TSTP Solution File: SET962+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET962+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 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 03:02:07 EDT 2024

% Result   : Theorem 0.45s 1.14s
% Output   : CNFRefutation 0.45s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% 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] :
      ( cartesian_product2(X0,X0) = cartesian_product2(X1,X1)
     => X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_zfmisc_1) ).

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

fof(f10,axiom,
    ! [X0,X1] :
      ( ! [X2] :
          ( in(X2,X0)
        <=> in(X2,X1) )
     => X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).

fof(f12,plain,
    ? [X0,X1] :
      ( X0 != X1
      & cartesian_product2(X0,X0) = cartesian_product2(X1,X1) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f13,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ? [X2] :
          ( in(X2,X0)
        <~> in(X2,X1) ) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f14,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(f15,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,[],[f14]) ).

fof(f20,plain,
    ( ? [X0,X1] :
        ( X0 != X1
        & cartesian_product2(X0,X0) = cartesian_product2(X1,X1) )
   => ( sK2 != sK3
      & cartesian_product2(sK2,sK2) = cartesian_product2(sK3,sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f21,plain,
    ( sK2 != sK3
    & cartesian_product2(sK2,sK2) = cartesian_product2(sK3,sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f12,f20]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ? [X2] :
          ( ( ~ in(X2,X1)
            | ~ in(X2,X0) )
          & ( in(X2,X1)
            | in(X2,X0) ) ) ),
    inference(nnf_transformation,[],[f13]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ in(X2,X1)
            | ~ in(X2,X0) )
          & ( in(X2,X1)
            | in(X2,X0) ) )
     => ( ( ~ in(sK4(X0,X1),X1)
          | ~ in(sK4(X0,X1),X0) )
        & ( in(sK4(X0,X1),X1)
          | in(sK4(X0,X1),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ( ( ~ in(sK4(X0,X1),X1)
          | ~ in(sK4(X0,X1),X0) )
        & ( in(sK4(X0,X1),X1)
          | in(sK4(X0,X1),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f22,f23]) ).

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

fof(f27,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    inference(cnf_transformation,[],[f3]) ).

fof(f30,plain,
    ! [X2,X3,X0,X1] :
      ( in(X1,X3)
      | ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f31,plain,
    ! [X2,X3,X0,X1] :
      ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
      | ~ in(X1,X3)
      | ~ in(X0,X2) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f34,plain,
    cartesian_product2(sK2,sK2) = cartesian_product2(sK3,sK3),
    inference(cnf_transformation,[],[f21]) ).

fof(f35,plain,
    sK2 != sK3,
    inference(cnf_transformation,[],[f21]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( X0 = X1
      | in(sK4(X0,X1),X1)
      | in(sK4(X0,X1),X0) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ in(sK4(X0,X1),X1)
      | ~ in(sK4(X0,X1),X0) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f39,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,[],[f31,f27]) ).

fof(f40,plain,
    ! [X2,X3,X0,X1] :
      ( in(X1,X3)
      | ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
    inference(definition_unfolding,[],[f30,f27]) ).

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

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,[],[f39]) ).

cnf(c_53,plain,
    ( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
    | in(X1,X3) ),
    inference(cnf_transformation,[],[f40]) ).

cnf(c_57,negated_conjecture,
    sK2 != sK3,
    inference(cnf_transformation,[],[f35]) ).

cnf(c_58,negated_conjecture,
    cartesian_product2(sK2,sK2) = cartesian_product2(sK3,sK3),
    inference(cnf_transformation,[],[f34]) ).

cnf(c_59,plain,
    ( ~ in(sK4(X0,X1),X0)
    | ~ in(sK4(X0,X1),X1)
    | X0 = X1 ),
    inference(cnf_transformation,[],[f37]) ).

cnf(c_60,plain,
    ( X0 = X1
    | in(sK4(X0,X1),X0)
    | in(sK4(X0,X1),X1) ),
    inference(cnf_transformation,[],[f36]) ).

cnf(c_123,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_134,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_161,plain,
    cartesian_product2(sK2,sK2) = sP0_iProver_def,
    definition ).

cnf(c_162,plain,
    cartesian_product2(sK3,sK3) = sP1_iProver_def,
    definition ).

cnf(c_163,negated_conjecture,
    sP0_iProver_def = sP1_iProver_def,
    inference(demodulation,[status(thm)],[c_58,c_162,c_161]) ).

cnf(c_164,negated_conjecture,
    sK2 != sK3,
    inference(demodulation,[status(thm)],[c_57]) ).

cnf(c_337,plain,
    cartesian_product2(sK3,sK3) = sP0_iProver_def,
    inference(light_normalisation,[status(thm)],[c_162,c_163]) ).

cnf(c_380,plain,
    ( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sP0_iProver_def)
    | in(X1,sK2) ),
    inference(superposition,[status(thm)],[c_161,c_123]) ).

cnf(c_381,plain,
    ( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sP0_iProver_def)
    | in(X1,sK3) ),
    inference(superposition,[status(thm)],[c_337,c_123]) ).

cnf(c_418,plain,
    ( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sP0_iProver_def)
    | in(X1,sK2) ),
    inference(superposition,[status(thm)],[c_50,c_380]) ).

cnf(c_426,plain,
    ( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sP0_iProver_def)
    | in(X1,sK3) ),
    inference(superposition,[status(thm)],[c_50,c_381]) ).

cnf(c_484,plain,
    ( ~ in(X0,sK2)
    | ~ in(X1,sK2)
    | in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_161,c_134]) ).

cnf(c_485,plain,
    ( ~ in(X0,sK3)
    | ~ in(X1,sK3)
    | in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_337,c_134]) ).

cnf(c_525,plain,
    ( ~ in(X0,sK2)
    | in(X0,sK3) ),
    inference(superposition,[status(thm)],[c_484,c_426]) ).

cnf(c_543,plain,
    ( ~ in(sK4(sK2,sK3),sK2)
    | ~ in(sK4(sK2,sK3),sK3)
    | sK2 = sK3 ),
    inference(instantiation,[status(thm)],[c_59]) ).

cnf(c_557,plain,
    ( ~ in(X0,sK3)
    | in(X0,sK2) ),
    inference(superposition,[status(thm)],[c_485,c_418]) ).

cnf(c_632,plain,
    ( X0 = sK3
    | in(sK4(X0,sK3),X0)
    | in(sK4(X0,sK3),sK2) ),
    inference(superposition,[status(thm)],[c_60,c_557]) ).

cnf(c_641,plain,
    ( sK2 = sK3
    | in(sK4(sK2,sK3),sK2) ),
    inference(instantiation,[status(thm)],[c_632]) ).

cnf(c_692,plain,
    ( sK2 = sK3
    | in(sK4(sK2,sK3),sK2) ),
    inference(equality_factoring,[status(thm)],[c_632]) ).

cnf(c_694,plain,
    in(sK4(sK2,sK3),sK2),
    inference(forward_subsumption_resolution,[status(thm)],[c_692,c_164]) ).

cnf(c_712,plain,
    in(sK4(sK2,sK3),sK3),
    inference(superposition,[status(thm)],[c_694,c_525]) ).

cnf(c_713,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_712,c_641,c_543,c_57]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11  % Problem  : SET962+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.09/0.12  % Command  : run_iprover %s %d THM
% 0.11/0.32  % Computer : n010.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Thu May  2 20:03:49 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.17/0.44  Running first-order theorem proving
% 0.17/0.44  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
% 0.45/1.14  % SZS status Started for theBenchmark.p
% 0.45/1.14  % SZS status Theorem for theBenchmark.p
% 0.45/1.14  
% 0.45/1.14  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 0.45/1.14  
% 0.45/1.14  ------  iProver source info
% 0.45/1.14  
% 0.45/1.14  git: date: 2024-05-02 19:28:25 +0000
% 0.45/1.14  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 0.45/1.14  git: non_committed_changes: false
% 0.45/1.14  
% 0.45/1.14  ------ Parsing...
% 0.45/1.14  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 0.45/1.14  
% 0.45/1.14  ------ Preprocessing... sup_sim: 4  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 0.45/1.14  
% 0.45/1.14  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 0.45/1.14  
% 0.45/1.14  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 0.45/1.14  ------ Proving...
% 0.45/1.14  ------ Problem Properties 
% 0.45/1.14  
% 0.45/1.14  
% 0.45/1.14  clauses                                 14
% 0.45/1.14  conjectures                             2
% 0.45/1.14  EPR                                     5
% 0.45/1.14  Horn                                    13
% 0.45/1.14  unary                                   8
% 0.45/1.14  binary                                  3
% 0.45/1.14  lits                                    23
% 0.45/1.14  lits eq                                 7
% 0.45/1.14  fd_pure                                 0
% 0.45/1.14  fd_pseudo                               0
% 0.45/1.14  fd_cond                                 0
% 0.45/1.14  fd_pseudo_cond                          2
% 0.45/1.14  AC symbols                              0
% 0.45/1.14  
% 0.45/1.14  ------ Schedule dynamic 5 is on 
% 0.45/1.14  
% 0.45/1.14  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.45/1.14  
% 0.45/1.14  
% 0.45/1.14  ------ 
% 0.45/1.14  Current options:
% 0.45/1.14  ------ 
% 0.45/1.14  
% 0.45/1.14  
% 0.45/1.14  
% 0.45/1.14  
% 0.45/1.14  ------ Proving...
% 0.45/1.14  
% 0.45/1.14  
% 0.45/1.14  % SZS status Theorem for theBenchmark.p
% 0.45/1.14  
% 0.45/1.14  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.45/1.14  
% 0.45/1.15  
%------------------------------------------------------------------------------