TSTP Solution File: SET907+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET907+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : Fri May  3 03:01:57 EDT 2024

% Result   : Theorem 1.79s 1.21s
% Output   : CNFRefutation 1.79s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   32 (  14 unt;   0 def)
%            Number of atoms       :   71 (  21 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   65 (  26   ~;  17   |;  17   &)
%                                         (   1 <=>;   4  =>;   0  <=;   0 <~>)
%            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   :   49 (   0 sgn  28   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
     => set_union2(X0,X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).

fof(f11,axiom,
    ! [X0,X1,X2] :
      ( subset(unordered_pair(X0,X1),X2)
    <=> ( in(X1,X2)
        & in(X0,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).

fof(f12,conjecture,
    ! [X0,X1,X2] :
      ( ( in(X2,X1)
        & in(X0,X1) )
     => set_union2(unordered_pair(X0,X2),X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_zfmisc_1) ).

fof(f13,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ( in(X2,X1)
          & in(X0,X1) )
       => set_union2(unordered_pair(X0,X2),X1) = X1 ),
    inference(negated_conjecture,[],[f12]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( set_union2(X0,X1) = X1
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f20,plain,
    ? [X0,X1,X2] :
      ( set_union2(unordered_pair(X0,X2),X1) != X1
      & in(X2,X1)
      & in(X0,X1) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f21,plain,
    ? [X0,X1,X2] :
      ( set_union2(unordered_pair(X0,X2),X1) != X1
      & in(X2,X1)
      & in(X0,X1) ),
    inference(flattening,[],[f20]) ).

fof(f26,plain,
    ! [X0,X1,X2] :
      ( ( subset(unordered_pair(X0,X1),X2)
        | ~ in(X1,X2)
        | ~ in(X0,X2) )
      & ( ( in(X1,X2)
          & in(X0,X2) )
        | ~ subset(unordered_pair(X0,X1),X2) ) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( ( subset(unordered_pair(X0,X1),X2)
        | ~ in(X1,X2)
        | ~ in(X0,X2) )
      & ( ( in(X1,X2)
          & in(X0,X2) )
        | ~ subset(unordered_pair(X0,X1),X2) ) ),
    inference(flattening,[],[f26]) ).

fof(f28,plain,
    ( ? [X0,X1,X2] :
        ( set_union2(unordered_pair(X0,X2),X1) != X1
        & in(X2,X1)
        & in(X0,X1) )
   => ( sK3 != set_union2(unordered_pair(sK2,sK4),sK3)
      & in(sK4,sK3)
      & in(sK2,sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f29,plain,
    ( sK3 != set_union2(unordered_pair(sK2,sK4),sK3)
    & in(sK4,sK3)
    & in(sK2,sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f21,f28]) ).

fof(f32,plain,
    ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
    inference(cnf_transformation,[],[f3]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( set_union2(X0,X1) = X1
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f42,plain,
    ! [X2,X0,X1] :
      ( subset(unordered_pair(X0,X1),X2)
      | ~ in(X1,X2)
      | ~ in(X0,X2) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f43,plain,
    in(sK2,sK3),
    inference(cnf_transformation,[],[f29]) ).

fof(f44,plain,
    in(sK4,sK3),
    inference(cnf_transformation,[],[f29]) ).

fof(f45,plain,
    sK3 != set_union2(unordered_pair(sK2,sK4),sK3),
    inference(cnf_transformation,[],[f29]) ).

cnf(c_51,plain,
    set_union2(X0,X1) = set_union2(X1,X0),
    inference(cnf_transformation,[],[f32]) ).

cnf(c_58,plain,
    ( ~ subset(X0,X1)
    | set_union2(X0,X1) = X1 ),
    inference(cnf_transformation,[],[f39]) ).

cnf(c_59,plain,
    ( ~ in(X0,X1)
    | ~ in(X2,X1)
    | subset(unordered_pair(X2,X0),X1) ),
    inference(cnf_transformation,[],[f42]) ).

cnf(c_62,negated_conjecture,
    set_union2(unordered_pair(sK2,sK4),sK3) != sK3,
    inference(cnf_transformation,[],[f45]) ).

cnf(c_63,negated_conjecture,
    in(sK4,sK3),
    inference(cnf_transformation,[],[f44]) ).

cnf(c_64,negated_conjecture,
    in(sK2,sK3),
    inference(cnf_transformation,[],[f43]) ).

cnf(c_130,plain,
    set_union2(sK3,unordered_pair(sK2,sK4)) != sK3,
    inference(demodulation,[status(thm)],[c_62,c_51]) ).

cnf(c_222,negated_conjecture,
    in(sK2,sK3),
    inference(demodulation,[status(thm)],[c_64]) ).

cnf(c_223,negated_conjecture,
    in(sK4,sK3),
    inference(demodulation,[status(thm)],[c_63]) ).

cnf(c_468,plain,
    ( ~ in(X0,X1)
    | ~ in(X2,X1)
    | set_union2(unordered_pair(X2,X0),X1) = X1 ),
    inference(superposition,[status(thm)],[c_59,c_58]) ).

cnf(c_480,plain,
    ( ~ in(X0,sK3)
    | set_union2(unordered_pair(X0,sK4),sK3) = sK3 ),
    inference(superposition,[status(thm)],[c_223,c_468]) ).

cnf(c_493,plain,
    ( ~ in(X0,sK3)
    | set_union2(sK3,unordered_pair(X0,sK4)) = sK3 ),
    inference(demodulation,[status(thm)],[c_480,c_51]) ).

cnf(c_499,plain,
    set_union2(sK3,unordered_pair(sK2,sK4)) = sK3,
    inference(superposition,[status(thm)],[c_222,c_493]) ).

cnf(c_500,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_499,c_130]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SET907+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14  % Command  : run_iprover %s %d THM
% 0.14/0.35  % Computer : n028.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 : Thu May  2 20:37:48 EDT 2024
% 0.14/0.35  % 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 --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 1.79/1.21  % SZS status Started for theBenchmark.p
% 1.79/1.21  % SZS status Theorem for theBenchmark.p
% 1.79/1.21  
% 1.79/1.21  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 1.79/1.21  
% 1.79/1.21  ------  iProver source info
% 1.79/1.21  
% 1.79/1.21  git: date: 2024-05-02 19:28:25 +0000
% 1.79/1.21  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 1.79/1.21  git: non_committed_changes: false
% 1.79/1.21  
% 1.79/1.21  ------ Parsing...
% 1.79/1.21  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 1.79/1.21  
% 1.79/1.21  ------ Preprocessing... sup_sim: 1  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 1.79/1.21  
% 1.79/1.21  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 1.79/1.21  
% 1.79/1.21  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 1.79/1.21  ------ Proving...
% 1.79/1.21  ------ Problem Properties 
% 1.79/1.21  
% 1.79/1.21  
% 1.79/1.21  clauses                                 16
% 1.79/1.21  conjectures                             2
% 1.79/1.21  EPR                                     6
% 1.79/1.21  Horn                                    16
% 1.79/1.21  unary                                   9
% 1.79/1.21  binary                                  6
% 1.79/1.21  lits                                    24
% 1.79/1.21  lits eq                                 5
% 1.79/1.21  fd_pure                                 0
% 1.79/1.21  fd_pseudo                               0
% 1.79/1.21  fd_cond                                 0
% 1.79/1.21  fd_pseudo_cond                          0
% 1.79/1.21  AC symbols                              0
% 1.79/1.21  
% 1.79/1.21  ------ Schedule dynamic 5 is on 
% 1.79/1.21  
% 1.79/1.21  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.79/1.21  
% 1.79/1.21  
% 1.79/1.21  ------ 
% 1.79/1.21  Current options:
% 1.79/1.21  ------ 
% 1.79/1.21  
% 1.79/1.21  
% 1.79/1.21  
% 1.79/1.21  
% 1.79/1.21  ------ Proving...
% 1.79/1.21  
% 1.79/1.21  
% 1.79/1.21  % SZS status Theorem for theBenchmark.p
% 1.79/1.21  
% 1.79/1.21  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.79/1.21  
% 1.79/1.21  
%------------------------------------------------------------------------------