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iProver---3.9.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : GEO111+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM

% Computer : n020.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 01:19:54 PM UTC 2026

% Result   : Theorem 2.86s 1.29s
% Output   : CNFRefutation 2.86s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   80 (  23 unt;   1 def)
%            Number of atoms       :  319 (  55 equ)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives :  365 ( 143   ~; 137   |;  73   &)
%                                         (   7 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 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  :    8 (   6 usr;   2 prp; 0-4 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-4 aty)
%            Number of variables   :  170 (   0 sgn 155   !;  15   ?;  50   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1] :
      ( part_of(X1,X0)
    <=> ! [X2] :
          ( incident_c(X2,X1)
         => incident_c(X2,X0) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax',part_of_defn) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( end_point(X0,X1)
    <=> ( ! [X2,X3] :
            ( ( incident_c(X0,X3)
              & incident_c(X0,X2)
              & part_of(X3,X1)
              & part_of(X2,X1) )
           => ( part_of(X3,X2)
              | part_of(X2,X3) ) )
        & incident_c(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax',end_point_defn) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( inner_point(X0,X1)
    <=> ( ~ end_point(X0,X1)
        & incident_c(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax',inner_point_defn) ).

fof(f17,axiom,
    ! [X0,X1,X2,X3] :
      ( between_c(X0,X1,X2,X3)
    <=> ( ? [X4] :
            ( inner_point(X2,X4)
            & end_point(X3,X4)
            & end_point(X1,X4)
            & part_of(X4,X0) )
        & X1 != X3 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO004+1.ax',between_c_defn) ).

fof(f18,conjecture,
    ! [X0,X1,X2,X3] :
      ( between_c(X0,X1,X2,X3)
     => ( X1 != X3
        & X2 != X3
        & X1 != X2
        & incident_c(X3,X0)
        & incident_c(X2,X0)
        & incident_c(X1,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_3_8_1) ).

fof(f19,negated_conjecture,
    ~ ! [X0,X1,X2,X3] :
        ( between_c(X0,X1,X2,X3)
       => ( X1 != X3
          & X2 != X3
          & X1 != X2
          & incident_c(X3,X0)
          & incident_c(X2,X0)
          & incident_c(X1,X0) ) ),
    inference(negated_conjecture,[status(cth)],[f18]) ).

fof(f20,plain,
    ! [X0,X1,X2,X3] :
      ( between_c(X0,X1,X2,X3)
     => ( ? [X4] :
            ( inner_point(X2,X4)
            & end_point(X3,X4)
            & end_point(X1,X4)
            & part_of(X4,X0) )
        & X1 != X3 ) ),
    inference(unused_predicate_definition_removal,[],[f17]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( part_of(X1,X0)
    <=> ! [X2] :
          ( ~ incident_c(X2,X1)
          | incident_c(X2,X0) ) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( end_point(X0,X1)
    <=> ( ! [X2,X3] :
            ( ~ incident_c(X0,X3)
            | ~ incident_c(X0,X2)
            | ~ part_of(X3,X1)
            | ~ part_of(X2,X1)
            | part_of(X3,X2)
            | part_of(X2,X3) )
        & incident_c(X0,X1) ) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( end_point(X0,X1)
    <=> ( ! [X2,X3] :
            ( ~ incident_c(X0,X3)
            | ~ incident_c(X0,X2)
            | ~ part_of(X3,X1)
            | ~ part_of(X2,X1)
            | part_of(X3,X2)
            | part_of(X2,X3) )
        & incident_c(X0,X1) ) ),
    inference(flattening,[],[f24]) ).

fof(f42,plain,
    ! [X0,X1,X2,X3] :
      ( ~ between_c(X0,X1,X2,X3)
      | ( ? [X4] :
            ( inner_point(X2,X4)
            & end_point(X3,X4)
            & end_point(X1,X4)
            & part_of(X4,X0) )
        & X1 != X3 ) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f43,plain,
    ? [X0,X1,X2,X3] :
      ( between_c(X0,X1,X2,X3)
      & ( X1 = X3
        | X2 = X3
        | X1 = X2
        | ~ incident_c(X3,X0)
        | ~ incident_c(X2,X0)
        | ~ incident_c(X1,X0) ) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ( ~ part_of(X1,X0)
        | ! [X2] :
            ( ~ incident_c(X2,X1)
            | incident_c(X2,X0) ) )
      & ( ? [X2] :
            ( incident_c(X2,X1)
            & ~ incident_c(X2,X0) )
        | part_of(X1,X0) ) ),
    inference(nnf_transformation,[],[f23]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( ( ~ part_of(X1,X0)
        | ! [X3] :
            ( ~ incident_c(X3,X1)
            | incident_c(X3,X0) ) )
      & ( ? [X2] :
            ( incident_c(X2,X1)
            & ~ incident_c(X2,X0) )
        | part_of(X1,X0) ) ),
    inference(rectify,[],[f44]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( ( ~ part_of(X1,X0)
        | ! [X3] :
            ( ~ incident_c(X3,X1)
            | incident_c(X3,X0) ) )
      & ( ( incident_c(sK0(X0,X1),X1)
          & ~ incident_c(sK0(X0,X1),X0) )
        | part_of(X1,X0) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f45]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( ( ~ end_point(X0,X1)
        | ( ! [X2,X3] :
              ( ~ incident_c(X0,X3)
              | ~ incident_c(X0,X2)
              | ~ part_of(X3,X1)
              | ~ part_of(X2,X1)
              | part_of(X3,X2)
              | part_of(X2,X3) )
          & incident_c(X0,X1) ) )
      & ( ? [X2,X3] :
            ( incident_c(X0,X3)
            & incident_c(X0,X2)
            & part_of(X3,X1)
            & part_of(X2,X1)
            & ~ part_of(X3,X2)
            & ~ part_of(X2,X3) )
        | ~ incident_c(X0,X1)
        | end_point(X0,X1) ) ),
    inference(nnf_transformation,[],[f25]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( ( ~ end_point(X0,X1)
        | ( ! [X2,X3] :
              ( ~ incident_c(X0,X3)
              | ~ incident_c(X0,X2)
              | ~ part_of(X3,X1)
              | ~ part_of(X2,X1)
              | part_of(X3,X2)
              | part_of(X2,X3) )
          & incident_c(X0,X1) ) )
      & ( ? [X2,X3] :
            ( incident_c(X0,X3)
            & incident_c(X0,X2)
            & part_of(X3,X1)
            & part_of(X2,X1)
            & ~ part_of(X3,X2)
            & ~ part_of(X2,X3) )
        | ~ incident_c(X0,X1)
        | end_point(X0,X1) ) ),
    inference(flattening,[],[f51]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( ( ~ end_point(X0,X1)
        | ( ! [X4,X5] :
              ( ~ incident_c(X0,X5)
              | ~ incident_c(X0,X4)
              | ~ part_of(X5,X1)
              | ~ part_of(X4,X1)
              | part_of(X5,X4)
              | part_of(X4,X5) )
          & incident_c(X0,X1) ) )
      & ( ? [X2,X3] :
            ( incident_c(X0,X3)
            & incident_c(X0,X2)
            & part_of(X3,X1)
            & part_of(X2,X1)
            & ~ part_of(X3,X2)
            & ~ part_of(X2,X3) )
        | ~ incident_c(X0,X1)
        | end_point(X0,X1) ) ),
    inference(rectify,[],[f52]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( ( ~ end_point(X0,X1)
        | ( ! [X4,X5] :
              ( ~ incident_c(X0,X5)
              | ~ incident_c(X0,X4)
              | ~ part_of(X5,X1)
              | ~ part_of(X4,X1)
              | part_of(X5,X4)
              | part_of(X4,X5) )
          & incident_c(X0,X1) ) )
      & ( ( incident_c(X0,sK3(X0,X1))
          & incident_c(X0,sK2(X0,X1))
          & part_of(sK3(X0,X1),X1)
          & part_of(sK2(X0,X1),X1)
          & ~ part_of(sK3(X0,X1),sK2(X0,X1))
          & ~ part_of(sK2(X0,X1),sK3(X0,X1)) )
        | ~ incident_c(X0,X1)
        | end_point(X0,X1) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X2,sK2(X0,X1)),skolemize(X3,sK3(X0,X1))],[f53]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( ( ~ inner_point(X0,X1)
        | ( ~ end_point(X0,X1)
          & incident_c(X0,X1) ) )
      & ( end_point(X0,X1)
        | ~ incident_c(X0,X1)
        | inner_point(X0,X1) ) ),
    inference(nnf_transformation,[],[f4]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( ( ~ inner_point(X0,X1)
        | ( ~ end_point(X0,X1)
          & incident_c(X0,X1) ) )
      & ( end_point(X0,X1)
        | ~ incident_c(X0,X1)
        | inner_point(X0,X1) ) ),
    inference(flattening,[],[f55]) ).

fof(f70,plain,
    ! [X0,X1,X2,X3] :
      ( ~ between_c(X0,X1,X2,X3)
      | ( inner_point(X2,sK13(X0,X1,X2,X3))
        & end_point(X3,sK13(X0,X1,X2,X3))
        & end_point(X1,sK13(X0,X1,X2,X3))
        & part_of(sK13(X0,X1,X2,X3),X0)
        & X1 != X3 ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X4,sK13(X0,X1,X2,X3))],[f42]) ).

fof(f71,plain,
    ( between_c(sK14,sK15,sK16,sK17)
    & ( sK15 = sK17
      | sK16 = sK17
      | sK15 = sK16
      | ~ incident_c(sK17,sK14)
      | ~ incident_c(sK16,sK14)
      | ~ incident_c(sK15,sK14) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,sK17]),skolemize(X0,sK14),skolemize(X1,sK15),skolemize(X2,sK16),skolemize(X3,sK17)],[f43]) ).

fof(f72,plain,
    ! [X3,X0,X1] :
      ( ~ part_of(X1,X0)
      | ~ incident_c(X3,X1)
      | incident_c(X3,X0) ),
    inference(cnf_transformation,[],[f46]) ).

fof(f82,plain,
    ! [X0,X1] :
      ( ~ end_point(X0,X1)
      | incident_c(X0,X1) ),
    inference(cnf_transformation,[],[f54]) ).

fof(f89,plain,
    ! [X0,X1] :
      ( ~ inner_point(X0,X1)
      | ~ end_point(X0,X1) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f90,plain,
    ! [X0,X1] :
      ( ~ inner_point(X0,X1)
      | incident_c(X0,X1) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f113,plain,
    ! [X2,X3,X0,X1] :
      ( ~ between_c(X0,X1,X2,X3)
      | inner_point(X2,sK13(X0,X1,X2,X3)) ),
    inference(cnf_transformation,[],[f70]) ).

fof(f114,plain,
    ! [X2,X3,X0,X1] :
      ( ~ between_c(X0,X1,X2,X3)
      | end_point(X3,sK13(X0,X1,X2,X3)) ),
    inference(cnf_transformation,[],[f70]) ).

fof(f115,plain,
    ! [X2,X3,X0,X1] :
      ( ~ between_c(X0,X1,X2,X3)
      | end_point(X1,sK13(X0,X1,X2,X3)) ),
    inference(cnf_transformation,[],[f70]) ).

fof(f116,plain,
    ! [X2,X3,X0,X1] :
      ( ~ between_c(X0,X1,X2,X3)
      | part_of(sK13(X0,X1,X2,X3),X0) ),
    inference(cnf_transformation,[],[f70]) ).

fof(f117,plain,
    ! [X2,X3,X0,X1] :
      ( ~ between_c(X0,X1,X2,X3)
      | X1 != X3 ),
    inference(cnf_transformation,[],[f70]) ).

fof(f118,plain,
    between_c(sK14,sK15,sK16,sK17),
    inference(cnf_transformation,[],[f71]) ).

fof(f119,plain,
    ( sK15 = sK17
    | sK16 = sK17
    | sK15 = sK16
    | ~ incident_c(sK17,sK14)
    | ~ incident_c(sK16,sK14)
    | ~ incident_c(sK15,sK14) ),
    inference(cnf_transformation,[],[f71]) ).

fof(f124,plain,
    ! [X2,X3,X0] : ~ between_c(X0,X3,X2,X3),
    inference(equality_resolution,[],[f117]) ).

tcf(c_51,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( incident_c(X2,X1)
      | ~ incident_c(X2,X0)
      | ~ part_of(X0,X1) ),
    inference(cnf_transformation,[],[f72]) ).

tcf(c_64,plain,
    ! [X0: $i,X1: $i] :
      ( incident_c(X0,X1)
      | ~ end_point(X0,X1) ),
    inference(cnf_transformation,[],[f82]) ).

tcf(c_67,plain,
    ! [X0: $i,X1: $i] :
      ( incident_c(X0,X1)
      | ~ inner_point(X0,X1) ),
    inference(cnf_transformation,[],[f90]) ).

tcf(c_68,plain,
    ! [X0: $i,X1: $i] :
      ( ~ inner_point(X0,X1)
      | ~ end_point(X0,X1) ),
    inference(cnf_transformation,[],[f89]) ).

tcf(c_90,plain,
    ! [X0: $i,X1: $i,X2: $i] : ~ between_c(X0,X1,X2,X1),
    inference(cnf_transformation,[],[f124]) ).

tcf(c_91,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( part_of(sK13(X0,X1,X2,X3),X0)
      | ~ between_c(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f116]) ).

tcf(c_92,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( end_point(X1,sK13(X0,X1,X2,X3))
      | ~ between_c(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f115]) ).

tcf(c_93,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( end_point(X3,sK13(X0,X1,X2,X3))
      | ~ between_c(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f114]) ).

tcf(c_94,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( inner_point(X2,sK13(X0,X1,X2,X3))
      | ~ between_c(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f113]) ).

tcf(c_95,negated_conjecture,
    ( ( sK16 = sK17 )
    | ( sK15 = sK17 )
    | ( sK15 = sK16 )
    | ~ incident_c(sK17,sK14)
    | ~ incident_c(sK16,sK14)
    | ~ incident_c(sK15,sK14) ),
    inference(cnf_transformation,[],[f119]) ).

tcf(c_96,negated_conjecture,
    between_c(sK14,sK15,sK16,sK17),
    inference(cnf_transformation,[],[f118]) ).

tcf(c_746,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X2 != sK16 )
      | ( X1 != sK17 )
      | ( X1 != sK15 )
      | ( X0 != sK14 ) ),
    inference(resolution_lifted,[status(thm)],[c_90,c_96]) ).

tcf(c_747,plain,
    sK15 != sK17,
    inference(unflattening,[status(thm)],[c_746]) ).

tcf(c_751,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( inner_point(X2,sK13(X0,X1,X2,X3))
      | ( X3 != sK17 )
      | ( X2 != sK16 )
      | ( X1 != sK15 )
      | ( X0 != sK14 ) ),
    inference(resolution_lifted,[status(thm)],[c_94,c_96]) ).

tcf(c_752,plain,
    inner_point(sK16,sK13(sK14,sK15,sK16,sK17)),
    inference(unflattening,[status(thm)],[c_751]) ).

tcf(c_756,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( end_point(X3,sK13(X0,X1,X2,X3))
      | ( X3 != sK17 )
      | ( X2 != sK16 )
      | ( X1 != sK15 )
      | ( X0 != sK14 ) ),
    inference(resolution_lifted,[status(thm)],[c_93,c_96]) ).

tcf(c_757,plain,
    end_point(sK17,sK13(sK14,sK15,sK16,sK17)),
    inference(unflattening,[status(thm)],[c_756]) ).

tcf(c_761,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( end_point(X1,sK13(X0,X1,X2,X3))
      | ( X3 != sK17 )
      | ( X2 != sK16 )
      | ( X1 != sK15 )
      | ( X0 != sK14 ) ),
    inference(resolution_lifted,[status(thm)],[c_92,c_96]) ).

tcf(c_762,plain,
    end_point(sK15,sK13(sK14,sK15,sK16,sK17)),
    inference(unflattening,[status(thm)],[c_761]) ).

tcf(c_766,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( part_of(sK13(X0,X1,X2,X3),X0)
      | ( X3 != sK17 )
      | ( X2 != sK16 )
      | ( X1 != sK15 )
      | ( X0 != sK14 ) ),
    inference(resolution_lifted,[status(thm)],[c_91,c_96]) ).

tcf(c_767,plain,
    part_of(sK13(sK14,sK15,sK16,sK17),sK14),
    inference(unflattening,[status(thm)],[c_766]) ).

tcf(c_772,plain,
    ( ( sK16 = sK17 )
    | ( sK15 = sK16 )
    | ~ incident_c(sK17,sK14)
    | ~ incident_c(sK16,sK14)
    | ~ incident_c(sK15,sK14) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_95,c_747]) ).

tcf(c_1528,definition,
    iPr_def_10 = sK13(sK14,sK15,sK16,sK17),
    introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).

tcf(c_1529,plain,
    ( ( sK16 = sK17 )
    | ( sK15 = sK16 )
    | ~ incident_c(sK17,sK14)
    | ~ incident_c(sK16,sK14)
    | ~ incident_c(sK15,sK14) ),
    inference(demodulation,[status(thm)],[c_772]) ).

tcf(c_1530,plain,
    part_of(iPr_def_10,sK14),
    inference(demodulation,[status(thm)],[c_767,c_1528]) ).

tcf(c_1531,plain,
    end_point(sK15,iPr_def_10),
    inference(demodulation,[status(thm)],[c_762]) ).

tcf(c_1532,plain,
    end_point(sK17,iPr_def_10),
    inference(demodulation,[status(thm)],[c_757]) ).

tcf(c_1533,plain,
    inner_point(sK16,iPr_def_10),
    inference(demodulation,[status(thm)],[c_752]) ).

tcf(c_2266,plain,
    incident_c(sK15,iPr_def_10),
    inference(superposition,[status(thm)],[c_1531,c_64]) ).

tcf(c_2267,plain,
    incident_c(sK17,iPr_def_10),
    inference(superposition,[status(thm)],[c_1532,c_64]) ).

tcf(c_2276,plain,
    incident_c(sK16,iPr_def_10),
    inference(superposition,[status(thm)],[c_1533,c_67]) ).

tcf(c_2303,plain,
    ~ inner_point(sK15,iPr_def_10),
    inference(superposition,[status(thm)],[c_1531,c_68]) ).

tcf(c_2304,plain,
    ~ inner_point(sK17,iPr_def_10),
    inference(superposition,[status(thm)],[c_1532,c_68]) ).

tcf(c_2424,plain,
    ! [X0: $i] :
      ( incident_c(sK15,X0)
      | ~ part_of(iPr_def_10,X0) ),
    inference(superposition,[status(thm)],[c_2266,c_51]) ).

tcf(c_2425,plain,
    ! [X0: $i] :
      ( incident_c(sK17,X0)
      | ~ part_of(iPr_def_10,X0) ),
    inference(superposition,[status(thm)],[c_2267,c_51]) ).

tcf(c_2426,plain,
    ! [X0: $i] :
      ( incident_c(sK16,X0)
      | ~ part_of(iPr_def_10,X0) ),
    inference(superposition,[status(thm)],[c_2276,c_51]) ).

tcf(c_2455,plain,
    ( incident_c(sK16,sK14)
    | ~ part_of(iPr_def_10,sK14) ),
    inference(instantiation,[status(thm)],[c_2426]) ).

tcf(c_2456,plain,
    ( incident_c(sK17,sK14)
    | ~ part_of(iPr_def_10,sK14) ),
    inference(instantiation,[status(thm)],[c_2425]) ).

tcf(c_2465,plain,
    incident_c(sK15,sK14),
    inference(superposition,[status(thm)],[c_1530,c_2424]) ).

tcf(c_2467,plain,
    ( ( sK16 = sK17 )
    | ( sK15 = sK16 )
    | ~ incident_c(sK17,sK14)
    | ~ incident_c(sK16,sK14) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_1529,c_2465]) ).

tcf(c_2478,plain,
    ( ( sK16 = sK17 )
    | ( sK15 = sK16 ) ),
    inference(global_subsumption_just,[status(thm)],[c_2467,c_1530,c_2455,c_2456,c_2467]) ).

tcf(c_2484,plain,
    ( ( sK15 = sK16 )
    | ~ inner_point(sK16,iPr_def_10) ),
    inference(superposition,[status(thm)],[c_2478,c_2304]) ).

tcf(c_2491,plain,
    sK15 = sK16,
    inference(forward_subsumption_resolution,[status(thm)],[c_2484,c_1533]) ).

tcf(c_2494,plain,
    inner_point(sK15,iPr_def_10),
    inference(demodulation,[status(thm)],[c_1533,c_2491]) ).

tcf(c_2495,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_2494,c_2303]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : GEO111+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.39  % Computer : n020.cluster.edu
% 0.11/0.39  % Model    : x86_64 x86_64
% 0.11/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39  % Memory   : 8046.5625MB
% 0.11/0.39  % OS       : Linux 6.8.0-71-generic
% 0.11/0.39  % CPULimit : 300
% 0.11/0.39  % WCLimit  : 300
% 0.11/0.39  % DateTime : Wed Sep 23 10:57:04 UTC 2026
% 0.11/0.39  % CPUTime  : 
% 0.11/0.39  Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.42  Running first-order theorem proving
% 0.11/0.42  Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.43  
% 0.11/0.43  % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43  
% 0.11/0.43  % Detected problem language: tptp
% 0.11/0.44  % Proving...
% 2.86/1.29  % SZS status Started for theBenchmark.p
% 2.86/1.29  % SZS status Theorem for theBenchmark.p
% 2.86/1.29  
% 2.86/1.29  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.86/1.29  
% 2.86/1.29  % ------  iProver source info
% 2.86/1.29  
% 2.86/1.29  % git: date: 2026-07-19 20:42:38 +0200
% 2.86/1.29  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.86/1.29  % git: non_committed_changes: false
% 2.86/1.29  
% 2.86/1.29  % ------ Parsing...
% 2.86/1.29  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 2.86/1.29  
% 2.86/1.29  % ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e % 
% 2.86/1.29  
% 2.86/1.29  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 2.86/1.29  
% 2.86/1.29  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.86/1.29  % ------ Proving...
% 2.86/1.29  % ------ Problem Properties 
% 2.86/1.29  
% 2.86/1.29  % 
% 2.86/1.29  % clauses                               48
% 2.86/1.29  % conjectures                           0
% 2.86/1.29  % EPR                                   19
% 2.86/1.29  % Horn                                  31
% 2.86/1.29  % unary                                 7
% 2.86/1.29  % binary                                16
% 2.86/1.29  % lits                                  140
% 2.86/1.29  % lits eq                               16
% 2.86/1.29  % fd_pure                               0
% 2.86/1.29  % fd_pseudo                             0
% 2.86/1.29  % fd_cond                               0
% 2.86/1.29  % fd_pseudo_cond                        7
% 2.86/1.29  % AC symbols                            0
% 2.86/1.29  
% 2.86/1.29  % ------ Schedule dynamic 5 is on 
% 2.86/1.29  
% 2.86/1.29  % ------ no conjectures: strip conj schedule 
% 2.86/1.29  
% 2.86/1.29  % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.86/1.29  
% 2.86/1.29  
% 2.86/1.29  % ------ 
% 2.86/1.29  % Current options:
% 2.86/1.29  % ------ 
% 2.86/1.29  
% 2.86/1.29  
% 2.86/1.29  % 
% 2.86/1.29  
% 2.86/1.29  % ------ Proving...
% 2.86/1.29  % 
% 2.86/1.29  
% 2.86/1.29  % SZS status Theorem for theBenchmark.p
% 2.86/1.29  
% 2.86/1.29  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.86/1.30  
% 2.86/1.30  
%------------------------------------------------------------------------------