TSTP Solution File: NUN062+2 by iProver---3.8

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%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : NUN062+2 : TPTP v8.1.2. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n025.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 12:49:13 EDT 2023

% Result   : Theorem 1.89s 1.19s
% Output   : CNFRefutation 1.89s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   39 (   9 unt;   0 def)
%            Number of atoms       :  120 (  54 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  147 (  66   ~;  45   |;  32   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   1 con; 0-2 aty)
%            Number of variables   :  113 (   9 sgn;  70   !;  21   ?)

% Comments : 
%------------------------------------------------------------------------------
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(f3,axiom,
    ! [X5,X6] :
    ? [X7] :
    ! [X8] :
      ( ( X7 = X8
        & r3(X5,X6,X8) )
      | ( X7 != X8
        & ~ r3(X5,X6,X8) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).

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,
    ! [X13] :
    ? [X21,X38] :
      ( ? [X22] :
          ( X21 = X22
          & r3(X13,X38,X22) )
      & ! [X15] :
          ( X15 != X38
          | ~ r1(X15) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infiniteNumbers) ).

fof(f13,negated_conjecture,
    ~ ! [X13] :
      ? [X21,X38] :
        ( ? [X22] :
            ( X21 = X22
            & r3(X13,X38,X22) )
        & ! [X15] :
            ( X15 != X38
            | ~ 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(f15,plain,
    ! [X0,X1] :
    ? [X2] :
    ! [X3] :
      ( ( X2 = X3
        & r3(X0,X1,X3) )
      | ( X2 != X3
        & ~ r3(X0,X1,X3) ) ),
    inference(rectify,[],[f3]) ).

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

fof(f24,plain,
    ~ ! [X0] :
      ? [X1,X2] :
        ( ? [X3] :
            ( X1 = X3
            & r3(X0,X2,X3) )
        & ! [X4] :
            ( X2 != X4
            | ~ r1(X4) ) ),
    inference(rectify,[],[f13]) ).

fof(f25,plain,
    ? [X0] :
    ! [X1,X2] :
      ( ! [X3] :
          ( X1 != X3
          | ~ r3(X0,X2,X3) )
      | ? [X4] :
          ( X2 = X4
          & r1(X4) ) ),
    inference(ennf_transformation,[],[f24]) ).

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(f30,plain,
    ! [X0,X1] :
      ( ? [X2] :
        ! [X3] :
          ( ( X2 = X3
            & r3(X0,X1,X3) )
          | ( X2 != X3
            & ~ r3(X0,X1,X3) ) )
     => ! [X3] :
          ( ( sK2(X0,X1) = X3
            & r3(X0,X1,X3) )
          | ( sK2(X0,X1) != X3
            & ~ r3(X0,X1,X3) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f31,plain,
    ! [X0,X1,X3] :
      ( ( sK2(X0,X1) = X3
        & r3(X0,X1,X3) )
      | ( sK2(X0,X1) != X3
        & ~ r3(X0,X1,X3) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f15,f30]) ).

fof(f54,plain,
    ( ? [X0] :
      ! [X1,X2] :
        ( ! [X3] :
            ( X1 != X3
            | ~ r3(X0,X2,X3) )
        | ? [X4] :
            ( X2 = X4
            & r1(X4) ) )
   => ! [X2,X1] :
        ( ! [X3] :
            ( X1 != X3
            | ~ r3(sK20,X2,X3) )
        | ? [X4] :
            ( X2 = X4
            & r1(X4) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f55,plain,
    ! [X2] :
      ( ? [X4] :
          ( X2 = X4
          & r1(X4) )
     => ( sK21(X2) = X2
        & r1(sK21(X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f56,plain,
    ! [X1,X2] :
      ( ! [X3] :
          ( X1 != X3
          | ~ r3(sK20,X2,X3) )
      | ( sK21(X2) = X2
        & r1(sK21(X2)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21])],[f25,f55,f54]) ).

fof(f62,plain,
    ! [X2,X0] :
      ( r2(X0,X2)
      | sK1(X0) != X2 ),
    inference(cnf_transformation,[],[f29]) ).

fof(f66,plain,
    ! [X3,X0,X1] :
      ( r3(X0,X1,X3)
      | sK2(X0,X1) != X3 ),
    inference(cnf_transformation,[],[f31]) ).

fof(f95,plain,
    ! [X2,X0,X1] :
      ( ~ r2(X0,X1)
      | X1 != X2
      | ~ r1(X2) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f96,plain,
    ! [X2,X3,X1] :
      ( X1 != X3
      | ~ r3(sK20,X2,X3)
      | r1(sK21(X2)) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f97,plain,
    ! [X2,X3,X1] :
      ( X1 != X3
      | ~ r3(sK20,X2,X3)
      | sK21(X2) = X2 ),
    inference(cnf_transformation,[],[f56]) ).

fof(f104,plain,
    ! [X0] : r2(X0,sK1(X0)),
    inference(equality_resolution,[],[f62]) ).

fof(f106,plain,
    ! [X0,X1] : r3(X0,X1,sK2(X0,X1)),
    inference(equality_resolution,[],[f66]) ).

fof(f110,plain,
    ! [X2,X0] :
      ( ~ r2(X0,X2)
      | ~ r1(X2) ),
    inference(equality_resolution,[],[f95]) ).

fof(f111,plain,
    ! [X2,X3] :
      ( ~ r3(sK20,X2,X3)
      | sK21(X2) = X2 ),
    inference(equality_resolution,[],[f97]) ).

fof(f112,plain,
    ! [X2,X3] :
      ( ~ r3(sK20,X2,X3)
      | r1(sK21(X2)) ),
    inference(equality_resolution,[],[f96]) ).

cnf(c_52,plain,
    r2(X0,sK1(X0)),
    inference(cnf_transformation,[],[f104]) ).

cnf(c_54,plain,
    r3(X0,X1,sK2(X0,X1)),
    inference(cnf_transformation,[],[f106]) ).

cnf(c_76,plain,
    ( ~ r2(X0,X1)
    | ~ r1(X1) ),
    inference(cnf_transformation,[],[f110]) ).

cnf(c_77,negated_conjecture,
    ( ~ r3(sK20,X0,X1)
    | sK21(X0) = X0 ),
    inference(cnf_transformation,[],[f111]) ).

cnf(c_78,negated_conjecture,
    ( ~ r3(sK20,X0,X1)
    | r1(sK21(X0)) ),
    inference(cnf_transformation,[],[f112]) ).

cnf(c_300,plain,
    ( sK2(X0,X1) != X2
    | X0 != sK20
    | X1 != X3
    | r1(sK21(X3)) ),
    inference(resolution_lifted,[status(thm)],[c_54,c_78]) ).

cnf(c_301,plain,
    r1(sK21(X0)),
    inference(unflattening,[status(thm)],[c_300]) ).

cnf(c_306,plain,
    ( sK2(X0,X1) != X2
    | X0 != sK20
    | X1 != X3
    | sK21(X3) = X3 ),
    inference(resolution_lifted,[status(thm)],[c_54,c_77]) ).

cnf(c_307,plain,
    sK21(X0) = X0,
    inference(unflattening,[status(thm)],[c_306]) ).

cnf(c_512,plain,
    r1(X0),
    inference(demodulation,[status(thm)],[c_301,c_307]) ).

cnf(c_513,plain,
    ~ r2(X0,X1),
    inference(forward_subsumption_resolution,[status(thm)],[c_76,c_512]) ).

cnf(c_514,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[c_52,c_513]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUN062+2 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n025.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 09:14:54 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.47  Running first-order theorem proving
% 0.20/0.47  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 1.89/1.19  % SZS status Started for theBenchmark.p
% 1.89/1.19  % SZS status Theorem for theBenchmark.p
% 1.89/1.19  
% 1.89/1.19  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 1.89/1.19  
% 1.89/1.19  ------  iProver source info
% 1.89/1.19  
% 1.89/1.19  git: date: 2023-05-31 18:12:56 +0000
% 1.89/1.19  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 1.89/1.19  git: non_committed_changes: false
% 1.89/1.19  git: last_make_outside_of_git: false
% 1.89/1.19  
% 1.89/1.19  ------ Parsing...
% 1.89/1.19  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 1.89/1.19  
% 1.89/1.19  ------ Preprocessing... sup_sim: 1  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe_e 
% 1.89/1.19  
% 1.89/1.19  % SZS status Theorem for theBenchmark.p
% 1.89/1.19  
% 1.89/1.19  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.89/1.19  
% 1.89/1.19  
%------------------------------------------------------------------------------