnf_transformation,[],[f59]) ).

fof(f108,plain,
    r2(sK21,sK23),
    inference(definition_unfolding,[],[f104,f101]) ).

fof(f110,plain,
    r1(sK0),
    inference(equality_resolution,[],[f61]) ).

fof(f117,plain,
    ! [X3,X0,X1] :
      ( X0 = X1
      | ~ r2(X1,X3)
      | ~ r2(X0,X3) ),
    inference(equality_resolution,[],[f86]) ).

fof(f118,plain,
    ! [X2,X0] :
      ( ~ r2(X0,X2)
      | ~ r1(X2) ),
    inference(equality_resolution,[],[f98]) ).

cnf(c_49,plain,
    ( ~ r1(X0)
    | X0 = sK0 ),
    inference(cnf_transformation,[],[f62]) ).

cnf(c_50,plain,
    r1(sK0),
    inference(cnf_transformation,[],[f110]) ).

cnf(c_51,plain,
    ( ~ r2(X0,X1)
    | sK1(X0) = X1 ),
    inference(cnf_transformation,[],[f66]) ).

cnf(c_65,plain,
    ( ~ r2(X0,X1)
    | ~ r2(X2,X1)
    | X0 = X2 ),
    inference(cnf_transformation,[],[f117]) ).

cnf(c_76,plain,
    ( ~ r2(X0,X1)
    | ~ r1(X1) ),
    inference(cnf_transformation,[],[f118]) ).

cnf(c_77,negated_conjecture,
    r2(sK21,sK23),
    inference(cnf_transformation,[],[f108]) ).

cnf(c_78,negated_conjecture,
    r2(sK22,sK21),
    inference(cnf_transformation,[],[f103]) ).

cnf(c_79,negated_conjecture,
    r1(sK22),
    inference(cnf_transformation,[],[f102]) ).

cnf(c_80,negated_conjecture,
    r2(sK24,sK23),
    inference(cnf_transformation,[],[f100]) ).

cnf(c_81,negated_conjecture,
    r1(sK24),
    inference(cnf_transformation,[],[f99]) ).

cnf(c_880,plain,
    sK0 = sK22,
    inference(superposition,[status(thm)],[c_79,c_49]) ).

cnf(c_881,plain,
    sK0 = sK24,
    inference(superposition,[status(thm)],[c_81,c_49]) ).

cnf(c_885,plain,
    r2(sK0,sK21),
    inference(demodulation,[status(thm)],[c_78,c_880]) ).

cnf(c_887,plain,
    r2(sK0,sK23),
    inference(demodulation,[status(thm)],[c_80,c_881]) ).

cnf(c_898,plain,
    ~ r1(sK21),
    inference(superposition,[status(thm)],[c_885,c_76]) ).

cnf(c_929,plain,
    sK1(sK0) = sK21,
    inference(superposition,[status(thm)],[c_885,c_51]) ).

cnf(c_930,plain,
    sK1(sK0) = sK23,
    inference(superposition,[status(thm)],[c_887,c_51]) ).

cnf(c_952,plain,
    sK21 = sK23,
    inference(light_normalisation,[status(thm)],[c_930,c_929]) ).

cnf(c_956,plain,
    r2(sK21,sK21),
    inference(demodulation,[status(thm)],[c_77,c_952]) ).

cnf(c_994,plain,
    ( ~ r2(X0,sK21)
    | X0 = sK0 ),
    inference(superposition,[status(thm)],[c_885,c_65]) ).

cnf(c_1075,plain,
    sK0 = sK21,
    inference(superposition,[status(thm)],[c_956,c_994]) ).

cnf(c_1086,plain,
    ~ r1(sK0),
    inference(demodulation,[status(thm)],[c_898,c_1075]) ).

cnf(c_1088,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_1086,c_50]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUN073+2 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n012.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sun Aug 27 09:23:55 EDT 2023
% 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 --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.34/1.15  % SZS status Started for theBenchmark.p
% 2.34/1.15  % SZS status Theorem for theBenchmark.p
% 2.34/1.15  
% 2.34/1.15  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.34/1.15  
% 2.34/1.15  ------  iProver source info
% 2.34/1.15  
% 2.34/1.15  git: date: 2023-05-31 18:12:56 +0000
% 2.34/1.15  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.34/1.15  git: non_committed_changes: false
% 2.34/1.15  git: last_make_outside_of_git: false
% 2.34/1.15  
% 2.34/1.15  ------ Parsing...
% 2.34/1.15  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 2.34/1.15  
% 2.34/1.15  ------ Preprocessing... sup_sim: 1  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe_e  sup_sim: 2  sf_s  rm: 3 0s  sf_e  pe_s  pe_e 
% 2.34/1.15  
% 2.34/1.15  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 2.34/1.15  
% 2.34/1.15  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.34/1.15  ------ Proving...
% 2.34/1.15  ------ Problem Properties 
% 2.34/1.15  
% 2.34/1.15  
% 2.34/1.15  clauses                                 29
% 2.34/1.15  conjectures                             5
% 2.34/1.15  EPR                                     9
% 2.34/1.15  Horn                                    25
% 2.34/1.15  unary                                   21
% 2.34/1.15  binary                                  7
% 2.34/1.15  lits                                    38
% 2.34/1.15  lits eq                                 15
% 2.34/1.15  fd_pure                                 0
% 2.34/1.15  fd_pseudo                               0
% 2.34/1.15  fd_cond                                 1
% 2.34/1.15  fd_pseudo_cond                          2
% 2.34/1.15  AC symbols                              0
% 2.34/1.15  
% 2.34/1.15  ------ Schedule dynamic 5 is on 
% 2.34/1.15  
% 2.34/1.15  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.34/1.15  
% 2.34/1.15  
% 2.34/1.15  ------ 
% 2.34/1.15  Current options:
% 2.34/1.15  ------ 
% 2.34/1.15  
% 2.34/1.15  
% 2.34/1.15  
% 2.34/1.15  
% 2.34/1.15  ------ Proving...
% 2.34/1.15  
% 2.34/1.15  
% 2.34/1.15  % SZS status Theorem for theBenchmark.p
% 2.34/1.15  
% 2.34/1.15  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.34/1.15  
% 2.34/1.15  
%------------------------------------------------------------------------------