TSTP Solution File: KLE150+2 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : KLE150+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n014.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 05:32:18 EDT 2023

% Result   : Theorem 21.33s 3.73s
% Output   : CNFRefutation 21.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   78 (  64 unt;   0 def)
%            Number of atoms       :   96 (  53 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   40 (  22   ~;  12   |;   4   &)
%                                         (   1 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :  119 (  14 sgn;  50   !;   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',idempotence) ).

fof(f5,axiom,
    ! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).

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',distributivity2) ).

fof(f10,axiom,
    ! [X0] : zero = multiplication(zero,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).

fof(f11,axiom,
    ! [X0] : star(X0) = addition(one,multiplication(X0,star(X0))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold1) ).

fof(f12,axiom,
    ! [X0] : star(X0) = addition(one,multiplication(star(X0),X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold2) ).

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

fof(f17,axiom,
    ! [X0] : strong_iteration(X0) = addition(star(X0),multiplication(strong_iteration(X0),zero)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',isolation) ).

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

fof(f19,conjecture,
    ! [X3] :
      ( leq(addition(one,multiplication(X3,zero)),strong_iteration(multiplication(X3,zero)))
      & leq(strong_iteration(multiplication(X3,zero)),addition(one,multiplication(X3,zero))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

fof(f20,negated_conjecture,
    ~ ! [X3] :
        ( leq(addition(one,multiplication(X3,zero)),strong_iteration(multiplication(X3,zero)))
        & leq(strong_iteration(multiplication(X3,zero)),addition(one,multiplication(X3,zero))) ),
    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] :
        ( leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero)))
        & leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero))) ),
    inference(rectify,[],[f20]) ).

fof(f26,plain,
    ? [X0] :
      ( ~ leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero)))
      | ~ leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero))) ),
    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] :
        ( ~ leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero)))
        | ~ leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero))) )
   => ( ~ leq(addition(one,multiplication(sK0,zero)),strong_iteration(multiplication(sK0,zero)))
      | ~ leq(strong_iteration(multiplication(sK0,zero)),addition(one,multiplication(sK0,zero))) ) ),
    introduced(choice_axiom,[]) ).

fof(f29,plain,
    ( ~ leq(addition(one,multiplication(sK0,zero)),strong_iteration(multiplication(sK0,zero)))
    | ~ leq(strong_iteration(multiplication(sK0,zero)),addition(one,multiplication(sK0,zero))) ),
    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(f34,plain,
    ! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
    inference(cnf_transformation,[],[f5]) ).

fof(f36,plain,
    ! [X0] : multiplication(one,X0) = X0,
    inference(cnf_transformation,[],[f7]) ).

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

fof(f39,plain,
    ! [X0] : zero = multiplication(zero,X0),
    inference(cnf_transformation,[],[f10]) ).

fof(f40,plain,
    ! [X0] : star(X0) = addition(one,multiplication(X0,star(X0))),
    inference(cnf_transformation,[],[f11]) ).

fof(f41,plain,
    ! [X0] : star(X0) = addition(one,multiplication(star(X0),X0)),
    inference(cnf_transformation,[],[f12]) ).

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

fof(f46,plain,
    ! [X0] : strong_iteration(X0) = addition(star(X0),multiplication(strong_iteration(X0),zero)),
    inference(cnf_transformation,[],[f17]) ).

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(addition(one,multiplication(sK0,zero)),strong_iteration(multiplication(sK0,zero)))
    | ~ leq(strong_iteration(multiplication(sK0,zero)),addition(one,multiplication(sK0,zero))) ),
    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_53,plain,
    multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
    inference(cnf_transformation,[],[f34]) ).

cnf(c_55,plain,
    multiplication(one,X0) = X0,
    inference(cnf_transformation,[],[f36]) ).

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

cnf(c_58,plain,
    multiplication(zero,X0) = zero,
    inference(cnf_transformation,[],[f39]) ).

cnf(c_59,plain,
    addition(one,multiplication(X0,star(X0))) = star(X0),
    inference(cnf_transformation,[],[f40]) ).

cnf(c_60,plain,
    addition(one,multiplication(star(X0),X0)) = star(X0),
    inference(cnf_transformation,[],[f41]) ).

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

cnf(c_65,plain,
    addition(star(X0),multiplication(strong_iteration(X0),zero)) = strong_iteration(X0),
    inference(cnf_transformation,[],[f46]) ).

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(addition(one,multiplication(sK0,zero)),strong_iteration(multiplication(sK0,zero)))
    | ~ leq(strong_iteration(multiplication(sK0,zero)),addition(one,multiplication(sK0,zero))) ),
    inference(cnf_transformation,[],[f49]) ).

cnf(c_86,plain,
    addition(one,multiplication(X0,strong_iteration(X0))) = strong_iteration(X0),
    inference(theory_normalisation,[status(thm)],[c_63,c_50,c_49]) ).

cnf(c_1079,plain,
    leq(X0,X0),
    inference(superposition,[status(thm)],[c_52,c_66]) ).

cnf(c_10311,plain,
    addition(X0,addition(X0,X1)) = addition(X0,X1),
    inference(superposition,[status(thm)],[c_52,c_50]) ).

cnf(c_10391,plain,
    addition(one,multiplication(X0,multiplication(X1,strong_iteration(multiplication(X0,X1))))) = strong_iteration(multiplication(X0,X1)),
    inference(superposition,[status(thm)],[c_53,c_86]) ).

cnf(c_10512,plain,
    addition(one,star(X0)) = star(X0),
    inference(superposition,[status(thm)],[c_59,c_10311]) ).

cnf(c_10514,plain,
    addition(star(X0),strong_iteration(X0)) = strong_iteration(X0),
    inference(superposition,[status(thm)],[c_65,c_10311]) ).

cnf(c_10517,plain,
    leq(X0,addition(X0,X1)),
    inference(superposition,[status(thm)],[c_10311,c_66]) ).

cnf(c_10530,plain,
    leq(X0,addition(X1,X0)),
    inference(superposition,[status(thm)],[c_49,c_10517]) ).

cnf(c_10532,plain,
    leq(addition(X0,X1),addition(X0,addition(X1,X2))),
    inference(superposition,[status(thm)],[c_50,c_10517]) ).

cnf(c_10549,plain,
    leq(X0,addition(X1,addition(X2,X0))),
    inference(superposition,[status(thm)],[c_50,c_10530]) ).

cnf(c_10553,plain,
    leq(multiplication(star(X0),X0),star(X0)),
    inference(superposition,[status(thm)],[c_60,c_10530]) ).

cnf(c_10770,plain,
    leq(addition(X0,one),addition(X0,strong_iteration(X1))),
    inference(superposition,[status(thm)],[c_86,c_10532]) ).

cnf(c_10812,plain,
    leq(X0,addition(X1,addition(X0,X2))),
    inference(superposition,[status(thm)],[c_49,c_10549]) ).

cnf(c_10843,plain,
    addition(multiplication(star(X0),X0),star(X0)) = star(X0),
    inference(superposition,[status(thm)],[c_10553,c_67]) ).

cnf(c_10844,plain,
    addition(star(X0),multiplication(star(X0),X0)) = star(X0),
    inference(theory_normalisation,[status(thm)],[c_10843,c_50,c_49]) ).

cnf(c_11569,plain,
    addition(multiplication(one,X0),multiplication(star(X1),X0)) = multiplication(star(X1),X0),
    inference(superposition,[status(thm)],[c_10512,c_57]) ).

cnf(c_11581,plain,
    addition(X0,multiplication(star(X1),X0)) = multiplication(star(X1),X0),
    inference(light_normalisation,[status(thm)],[c_11569,c_55]) ).

cnf(c_12432,plain,
    leq(addition(one,X0),addition(X0,strong_iteration(X1))),
    inference(superposition,[status(thm)],[c_49,c_10770]) ).

cnf(c_43229,plain,
    leq(X0,addition(X1,multiplication(star(X2),X0))),
    inference(superposition,[status(thm)],[c_11581,c_10812]) ).

cnf(c_49848,plain,
    leq(X0,star(X0)),
    inference(superposition,[status(thm)],[c_10844,c_43229]) ).

cnf(c_50222,plain,
    addition(X0,star(X0)) = star(X0),
    inference(superposition,[status(thm)],[c_49848,c_67]) ).

cnf(c_50977,plain,
    leq(X0,addition(X1,star(X0))),
    inference(superposition,[status(thm)],[c_50222,c_10812]) ).

cnf(c_52976,plain,
    leq(X0,addition(star(X0),X1)),
    inference(superposition,[status(thm)],[c_49,c_50977]) ).

cnf(c_53589,plain,
    leq(X0,strong_iteration(X0)),
    inference(superposition,[status(thm)],[c_10514,c_52976]) ).

cnf(c_53639,plain,
    addition(X0,strong_iteration(X0)) = strong_iteration(X0),
    inference(superposition,[status(thm)],[c_53589,c_67]) ).

cnf(c_59967,plain,
    leq(addition(one,X0),strong_iteration(X0)),
    inference(superposition,[status(thm)],[c_53639,c_12432]) ).

cnf(c_60038,plain,
    ~ leq(strong_iteration(multiplication(sK0,zero)),addition(one,multiplication(sK0,zero))),
    inference(backward_subsumption_resolution,[status(thm)],[c_68,c_59967]) ).

cnf(c_115957,plain,
    addition(one,multiplication(X0,zero)) = strong_iteration(multiplication(X0,zero)),
    inference(superposition,[status(thm)],[c_58,c_10391]) ).

cnf(c_116074,plain,
    ~ leq(addition(one,multiplication(sK0,zero)),addition(one,multiplication(sK0,zero))),
    inference(demodulation,[status(thm)],[c_60038,c_115957]) ).

cnf(c_116075,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_116074,c_1079]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : KLE150+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n014.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Tue Aug 29 11:06:45 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
% 21.33/3.73  % SZS status Started for theBenchmark.p
% 21.33/3.73  % SZS status Theorem for theBenchmark.p
% 21.33/3.73  
% 21.33/3.73  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 21.33/3.73  
% 21.33/3.73  ------  iProver source info
% 21.33/3.73  
% 21.33/3.73  git: date: 2023-05-31 18:12:56 +0000
% 21.33/3.73  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 21.33/3.73  git: non_committed_changes: false
% 21.33/3.73  git: last_make_outside_of_git: false
% 21.33/3.73  
% 21.33/3.73  ------ Parsing...
% 21.33/3.73  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 21.33/3.73  
% 21.33/3.73  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 21.33/3.73  
% 21.33/3.73  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 21.33/3.73  
% 21.33/3.73  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 21.33/3.73  ------ Proving...
% 21.33/3.73  ------ Problem Properties 
% 21.33/3.73  
% 21.33/3.73  
% 21.33/3.73  clauses                                 20
% 21.33/3.73  conjectures                             1
% 21.33/3.73  EPR                                     0
% 21.33/3.73  Horn                                    20
% 21.33/3.73  unary                                   14
% 21.33/3.73  binary                                  6
% 21.33/3.73  lits                                    26
% 21.33/3.73  lits eq                                 16
% 21.33/3.73  fd_pure                                 0
% 21.33/3.73  fd_pseudo                               0
% 21.33/3.73  fd_cond                                 0
% 21.33/3.73  fd_pseudo_cond                          0
% 21.33/3.73  AC symbols                              1
% 21.33/3.73  
% 21.33/3.73  ------ Schedule dynamic 5 is on 
% 21.33/3.73  
% 21.33/3.73  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 21.33/3.73  
% 21.33/3.73  
% 21.33/3.73  ------ 
% 21.33/3.73  Current options:
% 21.33/3.73  ------ 
% 21.33/3.73  
% 21.33/3.73  
% 21.33/3.73  
% 21.33/3.73  
% 21.33/3.73  ------ Proving...
% 21.33/3.73  
% 21.33/3.73  
% 21.33/3.73  % SZS status Theorem for theBenchmark.p
% 21.33/3.73  
% 21.33/3.73  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 21.33/3.73  
% 21.33/3.73  
%------------------------------------------------------------------------------