TSTP Solution File: KLE025+2 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : KLE025+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n028.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 05:31:46 EDT 2023

% Result   : Theorem 17.36s 3.17s
% Output   : CNFRefutation 17.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   66 (  33 unt;   0 def)
%            Number of atoms       :  151 ( 107 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  136 (  51   ~;  42   |;  29   &)
%                                         (   5 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   97 (   0 sgn;  53   !;   9   ?)

% 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(f3,axiom,
    ! [X0] : addition(X0,zero) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).

fof(f6,axiom,
    ! [X0] : multiplication(X0,one) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_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(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,X5] :
      ( ( test(X5)
        & test(X4) )
     => ( zero = multiplication(multiplication(X4,X3),c(X5))
       => multiplication(X4,X3) = multiplication(multiplication(X4,X3),X5) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

fof(f20,negated_conjecture,
    ~ ! [X3,X4,X5] :
        ( ( test(X5)
          & test(X4) )
       => ( zero = multiplication(multiplication(X4,X3),c(X5))
         => multiplication(X4,X3) = multiplication(multiplication(X4,X3),X5) ) ),
    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,X2] :
        ( ( test(X2)
          & test(X1) )
       => ( zero = multiplication(multiplication(X1,X0),c(X2))
         => multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2) ) ),
    inference(rectify,[],[f20]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ( c(X0) = X1
      <=> complement(X0,X1) )
      | ~ test(X0) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f35,plain,
    ? [X0,X1,X2] :
      ( multiplication(X1,X0) != multiplication(multiplication(X1,X0),X2)
      & zero = multiplication(multiplication(X1,X0),c(X2))
      & test(X2)
      & test(X1) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f36,plain,
    ? [X0,X1,X2] :
      ( multiplication(X1,X0) != multiplication(multiplication(X1,X0),X2)
      & zero = multiplication(multiplication(X1,X0),c(X2))
      & test(X2)
      & test(X1) ),
    inference(flattening,[],[f35]) ).

fof(f41,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(f42,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,[],[f41]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( ( ( c(X0) = X1
          | ~ complement(X0,X1) )
        & ( complement(X0,X1)
          | c(X0) != X1 ) )
      | ~ test(X0) ),
    inference(nnf_transformation,[],[f29]) ).

fof(f44,plain,
    ( ? [X0,X1,X2] :
        ( multiplication(X1,X0) != multiplication(multiplication(X1,X0),X2)
        & zero = multiplication(multiplication(X1,X0),c(X2))
        & test(X2)
        & test(X1) )
   => ( multiplication(sK2,sK1) != multiplication(multiplication(sK2,sK1),sK3)
      & zero = multiplication(multiplication(sK2,sK1),c(sK3))
      & test(sK3)
      & test(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f45,plain,
    ( multiplication(sK2,sK1) != multiplication(multiplication(sK2,sK1),sK3)
    & zero = multiplication(multiplication(sK2,sK1),c(sK3))
    & test(sK3)
    & test(sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f36,f44]) ).

fof(f46,plain,
    ! [X0,X1] : addition(X0,X1) = addition(X1,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f47,plain,
    ! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
    inference(cnf_transformation,[],[f21]) ).

fof(f48,plain,
    ! [X0] : addition(X0,zero) = X0,
    inference(cnf_transformation,[],[f3]) ).

fof(f51,plain,
    ! [X0] : multiplication(X0,one) = X0,
    inference(cnf_transformation,[],[f6]) ).

fof(f53,plain,
    ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
    inference(cnf_transformation,[],[f8]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( addition(X0,X1) = one
      | ~ complement(X1,X0) ),
    inference(cnf_transformation,[],[f42]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( complement(X0,X1)
      | c(X0) != X1
      | ~ test(X0) ),
    inference(cnf_transformation,[],[f43]) ).

fof(f69,plain,
    test(sK3),
    inference(cnf_transformation,[],[f45]) ).

fof(f70,plain,
    zero = multiplication(multiplication(sK2,sK1),c(sK3)),
    inference(cnf_transformation,[],[f45]) ).

fof(f71,plain,
    multiplication(sK2,sK1) != multiplication(multiplication(sK2,sK1),sK3),
    inference(cnf_transformation,[],[f45]) ).

fof(f72,plain,
    ! [X0] :
      ( complement(X0,c(X0))
      | ~ test(X0) ),
    inference(equality_resolution,[],[f63]) ).

cnf(c_49,plain,
    addition(X0,X1) = addition(X1,X0),
    inference(cnf_transformation,[],[f46]) ).

cnf(c_50,plain,
    addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
    inference(cnf_transformation,[],[f47]) ).

cnf(c_51,plain,
    addition(X0,zero) = X0,
    inference(cnf_transformation,[],[f48]) ).

cnf(c_54,plain,
    multiplication(X0,one) = X0,
    inference(cnf_transformation,[],[f51]) ).

cnf(c_56,plain,
    addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
    inference(cnf_transformation,[],[f53]) ).

cnf(c_63,plain,
    ( ~ complement(X0,X1)
    | addition(X1,X0) = one ),
    inference(cnf_transformation,[],[f61]) ).

cnf(c_67,plain,
    ( ~ test(X0)
    | complement(X0,c(X0)) ),
    inference(cnf_transformation,[],[f72]) ).

cnf(c_71,negated_conjecture,
    multiplication(multiplication(sK2,sK1),sK3) != multiplication(sK2,sK1),
    inference(cnf_transformation,[],[f71]) ).

cnf(c_72,negated_conjecture,
    multiplication(multiplication(sK2,sK1),c(sK3)) = zero,
    inference(cnf_transformation,[],[f70]) ).

cnf(c_73,negated_conjecture,
    test(sK3),
    inference(cnf_transformation,[],[f69]) ).

cnf(c_329,plain,
    X0 = X0,
    theory(equality) ).

cnf(c_331,plain,
    ( X0 != X1
    | X2 != X1
    | X2 = X0 ),
    theory(equality) ).

cnf(c_589,plain,
    ( multiplication(multiplication(sK2,sK1),sK3) != X0
    | multiplication(sK2,sK1) != X0
    | multiplication(multiplication(sK2,sK1),sK3) = multiplication(sK2,sK1) ),
    inference(instantiation,[status(thm)],[c_331]) ).

cnf(c_597,plain,
    ( multiplication(sK2,sK1) != X0
    | X1 != X0
    | multiplication(sK2,sK1) = X1 ),
    inference(instantiation,[status(thm)],[c_331]) ).

cnf(c_598,plain,
    ( multiplication(multiplication(sK2,sK1),sK3) != multiplication(X0,X1)
    | multiplication(sK2,sK1) != multiplication(X0,X1)
    | multiplication(multiplication(sK2,sK1),sK3) = multiplication(sK2,sK1) ),
    inference(instantiation,[status(thm)],[c_589]) ).

cnf(c_605,plain,
    ( multiplication(sK2,sK1) != multiplication(sK2,sK1)
    | X0 != multiplication(sK2,sK1)
    | multiplication(sK2,sK1) = X0 ),
    inference(instantiation,[status(thm)],[c_597]) ).

cnf(c_633,plain,
    ( multiplication(multiplication(sK2,sK1),one) != multiplication(sK2,sK1)
    | multiplication(sK2,sK1) != multiplication(sK2,sK1)
    | multiplication(sK2,sK1) = multiplication(multiplication(sK2,sK1),one) ),
    inference(instantiation,[status(thm)],[c_605]) ).

cnf(c_659,plain,
    ( multiplication(X0,X1) != X2
    | X3 != X2
    | X3 = multiplication(X0,X1) ),
    inference(instantiation,[status(thm)],[c_331]) ).

cnf(c_670,plain,
    multiplication(sK2,sK1) = multiplication(sK2,sK1),
    inference(instantiation,[status(thm)],[c_329]) ).

cnf(c_712,plain,
    multiplication(multiplication(sK2,sK1),one) = multiplication(sK2,sK1),
    inference(instantiation,[status(thm)],[c_54]) ).

cnf(c_860,plain,
    ( multiplication(multiplication(sK2,sK1),sK3) != multiplication(multiplication(sK2,sK1),one)
    | multiplication(sK2,sK1) != multiplication(multiplication(sK2,sK1),one)
    | multiplication(multiplication(sK2,sK1),sK3) = multiplication(sK2,sK1) ),
    inference(instantiation,[status(thm)],[c_598]) ).

cnf(c_954,plain,
    ( ~ test(X0)
    | addition(c(X0),X0) = one ),
    inference(superposition,[status(thm)],[c_67,c_63]) ).

cnf(c_955,plain,
    ( ~ test(X0)
    | addition(X0,c(X0)) = one ),
    inference(theory_normalisation,[status(thm)],[c_954,c_50,c_49]) ).

cnf(c_1024,plain,
    ( multiplication(multiplication(sK2,sK1),one) != X0
    | multiplication(multiplication(sK2,sK1),sK3) != X0
    | multiplication(multiplication(sK2,sK1),sK3) = multiplication(multiplication(sK2,sK1),one) ),
    inference(instantiation,[status(thm)],[c_659]) ).

cnf(c_1051,plain,
    addition(sK3,c(sK3)) = one,
    inference(superposition,[status(thm)],[c_73,c_955]) ).

cnf(c_2411,plain,
    ( multiplication(multiplication(sK2,sK1),one) != multiplication(X0,X1)
    | multiplication(multiplication(sK2,sK1),sK3) != multiplication(X0,X1)
    | multiplication(multiplication(sK2,sK1),sK3) = multiplication(multiplication(sK2,sK1),one) ),
    inference(instantiation,[status(thm)],[c_1024]) ).

cnf(c_6173,plain,
    ( multiplication(multiplication(sK2,sK1),one) != multiplication(multiplication(sK2,sK1),sK3)
    | multiplication(multiplication(sK2,sK1),sK3) != multiplication(multiplication(sK2,sK1),sK3)
    | multiplication(multiplication(sK2,sK1),sK3) = multiplication(multiplication(sK2,sK1),one) ),
    inference(instantiation,[status(thm)],[c_2411]) ).

cnf(c_16898,plain,
    multiplication(multiplication(sK2,sK1),sK3) = multiplication(multiplication(sK2,sK1),sK3),
    inference(instantiation,[status(thm)],[c_329]) ).

cnf(c_57730,plain,
    addition(zero,X0) = X0,
    inference(superposition,[status(thm)],[c_51,c_49]) ).

cnf(c_57947,plain,
    multiplication(multiplication(sK2,sK1),addition(X0,c(sK3))) = addition(multiplication(multiplication(sK2,sK1),X0),zero),
    inference(superposition,[status(thm)],[c_72,c_56]) ).

cnf(c_57971,plain,
    multiplication(multiplication(sK2,sK1),addition(X0,c(sK3))) = addition(zero,multiplication(multiplication(sK2,sK1),X0)),
    inference(theory_normalisation,[status(thm)],[c_57947,c_50,c_49]) ).

cnf(c_61767,plain,
    addition(zero,multiplication(multiplication(sK2,sK1),sK3)) = multiplication(multiplication(sK2,sK1),one),
    inference(superposition,[status(thm)],[c_1051,c_57971]) ).

cnf(c_61802,plain,
    multiplication(multiplication(sK2,sK1),one) = multiplication(multiplication(sK2,sK1),sK3),
    inference(superposition,[status(thm)],[c_61767,c_57730]) ).

cnf(c_61804,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_61802,c_16898,c_6173,c_860,c_712,c_670,c_633,c_71]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : KLE025+2 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n028.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 11:39:56 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.46  Running first-order theorem proving
% 0.20/0.46  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 17.36/3.17  % SZS status Started for theBenchmark.p
% 17.36/3.17  % SZS status Theorem for theBenchmark.p
% 17.36/3.17  
% 17.36/3.17  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 17.36/3.17  
% 17.36/3.17  ------  iProver source info
% 17.36/3.17  
% 17.36/3.17  git: date: 2023-05-31 18:12:56 +0000
% 17.36/3.17  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 17.36/3.17  git: non_committed_changes: false
% 17.36/3.17  git: last_make_outside_of_git: false
% 17.36/3.17  
% 17.36/3.17  ------ Parsing...
% 17.36/3.17  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 17.36/3.17  
% 17.36/3.17  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 17.36/3.17  
% 17.36/3.17  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 17.36/3.17  
% 17.36/3.17  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 17.36/3.17  ------ Proving...
% 17.36/3.17  ------ Problem Properties 
% 17.36/3.17  
% 17.36/3.17  
% 17.36/3.17  clauses                                 26
% 17.36/3.17  conjectures                             4
% 17.36/3.17  EPR                                     3
% 17.36/3.17  Horn                                    25
% 17.36/3.17  unary                                   15
% 17.36/3.17  binary                                  7
% 17.36/3.17  lits                                    42
% 17.36/3.17  lits eq                                 23
% 17.36/3.17  fd_pure                                 0
% 17.36/3.17  fd_pseudo                               0
% 17.36/3.17  fd_cond                                 0
% 17.36/3.17  fd_pseudo_cond                          1
% 17.36/3.17  AC symbols                              1
% 17.36/3.17  
% 17.36/3.17  ------ Input Options Time Limit: Unbounded
% 17.36/3.17  
% 17.36/3.17  
% 17.36/3.17  ------ 
% 17.36/3.17  Current options:
% 17.36/3.17  ------ 
% 17.36/3.17  
% 17.36/3.17  
% 17.36/3.17  
% 17.36/3.17  
% 17.36/3.17  ------ Proving...
% 17.36/3.17  
% 17.36/3.17  
% 17.36/3.17  % SZS status Theorem for theBenchmark.p
% 17.36/3.17  
% 17.36/3.17  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.36/3.17  
% 17.36/3.17  
%------------------------------------------------------------------------------