TSTP Solution File: KLE007+4 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : KLE007+4 : 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 05:31:36 EDT 2023

% Result   : Theorem 3.53s 1.22s
% Output   : CNFRefutation 3.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   55 (  25 unt;   0 def)
%            Number of atoms       :  126 (  51 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  113 (  42   ~;  31   |;  27   &)
%                                         (   6 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   82 (   0 sgn;  58   !;   6   ?)

% 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',additive_idempotence) ).

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

fof(f8,axiom,
    ! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).

fof(f12,axiom,
    ! [X0,X1] :
      ( leq(X0,X1)
    <=> addition(X0,X1) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).

fof(f14,axiom,
    ! [X3,X4] :
      ( complement(X4,X3)
    <=> ( one = addition(X3,X4)
        & zero = multiplication(X4,X3)
        & zero = multiplication(X3,X4) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_2) ).

fof(f15,axiom,
    ! [X3,X4] :
      ( test(X3)
     => ( c(X3) = X4
      <=> complement(X3,X4) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_3) ).

fof(f19,conjecture,
    ! [X3,X4] :
      ( ( test(X3)
        & test(X4) )
     => ( leq(addition(multiplication(addition(X3,c(X3)),X4),multiplication(addition(X3,c(X3)),c(X4))),one)
        & leq(one,addition(multiplication(addition(X3,c(X3)),X4),multiplication(addition(X3,c(X3)),c(X4)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

fof(f20,negated_conjecture,
    ~ ! [X3,X4] :
        ( ( test(X3)
          & test(X4) )
       => ( leq(addition(multiplication(addition(X3,c(X3)),X4),multiplication(addition(X3,c(X3)),c(X4))),one)
          & leq(one,addition(multiplication(addition(X3,c(X3)),X4),multiplication(addition(X3,c(X3)),c(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(f23,plain,
    ! [X0,X1] :
      ( complement(X1,X0)
    <=> ( addition(X0,X1) = one
        & zero = multiplication(X1,X0)
        & zero = multiplication(X0,X1) ) ),
    inference(rectify,[],[f14]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( test(X0)
     => ( c(X0) = X1
      <=> complement(X0,X1) ) ),
    inference(rectify,[],[f15]) ).

fof(f28,plain,
    ~ ! [X0,X1] :
        ( ( test(X0)
          & test(X1) )
       => ( leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one)
          & leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1)))) ) ),
    inference(rectify,[],[f20]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( addition(X0,X1) = X1
     => leq(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f12]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( leq(X0,X1)
      | addition(X0,X1) != X1 ),
    inference(ennf_transformation,[],[f29]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ( c(X0) = X1
      <=> complement(X0,X1) )
      | ~ test(X0) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f37,plain,
    ? [X0,X1] :
      ( ( ~ leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one)
        | ~ leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1)))) )
      & test(X0)
      & test(X1) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f38,plain,
    ? [X0,X1] :
      ( ( ~ leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one)
        | ~ leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1)))) )
      & test(X0)
      & test(X1) ),
    inference(flattening,[],[f37]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( ( complement(X1,X0)
        | addition(X0,X1) != one
        | zero != multiplication(X1,X0)
        | zero != multiplication(X0,X1) )
      & ( ( addition(X0,X1) = one
          & zero = multiplication(X1,X0)
          & zero = multiplication(X0,X1) )
        | ~ complement(X1,X0) ) ),
    inference(nnf_transformation,[],[f23]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ( complement(X1,X0)
        | addition(X0,X1) != one
        | zero != multiplication(X1,X0)
        | zero != multiplication(X0,X1) )
      & ( ( addition(X0,X1) = one
          & zero = multiplication(X1,X0)
          & zero = multiplication(X0,X1) )
        | ~ complement(X1,X0) ) ),
    inference(flattening,[],[f43]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( ( ( c(X0) = X1
          | ~ complement(X0,X1) )
        & ( complement(X0,X1)
          | c(X0) != X1 ) )
      | ~ test(X0) ),
    inference(nnf_transformation,[],[f31]) ).

fof(f46,plain,
    ( ? [X0,X1] :
        ( ( ~ leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one)
          | ~ leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1)))) )
        & test(X0)
        & test(X1) )
   => ( ( ~ leq(addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2))),one)
        | ~ leq(one,addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2)))) )
      & test(sK1)
      & test(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f47,plain,
    ( ( ~ leq(addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2))),one)
      | ~ leq(one,addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2)))) )
    & test(sK1)
    & test(sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f38,f46]) ).

fof(f48,plain,
    ! [X0,X1] : addition(X0,X1) = addition(X1,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f49,plain,
    ! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
    inference(cnf_transformation,[],[f21]) ).

fof(f51,plain,
    ! [X0] : addition(X0,X0) = X0,
    inference(cnf_transformation,[],[f4]) ).

fof(f54,plain,
    ! [X0] : multiplication(one,X0) = X0,
    inference(cnf_transformation,[],[f7]) ).

fof(f55,plain,
    ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
    inference(cnf_transformation,[],[f8]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( leq(X0,X1)
      | addition(X0,X1) != X1 ),
    inference(cnf_transformation,[],[f30]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( addition(X0,X1) = one
      | ~ complement(X1,X0) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f66,plain,
    ! [X0,X1] :
      ( complement(X0,X1)
      | c(X0) != X1
      | ~ test(X0) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f71,plain,
    test(sK2),
    inference(cnf_transformation,[],[f47]) ).

fof(f72,plain,
    test(sK1),
    inference(cnf_transformation,[],[f47]) ).

fof(f73,plain,
    ( ~ leq(addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2))),one)
    | ~ leq(one,addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2)))) ),
    inference(cnf_transformation,[],[f47]) ).

fof(f74,plain,
    ! [X0] :
      ( complement(X0,c(X0))
      | ~ test(X0) ),
    inference(equality_resolution,[],[f66]) ).

cnf(c_49,plain,
    addition(X0,X1) = addition(X1,X0),
    inference(cnf_transformation,[],[f48]) ).

cnf(c_50,plain,
    addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
    inference(cnf_transformation,[],[f49]) ).

cnf(c_52,plain,
    addition(X0,X0) = X0,
    inference(cnf_transformation,[],[f51]) ).

cnf(c_55,plain,
    multiplication(one,X0) = X0,
    inference(cnf_transformation,[],[f54]) ).

cnf(c_56,plain,
    addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
    inference(cnf_transformation,[],[f55]) ).

cnf(c_60,plain,
    ( addition(X0,X1) != X1
    | leq(X0,X1) ),
    inference(cnf_transformation,[],[f59]) ).

cnf(c_64,plain,
    ( ~ complement(X0,X1)
    | addition(X1,X0) = one ),
    inference(cnf_transformation,[],[f64]) ).

cnf(c_68,plain,
    ( ~ test(X0)
    | complement(X0,c(X0)) ),
    inference(cnf_transformation,[],[f74]) ).

cnf(c_72,negated_conjecture,
    ( ~ leq(addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2))),one)
    | ~ leq(one,addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2)))) ),
    inference(cnf_transformation,[],[f73]) ).

cnf(c_73,negated_conjecture,
    test(sK1),
    inference(cnf_transformation,[],[f72]) ).

cnf(c_74,negated_conjecture,
    test(sK2),
    inference(cnf_transformation,[],[f71]) ).

cnf(c_551,plain,
    ( ~ test(X0)
    | addition(c(X0),X0) = one ),
    inference(superposition,[status(thm)],[c_68,c_64]) ).

cnf(c_556,plain,
    ( ~ test(X0)
    | addition(X0,c(X0)) = one ),
    inference(theory_normalisation,[status(thm)],[c_551,c_50,c_49]) ).

cnf(c_581,plain,
    leq(X0,X0),
    inference(superposition,[status(thm)],[c_52,c_60]) ).

cnf(c_682,plain,
    ( ~ leq(multiplication(addition(sK1,c(sK1)),addition(sK2,c(sK2))),one)
    | ~ leq(one,multiplication(addition(sK1,c(sK1)),addition(sK2,c(sK2)))) ),
    inference(demodulation,[status(thm)],[c_72,c_56]) ).

cnf(c_1205,plain,
    addition(sK1,c(sK1)) = one,
    inference(superposition,[status(thm)],[c_73,c_556]) ).

cnf(c_1206,plain,
    addition(sK2,c(sK2)) = one,
    inference(superposition,[status(thm)],[c_74,c_556]) ).

cnf(c_3566,plain,
    ~ leq(one,one),
    inference(demodulation,[status(thm)],[c_682,c_55,c_1205,c_1206]) ).

cnf(c_3567,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_3566,c_581]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : KLE007+4 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15  % Command  : run_iprover %s %d THM
% 0.16/0.37  % Computer : n008.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Tue Aug 29 12:02:47 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 0.23/0.52  Running first-order theorem proving
% 0.23/0.52  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.53/1.22  % SZS status Started for theBenchmark.p
% 3.53/1.22  % SZS status Theorem for theBenchmark.p
% 3.53/1.22  
% 3.53/1.22  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.53/1.22  
% 3.53/1.22  ------  iProver source info
% 3.53/1.22  
% 3.53/1.22  git: date: 2023-05-31 18:12:56 +0000
% 3.53/1.22  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.53/1.22  git: non_committed_changes: false
% 3.53/1.22  git: last_make_outside_of_git: false
% 3.53/1.22  
% 3.53/1.22  ------ Parsing...
% 3.53/1.22  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.53/1.22  
% 3.53/1.22  ------ Preprocessing... sup_sim: 0  pe_s  pe_e 
% 3.53/1.22  
% 3.53/1.22  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  scvd_s sp: 0 0s scvd_e  snvd_s sp: 0 0s snvd_e 
% 3.53/1.22  
% 3.53/1.22  ------ Preprocessing...
% 3.53/1.22  ------ Proving...
% 3.53/1.22  ------ Problem Properties 
% 3.53/1.22  
% 3.53/1.22  
% 3.53/1.22  clauses                                 28
% 3.53/1.22  conjectures                             3
% 3.53/1.22  EPR                                     3
% 3.53/1.22  Horn                                    25
% 3.53/1.22  unary                                   13
% 3.53/1.22  binary                                  11
% 3.53/1.22  lits                                    48
% 3.53/1.22  lits eq                                 24
% 3.53/1.22  fd_pure                                 0
% 3.53/1.22  fd_pseudo                               0
% 3.53/1.22  fd_cond                                 0
% 3.53/1.22  fd_pseudo_cond                          1
% 3.53/1.22  AC symbols                              1
% 3.53/1.22  
% 3.53/1.22  ------ Input Options Time Limit: Unbounded
% 3.53/1.22  
% 3.53/1.22  
% 3.53/1.22  ------ 
% 3.53/1.22  Current options:
% 3.53/1.22  ------ 
% 3.53/1.22  
% 3.53/1.22  
% 3.53/1.22  
% 3.53/1.22  
% 3.53/1.22  ------ Proving...
% 3.53/1.22  
% 3.53/1.22  
% 3.53/1.22  % SZS status Theorem for theBenchmark.p
% 3.53/1.22  
% 3.53/1.22  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.53/1.23  
% 3.53/1.23  
%------------------------------------------------------------------------------