TSTP Solution File: KLE140+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : KLE140+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n019.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 : Thu Aug 31 05:32:14 EDT 2023

% Result   : Theorem 7.52s 1.66s
% Output   : CNFRefutation 7.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   51 (  34 unt;   0 def)
%            Number of atoms       :   72 (  30 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   39 (  18   ~;  10   |;   5   &)
%                                         (   1 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   84 (   2 sgn;  48   !;   4   ?)

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

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

fof(f4,axiom,
    ! [X0] : addition(X0,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence) ).

fof(f6,axiom,
    ! [X0] : multiplication(X0,one) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).

fof(f9,axiom,
    ! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity2) ).

fof(f15,axiom,
    ! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infty_unfold1) ).

fof(f16,axiom,
    ! [X0,X1,X2] :
      ( leq(X2,addition(multiplication(X0,X2),X1))
     => leq(X2,multiplication(strong_iteration(X0),X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infty_coinduction) ).

fof(f18,axiom,
    ! [X0,X1] :
      ( leq(X0,X1)
    <=> addition(X0,X1) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).

fof(f19,conjecture,
    ! [X3,X4] :
      ( leq(X3,X4)
     => leq(strong_iteration(X3),strong_iteration(X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

fof(f20,negated_conjecture,
    ~ ! [X3,X4] :
        ( leq(X3,X4)
       => leq(strong_iteration(X3),strong_iteration(X4)) ),
    inference(negated_conjecture,[],[f19]) ).

fof(f21,plain,
    ! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
    inference(rectify,[],[f2]) ).

fof(f22,plain,
    ~ ! [X0,X1] :
        ( leq(X0,X1)
       => leq(strong_iteration(X0),strong_iteration(X1)) ),
    inference(rectify,[],[f20]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( leq(X2,multiplication(strong_iteration(X0),X1))
      | ~ leq(X2,addition(multiplication(X0,X2),X1)) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f26,plain,
    ? [X0,X1] :
      ( ~ leq(strong_iteration(X0),strong_iteration(X1))
      & leq(X0,X1) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( ( leq(X0,X1)
        | addition(X0,X1) != X1 )
      & ( addition(X0,X1) = X1
        | ~ leq(X0,X1) ) ),
    inference(nnf_transformation,[],[f18]) ).

fof(f28,plain,
    ( ? [X0,X1] :
        ( ~ leq(strong_iteration(X0),strong_iteration(X1))
        & leq(X0,X1) )
   => ( ~ leq(strong_iteration(sK0),strong_iteration(sK1))
      & leq(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f29,plain,
    ( ~ leq(strong_iteration(sK0),strong_iteration(sK1))
    & leq(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f26,f28]) ).

fof(f30,plain,
    ! [X0,X1] : addition(X0,X1) = addition(X1,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f31,plain,
    ! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
    inference(cnf_transformation,[],[f21]) ).

fof(f33,plain,
    ! [X0] : addition(X0,X0) = X0,
    inference(cnf_transformation,[],[f4]) ).

fof(f35,plain,
    ! [X0] : multiplication(X0,one) = X0,
    inference(cnf_transformation,[],[f6]) ).

fof(f38,plain,
    ! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
    inference(cnf_transformation,[],[f9]) ).

fof(f44,plain,
    ! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
    inference(cnf_transformation,[],[f15]) ).

fof(f45,plain,
    ! [X2,X0,X1] :
      ( leq(X2,multiplication(strong_iteration(X0),X1))
      | ~ leq(X2,addition(multiplication(X0,X2),X1)) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( addition(X0,X1) = X1
      | ~ leq(X0,X1) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( leq(X0,X1)
      | addition(X0,X1) != X1 ),
    inference(cnf_transformation,[],[f27]) ).

fof(f49,plain,
    leq(sK0,sK1),
    inference(cnf_transformation,[],[f29]) ).

fof(f50,plain,
    ~ leq(strong_iteration(sK0),strong_iteration(sK1)),
    inference(cnf_transformation,[],[f29]) ).

cnf(c_49,plain,
    addition(X0,X1) = addition(X1,X0),
    inference(cnf_transformation,[],[f30]) ).

cnf(c_50,plain,
    addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
    inference(cnf_transformation,[],[f31]) ).

cnf(c_52,plain,
    addition(X0,X0) = X0,
    inference(cnf_transformation,[],[f33]) ).

cnf(c_54,plain,
    multiplication(X0,one) = X0,
    inference(cnf_transformation,[],[f35]) ).

cnf(c_57,plain,
    addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
    inference(cnf_transformation,[],[f38]) ).

cnf(c_63,plain,
    addition(multiplication(X0,strong_iteration(X0)),one) = strong_iteration(X0),
    inference(cnf_transformation,[],[f44]) ).

cnf(c_64,plain,
    ( ~ leq(X0,addition(multiplication(X1,X0),X2))
    | leq(X0,multiplication(strong_iteration(X1),X2)) ),
    inference(cnf_transformation,[],[f45]) ).

cnf(c_66,plain,
    ( addition(X0,X1) != X1
    | leq(X0,X1) ),
    inference(cnf_transformation,[],[f48]) ).

cnf(c_67,plain,
    ( ~ leq(X0,X1)
    | addition(X0,X1) = X1 ),
    inference(cnf_transformation,[],[f47]) ).

cnf(c_68,negated_conjecture,
    ~ leq(strong_iteration(sK0),strong_iteration(sK1)),
    inference(cnf_transformation,[],[f50]) ).

cnf(c_69,negated_conjecture,
    leq(sK0,sK1),
    inference(cnf_transformation,[],[f49]) ).

cnf(c_87,plain,
    addition(one,multiplication(X0,strong_iteration(X0))) = strong_iteration(X0),
    inference(theory_normalisation,[status(thm)],[c_63,c_50,c_49]) ).

cnf(c_548,plain,
    addition(sK0,sK1) = sK1,
    inference(superposition,[status(thm)],[c_69,c_67]) ).

cnf(c_586,plain,
    addition(X0,addition(X0,X1)) = addition(X0,X1),
    inference(superposition,[status(thm)],[c_52,c_50]) ).

cnf(c_710,plain,
    addition(multiplication(sK0,X0),multiplication(sK1,X0)) = multiplication(sK1,X0),
    inference(superposition,[status(thm)],[c_548,c_57]) ).

cnf(c_1200,plain,
    ( ~ leq(X0,addition(X1,multiplication(X2,X0)))
    | leq(X0,multiplication(strong_iteration(X2),X1)) ),
    inference(superposition,[status(thm)],[c_49,c_64]) ).

cnf(c_3366,plain,
    leq(X0,addition(X0,X1)),
    inference(superposition,[status(thm)],[c_586,c_66]) ).

cnf(c_3433,plain,
    leq(addition(X0,X1),addition(X0,addition(X1,X2))),
    inference(superposition,[status(thm)],[c_50,c_3366]) ).

cnf(c_7995,plain,
    leq(addition(X0,multiplication(sK0,X1)),addition(X0,multiplication(sK1,X1))),
    inference(superposition,[status(thm)],[c_710,c_3433]) ).

cnf(c_8655,plain,
    leq(strong_iteration(sK0),addition(one,multiplication(sK1,strong_iteration(sK0)))),
    inference(superposition,[status(thm)],[c_87,c_7995]) ).

cnf(c_16209,plain,
    leq(strong_iteration(sK0),multiplication(strong_iteration(sK1),one)),
    inference(superposition,[status(thm)],[c_8655,c_1200]) ).

cnf(c_16432,plain,
    leq(strong_iteration(sK0),strong_iteration(sK1)),
    inference(demodulation,[status(thm)],[c_16209,c_54]) ).

cnf(c_16433,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_16432,c_68]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14  % Problem  : KLE140+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.15  % Command  : run_iprover %s %d THM
% 0.15/0.36  % Computer : n019.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 : Tue Aug 29 12:03:58 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.21/0.49  Running first-order theorem proving
% 0.21/0.49  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.52/1.66  % SZS status Started for theBenchmark.p
% 7.52/1.66  % SZS status Theorem for theBenchmark.p
% 7.52/1.66  
% 7.52/1.66  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 7.52/1.66  
% 7.52/1.66  ------  iProver source info
% 7.52/1.66  
% 7.52/1.66  git: date: 2023-05-31 18:12:56 +0000
% 7.52/1.66  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 7.52/1.66  git: non_committed_changes: false
% 7.52/1.66  git: last_make_outside_of_git: false
% 7.52/1.66  
% 7.52/1.66  ------ Parsing...
% 7.52/1.66  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 7.52/1.66  
% 7.52/1.66  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 7.52/1.66  
% 7.52/1.66  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 7.52/1.66  
% 7.52/1.66  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 7.52/1.66  ------ Proving...
% 7.52/1.66  ------ Problem Properties 
% 7.52/1.66  
% 7.52/1.66  
% 7.52/1.66  clauses                                 21
% 7.52/1.66  conjectures                             2
% 7.52/1.66  EPR                                     1
% 7.52/1.66  Horn                                    21
% 7.52/1.66  unary                                   16
% 7.52/1.66  binary                                  5
% 7.52/1.66  lits                                    26
% 7.52/1.66  lits eq                                 16
% 7.52/1.66  fd_pure                                 0
% 7.52/1.66  fd_pseudo                               0
% 7.52/1.66  fd_cond                                 0
% 7.52/1.66  fd_pseudo_cond                          0
% 7.52/1.66  AC symbols                              1
% 7.52/1.66  
% 7.52/1.66  ------ Schedule dynamic 5 is on 
% 7.52/1.66  
% 7.52/1.66  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.52/1.66  
% 7.52/1.66  
% 7.52/1.66  ------ 
% 7.52/1.66  Current options:
% 7.52/1.66  ------ 
% 7.52/1.66  
% 7.52/1.66  
% 7.52/1.66  
% 7.52/1.66  
% 7.52/1.66  ------ Proving...
% 7.52/1.66  
% 7.52/1.66  
% 7.52/1.66  % SZS status Theorem for theBenchmark.p
% 7.52/1.66  
% 7.52/1.66  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.52/1.66  
% 7.52/1.67  
%------------------------------------------------------------------------------