TSTP Solution File: COM007+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : COM007+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n024.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 02:10:24 EDT 2024

% Result   : Theorem 0.46s 1.15s
% Output   : CNFRefutation 0.46s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   84 (  15 unt;   0 def)
%            Number of atoms       :  197 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  208 (  95   ~;  95   |;  10   &)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   2 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :  107 (   0 sgn  64   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ( reflexive_rewrite(a,c)
    & reflexive_rewrite(a,b) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption) ).

fof(f2,axiom,
    ! [X0] :
      ( ( reflexive_rewrite(c,X0)
        & reflexive_rewrite(b,X0) )
     => goal ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_ax) ).

fof(f3,axiom,
    ! [X0] : equalish(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( equalish(X0,X1)
     => equalish(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmtery) ).

fof(f5,axiom,
    ! [X0,X1,X2] :
      ( ( reflexive_rewrite(X1,X2)
        & equalish(X0,X1) )
     => reflexive_rewrite(X0,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( equalish(X0,X1)
     => reflexive_rewrite(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equalish_in_reflexive_rewrite) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( rewrite(X0,X1)
     => reflexive_rewrite(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rewrite_in_reflexive_rewrite) ).

fof(f8,axiom,
    ! [X0,X1] :
      ( reflexive_rewrite(X0,X1)
     => ( rewrite(X0,X1)
        | equalish(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equalish_or_rewrite) ).

fof(f9,axiom,
    ! [X0,X1,X2] :
      ( ( rewrite(X0,X2)
        & rewrite(X0,X1) )
     => ? [X3] :
          ( rewrite(X2,X3)
          & rewrite(X1,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rewrite_diamond) ).

fof(f10,conjecture,
    goal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_to_be_proved) ).

fof(f11,negated_conjecture,
    ~ goal,
    inference(negated_conjecture,[],[f10]) ).

fof(f12,plain,
    ~ goal,
    inference(flattening,[],[f11]) ).

fof(f13,plain,
    ! [X0] :
      ( goal
      | ~ reflexive_rewrite(c,X0)
      | ~ reflexive_rewrite(b,X0) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f14,plain,
    ! [X0] :
      ( goal
      | ~ reflexive_rewrite(c,X0)
      | ~ reflexive_rewrite(b,X0) ),
    inference(flattening,[],[f13]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( equalish(X1,X0)
      | ~ equalish(X0,X1) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f16,plain,
    ! [X0,X1,X2] :
      ( reflexive_rewrite(X0,X2)
      | ~ reflexive_rewrite(X1,X2)
      | ~ equalish(X0,X1) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f17,plain,
    ! [X0,X1,X2] :
      ( reflexive_rewrite(X0,X2)
      | ~ reflexive_rewrite(X1,X2)
      | ~ equalish(X0,X1) ),
    inference(flattening,[],[f16]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( reflexive_rewrite(X0,X1)
      | ~ equalish(X0,X1) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( reflexive_rewrite(X0,X1)
      | ~ rewrite(X0,X1) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( rewrite(X0,X1)
      | equalish(X0,X1)
      | ~ reflexive_rewrite(X0,X1) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( rewrite(X0,X1)
      | equalish(X0,X1)
      | ~ reflexive_rewrite(X0,X1) ),
    inference(flattening,[],[f20]) ).

fof(f22,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( rewrite(X2,X3)
          & rewrite(X1,X3) )
      | ~ rewrite(X0,X2)
      | ~ rewrite(X0,X1) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f23,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( rewrite(X2,X3)
          & rewrite(X1,X3) )
      | ~ rewrite(X0,X2)
      | ~ rewrite(X0,X1) ),
    inference(flattening,[],[f22]) ).

fof(f24,plain,
    ! [X1,X2] :
      ( ? [X3] :
          ( rewrite(X2,X3)
          & rewrite(X1,X3) )
     => ( rewrite(X2,sK0(X1,X2))
        & rewrite(X1,sK0(X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( ( rewrite(X2,sK0(X1,X2))
        & rewrite(X1,sK0(X1,X2)) )
      | ~ rewrite(X0,X2)
      | ~ rewrite(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f23,f24]) ).

fof(f26,plain,
    reflexive_rewrite(a,b),
    inference(cnf_transformation,[],[f1]) ).

fof(f27,plain,
    reflexive_rewrite(a,c),
    inference(cnf_transformation,[],[f1]) ).

fof(f28,plain,
    ! [X0] :
      ( goal
      | ~ reflexive_rewrite(c,X0)
      | ~ reflexive_rewrite(b,X0) ),
    inference(cnf_transformation,[],[f14]) ).

fof(f29,plain,
    ! [X0] : equalish(X0,X0),
    inference(cnf_transformation,[],[f3]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( equalish(X1,X0)
      | ~ equalish(X0,X1) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f31,plain,
    ! [X2,X0,X1] :
      ( reflexive_rewrite(X0,X2)
      | ~ reflexive_rewrite(X1,X2)
      | ~ equalish(X0,X1) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( reflexive_rewrite(X0,X1)
      | ~ equalish(X0,X1) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( reflexive_rewrite(X0,X1)
      | ~ rewrite(X0,X1) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( rewrite(X0,X1)
      | equalish(X0,X1)
      | ~ reflexive_rewrite(X0,X1) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f35,plain,
    ! [X2,X0,X1] :
      ( rewrite(X1,sK0(X1,X2))
      | ~ rewrite(X0,X2)
      | ~ rewrite(X0,X1) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f36,plain,
    ! [X2,X0,X1] :
      ( rewrite(X2,sK0(X1,X2))
      | ~ rewrite(X0,X2)
      | ~ rewrite(X0,X1) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f37,plain,
    ~ goal,
    inference(cnf_transformation,[],[f12]) ).

cnf(c_49,plain,
    reflexive_rewrite(a,c),
    inference(cnf_transformation,[],[f27]) ).

cnf(c_50,plain,
    reflexive_rewrite(a,b),
    inference(cnf_transformation,[],[f26]) ).

cnf(c_51,plain,
    ( ~ reflexive_rewrite(c,X0)
    | ~ reflexive_rewrite(b,X0)
    | goal ),
    inference(cnf_transformation,[],[f28]) ).

cnf(c_52,plain,
    equalish(X0,X0),
    inference(cnf_transformation,[],[f29]) ).

cnf(c_53,plain,
    ( ~ equalish(X0,X1)
    | equalish(X1,X0) ),
    inference(cnf_transformation,[],[f30]) ).

cnf(c_54,plain,
    ( ~ reflexive_rewrite(X0,X1)
    | ~ equalish(X2,X0)
    | reflexive_rewrite(X2,X1) ),
    inference(cnf_transformation,[],[f31]) ).

cnf(c_55,plain,
    ( ~ equalish(X0,X1)
    | reflexive_rewrite(X0,X1) ),
    inference(cnf_transformation,[],[f32]) ).

cnf(c_56,plain,
    ( ~ rewrite(X0,X1)
    | reflexive_rewrite(X0,X1) ),
    inference(cnf_transformation,[],[f33]) ).

cnf(c_57,plain,
    ( ~ reflexive_rewrite(X0,X1)
    | equalish(X0,X1)
    | rewrite(X0,X1) ),
    inference(cnf_transformation,[],[f34]) ).

cnf(c_58,plain,
    ( ~ rewrite(X0,X1)
    | ~ rewrite(X0,X2)
    | rewrite(X2,sK0(X1,X2)) ),
    inference(cnf_transformation,[],[f36]) ).

cnf(c_59,plain,
    ( ~ rewrite(X0,X1)
    | ~ rewrite(X0,X2)
    | rewrite(X1,sK0(X1,X2)) ),
    inference(cnf_transformation,[],[f35]) ).

cnf(c_60,negated_conjecture,
    ~ goal,
    inference(cnf_transformation,[],[f37]) ).

cnf(c_66,plain,
    ( ~ reflexive_rewrite(b,X0)
    | ~ reflexive_rewrite(c,X0) ),
    inference(global_subsumption_just,[status(thm)],[c_51,c_60,c_51]) ).

cnf(c_67,plain,
    ( ~ reflexive_rewrite(c,X0)
    | ~ reflexive_rewrite(b,X0) ),
    inference(renaming,[status(thm)],[c_66]) ).

cnf(c_163,plain,
    ( ~ equalish(c,X0)
    | reflexive_rewrite(c,X0) ),
    inference(instantiation,[status(thm)],[c_55]) ).

cnf(c_165,plain,
    ( ~ rewrite(c,X0)
    | reflexive_rewrite(c,X0) ),
    inference(instantiation,[status(thm)],[c_56]) ).

cnf(c_167,plain,
    ( ~ reflexive_rewrite(X0,X1)
    | ~ equalish(c,X0)
    | reflexive_rewrite(c,X1) ),
    inference(instantiation,[status(thm)],[c_54]) ).

cnf(c_168,plain,
    ( ~ equalish(c,c)
    | reflexive_rewrite(c,c) ),
    inference(instantiation,[status(thm)],[c_163]) ).

cnf(c_169,plain,
    equalish(c,c),
    inference(instantiation,[status(thm)],[c_52]) ).

cnf(c_170,plain,
    ( ~ equalish(X0,c)
    | equalish(c,X0) ),
    inference(instantiation,[status(thm)],[c_53]) ).

cnf(c_171,plain,
    ( ~ equalish(a,c)
    | equalish(c,a) ),
    inference(instantiation,[status(thm)],[c_170]) ).

cnf(c_177,plain,
    ( ~ reflexive_rewrite(c,c)
    | ~ reflexive_rewrite(b,c) ),
    inference(instantiation,[status(thm)],[c_67]) ).

cnf(c_183,plain,
    ( ~ reflexive_rewrite(X0,c)
    | equalish(X0,c)
    | rewrite(X0,c) ),
    inference(instantiation,[status(thm)],[c_57]) ).

cnf(c_184,plain,
    ( ~ reflexive_rewrite(a,c)
    | equalish(a,c)
    | rewrite(a,c) ),
    inference(instantiation,[status(thm)],[c_183]) ).

cnf(c_192,plain,
    ( ~ reflexive_rewrite(X0,c)
    | ~ equalish(b,X0)
    | reflexive_rewrite(b,c) ),
    inference(instantiation,[status(thm)],[c_54]) ).

cnf(c_193,plain,
    ( ~ reflexive_rewrite(a,c)
    | ~ equalish(b,a)
    | reflexive_rewrite(b,c) ),
    inference(instantiation,[status(thm)],[c_192]) ).

cnf(c_194,plain,
    ( ~ rewrite(b,X0)
    | reflexive_rewrite(b,X0) ),
    inference(instantiation,[status(thm)],[c_56]) ).

cnf(c_195,plain,
    ( ~ equalish(b,X0)
    | reflexive_rewrite(b,X0) ),
    inference(instantiation,[status(thm)],[c_55]) ).

cnf(c_204,plain,
    ( ~ equalish(X0,b)
    | equalish(b,X0) ),
    inference(instantiation,[status(thm)],[c_53]) ).

cnf(c_205,plain,
    ( ~ equalish(a,b)
    | equalish(b,a) ),
    inference(instantiation,[status(thm)],[c_204]) ).

cnf(c_209,plain,
    ( ~ equalish(b,b)
    | reflexive_rewrite(b,b) ),
    inference(instantiation,[status(thm)],[c_195]) ).

cnf(c_210,plain,
    equalish(b,b),
    inference(instantiation,[status(thm)],[c_52]) ).

cnf(c_227,plain,
    ( ~ reflexive_rewrite(c,b)
    | ~ reflexive_rewrite(b,b) ),
    inference(instantiation,[status(thm)],[c_67]) ).

cnf(c_234,plain,
    ( ~ reflexive_rewrite(X0,b)
    | equalish(X0,b)
    | rewrite(X0,b) ),
    inference(instantiation,[status(thm)],[c_57]) ).

cnf(c_235,plain,
    ( ~ reflexive_rewrite(a,b)
    | equalish(a,b)
    | rewrite(a,b) ),
    inference(instantiation,[status(thm)],[c_234]) ).

cnf(c_255,plain,
    ( ~ reflexive_rewrite(X0,b)
    | ~ equalish(c,X0)
    | reflexive_rewrite(c,b) ),
    inference(instantiation,[status(thm)],[c_167]) ).

cnf(c_256,plain,
    ( ~ reflexive_rewrite(a,b)
    | ~ equalish(c,a)
    | reflexive_rewrite(c,b) ),
    inference(instantiation,[status(thm)],[c_255]) ).

cnf(c_262,plain,
    ( ~ rewrite(X0,X1)
    | ~ rewrite(X0,b)
    | rewrite(b,sK0(b,X1)) ),
    inference(instantiation,[status(thm)],[c_59]) ).

cnf(c_263,plain,
    ( ~ rewrite(X0,X1)
    | ~ rewrite(X0,b)
    | rewrite(X1,sK0(b,X1)) ),
    inference(instantiation,[status(thm)],[c_58]) ).

cnf(c_311,plain,
    ( ~ rewrite(X0,c)
    | ~ rewrite(X0,b)
    | rewrite(b,sK0(b,c)) ),
    inference(instantiation,[status(thm)],[c_262]) ).

cnf(c_312,plain,
    ( ~ rewrite(a,c)
    | ~ rewrite(a,b)
    | rewrite(b,sK0(b,c)) ),
    inference(instantiation,[status(thm)],[c_311]) ).

cnf(c_315,plain,
    ( ~ rewrite(X0,c)
    | ~ rewrite(X0,b)
    | rewrite(c,sK0(b,c)) ),
    inference(instantiation,[status(thm)],[c_263]) ).

cnf(c_316,plain,
    ( ~ rewrite(a,c)
    | ~ rewrite(a,b)
    | rewrite(c,sK0(b,c)) ),
    inference(instantiation,[status(thm)],[c_315]) ).

cnf(c_331,plain,
    ( ~ rewrite(b,sK0(b,c))
    | reflexive_rewrite(b,sK0(b,c)) ),
    inference(instantiation,[status(thm)],[c_194]) ).

cnf(c_355,plain,
    ( ~ rewrite(c,sK0(b,c))
    | reflexive_rewrite(c,sK0(b,c)) ),
    inference(instantiation,[status(thm)],[c_165]) ).

cnf(c_540,plain,
    ( ~ reflexive_rewrite(c,sK0(b,c))
    | ~ reflexive_rewrite(b,sK0(b,c)) ),
    inference(instantiation,[status(thm)],[c_67]) ).

cnf(c_541,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_540,c_355,c_331,c_316,c_312,c_256,c_235,c_227,c_210,c_209,c_205,c_193,c_184,c_177,c_171,c_169,c_168,c_49,c_50]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : COM007+1 : TPTP v8.1.2. Released v3.2.0.
% 0.10/0.12  % Command  : run_iprover %s %d THM
% 0.11/0.33  % Computer : n024.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 : Fri May  3 00:40:20 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
% 0.46/1.15  % SZS status Started for theBenchmark.p
% 0.46/1.15  % SZS status Theorem for theBenchmark.p
% 0.46/1.15  
% 0.46/1.15  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 0.46/1.15  
% 0.46/1.15  ------  iProver source info
% 0.46/1.15  
% 0.46/1.15  git: date: 2024-05-02 19:28:25 +0000
% 0.46/1.15  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 0.46/1.15  git: non_committed_changes: false
% 0.46/1.15  
% 0.46/1.15  ------ Parsing...
% 0.46/1.15  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 0.46/1.15  
% 0.46/1.15  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  pe_s  pe_e  sf_s  rm: 0 0s  sf_e  pe_s  pe_e 
% 0.46/1.15  
% 0.46/1.15  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 0.46/1.15  ------ Proving...
% 0.46/1.15  ------ Problem Properties 
% 0.46/1.15  
% 0.46/1.15  
% 0.46/1.15  clauses                                 11
% 0.46/1.15  conjectures                             0
% 0.46/1.15  EPR                                     9
% 0.46/1.15  Horn                                    10
% 0.46/1.15  unary                                   3
% 0.46/1.15  binary                                  4
% 0.46/1.15  lits                                    23
% 0.46/1.15  lits eq                                 0
% 0.46/1.15  fd_pure                                 0
% 0.46/1.15  fd_pseudo                               0
% 0.46/1.15  fd_cond                                 0
% 0.46/1.15  fd_pseudo_cond                          0
% 0.46/1.15  AC symbols                              0
% 0.46/1.15  
% 0.46/1.15  ------ Schedule dynamic 5 is on 
% 0.46/1.15  
% 0.46/1.15  ------ no conjectures: strip conj schedule 
% 0.46/1.15  
% 0.46/1.15  ------ no equalities: superposition off 
% 0.46/1.15  
% 0.46/1.15  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 0.46/1.15  
% 0.46/1.15  
% 0.46/1.15  ------ 
% 0.46/1.15  Current options:
% 0.46/1.15  ------ 
% 0.46/1.15  
% 0.46/1.15  
% 0.46/1.15  
% 0.46/1.15  
% 0.46/1.15  ------ Proving...
% 0.46/1.15  
% 0.46/1.15  
% 0.46/1.15  % SZS status Theorem for theBenchmark.p
% 0.46/1.15  
% 0.46/1.15  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.46/1.15  
% 0.46/1.15  
%------------------------------------------------------------------------------