TSTP Solution File: REL009+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : REL009+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n015.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 02:56:35 EDT 2024

% Result   : Theorem 209.24s 27.76s
% Output   : CNFRefutation 209.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   43 (  34 unt;   0 def)
%            Number of atoms       :   60 (  59 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   38 (  21   ~;   8   |;   6   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   72 (   0 sgn  32   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1] : join(X0,X1) = join(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity) ).

fof(f2,axiom,
    ! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux2_join_associativity) ).

fof(f7,axiom,
    ! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_distributivity) ).

fof(f8,axiom,
    ! [X0] : converse(converse(X0)) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence) ).

fof(f9,axiom,
    ! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_additivity) ).

fof(f10,axiom,
    ! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_multiplicativity) ).

fof(f14,conjecture,
    ! [X0,X1,X2] :
      ( join(X0,X1) = X1
     => ( composition(X2,X1) = join(composition(X2,X0),composition(X2,X1))
        & composition(X1,X2) = join(composition(X0,X2),composition(X1,X2)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

fof(f15,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( join(X0,X1) = X1
       => ( composition(X2,X1) = join(composition(X2,X0),composition(X2,X1))
          & composition(X1,X2) = join(composition(X0,X2),composition(X1,X2)) ) ),
    inference(negated_conjecture,[],[f14]) ).

fof(f16,plain,
    ? [X0,X1,X2] :
      ( ( composition(X2,X1) != join(composition(X2,X0),composition(X2,X1))
        | composition(X1,X2) != join(composition(X0,X2),composition(X1,X2)) )
      & join(X0,X1) = X1 ),
    inference(ennf_transformation,[],[f15]) ).

fof(f17,plain,
    ( ? [X0,X1,X2] :
        ( ( composition(X2,X1) != join(composition(X2,X0),composition(X2,X1))
          | composition(X1,X2) != join(composition(X0,X2),composition(X1,X2)) )
        & join(X0,X1) = X1 )
   => ( ( composition(sK2,sK1) != join(composition(sK2,sK0),composition(sK2,sK1))
        | composition(sK1,sK2) != join(composition(sK0,sK2),composition(sK1,sK2)) )
      & sK1 = join(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ( ( composition(sK2,sK1) != join(composition(sK2,sK0),composition(sK2,sK1))
      | composition(sK1,sK2) != join(composition(sK0,sK2),composition(sK1,sK2)) )
    & sK1 = join(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f16,f17]) ).

fof(f19,plain,
    ! [X0,X1] : join(X0,X1) = join(X1,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f20,plain,
    ! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
    inference(cnf_transformation,[],[f2]) ).

fof(f25,plain,
    ! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
    inference(cnf_transformation,[],[f7]) ).

fof(f26,plain,
    ! [X0] : converse(converse(X0)) = X0,
    inference(cnf_transformation,[],[f8]) ).

fof(f27,plain,
    ! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
    inference(cnf_transformation,[],[f9]) ).

fof(f28,plain,
    ! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
    inference(cnf_transformation,[],[f10]) ).

fof(f32,plain,
    sK1 = join(sK0,sK1),
    inference(cnf_transformation,[],[f18]) ).

fof(f33,plain,
    ( composition(sK2,sK1) != join(composition(sK2,sK0),composition(sK2,sK1))
    | composition(sK1,sK2) != join(composition(sK0,sK2),composition(sK1,sK2)) ),
    inference(cnf_transformation,[],[f18]) ).

cnf(c_49,plain,
    join(X0,X1) = join(X1,X0),
    inference(cnf_transformation,[],[f19]) ).

cnf(c_50,plain,
    join(join(X0,X1),X2) = join(X0,join(X1,X2)),
    inference(cnf_transformation,[],[f20]) ).

cnf(c_54,plain,
    join(composition(X0,X1),composition(X2,X1)) = composition(join(X0,X2),X1),
    inference(cnf_transformation,[],[f25]) ).

cnf(c_55,plain,
    converse(converse(X0)) = X0,
    inference(cnf_transformation,[],[f26]) ).

cnf(c_56,plain,
    join(converse(X0),converse(X1)) = converse(join(X0,X1)),
    inference(cnf_transformation,[],[f27]) ).

cnf(c_57,plain,
    composition(converse(X0),converse(X1)) = converse(composition(X1,X0)),
    inference(cnf_transformation,[],[f28]) ).

cnf(c_61,negated_conjecture,
    ( join(composition(sK2,sK0),composition(sK2,sK1)) != composition(sK2,sK1)
    | join(composition(sK0,sK2),composition(sK1,sK2)) != composition(sK1,sK2) ),
    inference(cnf_transformation,[],[f33]) ).

cnf(c_62,negated_conjecture,
    join(sK0,sK1) = sK1,
    inference(cnf_transformation,[],[f32]) ).

cnf(c_77,negated_conjecture,
    ( join(composition(sK2,sK1),composition(sK2,sK0)) != composition(sK2,sK1)
    | join(composition(sK1,sK2),composition(sK0,sK2)) != composition(sK1,sK2) ),
    inference(theory_normalisation,[status(thm)],[c_61,c_50,c_49]) ).

cnf(c_78,negated_conjecture,
    join(sK1,sK0) = sK1,
    inference(theory_normalisation,[status(thm)],[c_62,c_50,c_49]) ).

cnf(c_112,plain,
    ( join(composition(sK2,sK1),composition(sK2,sK0)) != composition(sK2,sK1)
    | composition(sK1,sK2) != composition(sK1,sK2) ),
    inference(demodulation,[status(thm)],[c_77,c_54,c_78]) ).

cnf(c_113,plain,
    join(composition(sK2,sK1),composition(sK2,sK0)) != composition(sK2,sK1),
    inference(equality_resolution_simp,[status(thm)],[c_112]) ).

cnf(c_79389,plain,
    converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
    inference(superposition,[status(thm)],[c_55,c_57]) ).

cnf(c_79517,plain,
    join(converse(X0),converse(X1)) = converse(join(X1,X0)),
    inference(superposition,[status(thm)],[c_56,c_49]) ).

cnf(c_79522,plain,
    join(converse(composition(X0,X1)),composition(X2,converse(X0))) = composition(join(converse(X1),X2),converse(X0)),
    inference(superposition,[status(thm)],[c_57,c_54]) ).

cnf(c_94512,plain,
    converse(join(converse(X0),X1)) = join(converse(X1),X0),
    inference(superposition,[status(thm)],[c_55,c_79517]) ).

cnf(c_94595,plain,
    composition(converse(X0),join(converse(X1),X2)) = converse(composition(join(converse(X2),X1),X0)),
    inference(superposition,[status(thm)],[c_94512,c_57]) ).

cnf(c_105830,plain,
    join(converse(X0),composition(converse(X1),X2)) = converse(join(X0,composition(converse(X2),X1))),
    inference(superposition,[status(thm)],[c_79389,c_56]) ).

cnf(c_105996,plain,
    join(converse(converse(composition(X0,X1))),composition(converse(converse(X0)),X2)) = converse(composition(join(converse(X1),converse(X2)),converse(X0))),
    inference(superposition,[status(thm)],[c_79522,c_105830]) ).

cnf(c_106084,plain,
    join(composition(X0,X1),composition(X0,X2)) = composition(X0,join(X2,X1)),
    inference(demodulation,[status(thm)],[c_105996,c_55,c_94595]) ).

cnf(c_106093,plain,
    composition(sK2,join(sK0,sK1)) != composition(sK2,sK1),
    inference(demodulation,[status(thm)],[c_113,c_106084]) ).

cnf(c_106094,plain,
    composition(sK2,join(sK1,sK0)) != composition(sK2,sK1),
    inference(theory_normalisation,[status(thm)],[c_106093,c_50,c_49]) ).

cnf(c_106095,plain,
    composition(sK2,sK1) != composition(sK2,sK1),
    inference(demodulation,[status(thm)],[c_106094,c_78]) ).

cnf(c_106096,plain,
    $false,
    inference(equality_resolution_simp,[status(thm)],[c_106095]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : REL009+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12  % Command  : run_iprover %s %d THM
% 0.11/0.33  % Computer : n015.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Thu May  2 20:16:51 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 0.18/0.45  Running first-order theorem proving
% 0.18/0.45  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 209.24/27.76  % SZS status Started for theBenchmark.p
% 209.24/27.76  % SZS status Theorem for theBenchmark.p
% 209.24/27.76  
% 209.24/27.76  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 209.24/27.76  
% 209.24/27.76  ------  iProver source info
% 209.24/27.76  
% 209.24/27.76  git: date: 2024-05-02 19:28:25 +0000
% 209.24/27.76  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 209.24/27.76  git: non_committed_changes: false
% 209.24/27.76  
% 209.24/27.76  ------ Parsing...
% 209.24/27.76  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 209.24/27.76  
% 209.24/27.76  ------ Preprocessing... sup_sim: 2  sf_s  rm: 0 0s  sf_e  pe_s  pe_e 
% 209.24/27.76  
% 209.24/27.76  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 209.24/27.76  
% 209.24/27.76  ------ Preprocessing... sf_s  rm: 0 0s  sf_e 
% 209.24/27.76  ------ Proving...
% 209.24/27.76  ------ Problem Properties 
% 209.24/27.76  
% 209.24/27.76  
% 209.24/27.76  clauses                                 14
% 209.24/27.76  conjectures                             1
% 209.24/27.76  EPR                                     0
% 209.24/27.76  Horn                                    14
% 209.24/27.76  unary                                   14
% 209.24/27.76  binary                                  0
% 209.24/27.76  lits                                    14
% 209.24/27.76  lits eq                                 14
% 209.24/27.76  fd_pure                                 0
% 209.24/27.76  fd_pseudo                               0
% 209.24/27.76  fd_cond                                 0
% 209.24/27.76  fd_pseudo_cond                          0
% 209.24/27.76  AC symbols                              1
% 209.24/27.76  
% 209.24/27.76  ------ Input Options Time Limit: Unbounded
% 209.24/27.76  
% 209.24/27.76  
% 209.24/27.76  ------ 
% 209.24/27.76  Current options:
% 209.24/27.76  ------ 
% 209.24/27.76  
% 209.24/27.76  
% 209.24/27.76  
% 209.24/27.76  
% 209.24/27.76  ------ Proving...
% 209.24/27.76  
% 209.24/27.76  
% 209.24/27.76  % SZS status Theorem for theBenchmark.p
% 209.24/27.76  
% 209.24/27.76  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 209.24/27.76  
% 209.24/27.77  
%------------------------------------------------------------------------------