TSTP Solution File: KLE040+2 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : KLE040+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n008.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 05:31:52 EDT 2023

% Result   : Theorem 4.16s 1.20s
% Output   : CNFRefutation 4.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   63 (  43 unt;   0 def)
%            Number of atoms       :   87 (  33 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   50 (  26   ~;  17   |;   4   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    5 (   2 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   :  104 (  11 sgn;  47   !;   2   ?)

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

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

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

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

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

fof(f12,axiom,
    ! [X0,X1] :
      ( leq(X0,X1)
    <=> addition(X0,X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).

fof(f13,axiom,
    ! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold_right) ).

fof(f14,axiom,
    ! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold_left) ).

fof(f15,axiom,
    ! [X0,X1,X2] :
      ( leq(addition(multiplication(X0,X1),X2),X1)
     => leq(multiplication(star(X0),X2),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_induction_left) ).

fof(f17,conjecture,
    ! [X3] :
      ( leq(star(X3),multiplication(star(X3),star(X3)))
      & leq(multiplication(star(X3),star(X3)),star(X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

fof(f18,negated_conjecture,
    ~ ! [X3] :
        ( leq(star(X3),multiplication(star(X3),star(X3)))
        & leq(multiplication(star(X3),star(X3)),star(X3)) ),
    inference(negated_conjecture,[],[f17]) ).

fof(f19,plain,
    ! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
    inference(rectify,[],[f2]) ).

fof(f20,plain,
    ~ ! [X0] :
        ( leq(star(X0),multiplication(star(X0),star(X0)))
        & leq(multiplication(star(X0),star(X0)),star(X0)) ),
    inference(rectify,[],[f18]) ).

fof(f21,plain,
    ! [X0,X1,X2] :
      ( leq(multiplication(star(X0),X2),X1)
      | ~ leq(addition(multiplication(X0,X1),X2),X1) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f23,plain,
    ? [X0] :
      ( ~ leq(star(X0),multiplication(star(X0),star(X0)))
      | ~ leq(multiplication(star(X0),star(X0)),star(X0)) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ( leq(X0,X1)
        | addition(X0,X1) != X1 )
      & ( addition(X0,X1) = X1
        | ~ leq(X0,X1) ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f25,plain,
    ( ? [X0] :
        ( ~ leq(star(X0),multiplication(star(X0),star(X0)))
        | ~ leq(multiplication(star(X0),star(X0)),star(X0)) )
   => ( ~ leq(star(sK0),multiplication(star(sK0),star(sK0)))
      | ~ leq(multiplication(star(sK0),star(sK0)),star(sK0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f26,plain,
    ( ~ leq(star(sK0),multiplication(star(sK0),star(sK0)))
    | ~ leq(multiplication(star(sK0),star(sK0)),star(sK0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f23,f25]) ).

fof(f27,plain,
    ! [X0,X1] : addition(X0,X1) = addition(X1,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f28,plain,
    ! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
    inference(cnf_transformation,[],[f19]) ).

fof(f30,plain,
    ! [X0] : addition(X0,X0) = X0,
    inference(cnf_transformation,[],[f4]) ).

fof(f33,plain,
    ! [X0] : multiplication(one,X0) = X0,
    inference(cnf_transformation,[],[f7]) ).

fof(f35,plain,
    ! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
    inference(cnf_transformation,[],[f9]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( addition(X0,X1) = X1
      | ~ leq(X0,X1) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( leq(X0,X1)
      | addition(X0,X1) != X1 ),
    inference(cnf_transformation,[],[f24]) ).

fof(f40,plain,
    ! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
    inference(cnf_transformation,[],[f13]) ).

fof(f41,plain,
    ! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
    inference(cnf_transformation,[],[f14]) ).

fof(f42,plain,
    ! [X2,X0,X1] :
      ( leq(multiplication(star(X0),X2),X1)
      | ~ leq(addition(multiplication(X0,X1),X2),X1) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f44,plain,
    ( ~ leq(star(sK0),multiplication(star(sK0),star(sK0)))
    | ~ leq(multiplication(star(sK0),star(sK0)),star(sK0)) ),
    inference(cnf_transformation,[],[f26]) ).

cnf(c_49,plain,
    addition(X0,X1) = addition(X1,X0),
    inference(cnf_transformation,[],[f27]) ).

cnf(c_50,plain,
    addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
    inference(cnf_transformation,[],[f28]) ).

cnf(c_52,plain,
    addition(X0,X0) = X0,
    inference(cnf_transformation,[],[f30]) ).

cnf(c_55,plain,
    multiplication(one,X0) = X0,
    inference(cnf_transformation,[],[f33]) ).

cnf(c_57,plain,
    addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
    inference(cnf_transformation,[],[f35]) ).

cnf(c_60,plain,
    ( addition(X0,X1) != X1
    | leq(X0,X1) ),
    inference(cnf_transformation,[],[f39]) ).

cnf(c_61,plain,
    ( ~ leq(X0,X1)
    | addition(X0,X1) = X1 ),
    inference(cnf_transformation,[],[f38]) ).

cnf(c_62,plain,
    leq(addition(one,multiplication(X0,star(X0))),star(X0)),
    inference(cnf_transformation,[],[f40]) ).

cnf(c_63,plain,
    leq(addition(one,multiplication(star(X0),X0)),star(X0)),
    inference(cnf_transformation,[],[f41]) ).

cnf(c_64,plain,
    ( ~ leq(addition(multiplication(X0,X1),X2),X1)
    | leq(multiplication(star(X0),X2),X1) ),
    inference(cnf_transformation,[],[f42]) ).

cnf(c_66,negated_conjecture,
    ( ~ leq(multiplication(star(sK0),star(sK0)),star(sK0))
    | ~ leq(star(sK0),multiplication(star(sK0),star(sK0))) ),
    inference(cnf_transformation,[],[f44]) ).

cnf(c_513,plain,
    leq(X0,X0),
    inference(superposition,[status(thm)],[c_52,c_60]) ).

cnf(c_524,plain,
    addition(addition(one,multiplication(X0,star(X0))),star(X0)) = star(X0),
    inference(superposition,[status(thm)],[c_62,c_61]) ).

cnf(c_525,plain,
    addition(addition(one,multiplication(star(X0),X0)),star(X0)) = star(X0),
    inference(superposition,[status(thm)],[c_63,c_61]) ).

cnf(c_526,plain,
    addition(one,addition(star(X0),multiplication(star(X0),X0))) = star(X0),
    inference(theory_normalisation,[status(thm)],[c_525,c_50,c_49]) ).

cnf(c_527,plain,
    addition(one,addition(star(X0),multiplication(X0,star(X0)))) = star(X0),
    inference(theory_normalisation,[status(thm)],[c_524,c_50,c_49]) ).

cnf(c_583,plain,
    addition(X0,addition(X0,X1)) = addition(X0,X1),
    inference(superposition,[status(thm)],[c_52,c_50]) ).

cnf(c_698,plain,
    ( ~ leq(addition(X0,multiplication(X1,X2)),X2)
    | leq(multiplication(star(X1),X0),X2) ),
    inference(superposition,[status(thm)],[c_49,c_64]) ).

cnf(c_798,plain,
    leq(X0,addition(X0,X1)),
    inference(superposition,[status(thm)],[c_583,c_60]) ).

cnf(c_817,plain,
    leq(X0,addition(X1,X0)),
    inference(superposition,[status(thm)],[c_49,c_798]) ).

cnf(c_831,plain,
    leq(X0,addition(X1,addition(X2,X0))),
    inference(superposition,[status(thm)],[c_50,c_817]) ).

cnf(c_845,plain,
    leq(X0,addition(X1,addition(X0,X2))),
    inference(superposition,[status(thm)],[c_49,c_831]) ).

cnf(c_5690,plain,
    addition(one,star(X0)) = star(X0),
    inference(superposition,[status(thm)],[c_526,c_583]) ).

cnf(c_5720,plain,
    leq(one,addition(X0,star(X1))),
    inference(superposition,[status(thm)],[c_526,c_845]) ).

cnf(c_6818,plain,
    leq(one,addition(star(X0),X1)),
    inference(superposition,[status(thm)],[c_49,c_5720]) ).

cnf(c_6837,plain,
    addition(one,addition(star(X0),X1)) = addition(star(X0),X1),
    inference(superposition,[status(thm)],[c_6818,c_61]) ).

cnf(c_6838,plain,
    addition(star(X0),multiplication(X0,star(X0))) = star(X0),
    inference(demodulation,[status(thm)],[c_527,c_6837]) ).

cnf(c_6955,plain,
    addition(multiplication(one,X0),multiplication(star(X1),X0)) = multiplication(star(X1),X0),
    inference(superposition,[status(thm)],[c_5690,c_57]) ).

cnf(c_7012,plain,
    addition(X0,multiplication(star(X1),X0)) = multiplication(star(X1),X0),
    inference(light_normalisation,[status(thm)],[c_6955,c_55]) ).

cnf(c_7499,plain,
    ( ~ leq(star(X0),star(X0))
    | leq(multiplication(star(X0),star(X0)),star(X0)) ),
    inference(superposition,[status(thm)],[c_6838,c_698]) ).

cnf(c_7525,plain,
    leq(multiplication(star(X0),star(X0)),star(X0)),
    inference(forward_subsumption_resolution,[status(thm)],[c_7499,c_513]) ).

cnf(c_7546,plain,
    ~ leq(star(sK0),multiplication(star(sK0),star(sK0))),
    inference(backward_subsumption_resolution,[status(thm)],[c_66,c_7525]) ).

cnf(c_8930,plain,
    leq(X0,multiplication(star(X1),X0)),
    inference(superposition,[status(thm)],[c_7012,c_60]) ).

cnf(c_9042,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[c_7546,c_8930]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : KLE040+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n008.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 11:22:47 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.16/1.20  % SZS status Started for theBenchmark.p
% 4.16/1.20  % SZS status Theorem for theBenchmark.p
% 4.16/1.20  
% 4.16/1.20  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 4.16/1.20  
% 4.16/1.20  ------  iProver source info
% 4.16/1.20  
% 4.16/1.20  git: date: 2023-05-31 18:12:56 +0000
% 4.16/1.20  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 4.16/1.20  git: non_committed_changes: false
% 4.16/1.20  git: last_make_outside_of_git: false
% 4.16/1.20  
% 4.16/1.20  ------ Parsing...
% 4.16/1.20  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 4.16/1.20  
% 4.16/1.20  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 4.16/1.20  
% 4.16/1.20  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 4.16/1.20  
% 4.16/1.20  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 4.16/1.20  ------ Proving...
% 4.16/1.20  ------ Problem Properties 
% 4.16/1.20  
% 4.16/1.20  
% 4.16/1.20  clauses                                 18
% 4.16/1.20  conjectures                             1
% 4.16/1.20  EPR                                     0
% 4.16/1.20  Horn                                    18
% 4.16/1.20  unary                                   13
% 4.16/1.20  binary                                  5
% 4.16/1.20  lits                                    23
% 4.16/1.20  lits eq                                 13
% 4.16/1.20  fd_pure                                 0
% 4.16/1.20  fd_pseudo                               0
% 4.16/1.20  fd_cond                                 0
% 4.16/1.20  fd_pseudo_cond                          0
% 4.16/1.20  AC symbols                              1
% 4.16/1.20  
% 4.16/1.20  ------ Schedule dynamic 5 is on 
% 4.16/1.20  
% 4.16/1.20  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.16/1.20  
% 4.16/1.20  
% 4.16/1.20  ------ 
% 4.16/1.20  Current options:
% 4.16/1.20  ------ 
% 4.16/1.20  
% 4.16/1.20  
% 4.16/1.20  
% 4.16/1.20  
% 4.16/1.20  ------ Proving...
% 4.16/1.20  
% 4.16/1.20  
% 4.16/1.20  % SZS status Theorem for theBenchmark.p
% 4.16/1.20  
% 4.16/1.20  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.16/1.20  
% 4.16/1.21  
%------------------------------------------------------------------------------