TSTP Solution File: SET928+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET928+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n020.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 : Mon Jun 24 14:36:36 EDT 2024

% Result   : Theorem 2.22s 1.18s
% Output   : CNFRefutation 2.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   51 (   9 unt;   0 def)
%            Number of atoms       :  129 (  42 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  138 (  60   ~;  56   |;  17   &)
%                                         (   3 <=>;   1  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    9 (   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   :   68 (   3 sgn  36   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

fof(f6,axiom,
    ! [X0,X1,X2] :
      ~ ( in(X0,X2)
        & disjoint(unordered_pair(X0,X1),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_zfmisc_1) ).

fof(f7,axiom,
    ! [X0,X1,X2] :
      ~ ( ~ disjoint(unordered_pair(X0,X2),X1)
        & ~ in(X2,X1)
        & ~ in(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_zfmisc_1) ).

fof(f8,conjecture,
    ! [X0,X1,X2] :
      ( unordered_pair(X0,X1) = set_difference(unordered_pair(X0,X1),X2)
    <=> ( ~ in(X1,X2)
        & ~ in(X0,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_zfmisc_1) ).

fof(f9,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( unordered_pair(X0,X1) = set_difference(unordered_pair(X0,X1),X2)
      <=> ( ~ in(X1,X2)
          & ~ in(X0,X2) ) ),
    inference(negated_conjecture,[],[f8]) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( disjoint(X0,X1)
    <=> set_difference(X0,X1) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).

fof(f13,plain,
    ! [X0,X1,X2] :
      ( ~ in(X0,X2)
      | ~ disjoint(unordered_pair(X0,X1),X2) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f14,plain,
    ! [X0,X1,X2] :
      ( disjoint(unordered_pair(X0,X2),X1)
      | in(X2,X1)
      | in(X0,X1) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f15,plain,
    ? [X0,X1,X2] :
      ( unordered_pair(X0,X1) = set_difference(unordered_pair(X0,X1),X2)
    <~> ( ~ in(X1,X2)
        & ~ in(X0,X2) ) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f20,plain,
    ? [X0,X1,X2] :
      ( ( in(X1,X2)
        | in(X0,X2)
        | unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2) )
      & ( ( ~ in(X1,X2)
          & ~ in(X0,X2) )
        | unordered_pair(X0,X1) = set_difference(unordered_pair(X0,X1),X2) ) ),
    inference(nnf_transformation,[],[f15]) ).

fof(f21,plain,
    ? [X0,X1,X2] :
      ( ( in(X1,X2)
        | in(X0,X2)
        | unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2) )
      & ( ( ~ in(X1,X2)
          & ~ in(X0,X2) )
        | unordered_pair(X0,X1) = set_difference(unordered_pair(X0,X1),X2) ) ),
    inference(flattening,[],[f20]) ).

fof(f22,plain,
    ( ? [X0,X1,X2] :
        ( ( in(X1,X2)
          | in(X0,X2)
          | unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2) )
        & ( ( ~ in(X1,X2)
            & ~ in(X0,X2) )
          | unordered_pair(X0,X1) = set_difference(unordered_pair(X0,X1),X2) ) )
   => ( ( in(sK3,sK4)
        | in(sK2,sK4)
        | unordered_pair(sK2,sK3) != set_difference(unordered_pair(sK2,sK3),sK4) )
      & ( ( ~ in(sK3,sK4)
          & ~ in(sK2,sK4) )
        | unordered_pair(sK2,sK3) = set_difference(unordered_pair(sK2,sK3),sK4) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f23,plain,
    ( ( in(sK3,sK4)
      | in(sK2,sK4)
      | unordered_pair(sK2,sK3) != set_difference(unordered_pair(sK2,sK3),sK4) )
    & ( ( ~ in(sK3,sK4)
        & ~ in(sK2,sK4) )
      | unordered_pair(sK2,sK3) = set_difference(unordered_pair(sK2,sK3),sK4) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f21,f22]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ( disjoint(X0,X1)
        | set_difference(X0,X1) != X0 )
      & ( set_difference(X0,X1) = X0
        | ~ disjoint(X0,X1) ) ),
    inference(nnf_transformation,[],[f10]) ).

fof(f26,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[],[f2]) ).

fof(f30,plain,
    ! [X2,X0,X1] :
      ( ~ in(X0,X2)
      | ~ disjoint(unordered_pair(X0,X1),X2) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f31,plain,
    ! [X2,X0,X1] :
      ( disjoint(unordered_pair(X0,X2),X1)
      | in(X2,X1)
      | in(X0,X1) ),
    inference(cnf_transformation,[],[f14]) ).

fof(f32,plain,
    ( ~ in(sK2,sK4)
    | unordered_pair(sK2,sK3) = set_difference(unordered_pair(sK2,sK3),sK4) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f33,plain,
    ( ~ in(sK3,sK4)
    | unordered_pair(sK2,sK3) = set_difference(unordered_pair(sK2,sK3),sK4) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f34,plain,
    ( in(sK3,sK4)
    | in(sK2,sK4)
    | unordered_pair(sK2,sK3) != set_difference(unordered_pair(sK2,sK3),sK4) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( set_difference(X0,X1) = X0
      | ~ disjoint(X0,X1) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( disjoint(X0,X1)
      | set_difference(X0,X1) != X0 ),
    inference(cnf_transformation,[],[f24]) ).

cnf(c_50,plain,
    unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[],[f26]) ).

cnf(c_54,plain,
    ( ~ disjoint(unordered_pair(X0,X1),X2)
    | ~ in(X0,X2) ),
    inference(cnf_transformation,[],[f30]) ).

cnf(c_55,plain,
    ( disjoint(unordered_pair(X0,X1),X2)
    | in(X0,X2)
    | in(X1,X2) ),
    inference(cnf_transformation,[],[f31]) ).

cnf(c_56,negated_conjecture,
    ( set_difference(unordered_pair(sK2,sK3),sK4) != unordered_pair(sK2,sK3)
    | in(sK3,sK4)
    | in(sK2,sK4) ),
    inference(cnf_transformation,[],[f34]) ).

cnf(c_57,negated_conjecture,
    ( ~ in(sK3,sK4)
    | set_difference(unordered_pair(sK2,sK3),sK4) = unordered_pair(sK2,sK3) ),
    inference(cnf_transformation,[],[f33]) ).

cnf(c_58,negated_conjecture,
    ( ~ in(sK2,sK4)
    | set_difference(unordered_pair(sK2,sK3),sK4) = unordered_pair(sK2,sK3) ),
    inference(cnf_transformation,[],[f32]) ).

cnf(c_59,plain,
    ( set_difference(X0,X1) != X0
    | disjoint(X0,X1) ),
    inference(cnf_transformation,[],[f36]) ).

cnf(c_60,plain,
    ( ~ disjoint(X0,X1)
    | set_difference(X0,X1) = X0 ),
    inference(cnf_transformation,[],[f35]) ).

cnf(c_82,plain,
    ( ~ in(sK3,sK4)
    | set_difference(unordered_pair(sK2,sK3),sK4) = unordered_pair(sK2,sK3) ),
    inference(prop_impl_just,[status(thm)],[c_57]) ).

cnf(c_84,plain,
    ( ~ in(sK2,sK4)
    | set_difference(unordered_pair(sK2,sK3),sK4) = unordered_pair(sK2,sK3) ),
    inference(prop_impl_just,[status(thm)],[c_58]) ).

cnf(c_183,plain,
    ( ~ in(sK2,sK4)
    | set_difference(unordered_pair(sK3,sK2),sK4) = unordered_pair(sK3,sK2) ),
    inference(demodulation,[status(thm)],[c_84,c_50]) ).

cnf(c_190,plain,
    ( ~ in(sK3,sK4)
    | set_difference(unordered_pair(sK3,sK2),sK4) = unordered_pair(sK3,sK2) ),
    inference(demodulation,[status(thm)],[c_82,c_50]) ).

cnf(c_197,plain,
    ( set_difference(unordered_pair(sK3,sK2),sK4) != unordered_pair(sK3,sK2)
    | in(sK3,sK4)
    | in(sK2,sK4) ),
    inference(demodulation,[status(thm)],[c_56,c_50]) ).

cnf(c_236,plain,
    ( ~ in(sK3,sK4)
    | set_difference(unordered_pair(sK3,sK2),sK4) = unordered_pair(sK3,sK2) ),
    inference(prop_impl_just,[status(thm)],[c_190]) ).

cnf(c_238,plain,
    ( ~ in(sK2,sK4)
    | set_difference(unordered_pair(sK3,sK2),sK4) = unordered_pair(sK3,sK2) ),
    inference(prop_impl_just,[status(thm)],[c_183]) ).

cnf(c_651,plain,
    ( ~ disjoint(unordered_pair(X0,X1),X2)
    | ~ in(X1,X2) ),
    inference(superposition,[status(thm)],[c_50,c_54]) ).

cnf(c_675,plain,
    ( set_difference(unordered_pair(X0,X1),X2) = unordered_pair(X0,X1)
    | in(X0,X2)
    | in(X1,X2) ),
    inference(superposition,[status(thm)],[c_55,c_60]) ).

cnf(c_808,plain,
    ( set_difference(unordered_pair(sK3,sK2),sK4) != unordered_pair(sK3,sK2)
    | disjoint(unordered_pair(sK3,sK2),sK4) ),
    inference(instantiation,[status(thm)],[c_59]) ).

cnf(c_844,plain,
    ( in(sK3,sK4)
    | in(sK2,sK4) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_197,c_675]) ).

cnf(c_857,plain,
    ( set_difference(unordered_pair(sK3,X0),sK4) = unordered_pair(sK3,X0)
    | set_difference(unordered_pair(sK3,sK2),sK4) = unordered_pair(sK3,sK2)
    | in(X0,sK4) ),
    inference(superposition,[status(thm)],[c_675,c_236]) ).

cnf(c_904,plain,
    ( set_difference(unordered_pair(sK3,sK2),sK4) = unordered_pair(sK3,sK2)
    | in(sK2,sK4) ),
    inference(instantiation,[status(thm)],[c_857]) ).

cnf(c_916,plain,
    ( ~ disjoint(unordered_pair(sK3,X0),sK4)
    | ~ in(sK3,sK4) ),
    inference(instantiation,[status(thm)],[c_54]) ).

cnf(c_917,plain,
    ( ~ disjoint(unordered_pair(sK3,sK2),sK4)
    | ~ in(sK3,sK4) ),
    inference(instantiation,[status(thm)],[c_916]) ).

cnf(c_920,plain,
    in(sK2,sK4),
    inference(global_subsumption_just,[status(thm)],[c_197,c_808,c_844,c_904,c_917]) ).

cnf(c_922,plain,
    in(sK2,sK4),
    inference(global_subsumption_just,[status(thm)],[c_844,c_920]) ).

cnf(c_924,plain,
    set_difference(unordered_pair(sK3,sK2),sK4) = unordered_pair(sK3,sK2),
    inference(backward_subsumption_resolution,[status(thm)],[c_238,c_922]) ).

cnf(c_965,plain,
    disjoint(unordered_pair(sK3,sK2),sK4),
    inference(superposition,[status(thm)],[c_924,c_59]) ).

cnf(c_1030,plain,
    ~ in(sK2,sK4),
    inference(superposition,[status(thm)],[c_965,c_651]) ).

cnf(c_1032,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_1030,c_922]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SET928+1 : TPTP v8.2.0. Released v3.2.0.
% 0.07/0.13  % Command  : run_iprover %s %d THM
% 0.14/0.35  % Computer : n020.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Sun Jun 23 15:32:24 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.22/0.49  Running first-order theorem proving
% 0.22/0.49  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.22/1.18  % SZS status Started for theBenchmark.p
% 2.22/1.18  % SZS status Theorem for theBenchmark.p
% 2.22/1.18  
% 2.22/1.18  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 2.22/1.18  
% 2.22/1.18  ------  iProver source info
% 2.22/1.18  
% 2.22/1.18  git: date: 2024-06-12 09:56:46 +0000
% 2.22/1.18  git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 2.22/1.18  git: non_committed_changes: false
% 2.22/1.18  
% 2.22/1.18  ------ Parsing...
% 2.22/1.18  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 2.22/1.18  
% 2.22/1.18  ------ Preprocessing... sup_sim: 3  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e 
% 2.22/1.18  
% 2.22/1.18  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 2.22/1.18  
% 2.22/1.18  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.22/1.18  ------ Proving...
% 2.22/1.18  ------ Problem Properties 
% 2.22/1.18  
% 2.22/1.18  
% 2.22/1.18  clauses                                 11
% 2.22/1.18  conjectures                             0
% 2.22/1.18  EPR                                     3
% 2.22/1.18  Horn                                    9
% 2.22/1.18  unary                                   2
% 2.22/1.18  binary                                  7
% 2.22/1.18  lits                                    22
% 2.22/1.18  lits eq                                 7
% 2.22/1.18  fd_pure                                 0
% 2.22/1.18  fd_pseudo                               0
% 2.22/1.18  fd_cond                                 0
% 2.22/1.18  fd_pseudo_cond                          0
% 2.22/1.18  AC symbols                              0
% 2.22/1.18  
% 2.22/1.18  ------ Schedule dynamic 5 is on 
% 2.22/1.18  
% 2.22/1.18  ------ no conjectures: strip conj schedule 
% 2.22/1.18  
% 2.22/1.18  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.22/1.18  
% 2.22/1.18  
% 2.22/1.18  ------ 
% 2.22/1.18  Current options:
% 2.22/1.18  ------ 
% 2.22/1.18  
% 2.22/1.18  
% 2.22/1.18  
% 2.22/1.18  
% 2.22/1.18  ------ Proving...
% 2.22/1.18  
% 2.22/1.18  
% 2.22/1.18  % SZS status Theorem for theBenchmark.p
% 2.22/1.18  
% 2.22/1.18  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.22/1.18  
% 2.22/1.18  
%------------------------------------------------------------------------------