TSTP Solution File: SET954+1 by iProver---3.8

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%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SET954+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n014.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 15:10:48 EDT 2023

% Result   : Theorem 2.31s 1.17s
% Output   : CNFRefutation 2.31s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   40 (  17 unt;   0 def)
%            Number of atoms       :   78 (   5 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   74 (  36   ~;  25   |;   9   &)
%                                         (   1 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   94 (   9 sgn;  52   !;   8   ?)

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

fof(f3,axiom,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).

fof(f5,axiom,
    ! [X0,X1,X2,X3] :
      ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
    <=> ( in(X1,X3)
        & in(X0,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).

fof(f8,conjecture,
    ! [X0,X1,X2,X3] :
      ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
     => in(ordered_pair(X1,X0),cartesian_product2(X3,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t107_zfmisc_1) ).

fof(f9,negated_conjecture,
    ~ ! [X0,X1,X2,X3] :
        ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
       => in(ordered_pair(X1,X0),cartesian_product2(X3,X2)) ),
    inference(negated_conjecture,[],[f8]) ).

fof(f11,plain,
    ? [X0,X1,X2,X3] :
      ( ~ in(ordered_pair(X1,X0),cartesian_product2(X3,X2))
      & in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f12,plain,
    ! [X0,X1,X2,X3] :
      ( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
        | ~ in(X1,X3)
        | ~ in(X0,X2) )
      & ( ( in(X1,X3)
          & in(X0,X2) )
        | ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
    inference(nnf_transformation,[],[f5]) ).

fof(f13,plain,
    ! [X0,X1,X2,X3] :
      ( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
        | ~ in(X1,X3)
        | ~ in(X0,X2) )
      & ( ( in(X1,X3)
          & in(X0,X2) )
        | ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
    inference(flattening,[],[f12]) ).

fof(f18,plain,
    ( ? [X0,X1,X2,X3] :
        ( ~ in(ordered_pair(X1,X0),cartesian_product2(X3,X2))
        & in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) )
   => ( ~ in(ordered_pair(sK3,sK2),cartesian_product2(sK5,sK4))
      & in(ordered_pair(sK2,sK3),cartesian_product2(sK4,sK5)) ) ),
    introduced(choice_axiom,[]) ).

fof(f19,plain,
    ( ~ in(ordered_pair(sK3,sK2),cartesian_product2(sK5,sK4))
    & in(ordered_pair(sK2,sK3),cartesian_product2(sK4,sK5)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f11,f18]) ).

fof(f21,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[],[f2]) ).

fof(f22,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    inference(cnf_transformation,[],[f3]) ).

fof(f24,plain,
    ! [X2,X3,X0,X1] :
      ( in(X0,X2)
      | ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f25,plain,
    ! [X2,X3,X0,X1] :
      ( in(X1,X3)
      | ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f26,plain,
    ! [X2,X3,X0,X1] :
      ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
      | ~ in(X1,X3)
      | ~ in(X0,X2) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f29,plain,
    in(ordered_pair(sK2,sK3),cartesian_product2(sK4,sK5)),
    inference(cnf_transformation,[],[f19]) ).

fof(f30,plain,
    ~ in(ordered_pair(sK3,sK2),cartesian_product2(sK5,sK4)),
    inference(cnf_transformation,[],[f19]) ).

fof(f32,plain,
    ! [X2,X3,X0,X1] :
      ( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
      | ~ in(X1,X3)
      | ~ in(X0,X2) ),
    inference(definition_unfolding,[],[f26,f22]) ).

fof(f33,plain,
    ! [X2,X3,X0,X1] :
      ( in(X1,X3)
      | ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
    inference(definition_unfolding,[],[f25,f22]) ).

fof(f34,plain,
    ! [X2,X3,X0,X1] :
      ( in(X0,X2)
      | ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
    inference(definition_unfolding,[],[f24,f22]) ).

fof(f35,plain,
    ~ in(unordered_pair(unordered_pair(sK3,sK2),singleton(sK3)),cartesian_product2(sK5,sK4)),
    inference(definition_unfolding,[],[f30,f22]) ).

fof(f36,plain,
    in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),cartesian_product2(sK4,sK5)),
    inference(definition_unfolding,[],[f29,f22]) ).

cnf(c_50,plain,
    unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[],[f21]) ).

cnf(c_52,plain,
    ( ~ in(X0,X1)
    | ~ in(X2,X3)
    | in(unordered_pair(unordered_pair(X2,X0),singleton(X2)),cartesian_product2(X3,X1)) ),
    inference(cnf_transformation,[],[f32]) ).

cnf(c_53,plain,
    ( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
    | in(X1,X3) ),
    inference(cnf_transformation,[],[f33]) ).

cnf(c_54,plain,
    ( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
    | in(X0,X2) ),
    inference(cnf_transformation,[],[f34]) ).

cnf(c_57,negated_conjecture,
    ~ in(unordered_pair(unordered_pair(sK3,sK2),singleton(sK3)),cartesian_product2(sK5,sK4)),
    inference(cnf_transformation,[],[f35]) ).

cnf(c_58,negated_conjecture,
    in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),cartesian_product2(sK4,sK5)),
    inference(cnf_transformation,[],[f36]) ).

cnf(c_96,plain,
    in(unordered_pair(singleton(sK2),unordered_pair(sK3,sK2)),cartesian_product2(sK4,sK5)),
    inference(demodulation,[status(thm)],[c_58,c_50]) ).

cnf(c_97,plain,
    ~ in(unordered_pair(singleton(sK3),unordered_pair(sK3,sK2)),cartesian_product2(sK5,sK4)),
    inference(demodulation,[status(thm)],[c_57,c_50]) ).

cnf(c_98,plain,
    ( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
    | in(X0,X2) ),
    inference(demodulation,[status(thm)],[c_54,c_50]) ).

cnf(c_103,plain,
    ( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
    | in(X1,X3) ),
    inference(demodulation,[status(thm)],[c_53,c_50]) ).

cnf(c_108,plain,
    ( ~ in(X0,X1)
    | ~ in(X2,X3)
    | in(unordered_pair(singleton(X2),unordered_pair(X2,X0)),cartesian_product2(X3,X1)) ),
    inference(demodulation,[status(thm)],[c_52,c_50]) ).

cnf(c_295,plain,
    ( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
    | in(X0,X2) ),
    inference(superposition,[status(thm)],[c_50,c_98]) ).

cnf(c_303,plain,
    ( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
    | in(X1,X3) ),
    inference(superposition,[status(thm)],[c_50,c_103]) ).

cnf(c_316,plain,
    ( ~ in(sK3,sK5)
    | ~ in(sK2,sK4) ),
    inference(superposition,[status(thm)],[c_108,c_97]) ).

cnf(c_337,plain,
    in(sK2,sK4),
    inference(superposition,[status(thm)],[c_96,c_295]) ).

cnf(c_341,plain,
    ~ in(sK3,sK5),
    inference(backward_subsumption_resolution,[status(thm)],[c_316,c_337]) ).

cnf(c_347,plain,
    in(sK3,sK5),
    inference(superposition,[status(thm)],[c_96,c_303]) ).

cnf(c_351,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_347,c_341]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET954+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14  % Command  : run_iprover %s %d THM
% 0.13/0.36  % Computer : n014.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit : 300
% 0.13/0.36  % WCLimit  : 300
% 0.13/0.36  % DateTime : Sat Aug 26 08:29:32 EDT 2023
% 0.13/0.36  % 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 --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.31/1.17  % SZS status Started for theBenchmark.p
% 2.31/1.17  % SZS status Theorem for theBenchmark.p
% 2.31/1.17  
% 2.31/1.17  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.31/1.17  
% 2.31/1.17  ------  iProver source info
% 2.31/1.17  
% 2.31/1.17  git: date: 2023-05-31 18:12:56 +0000
% 2.31/1.17  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.31/1.17  git: non_committed_changes: false
% 2.31/1.17  git: last_make_outside_of_git: false
% 2.31/1.17  
% 2.31/1.17  ------ Parsing...
% 2.31/1.17  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 2.31/1.17  
% 2.31/1.17  ------ Preprocessing... sup_sim: 6  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 2.31/1.17  
% 2.31/1.17  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 2.31/1.17  
% 2.31/1.17  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.31/1.17  ------ Proving...
% 2.31/1.17  ------ Problem Properties 
% 2.31/1.17  
% 2.31/1.17  
% 2.31/1.17  clauses                                 10
% 2.31/1.17  conjectures                             0
% 2.31/1.17  EPR                                     3
% 2.31/1.17  Horn                                    10
% 2.31/1.17  unary                                   6
% 2.31/1.17  binary                                  3
% 2.31/1.17  lits                                    15
% 2.31/1.17  lits eq                                 1
% 2.31/1.17  fd_pure                                 0
% 2.31/1.17  fd_pseudo                               0
% 2.31/1.17  fd_cond                                 0
% 2.31/1.17  fd_pseudo_cond                          0
% 2.31/1.17  AC symbols                              0
% 2.31/1.17  
% 2.31/1.17  ------ Schedule dynamic 5 is on 
% 2.31/1.17  
% 2.31/1.17  ------ no conjectures: strip conj schedule 
% 2.31/1.17  
% 2.31/1.17  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.31/1.17  
% 2.31/1.17  
% 2.31/1.17  ------ 
% 2.31/1.17  Current options:
% 2.31/1.17  ------ 
% 2.31/1.17  
% 2.31/1.17  
% 2.31/1.17  
% 2.31/1.17  
% 2.31/1.17  ------ Proving...
% 2.31/1.17  
% 2.31/1.17  
% 2.31/1.17  % SZS status Theorem for theBenchmark.p
% 2.31/1.17  
% 2.31/1.17  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.31/1.17  
% 2.31/1.17  
%------------------------------------------------------------------------------