TSTP Solution File: SYN074+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SYN074+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n002.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 03:29:09 EDT 2024

% Result   : Theorem 2.19s 1.23s
% Output   : CNFRefutation 2.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   52 (   6 unt;   0 def)
%            Number of atoms       :  201 ( 125 equ)
%            Maximal formula atoms :   20 (   3 avg)
%            Number of connectives :  244 (  95   ~; 106   |;  30   &)
%                                         (   8 <=>;   4  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :  116 (   3 sgn  53   !;  29   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ? [X0,X1] :
    ! [X2,X3] :
      ( big_f(X2,X3)
    <=> ( X1 = X3
        & X0 = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel51_1) ).

fof(f2,conjecture,
    ? [X0] :
    ! [X2] :
      ( ? [X1] :
        ! [X3] :
          ( big_f(X2,X3)
        <=> X1 = X3 )
    <=> X0 = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel51) ).

fof(f3,negated_conjecture,
    ~ ? [X0] :
      ! [X2] :
        ( ? [X1] :
          ! [X3] :
            ( big_f(X2,X3)
          <=> X1 = X3 )
      <=> X0 = X2 ),
    inference(negated_conjecture,[],[f2]) ).

fof(f4,plain,
    ~ ? [X0] :
      ! [X1] :
        ( ? [X2] :
          ! [X3] :
            ( big_f(X1,X3)
          <=> X2 = X3 )
      <=> X0 = X1 ),
    inference(rectify,[],[f3]) ).

fof(f5,plain,
    ! [X0] :
    ? [X1] :
      ( ? [X2] :
        ! [X3] :
          ( big_f(X1,X3)
        <=> X2 = X3 )
    <~> X0 = X1 ),
    inference(ennf_transformation,[],[f4]) ).

fof(f6,plain,
    ? [X0,X1] :
    ! [X2,X3] :
      ( ( big_f(X2,X3)
        | X1 != X3
        | X0 != X2 )
      & ( ( X1 = X3
          & X0 = X2 )
        | ~ big_f(X2,X3) ) ),
    inference(nnf_transformation,[],[f1]) ).

fof(f7,plain,
    ? [X0,X1] :
    ! [X2,X3] :
      ( ( big_f(X2,X3)
        | X1 != X3
        | X0 != X2 )
      & ( ( X1 = X3
          & X0 = X2 )
        | ~ big_f(X2,X3) ) ),
    inference(flattening,[],[f6]) ).

fof(f8,plain,
    ( ? [X0,X1] :
      ! [X2,X3] :
        ( ( big_f(X2,X3)
          | X1 != X3
          | X0 != X2 )
        & ( ( X1 = X3
            & X0 = X2 )
          | ~ big_f(X2,X3) ) )
   => ! [X3,X2] :
        ( ( big_f(X2,X3)
          | sK1 != X3
          | sK0 != X2 )
        & ( ( sK1 = X3
            & sK0 = X2 )
          | ~ big_f(X2,X3) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f9,plain,
    ! [X2,X3] :
      ( ( big_f(X2,X3)
        | sK1 != X3
        | sK0 != X2 )
      & ( ( sK1 = X3
          & sK0 = X2 )
        | ~ big_f(X2,X3) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f8]) ).

fof(f10,plain,
    ! [X0] :
    ? [X1] :
      ( ( X0 != X1
        | ! [X2] :
          ? [X3] :
            ( ( X2 != X3
              | ~ big_f(X1,X3) )
            & ( X2 = X3
              | big_f(X1,X3) ) ) )
      & ( X0 = X1
        | ? [X2] :
          ! [X3] :
            ( ( big_f(X1,X3)
              | X2 != X3 )
            & ( X2 = X3
              | ~ big_f(X1,X3) ) ) ) ),
    inference(nnf_transformation,[],[f5]) ).

fof(f11,plain,
    ! [X0] :
    ? [X1] :
      ( ( X0 != X1
        | ! [X2] :
          ? [X3] :
            ( ( X2 != X3
              | ~ big_f(X1,X3) )
            & ( X2 = X3
              | big_f(X1,X3) ) ) )
      & ( X0 = X1
        | ? [X4] :
          ! [X5] :
            ( ( big_f(X1,X5)
              | X4 != X5 )
            & ( X4 = X5
              | ~ big_f(X1,X5) ) ) ) ),
    inference(rectify,[],[f10]) ).

fof(f12,plain,
    ! [X0] :
      ( ? [X1] :
          ( ( X0 != X1
            | ! [X2] :
              ? [X3] :
                ( ( X2 != X3
                  | ~ big_f(X1,X3) )
                & ( X2 = X3
                  | big_f(X1,X3) ) ) )
          & ( X0 = X1
            | ? [X4] :
              ! [X5] :
                ( ( big_f(X1,X5)
                  | X4 != X5 )
                & ( X4 = X5
                  | ~ big_f(X1,X5) ) ) ) )
     => ( ( sK2(X0) != X0
          | ! [X2] :
            ? [X3] :
              ( ( X2 != X3
                | ~ big_f(sK2(X0),X3) )
              & ( X2 = X3
                | big_f(sK2(X0),X3) ) ) )
        & ( sK2(X0) = X0
          | ? [X4] :
            ! [X5] :
              ( ( big_f(sK2(X0),X5)
                | X4 != X5 )
              & ( X4 = X5
                | ~ big_f(sK2(X0),X5) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f13,plain,
    ! [X0,X2] :
      ( ? [X3] :
          ( ( X2 != X3
            | ~ big_f(sK2(X0),X3) )
          & ( X2 = X3
            | big_f(sK2(X0),X3) ) )
     => ( ( sK3(X0,X2) != X2
          | ~ big_f(sK2(X0),sK3(X0,X2)) )
        & ( sK3(X0,X2) = X2
          | big_f(sK2(X0),sK3(X0,X2)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f14,plain,
    ! [X0] :
      ( ? [X4] :
        ! [X5] :
          ( ( big_f(sK2(X0),X5)
            | X4 != X5 )
          & ( X4 = X5
            | ~ big_f(sK2(X0),X5) ) )
     => ! [X5] :
          ( ( big_f(sK2(X0),X5)
            | sK4(X0) != X5 )
          & ( sK4(X0) = X5
            | ~ big_f(sK2(X0),X5) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f15,plain,
    ! [X0] :
      ( ( sK2(X0) != X0
        | ! [X2] :
            ( ( sK3(X0,X2) != X2
              | ~ big_f(sK2(X0),sK3(X0,X2)) )
            & ( sK3(X0,X2) = X2
              | big_f(sK2(X0),sK3(X0,X2)) ) ) )
      & ( sK2(X0) = X0
        | ! [X5] :
            ( ( big_f(sK2(X0),X5)
              | sK4(X0) != X5 )
            & ( sK4(X0) = X5
              | ~ big_f(sK2(X0),X5) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f11,f14,f13,f12]) ).

fof(f16,plain,
    ! [X2,X3] :
      ( sK0 = X2
      | ~ big_f(X2,X3) ),
    inference(cnf_transformation,[],[f9]) ).

fof(f17,plain,
    ! [X2,X3] :
      ( sK1 = X3
      | ~ big_f(X2,X3) ),
    inference(cnf_transformation,[],[f9]) ).

fof(f18,plain,
    ! [X2,X3] :
      ( big_f(X2,X3)
      | sK1 != X3
      | sK0 != X2 ),
    inference(cnf_transformation,[],[f9]) ).

fof(f20,plain,
    ! [X0,X5] :
      ( sK2(X0) = X0
      | big_f(sK2(X0),X5)
      | sK4(X0) != X5 ),
    inference(cnf_transformation,[],[f15]) ).

fof(f21,plain,
    ! [X2,X0] :
      ( sK2(X0) != X0
      | sK3(X0,X2) = X2
      | big_f(sK2(X0),sK3(X0,X2)) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f22,plain,
    ! [X2,X0] :
      ( sK2(X0) != X0
      | sK3(X0,X2) != X2
      | ~ big_f(sK2(X0),sK3(X0,X2)) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f23,plain,
    ! [X2] :
      ( big_f(X2,sK1)
      | sK0 != X2 ),
    inference(equality_resolution,[],[f18]) ).

fof(f24,plain,
    big_f(sK0,sK1),
    inference(equality_resolution,[],[f23]) ).

fof(f25,plain,
    ! [X0] :
      ( sK2(X0) = X0
      | big_f(sK2(X0),sK4(X0)) ),
    inference(equality_resolution,[],[f20]) ).

cnf(c_49,plain,
    big_f(sK0,sK1),
    inference(cnf_transformation,[],[f24]) ).

cnf(c_50,plain,
    ( ~ big_f(X0,X1)
    | X1 = sK1 ),
    inference(cnf_transformation,[],[f17]) ).

cnf(c_51,plain,
    ( ~ big_f(X0,X1)
    | X0 = sK0 ),
    inference(cnf_transformation,[],[f16]) ).

cnf(c_52,negated_conjecture,
    ( sK3(X0,X1) != X1
    | sK2(X0) != X0
    | ~ big_f(sK2(X0),sK3(X0,X1)) ),
    inference(cnf_transformation,[],[f22]) ).

cnf(c_53,negated_conjecture,
    ( sK2(X0) != X0
    | sK3(X0,X1) = X1
    | big_f(sK2(X0),sK3(X0,X1)) ),
    inference(cnf_transformation,[],[f21]) ).

cnf(c_54,negated_conjecture,
    ( sK2(X0) = X0
    | big_f(sK2(X0),sK4(X0)) ),
    inference(cnf_transformation,[],[f25]) ).

cnf(c_197,plain,
    ( sK2(X0) != X1
    | sK4(X0) != X2
    | sK2(X0) = X0
    | X1 = sK0 ),
    inference(resolution_lifted,[status(thm)],[c_51,c_54]) ).

cnf(c_198,plain,
    ( sK2(X0) = X0
    | sK2(X0) = sK0 ),
    inference(unflattening,[status(thm)],[c_197]) ).

cnf(c_199,plain,
    sK2(sK0) = sK0,
    inference(instantiation,[status(thm)],[c_198]) ).

cnf(c_291,negated_conjecture,
    ( sK2(X0) = X0
    | big_f(sK2(X0),sK4(X0)) ),
    inference(demodulation,[status(thm)],[c_54]) ).

cnf(c_292,negated_conjecture,
    ( sK2(X0) != X0
    | sK3(X0,X1) = X1
    | big_f(sK2(X0),sK3(X0,X1)) ),
    inference(demodulation,[status(thm)],[c_53]) ).

cnf(c_293,negated_conjecture,
    ( sK3(X0,X1) != X1
    | sK2(X0) != X0
    | ~ big_f(sK2(X0),sK3(X0,X1)) ),
    inference(demodulation,[status(thm)],[c_52]) ).

cnf(c_297,plain,
    ( X0 != X1
    | X2 != X3
    | ~ big_f(X1,X3)
    | big_f(X0,X2) ),
    theory(equality) ).

cnf(c_445,plain,
    ( sK2(X0) = X0
    | sK2(X0) = sK0 ),
    inference(superposition,[status(thm)],[c_291,c_51]) ).

cnf(c_465,plain,
    ( X0 != sK0
    | sK2(X0) = sK0 ),
    inference(equality_factoring,[status(thm)],[c_445]) ).

cnf(c_516,plain,
    sK2(sK0) = sK0,
    inference(equality_resolution,[status(thm)],[c_465]) ).

cnf(c_517,plain,
    ( X0 != sK0
    | X1 != sK1
    | ~ big_f(sK0,sK1)
    | big_f(X0,X1) ),
    inference(instantiation,[status(thm)],[c_297]) ).

cnf(c_520,plain,
    ( sK3(sK0,X0) = X0
    | big_f(sK2(sK0),sK3(sK0,X0)) ),
    inference(superposition,[status(thm)],[c_516,c_292]) ).

cnf(c_523,plain,
    ( sK3(sK0,X0) = X0
    | big_f(sK0,sK3(sK0,X0)) ),
    inference(light_normalisation,[status(thm)],[c_520,c_516]) ).

cnf(c_527,plain,
    ( sK3(X0,sK1) != sK1
    | X1 != sK0
    | ~ big_f(sK0,sK1)
    | big_f(X1,sK3(X0,sK1)) ),
    inference(instantiation,[status(thm)],[c_517]) ).

cnf(c_552,plain,
    ( sK3(sK0,X0) = X0
    | sK3(sK0,X0) = sK1 ),
    inference(superposition,[status(thm)],[c_523,c_50]) ).

cnf(c_738,plain,
    ( sK3(X0,sK1) != sK1
    | sK2(X0) != sK0
    | ~ big_f(sK0,sK1)
    | big_f(sK2(X0),sK3(X0,sK1)) ),
    inference(instantiation,[status(thm)],[c_527]) ).

cnf(c_739,plain,
    ( sK3(X0,sK1) != sK1
    | sK2(X0) != X0
    | ~ big_f(sK2(X0),sK3(X0,sK1)) ),
    inference(instantiation,[status(thm)],[c_293]) ).

cnf(c_740,plain,
    ( sK3(sK0,sK1) != sK1
    | sK2(sK0) != sK0
    | ~ big_f(sK0,sK1)
    | big_f(sK2(sK0),sK3(sK0,sK1)) ),
    inference(instantiation,[status(thm)],[c_738]) ).

cnf(c_741,plain,
    ( sK3(sK0,sK1) != sK1
    | sK2(sK0) != sK0
    | ~ big_f(sK2(sK0),sK3(sK0,sK1)) ),
    inference(instantiation,[status(thm)],[c_739]) ).

cnf(c_764,plain,
    ( X0 != sK1
    | sK3(sK0,X0) = sK1 ),
    inference(equality_factoring,[status(thm)],[c_552]) ).

cnf(c_869,plain,
    sK3(sK0,sK1) = sK1,
    inference(equality_resolution,[status(thm)],[c_764]) ).

cnf(c_870,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_869,c_741,c_740,c_199,c_49]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SYN074+1 : TPTP v8.1.2. Released v2.0.0.
% 0.08/0.14  % Command  : run_iprover %s %d THM
% 0.15/0.36  % Computer : n002.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu May  2 21:07:57 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.21/0.49  Running first-order theorem proving
% 0.21/0.49  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
% 2.19/1.23  % SZS status Started for theBenchmark.p
% 2.19/1.23  % SZS status Theorem for theBenchmark.p
% 2.19/1.23  
% 2.19/1.23  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 2.19/1.23  
% 2.19/1.23  ------  iProver source info
% 2.19/1.23  
% 2.19/1.23  git: date: 2024-05-02 19:28:25 +0000
% 2.19/1.23  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 2.19/1.23  git: non_committed_changes: false
% 2.19/1.23  
% 2.19/1.23  ------ Parsing...
% 2.19/1.23  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 2.19/1.23  
% 2.19/1.23  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 2.19/1.23  
% 2.19/1.23  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 2.19/1.23  
% 2.19/1.23  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.19/1.23  ------ Proving...
% 2.19/1.23  ------ Problem Properties 
% 2.19/1.23  
% 2.19/1.23  
% 2.19/1.23  clauses                                 7
% 2.19/1.23  conjectures                             4
% 2.19/1.23  EPR                                     3
% 2.19/1.23  Horn                                    4
% 2.19/1.23  unary                                   1
% 2.19/1.23  binary                                  3
% 2.19/1.23  lits                                    16
% 2.19/1.23  lits eq                                 9
% 2.19/1.23  fd_pure                                 0
% 2.19/1.23  fd_pseudo                               0
% 2.19/1.23  fd_cond                                 2
% 2.19/1.23  fd_pseudo_cond                          0
% 2.19/1.23  AC symbols                              0
% 2.19/1.23  
% 2.19/1.23  ------ Schedule dynamic 5 is on 
% 2.19/1.23  
% 2.19/1.23  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.19/1.23  
% 2.19/1.23  
% 2.19/1.23  ------ 
% 2.19/1.23  Current options:
% 2.19/1.23  ------ 
% 2.19/1.23  
% 2.19/1.23  
% 2.19/1.23  
% 2.19/1.23  
% 2.19/1.23  ------ Proving...
% 2.19/1.23  
% 2.19/1.23  
% 2.19/1.23  % SZS status Theorem for theBenchmark.p
% 2.19/1.23  
% 2.19/1.23  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.19/1.23  
% 2.19/1.23  
%------------------------------------------------------------------------------