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iProver---3.9.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : SEU187+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM

% Computer : n016.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri Sep 25 02:55:48 PM UTC 2026

% Result   : Theorem 3.55s 1.28s
% Output   : CNFRefutation 3.55s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   78 (  22 unt;   2 def)
%            Number of atoms       :  246 (  54 equ)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :  259 ( 114   ~; 110   |;  22   &)
%                                         (   8 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   6 usr;   3 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   1 con; 0-2 aty)
%            Number of variables   :  146 (   0 sgn 129   !;  17   ?;  40   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [X0] :
      ( empty(X0)
     => relation(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).

fof(f3,axiom,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

fof(f4,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X1] :
          ( X1 = relation_dom(X0)
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).

fof(f5,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X1] :
          ( X1 = relation_rng(X0)
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).

fof(f6,axiom,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).

fof(f14,axiom,
    ! [X0] :
    ? [X1] : element(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).

fof(f19,axiom,
    ( relation(empty_set)
    & empty(empty_set) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).

fof(f27,axiom,
    ! [X0,X1] :
      ( element(X0,X1)
     => ( in(X0,X1)
        | empty(X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).

fof(f29,conjecture,
    ( relation_rng(empty_set) = empty_set
    & relation_dom(empty_set) = empty_set ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_relat_1) ).

fof(f30,negated_conjecture,
    ~ ( relation_rng(empty_set) = empty_set
      & relation_dom(empty_set) = empty_set ),
    inference(negated_conjecture,[status(cth)],[f29]) ).

fof(f31,axiom,
    ! [X0] :
      ( empty(X0)
     => X0 = empty_set ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

fof(f32,axiom,
    ! [X0,X1] :
      ~ ( empty(X1)
        & in(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).

fof(f35,plain,
    ! [X0] :
      ( ~ empty(X0)
      | relation(X0) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f36,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ! [X1] :
          ( X1 = relation_dom(X0)
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f37,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ! [X1] :
          ( X1 = relation_rng(X0)
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( ~ element(X0,X1)
      | in(X0,X1)
      | empty(X1) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ~ element(X0,X1)
      | in(X0,X1)
      | empty(X1) ),
    inference(flattening,[],[f43]) ).

fof(f46,plain,
    ( empty_set != relation_rng(empty_set)
    | empty_set != relation_dom(empty_set) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f47,plain,
    ! [X0] :
      ( ~ empty(X0)
      | X0 = empty_set ),
    inference(ennf_transformation,[],[f31]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f50,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ! [X1] :
          ( ( relation_dom(X0) != X1
            | ! [X2] :
                ( ( ~ in(X2,X1)
                  | ? [X3] : in(ordered_pair(X2,X3),X0) )
                & ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
                  | in(X2,X1) ) ) )
          & ( ? [X2] :
                ( ( in(X2,X1)
                  | ? [X3] : in(ordered_pair(X2,X3),X0) )
                & ( ~ in(X2,X1)
                  | ! [X3] : ~ in(ordered_pair(X2,X3),X0) ) )
            | X1 = relation_dom(X0) ) ) ),
    inference(nnf_transformation,[],[f36]) ).

fof(f51,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ! [X1] :
          ( ( relation_dom(X0) != X1
            | ! [X5] :
                ( ( ~ in(X5,X1)
                  | ? [X7] : in(ordered_pair(X5,X7),X0) )
                & ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
                  | in(X5,X1) ) ) )
          & ( ? [X2] :
                ( ( in(X2,X1)
                  | ? [X4] : in(ordered_pair(X2,X4),X0) )
                & ( ~ in(X2,X1)
                  | ! [X3] : ~ in(ordered_pair(X2,X3),X0) ) )
            | X1 = relation_dom(X0) ) ) ),
    inference(rectify,[],[f50]) ).

fof(f52,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ! [X1] :
          ( ( relation_dom(X0) != X1
            | ! [X5] :
                ( ( ~ in(X5,X1)
                  | in(ordered_pair(X5,sK2(X0,X5)),X0) )
                & ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
                  | in(X5,X1) ) ) )
          & ( ( ( in(sK0(X0,X1),X1)
                | in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0) )
              & ( ~ in(sK0(X0,X1),X1)
                | ! [X3] : ~ in(ordered_pair(sK0(X0,X1),X3),X0) ) )
            | X1 = relation_dom(X0) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X2,sK0(X0,X1)),skolemize(X4,sK1(X0,X1)),skolemize(X7,sK2(X0,X5))],[f51]) ).

fof(f53,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ! [X1] :
          ( ( relation_rng(X0) != X1
            | ! [X2] :
                ( ( ~ in(X2,X1)
                  | ? [X3] : in(ordered_pair(X3,X2),X0) )
                & ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
                  | in(X2,X1) ) ) )
          & ( ? [X2] :
                ( ( in(X2,X1)
                  | ? [X3] : in(ordered_pair(X3,X2),X0) )
                & ( ~ in(X2,X1)
                  | ! [X3] : ~ in(ordered_pair(X3,X2),X0) ) )
            | X1 = relation_rng(X0) ) ) ),
    inference(nnf_transformation,[],[f37]) ).

fof(f54,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ! [X1] :
          ( ( relation_rng(X0) != X1
            | ! [X5] :
                ( ( ~ in(X5,X1)
                  | ? [X7] : in(ordered_pair(X7,X5),X0) )
                & ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
                  | in(X5,X1) ) ) )
          & ( ? [X2] :
                ( ( in(X2,X1)
                  | ? [X4] : in(ordered_pair(X4,X2),X0) )
                & ( ~ in(X2,X1)
                  | ! [X3] : ~ in(ordered_pair(X3,X2),X0) ) )
            | X1 = relation_rng(X0) ) ) ),
    inference(rectify,[],[f53]) ).

fof(f55,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ! [X1] :
          ( ( relation_rng(X0) != X1
            | ! [X5] :
                ( ( ~ in(X5,X1)
                  | in(ordered_pair(sK5(X0,X5),X5),X0) )
                & ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
                  | in(X5,X1) ) ) )
          & ( ( ( in(sK3(X0,X1),X1)
                | in(ordered_pair(sK4(X0,X1),sK3(X0,X1)),X0) )
              & ( ~ in(sK3(X0,X1),X1)
                | ! [X3] : ~ in(ordered_pair(X3,sK3(X0,X1)),X0) ) )
            | X1 = relation_rng(X0) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X2,sK3(X0,X1)),skolemize(X4,sK4(X0,X1)),skolemize(X7,sK5(X0,X5))],[f54]) ).

fof(f56,plain,
    ! [X0] : element(sK6(X0),X0),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X1,sK6(X0))],[f14]) ).

fof(f64,plain,
    ! [X0] :
      ( ~ empty(X0)
      | relation(X0) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f65,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[],[f3]) ).

fof(f66,plain,
    ! [X0,X1,X5] :
      ( ~ relation(X0)
      | relation_dom(X0) != X1
      | ~ in(X5,X1)
      | in(ordered_pair(X5,sK2(X0,X5)),X0) ),
    inference(cnf_transformation,[],[f52]) ).

fof(f70,plain,
    ! [X0,X1,X5] :
      ( ~ relation(X0)
      | relation_rng(X0) != X1
      | ~ in(X5,X1)
      | in(ordered_pair(sK5(X0,X5),X5),X0) ),
    inference(cnf_transformation,[],[f55]) ).

fof(f74,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    inference(cnf_transformation,[],[f6]) ).

fof(f75,plain,
    ! [X0] : element(sK6(X0),X0),
    inference(cnf_transformation,[],[f56]) ).

fof(f81,plain,
    empty(empty_set),
    inference(cnf_transformation,[],[f19]) ).

fof(f91,plain,
    ! [X0,X1] :
      ( ~ element(X0,X1)
      | in(X0,X1)
      | empty(X1) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f94,plain,
    ( empty_set != relation_rng(empty_set)
    | empty_set != relation_dom(empty_set) ),
    inference(cnf_transformation,[],[f46]) ).

fof(f95,plain,
    ! [X0] :
      ( ~ empty(X0)
      | empty_set = X0 ),
    inference(cnf_transformation,[],[f47]) ).

fof(f96,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f48]) ).

fof(f101,plain,
    ! [X0,X1,X5] :
      ( ~ relation(X0)
      | relation_dom(X0) != X1
      | ~ in(X5,X1)
      | in(unordered_pair(unordered_pair(X5,sK2(X0,X5)),singleton(X5)),X0) ),
    inference(definition_unfolding,[],[f66,f74]) ).

fof(f105,plain,
    ! [X0,X1,X5] :
      ( ~ relation(X0)
      | relation_rng(X0) != X1
      | ~ in(X5,X1)
      | in(unordered_pair(unordered_pair(sK5(X0,X5),X5),singleton(sK5(X0,X5))),X0) ),
    inference(definition_unfolding,[],[f70,f74]) ).

fof(f108,plain,
    ! [X0,X5] :
      ( ~ relation(X0)
      | ~ in(X5,relation_dom(X0))
      | in(unordered_pair(unordered_pair(X5,sK2(X0,X5)),singleton(X5)),X0) ),
    inference(equality_resolution,[],[f101]) ).

fof(f110,plain,
    ! [X0,X5] :
      ( ~ relation(X0)
      | ~ in(X5,relation_rng(X0))
      | in(unordered_pair(unordered_pair(sK5(X0,X5),X5),singleton(sK5(X0,X5))),X0) ),
    inference(equality_resolution,[],[f105]) ).

tcf(c_50,plain,
    ! [X0: $i] :
      ( relation(X0)
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f64]) ).

tcf(c_51,plain,
    ! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[],[f65]) ).

tcf(c_55,plain,
    ! [X0: $i,X1: $i] :
      ( in(unordered_pair(unordered_pair(X0,sK2(X1,X0)),singleton(X0)),X1)
      | ~ relation(X1)
      | ~ in(X0,relation_dom(X1)) ),
    inference(cnf_transformation,[],[f108]) ).

tcf(c_59,plain,
    ! [X0: $i,X1: $i] :
      ( in(unordered_pair(unordered_pair(sK5(X1,X0),X0),singleton(sK5(X1,X0))),X1)
      | ~ relation(X1)
      | ~ in(X0,relation_rng(X1)) ),
    inference(cnf_transformation,[],[f110]) ).

tcf(c_60,plain,
    ! [X0: $i] : element(sK6(X0),X0),
    inference(cnf_transformation,[],[f75]) ).

tcf(c_65,plain,
    empty(empty_set),
    inference(cnf_transformation,[],[f81]) ).

tcf(c_76,plain,
    ! [X0: $i,X1: $i] :
      ( empty(X1)
      | in(X0,X1)
      | ~ element(X0,X1) ),
    inference(cnf_transformation,[],[f91]) ).

tcf(c_79,negated_conjecture,
    ( ( relation_rng(empty_set) != empty_set )
    | ( relation_dom(empty_set) != empty_set ) ),
    inference(cnf_transformation,[],[f94]) ).

tcf(c_80,plain,
    ! [X0: $i] :
      ( ( X0 = empty_set )
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f95]) ).

tcf(c_81,plain,
    ! [X0: $i,X1: $i] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f96]) ).

tcf(c_320,plain,
    ! [X0: $i,X1: $i] :
      ( in(unordered_pair(singleton(X0),unordered_pair(X0,sK2(X1,X0))),X1)
      | ~ relation(X1)
      | ~ in(X0,relation_dom(X1)) ),
    inference(demodulation,[status(thm)],[c_55,c_51]) ).

tcf(c_330,plain,
    ! [X0: $i,X1: $i] :
      ( in(unordered_pair(singleton(sK5(X1,X0)),unordered_pair(X0,sK5(X1,X0))),X1)
      | ~ relation(X1)
      | ~ in(X0,relation_rng(X1)) ),
    inference(demodulation,[status(thm)],[c_59,c_51]) ).

tcf(c_413,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( empty(X2)
      | in(X1,X2)
      | ( X0 != X2 )
      | ( sK6(X0) != X1 ) ),
    inference(resolution_lifted,[status(thm)],[c_60,c_76]) ).

tcf(c_414,plain,
    ! [X0: $i] :
      ( empty(X0)
      | in(sK6(X0),X0) ),
    inference(unflattening,[status(thm)],[c_413]) ).

tcf(c_465,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( in(unordered_pair(singleton(sK5(X0,X2)),unordered_pair(X2,sK5(X0,X2))),X0)
      | ~ empty(X1)
      | ~ in(X2,relation_rng(X0))
      | ( X0 != X1 ) ),
    inference(resolution_lifted,[status(thm)],[c_330,c_50]) ).

tcf(c_466,plain,
    ! [X0: $i,X1: $i] :
      ( in(unordered_pair(singleton(sK5(X1,X0)),unordered_pair(X0,sK5(X1,X0))),X1)
      | ~ empty(X1)
      | ~ in(X0,relation_rng(X1)) ),
    inference(unflattening,[status(thm)],[c_465]) ).

tcf(c_474,plain,
    ! [X0: $i,X1: $i] :
      ( ~ empty(X1)
      | ~ in(X0,relation_rng(X1)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_466,c_81]) ).

tcf(c_478,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( in(unordered_pair(singleton(X2),unordered_pair(X2,sK2(X0,X2))),X0)
      | ~ empty(X1)
      | ~ in(X2,relation_dom(X0))
      | ( X0 != X1 ) ),
    inference(resolution_lifted,[status(thm)],[c_320,c_50]) ).

tcf(c_479,plain,
    ! [X0: $i,X1: $i] :
      ( in(unordered_pair(singleton(X0),unordered_pair(X0,sK2(X1,X0))),X1)
      | ~ empty(X1)
      | ~ in(X0,relation_dom(X1)) ),
    inference(unflattening,[status(thm)],[c_478]) ).

tcf(c_487,plain,
    ! [X0: $i,X1: $i] :
      ( ~ empty(X1)
      | ~ in(X0,relation_dom(X1)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_479,c_81]) ).

tcf(c_843,definition,
    iPr_def_10 = relation_dom(empty_set),
    introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).

tcf(c_844,definition,
    iPr_def_11 = relation_rng(empty_set),
    introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).

tcf(c_845,negated_conjecture,
    ( ( iPr_def_11 != empty_set )
    | ( iPr_def_10 != empty_set ) ),
    inference(demodulation,[status(thm)],[c_79,c_844,c_843]) ).

tcf(c_1444,plain,
    ! [X0: $i] :
      ( ~ empty(empty_set)
      | ~ in(X0,iPr_def_11) ),
    inference(superposition,[status(thm)],[c_844,c_474]) ).

tcf(c_1447,plain,
    ! [X0: $i] : ~ in(X0,iPr_def_11),
    inference(forward_subsumption_resolution,[status(thm)],[c_1444,c_65]) ).

tcf(c_1450,plain,
    empty(iPr_def_11),
    inference(superposition,[status(thm)],[c_414,c_1447]) ).

tcf(c_1451,plain,
    empty_set = iPr_def_11,
    inference(superposition,[status(thm)],[c_1450,c_80]) ).

tcf(c_1454,plain,
    ! [X0: $i] :
      ( ( X0 = iPr_def_11 )
      | ~ empty(X0) ),
    inference(demodulation,[status(thm)],[c_80,c_1451]) ).

tcf(c_1456,plain,
    relation_dom(iPr_def_11) = iPr_def_10,
    inference(demodulation,[status(thm)],[c_843,c_1451]) ).

tcf(c_1458,plain,
    ( ( iPr_def_11 != iPr_def_11 )
    | ( iPr_def_10 != iPr_def_11 ) ),
    inference(demodulation,[status(thm)],[c_845,c_1451]) ).

tcf(c_1459,plain,
    iPr_def_10 != iPr_def_11,
    inference(equality_resolution_simp,[status(thm)],[c_1458]) ).

tcf(c_1545,plain,
    ! [X0: $i] :
      ( ~ empty(iPr_def_11)
      | ~ in(X0,iPr_def_10) ),
    inference(superposition,[status(thm)],[c_1456,c_487]) ).

tcf(c_1548,plain,
    ! [X0: $i] : ~ in(X0,iPr_def_10),
    inference(forward_subsumption_resolution,[status(thm)],[c_1545,c_1450]) ).

tcf(c_1561,plain,
    empty(iPr_def_10),
    inference(superposition,[status(thm)],[c_414,c_1548]) ).

tcf(c_1569,plain,
    iPr_def_10 = iPr_def_11,
    inference(superposition,[status(thm)],[c_1561,c_1454]) ).

tcf(c_1570,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_1569,c_1459]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SEU187+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37  % Computer : n016.cluster.edu
% 0.10/0.37  % Model    : x86_64 x86_64
% 0.10/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37  % Memory   : 8046.5625MB
% 0.10/0.37  % OS       : Linux 6.8.0-71-generic
% 0.10/0.37  % CPULimit : 300
% 0.10/0.37  % WCLimit  : 300
% 0.10/0.37  % DateTime : Thu Sep 24 13:10:59 UTC 2026
% 0.10/0.38  % CPUTime  : 
% 0.10/0.38  Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.40  Running first-order theorem proving
% 0.15/0.40  Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.42  
% 0.15/0.42  % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.42  
% 0.15/0.42  % Detected problem language: tptp
% 0.15/0.43  % Proving...
% 3.55/1.28  % SZS status Started for theBenchmark.p
% 3.55/1.28  % SZS status Theorem for theBenchmark.p
% 3.55/1.28  
% 3.55/1.28  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.55/1.28  
% 3.55/1.28  % ------  iProver source info
% 3.55/1.28  
% 3.55/1.28  % git: date: 2026-07-19 20:42:38 +0200
% 3.55/1.28  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.55/1.28  % git: non_committed_changes: false
% 3.55/1.28  
% 3.55/1.28  % ------ Parsing...
% 3.55/1.28  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 3.55/1.28  
% 3.55/1.28  % ------ Preprocessing... sup_sim: 8  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe_e % 
% 3.55/1.28  
% 3.55/1.28  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 3.55/1.28  
% 3.55/1.28  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.55/1.28  % ------ Proving...
% 3.55/1.28  % ------ Problem Properties 
% 3.55/1.28  
% 3.55/1.28  % 
% 3.55/1.28  % clauses                               48
% 3.55/1.28  % conjectures                           1
% 3.55/1.28  % EPR                                   10
% 3.55/1.28  % Horn                                  38
% 3.55/1.28  % unary                                 12
% 3.55/1.28  % binary                                19
% 3.55/1.28  % lits                                  101
% 3.55/1.28  % lits eq                               23
% 3.55/1.28  % fd_pure                               0
% 3.55/1.28  % fd_pseudo                             0
% 3.55/1.28  % fd_cond                               13
% 3.55/1.28  % fd_pseudo_cond                        5
% 3.55/1.28  % AC symbols                            0
% 3.55/1.28  
% 3.55/1.28  % ------ Schedule dynamic 5 is on 
% 3.55/1.28  
% 3.55/1.28  % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.55/1.28  
% 3.55/1.28  
% 3.55/1.28  % ------ 
% 3.55/1.28  % Current options:
% 3.55/1.28  % ------ 
% 3.55/1.28  
% 3.55/1.28  
% 3.55/1.28  % 
% 3.55/1.28  
% 3.55/1.28  % ------ Proving...
% 3.55/1.28  % 
% 3.55/1.28  
% 3.55/1.28  % SZS status Theorem for theBenchmark.p
% 3.55/1.28  
% 3.55/1.28  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.55/1.28  
% 3.55/1.28  
%------------------------------------------------------------------------------