TSTP Solution File: SEU230+2 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SEU230+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n007.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 03:05:07 EDT 2024

% Result   : Theorem 9.06s 2.16s
% Output   : CNFRefutation 9.06s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% Comments : 
%------------------------------------------------------------------------------
fof(f7,axiom,
    ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

fof(f18,axiom,
    ! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).

fof(f26,axiom,
    ! [X0,X1,X2] :
      ( unordered_pair(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( X1 = X3
            | X0 = X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).

fof(f27,axiom,
    ! [X0,X1,X2] :
      ( set_union2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            | in(X3,X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).

fof(f143,conjecture,
    ! [X0] : in(X0,succ(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_ordinal1) ).

fof(f144,negated_conjecture,
    ~ ! [X0] : in(X0,succ(X0)),
    inference(negated_conjecture,[],[f143]) ).

fof(f233,axiom,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).

fof(f366,plain,
    ? [X0] : ~ in(X0,succ(X0)),
    inference(ennf_transformation,[],[f144]) ).

fof(f569,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X0,X1) = X2
        | ? [X3] :
            ( ( ( X1 != X3
                & X0 != X3 )
              | ~ in(X3,X2) )
            & ( X1 = X3
              | X0 = X3
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ( X1 != X3
                & X0 != X3 ) )
            & ( X1 = X3
              | X0 = X3
              | ~ in(X3,X2) ) )
        | unordered_pair(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f26]) ).

fof(f570,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X0,X1) = X2
        | ? [X3] :
            ( ( ( X1 != X3
                & X0 != X3 )
              | ~ in(X3,X2) )
            & ( X1 = X3
              | X0 = X3
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ( X1 != X3
                & X0 != X3 ) )
            & ( X1 = X3
              | X0 = X3
              | ~ in(X3,X2) ) )
        | unordered_pair(X0,X1) != X2 ) ),
    inference(flattening,[],[f569]) ).

fof(f571,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X0,X1) = X2
        | ? [X3] :
            ( ( ( X1 != X3
                & X0 != X3 )
              | ~ in(X3,X2) )
            & ( X1 = X3
              | X0 = X3
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ( X1 != X4
                & X0 != X4 ) )
            & ( X1 = X4
              | X0 = X4
              | ~ in(X4,X2) ) )
        | unordered_pair(X0,X1) != X2 ) ),
    inference(rectify,[],[f570]) ).

fof(f572,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ( X1 != X3
              & X0 != X3 )
            | ~ in(X3,X2) )
          & ( X1 = X3
            | X0 = X3
            | in(X3,X2) ) )
     => ( ( ( sK29(X0,X1,X2) != X1
            & sK29(X0,X1,X2) != X0 )
          | ~ in(sK29(X0,X1,X2),X2) )
        & ( sK29(X0,X1,X2) = X1
          | sK29(X0,X1,X2) = X0
          | in(sK29(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f573,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X0,X1) = X2
        | ( ( ( sK29(X0,X1,X2) != X1
              & sK29(X0,X1,X2) != X0 )
            | ~ in(sK29(X0,X1,X2),X2) )
          & ( sK29(X0,X1,X2) = X1
            | sK29(X0,X1,X2) = X0
            | in(sK29(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ( X1 != X4
                & X0 != X4 ) )
            & ( X1 = X4
              | X0 = X4
              | ~ in(X4,X2) ) )
        | unordered_pair(X0,X1) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK29])],[f571,f572]) ).

fof(f574,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ? [X3] :
            ( ( ( ~ in(X3,X1)
                & ~ in(X3,X0) )
              | ~ in(X3,X2) )
            & ( in(X3,X1)
              | in(X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ( ~ in(X3,X1)
                & ~ in(X3,X0) ) )
            & ( in(X3,X1)
              | in(X3,X0)
              | ~ in(X3,X2) ) )
        | set_union2(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f27]) ).

fof(f575,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ? [X3] :
            ( ( ( ~ in(X3,X1)
                & ~ in(X3,X0) )
              | ~ in(X3,X2) )
            & ( in(X3,X1)
              | in(X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ( ~ in(X3,X1)
                & ~ in(X3,X0) ) )
            & ( in(X3,X1)
              | in(X3,X0)
              | ~ in(X3,X2) ) )
        | set_union2(X0,X1) != X2 ) ),
    inference(flattening,[],[f574]) ).

fof(f576,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ? [X3] :
            ( ( ( ~ in(X3,X1)
                & ~ in(X3,X0) )
              | ~ in(X3,X2) )
            & ( in(X3,X1)
              | in(X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ( ~ in(X4,X1)
                & ~ in(X4,X0) ) )
            & ( in(X4,X1)
              | in(X4,X0)
              | ~ in(X4,X2) ) )
        | set_union2(X0,X1) != X2 ) ),
    inference(rectify,[],[f575]) ).

fof(f577,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ( ~ in(X3,X1)
              & ~ in(X3,X0) )
            | ~ in(X3,X2) )
          & ( in(X3,X1)
            | in(X3,X0)
            | in(X3,X2) ) )
     => ( ( ( ~ in(sK30(X0,X1,X2),X1)
            & ~ in(sK30(X0,X1,X2),X0) )
          | ~ in(sK30(X0,X1,X2),X2) )
        & ( in(sK30(X0,X1,X2),X1)
          | in(sK30(X0,X1,X2),X0)
          | in(sK30(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f578,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ( ( ( ~ in(sK30(X0,X1,X2),X1)
              & ~ in(sK30(X0,X1,X2),X0) )
            | ~ in(sK30(X0,X1,X2),X2) )
          & ( in(sK30(X0,X1,X2),X1)
            | in(sK30(X0,X1,X2),X0)
            | in(sK30(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ( ~ in(X4,X1)
                & ~ in(X4,X0) ) )
            & ( in(X4,X1)
              | in(X4,X0)
              | ~ in(X4,X2) ) )
        | set_union2(X0,X1) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f576,f577]) ).

fof(f684,plain,
    ( ? [X0] : ~ in(X0,succ(X0))
   => ~ in(sK75,succ(sK75)) ),
    introduced(choice_axiom,[]) ).

fof(f685,plain,
    ~ in(sK75,succ(sK75)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK75])],[f366,f684]) ).

fof(f759,plain,
    ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
    inference(cnf_transformation,[],[f7]) ).

fof(f816,plain,
    ! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
    inference(cnf_transformation,[],[f18]) ).

fof(f847,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X2)
      | X0 != X4
      | unordered_pair(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f573]) ).

fof(f853,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X2)
      | ~ in(X4,X0)
      | set_union2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f578]) ).

fof(f1047,plain,
    ~ in(sK75,succ(sK75)),
    inference(cnf_transformation,[],[f685]) ).

fof(f1189,plain,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    inference(cnf_transformation,[],[f233]) ).

fof(f1226,plain,
    ! [X0] : succ(X0) = set_union2(X0,unordered_pair(X0,X0)),
    inference(definition_unfolding,[],[f816,f1189]) ).

fof(f1320,plain,
    ~ in(sK75,set_union2(sK75,unordered_pair(sK75,sK75))),
    inference(definition_unfolding,[],[f1047,f1226]) ).

fof(f1413,plain,
    ! [X2,X1,X4] :
      ( in(X4,X2)
      | unordered_pair(X4,X1) != X2 ),
    inference(equality_resolution,[],[f847]) ).

fof(f1414,plain,
    ! [X1,X4] : in(X4,unordered_pair(X4,X1)),
    inference(equality_resolution,[],[f1413]) ).

fof(f1417,plain,
    ! [X0,X1,X4] :
      ( in(X4,set_union2(X0,X1))
      | ~ in(X4,X0) ),
    inference(equality_resolution,[],[f853]) ).

cnf(c_55,plain,
    set_union2(X0,X1) = set_union2(X1,X0),
    inference(cnf_transformation,[],[f759]) ).

cnf(c_145,plain,
    in(X0,unordered_pair(X0,X1)),
    inference(cnf_transformation,[],[f1414]) ).

cnf(c_151,plain,
    ( ~ in(X0,X1)
    | in(X0,set_union2(X1,X2)) ),
    inference(cnf_transformation,[],[f1417]) ).

cnf(c_341,negated_conjecture,
    ~ in(sK75,set_union2(sK75,unordered_pair(sK75,sK75))),
    inference(cnf_transformation,[],[f1320]) ).

cnf(c_12906,plain,
    unordered_pair(sK75,sK75) = sP0_iProver_def,
    definition ).

cnf(c_12907,plain,
    set_union2(sK75,sP0_iProver_def) = sP1_iProver_def,
    definition ).

cnf(c_12908,negated_conjecture,
    ~ in(sK75,sP1_iProver_def),
    inference(demodulation,[status(thm)],[c_341,c_12906,c_12907]) ).

cnf(c_20457,plain,
    in(sK75,sP0_iProver_def),
    inference(superposition,[status(thm)],[c_12906,c_145]) ).

cnf(c_20470,plain,
    set_union2(sP0_iProver_def,sK75) = sP1_iProver_def,
    inference(demodulation,[status(thm)],[c_12907,c_55]) ).

cnf(c_21401,plain,
    ( ~ in(X0,sP0_iProver_def)
    | in(X0,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_20470,c_151]) ).

cnf(c_21777,plain,
    in(sK75,sP1_iProver_def),
    inference(superposition,[status(thm)],[c_20457,c_21401]) ).

cnf(c_21779,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_21777,c_12908]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : SEU230+2 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.14  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n007.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 17:45:35 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.49  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
% 9.06/2.16  % SZS status Started for theBenchmark.p
% 9.06/2.16  % SZS status Theorem for theBenchmark.p
% 9.06/2.16  
% 9.06/2.16  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 9.06/2.16  
% 9.06/2.16  ------  iProver source info
% 9.06/2.16  
% 9.06/2.16  git: date: 2024-05-02 19:28:25 +0000
% 9.06/2.16  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 9.06/2.16  git: non_committed_changes: false
% 9.06/2.16  
% 9.06/2.16  ------ Parsing...
% 9.06/2.16  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 9.06/2.16  
% 9.06/2.16  ------ Preprocessing... sup_sim: 41  sf_s  rm: 6 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e 
% 9.06/2.16  
% 9.06/2.16  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 9.06/2.16  
% 9.06/2.16  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 9.06/2.16  ------ Proving...
% 9.06/2.16  ------ Problem Properties 
% 9.06/2.16  
% 9.06/2.16  
% 9.06/2.16  clauses                                 409
% 9.06/2.16  conjectures                             1
% 9.06/2.16  EPR                                     48
% 9.06/2.16  Horn                                    327
% 9.06/2.16  unary                                   63
% 9.06/2.16  binary                                  115
% 9.06/2.16  lits                                    1187
% 9.06/2.16  lits eq                                 234
% 9.06/2.16  fd_pure                                 0
% 9.06/2.16  fd_pseudo                               0
% 9.06/2.16  fd_cond                                 14
% 9.06/2.16  fd_pseudo_cond                          90
% 9.06/2.16  AC symbols                              0
% 9.06/2.16  
% 9.06/2.16  ------ Schedule dynamic 5 is on 
% 9.06/2.16  
% 9.06/2.16  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 9.06/2.16  
% 9.06/2.16  
% 9.06/2.16  ------ 
% 9.06/2.16  Current options:
% 9.06/2.16  ------ 
% 9.06/2.16  
% 9.06/2.16  
% 9.06/2.16  
% 9.06/2.16  
% 9.06/2.16  ------ Proving...
% 9.06/2.16  
% 9.06/2.16  
% 9.06/2.16  % SZS status Theorem for theBenchmark.p
% 9.06/2.16  
% 9.06/2.16  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 9.06/2.16  
% 9.06/2.16  
%------------------------------------------------------------------------------