TSTP Solution File: GEO084+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : GEO084+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n028.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 : Wed Aug 30 23:09:16 EDT 2023

% Result   : Theorem 0.42s 1.14s
% Output   : CNFRefutation 0.42s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   42 (   7 unt;   0 def)
%            Number of atoms       :  183 (  11 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  214 (  73   ~;  75   |;  53   &)
%                                         (   6 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-3 aty)
%            Number of variables   :  100 (   0 sgn;  70   !;  19   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1] :
      ( part_of(X1,X0)
    <=> ! [X2] :
          ( incident_c(X2,X1)
         => incident_c(X2,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',part_of_defn) ).

fof(f2,axiom,
    ! [X0,X1,X3] :
      ( sum(X1,X3) = X0
    <=> ! [X4] :
          ( incident_c(X4,X0)
        <=> ( incident_c(X4,X3)
            | incident_c(X4,X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_defn) ).

fof(f17,conjecture,
    ! [X1,X3,X5,X2] :
      ( ( meet(X2,X1,X3)
        & part_of(X3,X5)
        & part_of(X1,X5) )
     => part_of(sum(X1,X3),X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_6_2) ).

fof(f18,negated_conjecture,
    ~ ! [X1,X3,X5,X2] :
        ( ( meet(X2,X1,X3)
          & part_of(X3,X5)
          & part_of(X1,X5) )
       => part_of(sum(X1,X3),X5) ),
    inference(negated_conjecture,[],[f17]) ).

fof(f19,plain,
    ! [X0,X1,X2] :
      ( sum(X1,X2) = X0
    <=> ! [X3] :
          ( incident_c(X3,X0)
        <=> ( incident_c(X3,X2)
            | incident_c(X3,X1) ) ) ),
    inference(rectify,[],[f2]) ).

fof(f32,plain,
    ~ ! [X0,X1,X2,X3] :
        ( ( meet(X3,X0,X1)
          & part_of(X1,X2)
          & part_of(X0,X2) )
       => part_of(sum(X0,X1),X2) ),
    inference(rectify,[],[f18]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( part_of(X1,X0)
    <=> ! [X2] :
          ( incident_c(X2,X0)
          | ~ incident_c(X2,X1) ) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f54,plain,
    ? [X0,X1,X2,X3] :
      ( ~ part_of(sum(X0,X1),X2)
      & meet(X3,X0,X1)
      & part_of(X1,X2)
      & part_of(X0,X2) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f55,plain,
    ? [X0,X1,X2,X3] :
      ( ~ part_of(sum(X0,X1),X2)
      & meet(X3,X0,X1)
      & part_of(X1,X2)
      & part_of(X0,X2) ),
    inference(flattening,[],[f54]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( ( part_of(X1,X0)
        | ? [X2] :
            ( ~ incident_c(X2,X0)
            & incident_c(X2,X1) ) )
      & ( ! [X2] :
            ( incident_c(X2,X0)
            | ~ incident_c(X2,X1) )
        | ~ part_of(X1,X0) ) ),
    inference(nnf_transformation,[],[f35]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( ( part_of(X1,X0)
        | ? [X2] :
            ( ~ incident_c(X2,X0)
            & incident_c(X2,X1) ) )
      & ( ! [X3] :
            ( incident_c(X3,X0)
            | ~ incident_c(X3,X1) )
        | ~ part_of(X1,X0) ) ),
    inference(rectify,[],[f56]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ incident_c(X2,X0)
          & incident_c(X2,X1) )
     => ( ~ incident_c(sK0(X0,X1),X0)
        & incident_c(sK0(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( ( part_of(X1,X0)
        | ( ~ incident_c(sK0(X0,X1),X0)
          & incident_c(sK0(X0,X1),X1) ) )
      & ( ! [X3] :
            ( incident_c(X3,X0)
            | ~ incident_c(X3,X1) )
        | ~ part_of(X1,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f57,f58]) ).

fof(f60,plain,
    ! [X0,X1,X2] :
      ( ( sum(X1,X2) = X0
        | ? [X3] :
            ( ( ( ~ incident_c(X3,X2)
                & ~ incident_c(X3,X1) )
              | ~ incident_c(X3,X0) )
            & ( incident_c(X3,X2)
              | incident_c(X3,X1)
              | incident_c(X3,X0) ) ) )
      & ( ! [X3] :
            ( ( incident_c(X3,X0)
              | ( ~ incident_c(X3,X2)
                & ~ incident_c(X3,X1) ) )
            & ( incident_c(X3,X2)
              | incident_c(X3,X1)
              | ~ incident_c(X3,X0) ) )
        | sum(X1,X2) != X0 ) ),
    inference(nnf_transformation,[],[f19]) ).

fof(f61,plain,
    ! [X0,X1,X2] :
      ( ( sum(X1,X2) = X0
        | ? [X3] :
            ( ( ( ~ incident_c(X3,X2)
                & ~ incident_c(X3,X1) )
              | ~ incident_c(X3,X0) )
            & ( incident_c(X3,X2)
              | incident_c(X3,X1)
              | incident_c(X3,X0) ) ) )
      & ( ! [X3] :
            ( ( incident_c(X3,X0)
              | ( ~ incident_c(X3,X2)
                & ~ incident_c(X3,X1) ) )
            & ( incident_c(X3,X2)
              | incident_c(X3,X1)
              | ~ incident_c(X3,X0) ) )
        | sum(X1,X2) != X0 ) ),
    inference(flattening,[],[f60]) ).

fof(f62,plain,
    ! [X0,X1,X2] :
      ( ( sum(X1,X2) = X0
        | ? [X3] :
            ( ( ( ~ incident_c(X3,X2)
                & ~ incident_c(X3,X1) )
              | ~ incident_c(X3,X0) )
            & ( incident_c(X3,X2)
              | incident_c(X3,X1)
              | incident_c(X3,X0) ) ) )
      & ( ! [X4] :
            ( ( incident_c(X4,X0)
              | ( ~ incident_c(X4,X2)
                & ~ incident_c(X4,X1) ) )
            & ( incident_c(X4,X2)
              | incident_c(X4,X1)
              | ~ incident_c(X4,X0) ) )
        | sum(X1,X2) != X0 ) ),
    inference(rectify,[],[f61]) ).

fof(f63,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ( ~ incident_c(X3,X2)
              & ~ incident_c(X3,X1) )
            | ~ incident_c(X3,X0) )
          & ( incident_c(X3,X2)
            | incident_c(X3,X1)
            | incident_c(X3,X0) ) )
     => ( ( ( ~ incident_c(sK1(X0,X1,X2),X2)
            & ~ incident_c(sK1(X0,X1,X2),X1) )
          | ~ incident_c(sK1(X0,X1,X2),X0) )
        & ( incident_c(sK1(X0,X1,X2),X2)
          | incident_c(sK1(X0,X1,X2),X1)
          | incident_c(sK1(X0,X1,X2),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f64,plain,
    ! [X0,X1,X2] :
      ( ( sum(X1,X2) = X0
        | ( ( ( ~ incident_c(sK1(X0,X1,X2),X2)
              & ~ incident_c(sK1(X0,X1,X2),X1) )
            | ~ incident_c(sK1(X0,X1,X2),X0) )
          & ( incident_c(sK1(X0,X1,X2),X2)
            | incident_c(sK1(X0,X1,X2),X1)
            | incident_c(sK1(X0,X1,X2),X0) ) ) )
      & ( ! [X4] :
            ( ( incident_c(X4,X0)
              | ( ~ incident_c(X4,X2)
                & ~ incident_c(X4,X1) ) )
            & ( incident_c(X4,X2)
              | incident_c(X4,X1)
              | ~ incident_c(X4,X0) ) )
        | sum(X1,X2) != X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f62,f63]) ).

fof(f93,plain,
    ( ? [X0,X1,X2,X3] :
        ( ~ part_of(sum(X0,X1),X2)
        & meet(X3,X0,X1)
        & part_of(X1,X2)
        & part_of(X0,X2) )
   => ( ~ part_of(sum(sK13,sK14),sK15)
      & meet(sK16,sK13,sK14)
      & part_of(sK14,sK15)
      & part_of(sK13,sK15) ) ),
    introduced(choice_axiom,[]) ).

fof(f94,plain,
    ( ~ part_of(sum(sK13,sK14),sK15)
    & meet(sK16,sK13,sK14)
    & part_of(sK14,sK15)
    & part_of(sK13,sK15) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16])],[f55,f93]) ).

fof(f95,plain,
    ! [X3,X0,X1] :
      ( incident_c(X3,X0)
      | ~ incident_c(X3,X1)
      | ~ part_of(X1,X0) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f96,plain,
    ! [X0,X1] :
      ( part_of(X1,X0)
      | incident_c(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f97,plain,
    ! [X0,X1] :
      ( part_of(X1,X0)
      | ~ incident_c(sK0(X0,X1),X0) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f98,plain,
    ! [X2,X0,X1,X4] :
      ( incident_c(X4,X2)
      | incident_c(X4,X1)
      | ~ incident_c(X4,X0)
      | sum(X1,X2) != X0 ),
    inference(cnf_transformation,[],[f64]) ).

fof(f136,plain,
    part_of(sK13,sK15),
    inference(cnf_transformation,[],[f94]) ).

fof(f137,plain,
    part_of(sK14,sK15),
    inference(cnf_transformation,[],[f94]) ).

fof(f139,plain,
    ~ part_of(sum(sK13,sK14),sK15),
    inference(cnf_transformation,[],[f94]) ).

fof(f142,plain,
    ! [X2,X1,X4] :
      ( incident_c(X4,X2)
      | incident_c(X4,X1)
      | ~ incident_c(X4,sum(X1,X2)) ),
    inference(equality_resolution,[],[f98]) ).

cnf(c_49,plain,
    ( ~ incident_c(sK0(X0,X1),X0)
    | part_of(X1,X0) ),
    inference(cnf_transformation,[],[f97]) ).

cnf(c_50,plain,
    ( incident_c(sK0(X0,X1),X1)
    | part_of(X1,X0) ),
    inference(cnf_transformation,[],[f96]) ).

cnf(c_51,plain,
    ( ~ part_of(X0,X1)
    | ~ incident_c(X2,X0)
    | incident_c(X2,X1) ),
    inference(cnf_transformation,[],[f95]) ).

cnf(c_57,plain,
    ( ~ incident_c(X0,sum(X1,X2))
    | incident_c(X0,X1)
    | incident_c(X0,X2) ),
    inference(cnf_transformation,[],[f142]) ).

cnf(c_90,negated_conjecture,
    ~ part_of(sum(sK13,sK14),sK15),
    inference(cnf_transformation,[],[f139]) ).

cnf(c_92,negated_conjecture,
    part_of(sK14,sK15),
    inference(cnf_transformation,[],[f137]) ).

cnf(c_93,negated_conjecture,
    part_of(sK13,sK15),
    inference(cnf_transformation,[],[f136]) ).

cnf(c_2010,plain,
    ( ~ incident_c(sK0(sK15,sum(sK13,sK14)),sK15)
    | part_of(sum(sK13,sK14),sK15) ),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_2016,plain,
    ( incident_c(sK0(sK15,sum(sK13,sK14)),sum(sK13,sK14))
    | part_of(sum(sK13,sK14),sK15) ),
    inference(instantiation,[status(thm)],[c_50]) ).

cnf(c_2210,plain,
    ( ~ incident_c(sK0(sK15,sum(sK13,sK14)),sum(sK13,sK14))
    | incident_c(sK0(sK15,sum(sK13,sK14)),sK13)
    | incident_c(sK0(sK15,sum(sK13,sK14)),sK14) ),
    inference(instantiation,[status(thm)],[c_57]) ).

cnf(c_6758,plain,
    ( ~ incident_c(sK0(sK15,sum(sK13,sK14)),X0)
    | ~ part_of(X0,sK15)
    | incident_c(sK0(sK15,sum(sK13,sK14)),sK15) ),
    inference(instantiation,[status(thm)],[c_51]) ).

cnf(c_6759,plain,
    ( ~ incident_c(sK0(sK15,sum(sK13,sK14)),sK13)
    | ~ part_of(sK13,sK15)
    | incident_c(sK0(sK15,sum(sK13,sK14)),sK15) ),
    inference(instantiation,[status(thm)],[c_6758]) ).

cnf(c_10056,plain,
    ( ~ incident_c(sK0(sK15,sum(sK13,sK14)),sK14)
    | ~ part_of(sK14,sK15)
    | incident_c(sK0(sK15,sum(sK13,sK14)),sK15) ),
    inference(instantiation,[status(thm)],[c_6758]) ).

cnf(c_10057,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_10056,c_6759,c_2210,c_2016,c_2010,c_90,c_92,c_93]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13  % Problem  : GEO084+1 : TPTP v8.1.2. Released v2.4.0.
% 0.10/0.14  % Command  : run_iprover %s %d THM
% 0.11/0.35  % Computer : n028.cluster.edu
% 0.11/0.35  % Model    : x86_64 x86_64
% 0.11/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35  % Memory   : 8042.1875MB
% 0.11/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.35  % CPULimit : 300
% 0.11/0.35  % WCLimit  : 300
% 0.11/0.35  % DateTime : Tue Aug 29 21:37:41 EDT 2023
% 0.11/0.35  % CPUTime  : 
% 0.18/0.46  Running first-order theorem proving
% 0.18/0.46  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.42/1.14  % SZS status Started for theBenchmark.p
% 0.42/1.14  % SZS status Theorem for theBenchmark.p
% 0.42/1.14  
% 0.42/1.14  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.42/1.14  
% 0.42/1.14  ------  iProver source info
% 0.42/1.14  
% 0.42/1.14  git: date: 2023-05-31 18:12:56 +0000
% 0.42/1.14  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.42/1.14  git: non_committed_changes: false
% 0.42/1.14  git: last_make_outside_of_git: false
% 0.42/1.14  
% 0.42/1.14  ------ Parsing...
% 0.42/1.14  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 0.42/1.14  
% 0.42/1.14  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 0.42/1.14  
% 0.42/1.14  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 0.42/1.14  
% 0.42/1.14  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 0.42/1.14  ------ Proving...
% 0.42/1.14  ------ Problem Properties 
% 0.42/1.14  
% 0.42/1.14  
% 0.42/1.14  clauses                                 45
% 0.42/1.14  conjectures                             4
% 0.42/1.14  EPR                                     16
% 0.42/1.14  Horn                                    29
% 0.42/1.14  unary                                   5
% 0.42/1.14  binary                                  16
% 0.42/1.14  lits                                    133
% 0.42/1.14  lits eq                                 12
% 0.42/1.14  fd_pure                                 0
% 0.42/1.14  fd_pseudo                               0
% 0.42/1.14  fd_cond                                 0
% 0.42/1.14  fd_pseudo_cond                          7
% 0.42/1.14  AC symbols                              0
% 0.42/1.14  
% 0.42/1.14  ------ Schedule dynamic 5 is on 
% 0.42/1.14  
% 0.42/1.14  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.42/1.14  
% 0.42/1.14  
% 0.42/1.14  ------ 
% 0.42/1.14  Current options:
% 0.42/1.14  ------ 
% 0.42/1.14  
% 0.42/1.14  
% 0.42/1.14  
% 0.42/1.14  
% 0.42/1.14  ------ Proving...
% 0.42/1.14  
% 0.42/1.14  
% 0.42/1.14  % SZS status Theorem for theBenchmark.p
% 0.42/1.14  
% 0.42/1.14  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.42/1.14  
% 0.42/1.14  
%------------------------------------------------------------------------------