TSTP Solution File: SET600+3 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET600+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n010.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 : Fri May  3 03:00:54 EDT 2024

% Result   : Theorem 2.87s 1.16s
% Output   : CNFRefutation 2.87s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   68 (  14 unt;   0 def)
%            Number of atoms       :  193 (  93 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  199 (  74   ~;  85   |;  30   &)
%                                         (   6 <=>;   3  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :  100 (  11 sgn  55   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1,X2] :
      ( member(X2,union(X0,X1))
    <=> ( member(X2,X1)
        | member(X2,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).

fof(f2,axiom,
    ! [X0] : ~ member(X0,empty_set),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( X0 = X1
    <=> ( subset(X1,X0)
        & subset(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).

fof(f4,axiom,
    ! [X0,X1] : union(X0,X1) = union(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).

fof(f9,conjecture,
    ! [X0,X1] :
      ( union(X0,X1) = empty_set
    <=> ( empty_set = X1
        & empty_set = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th59) ).

fof(f10,negated_conjecture,
    ~ ! [X0,X1] :
        ( union(X0,X1) = empty_set
      <=> ( empty_set = X1
          & empty_set = X0 ) ),
    inference(negated_conjecture,[],[f9]) ).

fof(f11,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f12,plain,
    ? [X0,X1] :
      ( union(X0,X1) = empty_set
    <~> ( empty_set = X1
        & empty_set = X0 ) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f13,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,union(X0,X1))
        | ( ~ member(X2,X1)
          & ~ member(X2,X0) ) )
      & ( member(X2,X1)
        | member(X2,X0)
        | ~ member(X2,union(X0,X1)) ) ),
    inference(nnf_transformation,[],[f1]) ).

fof(f14,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,union(X0,X1))
        | ( ~ member(X2,X1)
          & ~ member(X2,X0) ) )
      & ( member(X2,X1)
        | member(X2,X0)
        | ~ member(X2,union(X0,X1)) ) ),
    inference(flattening,[],[f13]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f3]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(flattening,[],[f15]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X2] :
            ( member(X2,X1)
            | ~ member(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f17]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK0(X0,X1),X1)
        & member(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ member(sK0(X0,X1),X1)
          & member(sK0(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f18,f19]) ).

fof(f25,plain,
    ? [X0,X1] :
      ( ( empty_set != X1
        | empty_set != X0
        | union(X0,X1) != empty_set )
      & ( ( empty_set = X1
          & empty_set = X0 )
        | union(X0,X1) = empty_set ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f26,plain,
    ? [X0,X1] :
      ( ( empty_set != X1
        | empty_set != X0
        | union(X0,X1) != empty_set )
      & ( ( empty_set = X1
          & empty_set = X0 )
        | union(X0,X1) = empty_set ) ),
    inference(flattening,[],[f25]) ).

fof(f27,plain,
    ( ? [X0,X1] :
        ( ( empty_set != X1
          | empty_set != X0
          | union(X0,X1) != empty_set )
        & ( ( empty_set = X1
            & empty_set = X0 )
          | union(X0,X1) = empty_set ) )
   => ( ( empty_set != sK3
        | empty_set != sK2
        | empty_set != union(sK2,sK3) )
      & ( ( empty_set = sK3
          & empty_set = sK2 )
        | empty_set = union(sK2,sK3) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f28,plain,
    ( ( empty_set != sK3
      | empty_set != sK2
      | empty_set != union(sK2,sK3) )
    & ( ( empty_set = sK3
        & empty_set = sK2 )
      | empty_set = union(sK2,sK3) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f26,f27]) ).

fof(f29,plain,
    ! [X2,X0,X1] :
      ( member(X2,X1)
      | member(X2,X0)
      | ~ member(X2,union(X0,X1)) ),
    inference(cnf_transformation,[],[f14]) ).

fof(f30,plain,
    ! [X2,X0,X1] :
      ( member(X2,union(X0,X1))
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f14]) ).

fof(f31,plain,
    ! [X2,X0,X1] :
      ( member(X2,union(X0,X1))
      | ~ member(X2,X1) ),
    inference(cnf_transformation,[],[f14]) ).

fof(f32,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(cnf_transformation,[],[f2]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f36,plain,
    ! [X0,X1] : union(X0,X1) = union(X1,X0),
    inference(cnf_transformation,[],[f4]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK0(X0,X1),X0) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f45,plain,
    ( empty_set = sK2
    | empty_set = union(sK2,sK3) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f46,plain,
    ( empty_set = sK3
    | empty_set = union(sK2,sK3) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f47,plain,
    ( empty_set != sK3
    | empty_set != sK2
    | empty_set != union(sK2,sK3) ),
    inference(cnf_transformation,[],[f28]) ).

cnf(c_49,plain,
    ( ~ member(X0,X1)
    | member(X0,union(X2,X1)) ),
    inference(cnf_transformation,[],[f31]) ).

cnf(c_50,plain,
    ( ~ member(X0,X1)
    | member(X0,union(X1,X2)) ),
    inference(cnf_transformation,[],[f30]) ).

cnf(c_51,plain,
    ( ~ member(X0,union(X1,X2))
    | member(X0,X1)
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f29]) ).

cnf(c_52,plain,
    ~ member(X0,empty_set),
    inference(cnf_transformation,[],[f32]) ).

cnf(c_53,plain,
    ( ~ subset(X0,X1)
    | ~ subset(X1,X0)
    | X0 = X1 ),
    inference(cnf_transformation,[],[f35]) ).

cnf(c_56,plain,
    union(X0,X1) = union(X1,X0),
    inference(cnf_transformation,[],[f36]) ).

cnf(c_58,plain,
    ( member(sK0(X0,X1),X0)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f38]) ).

cnf(c_63,negated_conjecture,
    ( union(sK2,sK3) != empty_set
    | empty_set != sK3
    | empty_set != sK2 ),
    inference(cnf_transformation,[],[f47]) ).

cnf(c_64,negated_conjecture,
    ( union(sK2,sK3) = empty_set
    | empty_set = sK3 ),
    inference(cnf_transformation,[],[f46]) ).

cnf(c_65,negated_conjecture,
    ( union(sK2,sK3) = empty_set
    | empty_set = sK2 ),
    inference(cnf_transformation,[],[f45]) ).

cnf(c_153,plain,
    ( union(sK3,sK2) = empty_set
    | empty_set = sK2 ),
    inference(demodulation,[status(thm)],[c_65,c_56]) ).

cnf(c_158,plain,
    ( union(sK3,sK2) = empty_set
    | empty_set = sK3 ),
    inference(demodulation,[status(thm)],[c_64,c_56]) ).

cnf(c_193,plain,
    ( union(sK3,sK2) != empty_set
    | empty_set != sK3
    | empty_set != sK2 ),
    inference(demodulation,[status(thm)],[c_63,c_56]) ).

cnf(c_537,plain,
    subset(empty_set,X0),
    inference(superposition,[status(thm)],[c_58,c_52]) ).

cnf(c_544,plain,
    ( ~ member(X0,sK2)
    | empty_set = sK3
    | member(X0,empty_set) ),
    inference(superposition,[status(thm)],[c_158,c_49]) ).

cnf(c_545,plain,
    ( ~ member(X0,sK2)
    | empty_set = sK2
    | member(X0,empty_set) ),
    inference(superposition,[status(thm)],[c_153,c_49]) ).

cnf(c_546,plain,
    ( ~ member(X0,sK2)
    | empty_set = sK2 ),
    inference(forward_subsumption_resolution,[status(thm)],[c_545,c_52]) ).

cnf(c_549,plain,
    ( ~ member(X0,sK2)
    | empty_set = sK3 ),
    inference(forward_subsumption_resolution,[status(thm)],[c_544,c_52]) ).

cnf(c_560,plain,
    ( ~ member(X0,sK3)
    | empty_set = sK3
    | member(X0,empty_set) ),
    inference(superposition,[status(thm)],[c_158,c_50]) ).

cnf(c_565,plain,
    ( ~ member(X0,sK3)
    | empty_set = sK3 ),
    inference(forward_subsumption_resolution,[status(thm)],[c_560,c_52]) ).

cnf(c_608,plain,
    ( member(sK0(union(X0,X1),X2),X0)
    | member(sK0(union(X0,X1),X2),X1)
    | subset(union(X0,X1),X2) ),
    inference(superposition,[status(thm)],[c_58,c_51]) ).

cnf(c_621,plain,
    ( empty_set = sK2
    | subset(sK2,X0) ),
    inference(superposition,[status(thm)],[c_58,c_546]) ).

cnf(c_633,plain,
    ( empty_set = sK3
    | subset(sK2,X0) ),
    inference(superposition,[status(thm)],[c_58,c_549]) ).

cnf(c_653,plain,
    ( empty_set = sK3
    | subset(sK3,X0) ),
    inference(superposition,[status(thm)],[c_58,c_565]) ).

cnf(c_672,plain,
    ( ~ subset(X0,empty_set)
    | X0 = empty_set ),
    inference(superposition,[status(thm)],[c_537,c_53]) ).

cnf(c_673,plain,
    ( ~ subset(X0,sK2)
    | X0 = sK2
    | empty_set = sK3 ),
    inference(superposition,[status(thm)],[c_633,c_53]) ).

cnf(c_703,plain,
    ( empty_set = sK3
    | empty_set = sK2 ),
    inference(superposition,[status(thm)],[c_537,c_673]) ).

cnf(c_706,plain,
    ( empty_set = sK3
    | sK3 = sK2 ),
    inference(superposition,[status(thm)],[c_653,c_673]) ).

cnf(c_742,plain,
    empty_set = sK3,
    inference(superposition,[status(thm)],[c_706,c_703]) ).

cnf(c_752,plain,
    ( union(sK3,sK2) != empty_set
    | empty_set != sK2 ),
    inference(backward_subsumption_resolution,[status(thm)],[c_193,c_742]) ).

cnf(c_829,plain,
    empty_set = sK2,
    inference(superposition,[status(thm)],[c_621,c_672]) ).

cnf(c_871,plain,
    union(sK3,sK2) != empty_set,
    inference(global_subsumption_just,[status(thm)],[c_752,c_193,c_742,c_829]) ).

cnf(c_873,plain,
    union(empty_set,empty_set) != empty_set,
    inference(light_normalisation,[status(thm)],[c_871,c_742,c_829]) ).

cnf(c_1294,plain,
    ( member(sK0(union(X0,empty_set),X1),X0)
    | subset(union(X0,empty_set),X1) ),
    inference(superposition,[status(thm)],[c_608,c_52]) ).

cnf(c_1439,plain,
    subset(union(empty_set,empty_set),X0),
    inference(superposition,[status(thm)],[c_1294,c_52]) ).

cnf(c_1467,plain,
    union(empty_set,empty_set) = empty_set,
    inference(superposition,[status(thm)],[c_1439,c_672]) ).

cnf(c_1472,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_1467,c_873]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SET600+3 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.14  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n010.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 : Thu May  2 20:05:34 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.21/0.48  Running first-order theorem proving
% 0.21/0.48  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.87/1.16  % SZS status Started for theBenchmark.p
% 2.87/1.16  % SZS status Theorem for theBenchmark.p
% 2.87/1.16  
% 2.87/1.16  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 2.87/1.16  
% 2.87/1.16  ------  iProver source info
% 2.87/1.16  
% 2.87/1.16  git: date: 2024-05-02 19:28:25 +0000
% 2.87/1.16  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 2.87/1.16  git: non_committed_changes: false
% 2.87/1.16  
% 2.87/1.16  ------ Parsing...
% 2.87/1.16  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 2.87/1.16  
% 2.87/1.16  ------ Preprocessing... sup_sim: 3  sf_s  rm: 1 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 2.87/1.16  
% 2.87/1.16  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 2.87/1.16  
% 2.87/1.16  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.87/1.16  ------ Proving...
% 2.87/1.16  ------ Problem Properties 
% 2.87/1.16  
% 2.87/1.16  
% 2.87/1.16  clauses                                 15
% 2.87/1.16  conjectures                             0
% 2.87/1.16  EPR                                     4
% 2.87/1.16  Horn                                    10
% 2.87/1.16  unary                                   3
% 2.87/1.16  binary                                  6
% 2.87/1.16  lits                                    33
% 2.87/1.16  lits eq                                 11
% 2.87/1.16  fd_pure                                 0
% 2.87/1.16  fd_pseudo                               0
% 2.87/1.16  fd_cond                                 0
% 2.87/1.16  fd_pseudo_cond                          3
% 2.87/1.16  AC symbols                              0
% 2.87/1.16  
% 2.87/1.16  ------ Schedule dynamic 5 is on 
% 2.87/1.16  
% 2.87/1.16  ------ no conjectures: strip conj schedule 
% 2.87/1.16  
% 2.87/1.16  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.87/1.16  
% 2.87/1.16  
% 2.87/1.16  ------ 
% 2.87/1.16  Current options:
% 2.87/1.16  ------ 
% 2.87/1.16  
% 2.87/1.16  
% 2.87/1.16  
% 2.87/1.16  
% 2.87/1.16  ------ Proving...
% 2.87/1.16  
% 2.87/1.16  
% 2.87/1.16  % SZS status Theorem for theBenchmark.p
% 2.87/1.16  
% 2.87/1.16  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.87/1.16  
% 2.87/1.16  
%------------------------------------------------------------------------------