TSTP Solution File: SYN059+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SYN059+1 : TPTP v8.1.2. Released v2.0.0.
% 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 Sep  1 03:04:59 EDT 2023

% Result   : Theorem 0.48s 1.17s
% Output   : CNFRefutation 0.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   66 (  12 unt;   0 def)
%            Number of atoms       :  255 (   0 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  307 ( 118   ~; 117   |;  51   &)
%                                         (   4 <=>;  14  =>;   0  <=;   3 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   2 prp; 0-1 aty)
%            Number of functors    :    6 (   6 usr;   6 con; 0-0 aty)
%            Number of variables   :   83 (  12 sgn;  44   !;  19   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ? [X0] : big_f(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel29_1) ).

fof(f2,axiom,
    ? [X1] : big_g(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel29_2) ).

fof(f3,conjecture,
    ( ( ! [X2] :
          ( big_g(X2)
         => big_j(X2) )
      & ! [X0] :
          ( big_f(X0)
         => big_h(X0) ) )
  <=> ! [X3,X1] :
        ( ( big_g(X1)
          & big_f(X3) )
       => ( big_j(X1)
          & big_h(X3) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel29) ).

fof(f4,negated_conjecture,
    ~ ( ( ! [X2] :
            ( big_g(X2)
           => big_j(X2) )
        & ! [X0] :
            ( big_f(X0)
           => big_h(X0) ) )
    <=> ! [X3,X1] :
          ( ( big_g(X1)
            & big_f(X3) )
         => ( big_j(X1)
            & big_h(X3) ) ) ),
    inference(negated_conjecture,[],[f3]) ).

fof(f5,plain,
    ? [X0] : big_g(X0),
    inference(rectify,[],[f2]) ).

fof(f6,plain,
    ~ ( ( ! [X0] :
            ( big_g(X0)
           => big_j(X0) )
        & ! [X1] :
            ( big_f(X1)
           => big_h(X1) ) )
    <=> ! [X2,X3] :
          ( ( big_g(X3)
            & big_f(X2) )
         => ( big_j(X3)
            & big_h(X2) ) ) ),
    inference(rectify,[],[f4]) ).

fof(f7,plain,
    ( ( ! [X0] :
          ( big_j(X0)
          | ~ big_g(X0) )
      & ! [X1] :
          ( big_h(X1)
          | ~ big_f(X1) ) )
  <~> ! [X2,X3] :
        ( ( big_j(X3)
          & big_h(X2) )
        | ~ big_g(X3)
        | ~ big_f(X2) ) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f8,plain,
    ( ( ! [X0] :
          ( big_j(X0)
          | ~ big_g(X0) )
      & ! [X1] :
          ( big_h(X1)
          | ~ big_f(X1) ) )
  <~> ! [X2,X3] :
        ( ( big_j(X3)
          & big_h(X2) )
        | ~ big_g(X3)
        | ~ big_f(X2) ) ),
    inference(flattening,[],[f7]) ).

fof(f9,plain,
    ( sP0
  <=> ( ! [X0] :
          ( big_j(X0)
          | ~ big_g(X0) )
      & ! [X1] :
          ( big_h(X1)
          | ~ big_f(X1) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f10,plain,
    ( sP0
  <~> ! [X2,X3] :
        ( ( big_j(X3)
          & big_h(X2) )
        | ~ big_g(X3)
        | ~ big_f(X2) ) ),
    inference(definition_folding,[],[f8,f9]) ).

fof(f11,plain,
    ( ? [X0] : big_f(X0)
   => big_f(sK1) ),
    introduced(choice_axiom,[]) ).

fof(f12,plain,
    big_f(sK1),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f1,f11]) ).

fof(f13,plain,
    ( ? [X0] : big_g(X0)
   => big_g(sK2) ),
    introduced(choice_axiom,[]) ).

fof(f14,plain,
    big_g(sK2),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f5,f13]) ).

fof(f15,plain,
    ( ( sP0
      | ? [X0] :
          ( ~ big_j(X0)
          & big_g(X0) )
      | ? [X1] :
          ( ~ big_h(X1)
          & big_f(X1) ) )
    & ( ( ! [X0] :
            ( big_j(X0)
            | ~ big_g(X0) )
        & ! [X1] :
            ( big_h(X1)
            | ~ big_f(X1) ) )
      | ~ sP0 ) ),
    inference(nnf_transformation,[],[f9]) ).

fof(f16,plain,
    ( ( sP0
      | ? [X0] :
          ( ~ big_j(X0)
          & big_g(X0) )
      | ? [X1] :
          ( ~ big_h(X1)
          & big_f(X1) ) )
    & ( ( ! [X0] :
            ( big_j(X0)
            | ~ big_g(X0) )
        & ! [X1] :
            ( big_h(X1)
            | ~ big_f(X1) ) )
      | ~ sP0 ) ),
    inference(flattening,[],[f15]) ).

fof(f17,plain,
    ( ( sP0
      | ? [X0] :
          ( ~ big_j(X0)
          & big_g(X0) )
      | ? [X1] :
          ( ~ big_h(X1)
          & big_f(X1) ) )
    & ( ( ! [X2] :
            ( big_j(X2)
            | ~ big_g(X2) )
        & ! [X3] :
            ( big_h(X3)
            | ~ big_f(X3) ) )
      | ~ sP0 ) ),
    inference(rectify,[],[f16]) ).

fof(f18,plain,
    ( ? [X0] :
        ( ~ big_j(X0)
        & big_g(X0) )
   => ( ~ big_j(sK3)
      & big_g(sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f19,plain,
    ( ? [X1] :
        ( ~ big_h(X1)
        & big_f(X1) )
   => ( ~ big_h(sK4)
      & big_f(sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f20,plain,
    ( ( sP0
      | ( ~ big_j(sK3)
        & big_g(sK3) )
      | ( ~ big_h(sK4)
        & big_f(sK4) ) )
    & ( ( ! [X2] :
            ( big_j(X2)
            | ~ big_g(X2) )
        & ! [X3] :
            ( big_h(X3)
            | ~ big_f(X3) ) )
      | ~ sP0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f17,f19,f18]) ).

fof(f21,plain,
    ( ( ? [X2,X3] :
          ( ( ~ big_j(X3)
            | ~ big_h(X2) )
          & big_g(X3)
          & big_f(X2) )
      | ~ sP0 )
    & ( ! [X2,X3] :
          ( ( big_j(X3)
            & big_h(X2) )
          | ~ big_g(X3)
          | ~ big_f(X2) )
      | sP0 ) ),
    inference(nnf_transformation,[],[f10]) ).

fof(f22,plain,
    ( ( ? [X0,X1] :
          ( ( ~ big_j(X1)
            | ~ big_h(X0) )
          & big_g(X1)
          & big_f(X0) )
      | ~ sP0 )
    & ( ! [X2,X3] :
          ( ( big_j(X3)
            & big_h(X2) )
          | ~ big_g(X3)
          | ~ big_f(X2) )
      | sP0 ) ),
    inference(rectify,[],[f21]) ).

fof(f23,plain,
    ( ? [X0,X1] :
        ( ( ~ big_j(X1)
          | ~ big_h(X0) )
        & big_g(X1)
        & big_f(X0) )
   => ( ( ~ big_j(sK6)
        | ~ big_h(sK5) )
      & big_g(sK6)
      & big_f(sK5) ) ),
    introduced(choice_axiom,[]) ).

fof(f24,plain,
    ( ( ( ( ~ big_j(sK6)
          | ~ big_h(sK5) )
        & big_g(sK6)
        & big_f(sK5) )
      | ~ sP0 )
    & ( ! [X2,X3] :
          ( ( big_j(X3)
            & big_h(X2) )
          | ~ big_g(X3)
          | ~ big_f(X2) )
      | sP0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f22,f23]) ).

fof(f25,plain,
    big_f(sK1),
    inference(cnf_transformation,[],[f12]) ).

fof(f26,plain,
    big_g(sK2),
    inference(cnf_transformation,[],[f14]) ).

fof(f27,plain,
    ! [X3] :
      ( big_h(X3)
      | ~ big_f(X3)
      | ~ sP0 ),
    inference(cnf_transformation,[],[f20]) ).

fof(f28,plain,
    ! [X2] :
      ( big_j(X2)
      | ~ big_g(X2)
      | ~ sP0 ),
    inference(cnf_transformation,[],[f20]) ).

fof(f29,plain,
    ( sP0
    | big_g(sK3)
    | big_f(sK4) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f30,plain,
    ( sP0
    | big_g(sK3)
    | ~ big_h(sK4) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f31,plain,
    ( sP0
    | ~ big_j(sK3)
    | big_f(sK4) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f32,plain,
    ( sP0
    | ~ big_j(sK3)
    | ~ big_h(sK4) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f33,plain,
    ! [X2,X3] :
      ( big_h(X2)
      | ~ big_g(X3)
      | ~ big_f(X2)
      | sP0 ),
    inference(cnf_transformation,[],[f24]) ).

fof(f34,plain,
    ! [X2,X3] :
      ( big_j(X3)
      | ~ big_g(X3)
      | ~ big_f(X2)
      | sP0 ),
    inference(cnf_transformation,[],[f24]) ).

fof(f35,plain,
    ( big_f(sK5)
    | ~ sP0 ),
    inference(cnf_transformation,[],[f24]) ).

fof(f36,plain,
    ( big_g(sK6)
    | ~ sP0 ),
    inference(cnf_transformation,[],[f24]) ).

fof(f37,plain,
    ( ~ big_j(sK6)
    | ~ big_h(sK5)
    | ~ sP0 ),
    inference(cnf_transformation,[],[f24]) ).

cnf(c_49,plain,
    big_f(sK1),
    inference(cnf_transformation,[],[f25]) ).

cnf(c_50,plain,
    big_g(sK2),
    inference(cnf_transformation,[],[f26]) ).

cnf(c_51,plain,
    ( ~ big_j(sK3)
    | ~ big_h(sK4)
    | sP0 ),
    inference(cnf_transformation,[],[f32]) ).

cnf(c_52,plain,
    ( ~ big_j(sK3)
    | big_f(sK4)
    | sP0 ),
    inference(cnf_transformation,[],[f31]) ).

cnf(c_53,plain,
    ( ~ big_h(sK4)
    | big_g(sK3)
    | sP0 ),
    inference(cnf_transformation,[],[f30]) ).

cnf(c_54,plain,
    ( big_f(sK4)
    | big_g(sK3)
    | sP0 ),
    inference(cnf_transformation,[],[f29]) ).

cnf(c_55,plain,
    ( ~ big_g(X0)
    | ~ sP0
    | big_j(X0) ),
    inference(cnf_transformation,[],[f28]) ).

cnf(c_56,plain,
    ( ~ big_f(X0)
    | ~ sP0
    | big_h(X0) ),
    inference(cnf_transformation,[],[f27]) ).

cnf(c_57,negated_conjecture,
    ( ~ big_j(sK6)
    | ~ big_h(sK5)
    | ~ sP0 ),
    inference(cnf_transformation,[],[f37]) ).

cnf(c_58,negated_conjecture,
    ( ~ sP0
    | big_g(sK6) ),
    inference(cnf_transformation,[],[f36]) ).

cnf(c_59,negated_conjecture,
    ( ~ sP0
    | big_f(sK5) ),
    inference(cnf_transformation,[],[f35]) ).

cnf(c_60,negated_conjecture,
    ( ~ big_f(X0)
    | ~ big_g(X1)
    | big_j(X1)
    | sP0 ),
    inference(cnf_transformation,[],[f34]) ).

cnf(c_61,negated_conjecture,
    ( ~ big_f(X0)
    | ~ big_g(X1)
    | big_h(X0)
    | sP0 ),
    inference(cnf_transformation,[],[f33]) ).

cnf(c_66,plain,
    ( big_h(X0)
    | ~ big_g(X1)
    | ~ big_f(X0) ),
    inference(global_subsumption_just,[status(thm)],[c_61,c_56,c_61]) ).

cnf(c_67,negated_conjecture,
    ( ~ big_f(X0)
    | ~ big_g(X1)
    | big_h(X0) ),
    inference(renaming,[status(thm)],[c_66]) ).

cnf(c_110,plain,
    ( ~ big_f(X0)
    | ~ big_g(X1)
    | big_j(X1) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_60,c_55]) ).

cnf(c_139,plain,
    ( ~ big_f(X0)
    | ~ big_g(sK3)
    | big_f(sK4)
    | sP0 ),
    inference(resolution,[status(thm)],[c_52,c_110]) ).

cnf(c_141,plain,
    ( ~ big_f(X0)
    | big_f(sK4)
    | sP0 ),
    inference(global_subsumption_just,[status(thm)],[c_139,c_54,c_139]) ).

cnf(c_153,plain,
    ( ~ big_f(X0)
    | ~ big_g(sK3)
    | ~ big_h(sK4)
    | sP0 ),
    inference(resolution,[status(thm)],[c_51,c_110]) ).

cnf(c_155,plain,
    ( ~ big_f(X0)
    | ~ big_h(sK4)
    | sP0 ),
    inference(global_subsumption_just,[status(thm)],[c_153,c_53,c_153]) ).

cnf(c_167,plain,
    ( ~ big_g(sK6)
    | ~ big_h(sK5)
    | ~ sP0 ),
    inference(resolution,[status(thm)],[c_55,c_57]) ).

cnf(c_168,plain,
    ( ~ big_h(sK5)
    | ~ sP0 ),
    inference(global_subsumption_just,[status(thm)],[c_167,c_58,c_167]) ).

cnf(c_185,plain,
    ( ~ big_f(X0)
    | big_h(X0) ),
    inference(resolution,[status(thm)],[c_50,c_67]) ).

cnf(c_200,plain,
    ( ~ big_f(X0)
    | ~ big_f(sK4)
    | sP0 ),
    inference(resolution,[status(thm)],[c_155,c_185]) ).

cnf(c_202,plain,
    ( ~ big_f(X0)
    | sP0 ),
    inference(global_subsumption_just,[status(thm)],[c_200,c_141,c_200]) ).

cnf(c_211,plain,
    ( ~ big_f(sK5)
    | ~ sP0 ),
    inference(resolution,[status(thm)],[c_185,c_168]) ).

cnf(c_212,plain,
    ~ sP0,
    inference(global_subsumption_just,[status(thm)],[c_211,c_59,c_211]) ).

cnf(c_217,plain,
    ~ big_f(X0),
    inference(backward_subsumption_resolution,[status(thm)],[c_202,c_212]) ).

cnf(c_222,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[c_49,c_217]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SYN059+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n014.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Sat Aug 26 19:48:17 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.48/1.17  % SZS status Started for theBenchmark.p
% 0.48/1.17  % SZS status Theorem for theBenchmark.p
% 0.48/1.17  
% 0.48/1.17  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.48/1.17  
% 0.48/1.17  ------  iProver source info
% 0.48/1.17  
% 0.48/1.17  git: date: 2023-05-31 18:12:56 +0000
% 0.48/1.17  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.48/1.17  git: non_committed_changes: false
% 0.48/1.17  git: last_make_outside_of_git: false
% 0.48/1.17  
% 0.48/1.17  ------ Parsing...
% 0.48/1.17  ------ Clausification by vclausify_rel  & Parsing by iProver...------  preprocesses with Option_epr_non_horn_non_eq
% 0.48/1.17  
% 0.48/1.17  
% 0.48/1.17  ------ Preprocessing... sf_s  rm: 0 0s  sf_e  pe_s  pe:1:0s pe:2:0s
% 0.48/1.17  
% 0.48/1.17  % SZS status Theorem for theBenchmark.p
% 0.48/1.17  
% 0.48/1.17  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.48/1.17  
% 0.48/1.17  
%------------------------------------------------------------------------------