↑ Up

iProver---3.9.4.THM-CRf.s

View TPTP
Problem
Process solution in
SystemOnTSTP
Download .tgz
%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : NUM404+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM

% Computer : n004.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 02:24:10 PM UTC 2026

% Result   : Theorem 4.30s 1.53s
% Output   : CNFRefutation 4.30s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   83 (   4 unt;   0 def)
%            Number of atoms       :  288 (  23 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  332 ( 127   ~; 148   |;  40   &)
%                                         (  10 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   1 con; 0-2 aty)
%            Number of variables   :  136 (   0 sgn 126   !;  10   ?;  37   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1] :
      ( in(X0,X1)
     => ~ in(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

fof(f8,axiom,
    ! [X0] :
      ( epsilon_transitive(X0)
    <=> ! [X1] :
          ( in(X1,X0)
         => subset(X1,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).

fof(f9,axiom,
    ! [X0] :
      ( epsilon_connected(X0)
    <=> ! [X1,X2] :
          ~ ( ~ in(X2,X1)
            & X1 != X2
            & ~ in(X1,X2)
            & in(X2,X0)
            & in(X1,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_ordinal1) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

fof(f11,axiom,
    ! [X0] :
      ( ordinal(X0)
    <=> ( epsilon_connected(X0)
        & epsilon_transitive(X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_ordinal1) ).

fof(f32,axiom,
    ! [X0,X1] :
      ( ordinal(X1)
     => ( in(X0,X1)
       => ordinal(X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_ordinal1) ).

fof(f33,axiom,
    ! [X0] :
      ( ordinal(X0)
     => ! [X1] :
          ( ordinal(X1)
         => ~ ( ~ in(X1,X0)
              & X0 != X1
              & ~ in(X0,X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_ordinal1) ).

fof(f35,conjecture,
    ! [X0] :
      ~ ! [X1] :
          ( in(X1,X0)
        <=> ordinal(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_ordinal1) ).

fof(f36,negated_conjecture,
    ~ ! [X0] :
        ~ ! [X1] :
            ( in(X1,X0)
          <=> ordinal(X1) ),
    inference(negated_conjecture,[status(cth)],[f35]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | ~ in(X1,X0) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f62,plain,
    ! [X0] :
      ( epsilon_transitive(X0)
    <=> ! [X1] :
          ( ~ in(X1,X0)
          | subset(X1,X0) ) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f63,plain,
    ! [X0] :
      ( epsilon_connected(X0)
    <=> ! [X1,X2] :
          ( in(X2,X1)
          | X1 = X2
          | in(X1,X2)
          | ~ in(X2,X0)
          | ~ in(X1,X0) ) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( ~ in(X2,X0)
          | in(X2,X1) ) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f66,plain,
    ! [X0,X1] :
      ( ~ ordinal(X1)
      | ~ in(X0,X1)
      | ordinal(X0) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f67,plain,
    ! [X0,X1] :
      ( ~ ordinal(X1)
      | ~ in(X0,X1)
      | ordinal(X0) ),
    inference(flattening,[],[f66]) ).

fof(f68,plain,
    ! [X0] :
      ( ~ ordinal(X0)
      | ! [X1] :
          ( ~ ordinal(X1)
          | in(X1,X0)
          | X0 = X1
          | in(X0,X1) ) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f69,plain,
    ! [X0] :
      ( ~ ordinal(X0)
      | ! [X1] :
          ( ~ ordinal(X1)
          | in(X1,X0)
          | X0 = X1
          | in(X0,X1) ) ),
    inference(flattening,[],[f68]) ).

fof(f72,plain,
    ? [X0] :
    ! [X1] :
      ( in(X1,X0)
    <=> ordinal(X1) ),
    inference(ennf_transformation,[],[f36]) ).

fof(f79,plain,
    ! [X0] :
      ( ( ~ epsilon_transitive(X0)
        | ! [X1] :
            ( ~ in(X1,X0)
            | subset(X1,X0) ) )
      & ( ? [X1] :
            ( in(X1,X0)
            & ~ subset(X1,X0) )
        | epsilon_transitive(X0) ) ),
    inference(nnf_transformation,[],[f62]) ).

fof(f80,plain,
    ! [X0] :
      ( ( ~ epsilon_transitive(X0)
        | ! [X2] :
            ( ~ in(X2,X0)
            | subset(X2,X0) ) )
      & ( ? [X1] :
            ( in(X1,X0)
            & ~ subset(X1,X0) )
        | epsilon_transitive(X0) ) ),
    inference(rectify,[],[f79]) ).

fof(f81,plain,
    ! [X0] :
      ( ( ~ epsilon_transitive(X0)
        | ! [X2] :
            ( ~ in(X2,X0)
            | subset(X2,X0) ) )
      & ( ( in(sK0(X0),X0)
          & ~ subset(sK0(X0),X0) )
        | epsilon_transitive(X0) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f80]) ).

fof(f82,plain,
    ! [X0] :
      ( ( ~ epsilon_connected(X0)
        | ! [X1,X2] :
            ( in(X2,X1)
            | X1 = X2
            | in(X1,X2)
            | ~ in(X2,X0)
            | ~ in(X1,X0) ) )
      & ( ? [X1,X2] :
            ( ~ in(X2,X1)
            & X1 != X2
            & ~ in(X1,X2)
            & in(X2,X0)
            & in(X1,X0) )
        | epsilon_connected(X0) ) ),
    inference(nnf_transformation,[],[f63]) ).

fof(f83,plain,
    ! [X0] :
      ( ( ~ epsilon_connected(X0)
        | ! [X3,X4] :
            ( in(X4,X3)
            | X3 = X4
            | in(X3,X4)
            | ~ in(X4,X0)
            | ~ in(X3,X0) ) )
      & ( ? [X1,X2] :
            ( ~ in(X2,X1)
            & X1 != X2
            & ~ in(X1,X2)
            & in(X2,X0)
            & in(X1,X0) )
        | epsilon_connected(X0) ) ),
    inference(rectify,[],[f82]) ).

fof(f84,plain,
    ! [X0] :
      ( ( ~ epsilon_connected(X0)
        | ! [X3,X4] :
            ( in(X4,X3)
            | X3 = X4
            | in(X3,X4)
            | ~ in(X4,X0)
            | ~ in(X3,X0) ) )
      & ( ( ~ in(sK2(X0),sK1(X0))
          & sK1(X0) != sK2(X0)
          & ~ in(sK1(X0),sK2(X0))
          & in(sK2(X0),X0)
          & in(sK1(X0),X0) )
        | epsilon_connected(X0) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X1,sK1(X0)),skolemize(X2,sK2(X0))],[f83]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( ( ~ subset(X0,X1)
        | ! [X2] :
            ( ~ in(X2,X0)
            | in(X2,X1) ) )
      & ( ? [X2] :
            ( in(X2,X0)
            & ~ in(X2,X1) )
        | subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f64]) ).

fof(f86,plain,
    ! [X0,X1] :
      ( ( ~ subset(X0,X1)
        | ! [X3] :
            ( ~ in(X3,X0)
            | in(X3,X1) ) )
      & ( ? [X2] :
            ( in(X2,X0)
            & ~ in(X2,X1) )
        | subset(X0,X1) ) ),
    inference(rectify,[],[f85]) ).

fof(f87,plain,
    ! [X0,X1] :
      ( ( ~ subset(X0,X1)
        | ! [X3] :
            ( ~ in(X3,X0)
            | in(X3,X1) ) )
      & ( ( in(sK3(X0,X1),X0)
          & ~ in(sK3(X0,X1),X1) )
        | subset(X0,X1) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f86]) ).

fof(f88,plain,
    ! [X0] :
      ( ( ~ ordinal(X0)
        | ( epsilon_connected(X0)
          & epsilon_transitive(X0) ) )
      & ( ~ epsilon_connected(X0)
        | ~ epsilon_transitive(X0)
        | ordinal(X0) ) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f89,plain,
    ! [X0] :
      ( ( ~ ordinal(X0)
        | ( epsilon_connected(X0)
          & epsilon_transitive(X0) ) )
      & ( ~ epsilon_connected(X0)
        | ~ epsilon_transitive(X0)
        | ordinal(X0) ) ),
    inference(flattening,[],[f88]) ).

fof(f104,plain,
    ? [X0] :
    ! [X1] :
      ( ( ~ in(X1,X0)
        | ordinal(X1) )
      & ( ~ ordinal(X1)
        | in(X1,X0) ) ),
    inference(nnf_transformation,[],[f72]) ).

fof(f105,plain,
    ! [X1] :
      ( ( ~ in(X1,sK18)
        | ordinal(X1) )
      & ( ~ ordinal(X1)
        | in(X1,sK18) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(X0,sK18)],[f104]) ).

fof(f107,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | ~ in(X1,X0) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f119,plain,
    ! [X0] :
      ( in(sK0(X0),X0)
      | epsilon_transitive(X0) ),
    inference(cnf_transformation,[],[f81]) ).

fof(f120,plain,
    ! [X0] :
      ( ~ subset(sK0(X0),X0)
      | epsilon_transitive(X0) ),
    inference(cnf_transformation,[],[f81]) ).

fof(f121,plain,
    ! [X3,X0,X4] :
      ( ~ epsilon_connected(X0)
      | in(X4,X3)
      | X3 = X4
      | in(X3,X4)
      | ~ in(X4,X0)
      | ~ in(X3,X0) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f122,plain,
    ! [X0] :
      ( ~ in(sK2(X0),sK1(X0))
      | epsilon_connected(X0) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f123,plain,
    ! [X0] :
      ( sK1(X0) != sK2(X0)
      | epsilon_connected(X0) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f124,plain,
    ! [X0] :
      ( ~ in(sK1(X0),sK2(X0))
      | epsilon_connected(X0) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f125,plain,
    ! [X0] :
      ( in(sK2(X0),X0)
      | epsilon_connected(X0) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f126,plain,
    ! [X0] :
      ( in(sK1(X0),X0)
      | epsilon_connected(X0) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f128,plain,
    ! [X0,X1] :
      ( in(sK3(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f87]) ).

fof(f129,plain,
    ! [X0,X1] :
      ( ~ in(sK3(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f87]) ).

fof(f132,plain,
    ! [X0] :
      ( ~ epsilon_connected(X0)
      | ~ epsilon_transitive(X0)
      | ordinal(X0) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f178,plain,
    ! [X0,X1] :
      ( ~ ordinal(X1)
      | ~ in(X0,X1)
      | ordinal(X0) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f179,plain,
    ! [X0,X1] :
      ( ~ ordinal(X0)
      | ~ ordinal(X1)
      | in(X1,X0)
      | X0 = X1
      | in(X0,X1) ),
    inference(cnf_transformation,[],[f69]) ).

fof(f181,plain,
    ! [X1] :
      ( ~ in(X1,sK18)
      | ordinal(X1) ),
    inference(cnf_transformation,[],[f105]) ).

fof(f182,plain,
    ! [X1] :
      ( ~ ordinal(X1)
      | in(X1,sK18) ),
    inference(cnf_transformation,[],[f105]) ).

tcf(c_49,plain,
    ! [X0: $i,X1: $i] :
      ( ~ in(X1,X0)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f107]) ).

tcf(c_58,plain,
    ! [X0: $i] :
      ( epsilon_transitive(X0)
      | ~ subset(sK0(X0),X0) ),
    inference(cnf_transformation,[],[f120]) ).

tcf(c_59,plain,
    ! [X0: $i] :
      ( epsilon_transitive(X0)
      | in(sK0(X0),X0) ),
    inference(cnf_transformation,[],[f119]) ).

tcf(c_61,plain,
    ! [X0: $i] :
      ( epsilon_connected(X0)
      | in(sK1(X0),X0) ),
    inference(cnf_transformation,[],[f126]) ).

tcf(c_62,plain,
    ! [X0: $i] :
      ( epsilon_connected(X0)
      | in(sK2(X0),X0) ),
    inference(cnf_transformation,[],[f125]) ).

tcf(c_63,plain,
    ! [X0: $i] :
      ( epsilon_connected(X0)
      | ~ in(sK1(X0),sK2(X0)) ),
    inference(cnf_transformation,[],[f124]) ).

tcf(c_64,plain,
    ! [X0: $i] :
      ( epsilon_connected(X0)
      | ( sK1(X0) != sK2(X0) ) ),
    inference(cnf_transformation,[],[f123]) ).

tcf(c_65,plain,
    ! [X0: $i] :
      ( epsilon_connected(X0)
      | ~ in(sK2(X0),sK1(X0)) ),
    inference(cnf_transformation,[],[f122]) ).

tcf(c_66,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( in(X2,X0)
      | in(X0,X2)
      | ( X0 = X2 )
      | ~ epsilon_connected(X1)
      | ~ in(X2,X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f121]) ).

tcf(c_67,plain,
    ! [X0: $i,X1: $i] :
      ( subset(X0,X1)
      | ~ in(sK3(X0,X1),X1) ),
    inference(cnf_transformation,[],[f129]) ).

tcf(c_68,plain,
    ! [X0: $i,X1: $i] :
      ( subset(X0,X1)
      | in(sK3(X0,X1),X0) ),
    inference(cnf_transformation,[],[f128]) ).

tcf(c_70,plain,
    ! [X0: $i] :
      ( ordinal(X0)
      | ~ epsilon_connected(X0)
      | ~ epsilon_transitive(X0) ),
    inference(cnf_transformation,[],[f132]) ).

tcf(c_118,plain,
    ! [X0: $i,X1: $i] :
      ( ordinal(X0)
      | ~ ordinal(X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f178]) ).

tcf(c_119,plain,
    ! [X0: $i,X1: $i] :
      ( in(X1,X0)
      | in(X0,X1)
      | ( X0 = X1 )
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f179]) ).

tcf(c_121,negated_conjecture,
    ! [X0: $i] :
      ( in(X0,sK18)
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f182]) ).

tcf(c_122,negated_conjecture,
    ! [X0: $i] :
      ( ordinal(X0)
      | ~ in(X0,sK18) ),
    inference(cnf_transformation,[],[f181]) ).

tcf(c_2811,negated_conjecture,
    ! [X0: $i] :
      ( ordinal(X0)
      | ~ in(X0,sK18) ),
    inference(demodulation,[status(thm)],[c_122]) ).

tcf(c_2812,negated_conjecture,
    ! [X0: $i] :
      ( in(X0,sK18)
      | ~ ordinal(X0) ),
    inference(demodulation,[status(thm)],[c_121]) ).

tcf(c_3665,plain,
    ! [X0: $i] :
      ( ~ ordinal(X0)
      | ~ in(sK18,X0) ),
    inference(superposition,[status(thm)],[c_2812,c_49]) ).

tcf(c_3673,plain,
    ~ ordinal(sK18),
    inference(superposition,[status(thm)],[c_2812,c_3665]) ).

tcf(c_3734,plain,
    ( epsilon_connected(sK18)
    | ordinal(sK2(sK18)) ),
    inference(superposition,[status(thm)],[c_62,c_2811]) ).

tcf(c_3758,plain,
    ( epsilon_transitive(sK18)
    | ordinal(sK0(sK18)) ),
    inference(superposition,[status(thm)],[c_59,c_2811]) ).

tcf(c_3962,plain,
    ! [X0: $i,X1: $i] :
      ( in(X1,X0)
      | in(X0,X1)
      | ( X0 = X1 )
      | ~ epsilon_connected(sK18)
      | ~ ordinal(X1)
      | ~ in(X0,sK18) ),
    inference(superposition,[status(thm)],[c_2812,c_66]) ).

tcf(c_4036,plain,
    ! [X0: $i,X1: $i] :
      ( in(X1,X0)
      | in(X0,X1)
      | ( X0 = X1 )
      | ~ in(X0,sK18)
      | ~ ordinal(X1) ),
    inference(global_subsumption_just,[status(thm)],[c_3962,c_122,c_119]) ).

tcf(c_4037,plain,
    ! [X0: $i,X1: $i] :
      ( in(X1,X0)
      | in(X0,X1)
      | ( X0 = X1 )
      | ~ ordinal(X1)
      | ~ in(X0,sK18) ),
    inference(renaming,[status(thm)],[c_4036]) ).

tcf(c_4049,plain,
    ! [X0: $i] :
      ( epsilon_connected(sK18)
      | in(X0,sK1(sK18))
      | in(sK1(sK18),X0)
      | ( sK1(sK18) = X0 )
      | ~ ordinal(X0) ),
    inference(superposition,[status(thm)],[c_61,c_4037]) ).

tcf(c_4160,plain,
    ( epsilon_connected(sK18)
    | in(sK1(sK18),sK2(sK18))
    | ( sK1(sK18) = sK2(sK18) )
    | ~ ordinal(sK2(sK18)) ),
    inference(superposition,[status(thm)],[c_4049,c_65]) ).

tcf(c_4437,plain,
    ( epsilon_connected(sK18)
    | in(sK1(sK18),sK2(sK18))
    | ( sK1(sK18) = sK2(sK18) ) ),
    inference(global_subsumption_just,[status(thm)],[c_4160,c_3734,c_4160]) ).

tcf(c_4442,plain,
    epsilon_connected(sK18),
    inference(forward_subsumption_resolution,[status(thm)],[c_4437,c_63,c_64]) ).

tcf(c_4451,plain,
    ! [X0: $i] :
      ( subset(X0,sK18)
      | ~ ordinal(sK3(X0,sK18)) ),
    inference(superposition,[status(thm)],[c_2812,c_67]) ).

tcf(c_4490,plain,
    ! [X0: $i,X1: $i] :
      ( subset(X0,X1)
      | ordinal(sK3(X0,X1))
      | ~ ordinal(X0) ),
    inference(superposition,[status(thm)],[c_68,c_118]) ).

tcf(c_7045,plain,
    ! [X0: $i] :
      ( subset(X0,sK18)
      | ~ ordinal(X0) ),
    inference(superposition,[status(thm)],[c_4490,c_4451]) ).

tcf(c_7452,plain,
    ( epsilon_transitive(sK18)
    | ~ ordinal(sK0(sK18)) ),
    inference(superposition,[status(thm)],[c_7045,c_58]) ).

tcf(c_7468,plain,
    epsilon_transitive(sK18),
    inference(global_subsumption_just,[status(thm)],[c_7452,c_3758,c_7452]) ).

tcf(c_7477,plain,
    ( ordinal(sK18)
    | ~ epsilon_connected(sK18) ),
    inference(superposition,[status(thm)],[c_7468,c_70]) ).

tcf(c_7478,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_7477,c_3673,c_4442]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05  % Problem  : NUM404+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07  % Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.19/0.45  % Computer : n004.cluster.edu
% 0.19/0.45  % Model    : x86_64 x86_64
% 0.19/0.45  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45  % Memory   : 8046.5625MB
% 0.19/0.45  % OS       : Linux 6.8.0-71-generic
% 0.19/0.45  % CPULimit : 300
% 0.19/0.45  % WCLimit  : 300
% 0.19/0.45  % DateTime : Thu Sep 24 03:50:52 UTC 2026
% 0.19/0.46  % CPUTime  : 
% 0.19/0.46  Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.23/0.52  Running first-order theorem proving
% 0.23/0.52  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
% 0.23/0.54  
% 0.23/0.54  % ======== iProver multi-core TPTP/SMT =========
% 0.23/0.54  
% 0.23/0.54  % Detected problem language: tptp
% 0.23/0.56  % Proving...
% 4.30/1.53  % SZS status Started for theBenchmark.p
% 4.30/1.53  % SZS status Theorem for theBenchmark.p
% 4.30/1.53  
% 4.30/1.53  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.30/1.53  
% 4.30/1.53  % ------  iProver source info
% 4.30/1.53  
% 4.30/1.53  % git: date: 2026-07-19 20:42:38 +0200
% 4.30/1.53  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.30/1.53  % git: non_committed_changes: false
% 4.30/1.53  
% 4.30/1.53  % ------ Parsing...
% 4.30/1.53  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 4.30/1.53  
% 4.30/1.53  % ------ Preprocessing... sup_sim: 0  sf_s  rm: 22 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 3 0s  sf_e  pe_s  pe_e % 
% 4.30/1.53  
% 4.30/1.53  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 4.30/1.53  
% 4.30/1.53  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 4.30/1.53  % ------ Proving...
% 4.30/1.53  % ------ Problem Properties 
% 4.30/1.53  
% 4.30/1.53  % 
% 4.30/1.53  % clauses                               54
% 4.30/1.53  % conjectures                           2
% 4.30/1.53  % EPR                                   42
% 4.30/1.53  % Horn                                  47
% 4.30/1.53  % unary                                 22
% 4.30/1.53  % binary                                22
% 4.30/1.53  % lits                                  101
% 4.30/1.53  % lits eq                               5
% 4.30/1.53  % fd_pure                               0
% 4.30/1.53  % fd_pseudo                             0
% 4.30/1.53  % fd_cond                               1
% 4.30/1.53  % fd_pseudo_cond                        3
% 4.30/1.53  % AC symbols                            0
% 4.30/1.53  
% 4.30/1.53  % ------ Schedule dynamic 5 is on 
% 4.30/1.53  
% 4.30/1.53  % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.30/1.53  
% 4.30/1.53  
% 4.30/1.53  % ------ 
% 4.30/1.53  % Current options:
% 4.30/1.53  % ------ 
% 4.30/1.53  
% 4.30/1.53  
% 4.30/1.53  % 
% 4.30/1.53  
% 4.30/1.53  % ------ Proving...
% 4.30/1.53  % 
% 4.30/1.53  
% 4.30/1.53  % SZS status Theorem for theBenchmark.p
% 4.30/1.53  
% 4.30/1.53  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.30/1.54  
% 4.30/1.54  
%------------------------------------------------------------------------------