TSTP Solution File: KLE141+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : KLE141+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n011.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 05:32:15 EDT 2023

% Result   : Theorem 10.09s 2.18s
% Output   : CNFRefutation 10.09s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   44 (  32 unt;   0 def)
%            Number of atoms       :   58 (  37 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   32 (  18   ~;  10   |;   1   &)
%                                         (   1 <=>;   2  =>;   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    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   70 (   8 sgn;  39   !;   2   ?)

% 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(f7,axiom,
    ! [X0] : multiplication(one,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).

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] : strong_iteration(one) = multiplication(strong_iteration(one),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

fof(f20,negated_conjecture,
    ~ ! [X3] : strong_iteration(one) = multiplication(strong_iteration(one),X3),
    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] : strong_iteration(one) = multiplication(strong_iteration(one),X0),
    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] : strong_iteration(one) != multiplication(strong_iteration(one),X0),
    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] : strong_iteration(one) != multiplication(strong_iteration(one),X0)
   => strong_iteration(one) != multiplication(strong_iteration(one),sK0) ),
    introduced(choice_axiom,[]) ).

fof(f29,plain,
    strong_iteration(one) != multiplication(strong_iteration(one),sK0),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[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(f36,plain,
    ! [X0] : multiplication(one,X0) = X0,
    inference(cnf_transformation,[],[f7]) ).

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,
    strong_iteration(one) != multiplication(strong_iteration(one),sK0),
    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_55,plain,
    multiplication(one,X0) = X0,
    inference(cnf_transformation,[],[f36]) ).

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,
    multiplication(strong_iteration(one),sK0) != strong_iteration(one),
    inference(cnf_transformation,[],[f49]) ).

cnf(c_9091,plain,
    addition(X0,addition(X0,X1)) = addition(X0,X1),
    inference(superposition,[status(thm)],[c_52,c_50]) ).

cnf(c_9176,plain,
    leq(X0,addition(X0,X1)),
    inference(superposition,[status(thm)],[c_9091,c_66]) ).

cnf(c_9335,plain,
    ( ~ leq(X0,addition(X0,X1))
    | leq(X0,multiplication(strong_iteration(one),X1)) ),
    inference(superposition,[status(thm)],[c_55,c_64]) ).

cnf(c_9342,plain,
    leq(X0,multiplication(strong_iteration(one),X1)),
    inference(forward_subsumption_resolution,[status(thm)],[c_9335,c_9176]) ).

cnf(c_9471,plain,
    leq(X0,strong_iteration(one)),
    inference(superposition,[status(thm)],[c_54,c_9342]) ).

cnf(c_9475,plain,
    addition(X0,multiplication(strong_iteration(one),X1)) = multiplication(strong_iteration(one),X1),
    inference(superposition,[status(thm)],[c_9342,c_67]) ).

cnf(c_9478,plain,
    addition(X0,strong_iteration(one)) = strong_iteration(one),
    inference(superposition,[status(thm)],[c_9471,c_67]) ).

cnf(c_11084,plain,
    addition(strong_iteration(one),X0) = strong_iteration(one),
    inference(superposition,[status(thm)],[c_9478,c_49]) ).

cnf(c_40256,plain,
    multiplication(strong_iteration(one),X0) = strong_iteration(one),
    inference(superposition,[status(thm)],[c_9475,c_11084]) ).

cnf(c_40310,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[c_68,c_40256]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : KLE141+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n011.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 : Tue Aug 29 11:58:41 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 10.09/2.18  % SZS status Started for theBenchmark.p
% 10.09/2.18  % SZS status Theorem for theBenchmark.p
% 10.09/2.18  
% 10.09/2.18  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 10.09/2.18  
% 10.09/2.18  ------  iProver source info
% 10.09/2.18  
% 10.09/2.18  git: date: 2023-05-31 18:12:56 +0000
% 10.09/2.18  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 10.09/2.18  git: non_committed_changes: false
% 10.09/2.18  git: last_make_outside_of_git: false
% 10.09/2.18  
% 10.09/2.18  ------ Parsing...
% 10.09/2.18  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 10.09/2.18  
% 10.09/2.18  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 10.09/2.18  
% 10.09/2.18  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 10.09/2.18  
% 10.09/2.18  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 10.09/2.18  ------ Proving...
% 10.09/2.18  ------ Problem Properties 
% 10.09/2.18  
% 10.09/2.18  
% 10.09/2.18  clauses                                 20
% 10.09/2.18  conjectures                             1
% 10.09/2.18  EPR                                     0
% 10.09/2.18  Horn                                    20
% 10.09/2.18  unary                                   15
% 10.09/2.18  binary                                  5
% 10.09/2.18  lits                                    25
% 10.09/2.18  lits eq                                 17
% 10.09/2.18  fd_pure                                 0
% 10.09/2.18  fd_pseudo                               0
% 10.09/2.18  fd_cond                                 0
% 10.09/2.18  fd_pseudo_cond                          0
% 10.09/2.18  AC symbols                              1
% 10.09/2.18  
% 10.09/2.18  ------ Schedule dynamic 5 is on 
% 10.09/2.18  
% 10.09/2.18  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.09/2.18  
% 10.09/2.18  
% 10.09/2.18  ------ 
% 10.09/2.18  Current options:
% 10.09/2.18  ------ 
% 10.09/2.18  
% 10.09/2.18  
% 10.09/2.18  
% 10.09/2.18  
% 10.09/2.18  ------ Proving...
% 10.09/2.18  
% 10.09/2.18  
% 10.09/2.18  % SZS status Theorem for theBenchmark.p
% 10.09/2.18  
% 10.09/2.18  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.09/2.18  
% 10.09/2.18  
%------------------------------------------------------------------------------