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iProver---3.9.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : GEO094+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox2/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 01:19:52 PM UTC 2026

% Result   : Theorem 4.46s 1.31s
% Output   : CNFRefutation 4.46s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   76 (  22 unt;   0 def)
%            Number of atoms       :  330 (   0 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  405 ( 151   ~; 148   |;  92   &)
%                                         (   9 <=>;   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  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-2 aty)
%            Number of variables   :  167 (   0 sgn 147   !;  20   ?;  34   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1] :
      ( part_of(X1,X0)
    <=> ! [X2] :
          ( incident_c(X2,X1)
         => incident_c(X2,X0) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/GEO004+0.ax',inner_point_defn) ).

fof(f5,axiom,
    ! [X0,X1,X2] :
      ( meet(X0,X1,X2)
    <=> ( ! [X3] :
            ( ( incident_c(X3,X2)
              & incident_c(X3,X1) )
           => ( end_point(X3,X2)
              & end_point(X3,X1) ) )
        & incident_c(X0,X2)
        & incident_c(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax',meet_defn) ).

fof(f10,axiom,
    ! [X0] :
    ? [X1] : inner_point(X1,X0),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax',c3) ).

fof(f17,conjecture,
    ! [X0,X1,X2,X3] :
      ( ( part_of(X2,X0)
        & part_of(X1,X0)
        & meet(X3,X1,X2) )
     => ~ end_point(X3,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',proposition_2_14_3) ).

fof(f18,negated_conjecture,
    ~ ! [X0,X1,X2,X3] :
        ( ( part_of(X2,X0)
          & part_of(X1,X0)
          & meet(X3,X1,X2) )
       => ~ end_point(X3,X0) ),
    inference(negated_conjecture,[status(cth)],[f17]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( part_of(X1,X0)
    <=> ! [X2] :
          ( ~ incident_c(X2,X1)
          | incident_c(X2,X0) ) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f22,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(f23,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,[],[f22]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( meet(X0,X1,X2)
    <=> ( ! [X3] :
            ( ~ incident_c(X3,X2)
            | ~ incident_c(X3,X1)
            | ( end_point(X3,X2)
              & end_point(X3,X1) ) )
        & incident_c(X0,X2)
        & incident_c(X0,X1) ) ),
    inference(ennf_transformation,[],[f5]) ).

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

fof(f40,plain,
    ? [X0,X1,X2,X3] :
      ( part_of(X2,X0)
      & part_of(X1,X0)
      & meet(X3,X1,X2)
      & end_point(X3,X0) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f41,plain,
    ? [X0,X1,X2,X3] :
      ( part_of(X2,X0)
      & part_of(X1,X0)
      & meet(X3,X1,X2)
      & end_point(X3,X0) ),
    inference(flattening,[],[f40]) ).

fof(f42,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,[],[f21]) ).

fof(f43,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,[],[f42]) ).

fof(f44,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))],[f43]) ).

fof(f49,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,[],[f23]) ).

fof(f50,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,[],[f49]) ).

fof(f51,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,[],[f50]) ).

fof(f52,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))],[f51]) ).

fof(f53,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(f54,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,[],[f53]) ).

fof(f55,plain,
    ! [X0,X1,X2] :
      ( ( ~ meet(X0,X1,X2)
        | ( ! [X3] :
              ( ~ incident_c(X3,X2)
              | ~ incident_c(X3,X1)
              | ( end_point(X3,X2)
                & end_point(X3,X1) ) )
          & incident_c(X0,X2)
          & incident_c(X0,X1) ) )
      & ( ? [X3] :
            ( incident_c(X3,X2)
            & incident_c(X3,X1)
            & ( ~ end_point(X3,X2)
              | ~ end_point(X3,X1) ) )
        | ~ incident_c(X0,X2)
        | ~ incident_c(X0,X1)
        | meet(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f25]) ).

fof(f56,plain,
    ! [X0,X1,X2] :
      ( ( ~ meet(X0,X1,X2)
        | ( ! [X3] :
              ( ~ incident_c(X3,X2)
              | ~ incident_c(X3,X1)
              | ( end_point(X3,X2)
                & end_point(X3,X1) ) )
          & incident_c(X0,X2)
          & incident_c(X0,X1) ) )
      & ( ? [X3] :
            ( incident_c(X3,X2)
            & incident_c(X3,X1)
            & ( ~ end_point(X3,X2)
              | ~ end_point(X3,X1) ) )
        | ~ incident_c(X0,X2)
        | ~ incident_c(X0,X1)
        | meet(X0,X1,X2) ) ),
    inference(flattening,[],[f55]) ).

fof(f57,plain,
    ! [X0,X1,X2] :
      ( ( ~ meet(X0,X1,X2)
        | ( ! [X4] :
              ( ~ incident_c(X4,X2)
              | ~ incident_c(X4,X1)
              | ( end_point(X4,X2)
                & end_point(X4,X1) ) )
          & incident_c(X0,X2)
          & incident_c(X0,X1) ) )
      & ( ? [X3] :
            ( incident_c(X3,X2)
            & incident_c(X3,X1)
            & ( ~ end_point(X3,X2)
              | ~ end_point(X3,X1) ) )
        | ~ incident_c(X0,X2)
        | ~ incident_c(X0,X1)
        | meet(X0,X1,X2) ) ),
    inference(rectify,[],[f56]) ).

fof(f58,plain,
    ! [X0,X1,X2] :
      ( ( ~ meet(X0,X1,X2)
        | ( ! [X4] :
              ( ~ incident_c(X4,X2)
              | ~ incident_c(X4,X1)
              | ( end_point(X4,X2)
                & end_point(X4,X1) ) )
          & incident_c(X0,X2)
          & incident_c(X0,X1) ) )
      & ( ( incident_c(sK4(X1,X2),X2)
          & incident_c(sK4(X1,X2),X1)
          & ( ~ end_point(sK4(X1,X2),X2)
            | ~ end_point(sK4(X1,X2),X1) ) )
        | ~ incident_c(X0,X2)
        | ~ incident_c(X0,X1)
        | meet(X0,X1,X2) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X1,X2))],[f57]) ).

fof(f61,plain,
    ! [X0] : inner_point(sK7(X0),X0),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X1,sK7(X0))],[f10]) ).

fof(f68,plain,
    ( part_of(sK15,sK13)
    & part_of(sK14,sK13)
    & meet(sK16,sK14,sK15)
    & end_point(sK16,sK13) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16]),skolemize(X0,sK13),skolemize(X1,sK14),skolemize(X2,sK15),skolemize(X3,sK16)],[f41]) ).

fof(f69,plain,
    ! [X3,X0,X1] :
      ( ~ part_of(X1,X0)
      | ~ incident_c(X3,X1)
      | incident_c(X3,X0) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f78,plain,
    ! [X0,X1,X4,X5] :
      ( ~ end_point(X0,X1)
      | ~ incident_c(X0,X5)
      | ~ incident_c(X0,X4)
      | ~ part_of(X5,X1)
      | ~ part_of(X4,X1)
      | part_of(X5,X4)
      | part_of(X4,X5) ),
    inference(cnf_transformation,[],[f52]) ).

fof(f86,plain,
    ! [X0,X1] :
      ( ~ inner_point(X0,X1)
      | ~ end_point(X0,X1) ),
    inference(cnf_transformation,[],[f54]) ).

fof(f87,plain,
    ! [X0,X1] :
      ( ~ inner_point(X0,X1)
      | incident_c(X0,X1) ),
    inference(cnf_transformation,[],[f54]) ).

fof(f89,plain,
    ! [X2,X0,X1,X4] :
      ( ~ meet(X0,X1,X2)
      | ~ incident_c(X4,X2)
      | ~ incident_c(X4,X1)
      | end_point(X4,X2) ),
    inference(cnf_transformation,[],[f58]) ).

fof(f90,plain,
    ! [X2,X0,X1,X4] :
      ( ~ meet(X0,X1,X2)
      | ~ incident_c(X4,X2)
      | ~ incident_c(X4,X1)
      | end_point(X4,X1) ),
    inference(cnf_transformation,[],[f58]) ).

fof(f91,plain,
    ! [X2,X0,X1] :
      ( ~ meet(X0,X1,X2)
      | incident_c(X0,X2) ),
    inference(cnf_transformation,[],[f58]) ).

fof(f92,plain,
    ! [X2,X0,X1] :
      ( ~ meet(X0,X1,X2)
      | incident_c(X0,X1) ),
    inference(cnf_transformation,[],[f58]) ).

fof(f100,plain,
    ! [X0] : inner_point(sK7(X0),X0),
    inference(cnf_transformation,[],[f61]) ).

fof(f110,plain,
    part_of(sK15,sK13),
    inference(cnf_transformation,[],[f68]) ).

fof(f111,plain,
    part_of(sK14,sK13),
    inference(cnf_transformation,[],[f68]) ).

fof(f112,plain,
    meet(sK16,sK14,sK15),
    inference(cnf_transformation,[],[f68]) ).

fof(f113,plain,
    end_point(sK16,sK13),
    inference(cnf_transformation,[],[f68]) ).

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,[],[f69]) ).

tcf(c_65,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( part_of(X2,X0)
      | part_of(X0,X2)
      | ~ end_point(X3,X1)
      | ~ incident_c(X3,X2)
      | ~ incident_c(X3,X0)
      | ~ part_of(X2,X1)
      | ~ part_of(X0,X1) ),
    inference(cnf_transformation,[],[f78]) ).

tcf(c_67,plain,
    ! [X0: $i,X1: $i] :
      ( incident_c(X0,X1)
      | ~ inner_point(X0,X1) ),
    inference(cnf_transformation,[],[f87]) ).

tcf(c_68,plain,
    ! [X0: $i,X1: $i] :
      ( ~ inner_point(X0,X1)
      | ~ end_point(X0,X1) ),
    inference(cnf_transformation,[],[f86]) ).

tcf(c_72,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( incident_c(X0,X1)
      | ~ meet(X0,X1,X2) ),
    inference(cnf_transformation,[],[f92]) ).

tcf(c_73,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( incident_c(X0,X2)
      | ~ meet(X0,X1,X2) ),
    inference(cnf_transformation,[],[f91]) ).

tcf(c_74,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( end_point(X3,X1)
      | ~ incident_c(X3,X2)
      | ~ incident_c(X3,X1)
      | ~ meet(X0,X1,X2) ),
    inference(cnf_transformation,[],[f90]) ).

tcf(c_75,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( end_point(X3,X2)
      | ~ incident_c(X3,X2)
      | ~ incident_c(X3,X1)
      | ~ meet(X0,X1,X2) ),
    inference(cnf_transformation,[],[f89]) ).

tcf(c_80,plain,
    ! [X0: $i] : inner_point(sK7(X0),X0),
    inference(cnf_transformation,[],[f100]) ).

tcf(c_90,negated_conjecture,
    end_point(sK16,sK13),
    inference(cnf_transformation,[],[f113]) ).

tcf(c_91,negated_conjecture,
    meet(sK16,sK14,sK15),
    inference(cnf_transformation,[],[f112]) ).

tcf(c_92,negated_conjecture,
    part_of(sK14,sK13),
    inference(cnf_transformation,[],[f111]) ).

tcf(c_93,negated_conjecture,
    part_of(sK15,sK13),
    inference(cnf_transformation,[],[f110]) ).

tcf(c_751,negated_conjecture,
    part_of(sK15,sK13),
    inference(demodulation,[status(thm)],[c_93]) ).

tcf(c_752,negated_conjecture,
    part_of(sK14,sK13),
    inference(demodulation,[status(thm)],[c_92]) ).

tcf(c_753,negated_conjecture,
    meet(sK16,sK14,sK15),
    inference(demodulation,[status(thm)],[c_91]) ).

tcf(c_754,negated_conjecture,
    end_point(sK16,sK13),
    inference(demodulation,[status(thm)],[c_90]) ).

tcf(c_1449,plain,
    ! [X0: $i] : incident_c(sK7(X0),X0),
    inference(superposition,[status(thm)],[c_80,c_67]) ).

tcf(c_1499,plain,
    incident_c(sK16,sK14),
    inference(superposition,[status(thm)],[c_753,c_72]) ).

tcf(c_1504,plain,
    incident_c(sK16,sK15),
    inference(superposition,[status(thm)],[c_753,c_73]) ).

tcf(c_1904,plain,
    ! [X0: $i,X1: $i] :
      ( incident_c(sK7(X0),X1)
      | ~ part_of(X0,X1) ),
    inference(superposition,[status(thm)],[c_1449,c_51]) ).

tcf(c_2586,plain,
    ! [X0: $i] :
      ( end_point(X0,sK14)
      | ~ incident_c(X0,sK15)
      | ~ incident_c(X0,sK14) ),
    inference(superposition,[status(thm)],[c_753,c_74]) ).

tcf(c_2605,plain,
    ! [X0: $i] :
      ( end_point(X0,sK15)
      | ~ incident_c(X0,sK15)
      | ~ incident_c(X0,sK14) ),
    inference(superposition,[status(thm)],[c_753,c_75]) ).

tcf(c_2870,plain,
    ( end_point(sK7(sK14),sK14)
    | ~ incident_c(sK7(sK14),sK15) ),
    inference(superposition,[status(thm)],[c_1449,c_2586]) ).

tcf(c_3024,plain,
    ! [X0: $i] :
      ( end_point(sK7(X0),sK15)
      | ~ part_of(X0,sK14)
      | ~ incident_c(sK7(X0),sK15) ),
    inference(superposition,[status(thm)],[c_1904,c_2605]) ).

tcf(c_3234,plain,
    ( end_point(sK7(sK14),sK14)
    | ~ part_of(sK14,sK15) ),
    inference(superposition,[status(thm)],[c_1904,c_2870]) ).

tcf(c_3250,plain,
    ( ~ part_of(sK14,sK15)
    | ~ inner_point(sK7(sK14),sK14) ),
    inference(superposition,[status(thm)],[c_3234,c_68]) ).

tcf(c_3252,plain,
    ~ part_of(sK14,sK15),
    inference(forward_subsumption_resolution,[status(thm)],[c_3250,c_80]) ).

tcf(c_3556,plain,
    ( end_point(sK7(sK15),sK15)
    | ~ part_of(sK15,sK14) ),
    inference(superposition,[status(thm)],[c_1449,c_3024]) ).

tcf(c_4002,plain,
    ! [X0: $i,X1: $i] :
      ( part_of(sK14,X1)
      | part_of(X1,sK14)
      | ~ end_point(X0,sK13)
      | ~ incident_c(X0,sK14)
      | ~ part_of(X1,sK13)
      | ~ incident_c(X0,X1) ),
    inference(superposition,[status(thm)],[c_752,c_65]) ).

tcf(c_4115,plain,
    ( ~ part_of(sK15,sK14)
    | ~ inner_point(sK7(sK15),sK15) ),
    inference(superposition,[status(thm)],[c_3556,c_68]) ).

tcf(c_4117,plain,
    ~ part_of(sK15,sK14),
    inference(forward_subsumption_resolution,[status(thm)],[c_4115,c_80]) ).

tcf(c_4186,plain,
    ( part_of(sK15,sK14)
    | part_of(sK14,sK15)
    | ~ end_point(sK16,sK13)
    | ~ incident_c(sK16,sK14)
    | ~ part_of(sK15,sK13) ),
    inference(superposition,[status(thm)],[c_1504,c_4002]) ).

tcf(c_4196,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_4186,c_4117,c_3252,c_754,c_1499,c_751]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05  % Problem  : GEO094+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07  % Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.19/0.44  % Computer : n020.cluster.edu
% 0.19/0.44  % Model    : x86_64 x86_64
% 0.19/0.44  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44  % Memory   : 8046.5625MB
% 0.19/0.44  % OS       : Linux 6.8.0-71-generic
% 0.19/0.44  % CPULimit : 300
% 0.19/0.44  % WCLimit  : 300
% 0.19/0.44  % DateTime : Wed Sep 23 10:50:48 UTC 2026
% 0.19/0.44  % CPUTime  : 
% 0.19/0.44  Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.19/0.50  Running first-order theorem proving
% 0.19/0.50  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
% 0.25/0.51  
% 0.25/0.51  % ======== iProver multi-core TPTP/SMT =========
% 0.25/0.51  
% 0.25/0.51  % Detected problem language: tptp
% 0.25/0.53  % Proving...
% 4.46/1.31  % SZS status Started for theBenchmark.p
% 4.46/1.31  % SZS status Theorem for theBenchmark.p
% 4.46/1.31  
% 4.46/1.31  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.46/1.31  
% 4.46/1.31  % ------  iProver source info
% 4.46/1.31  
% 4.46/1.31  % git: date: 2026-07-19 20:42:38 +0200
% 4.46/1.31  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.46/1.31  % git: non_committed_changes: false
% 4.46/1.31  
% 4.46/1.31  % ------ Parsing...
% 4.46/1.31  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 4.46/1.31  
% 4.46/1.31  % ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e % 
% 4.46/1.31  
% 4.46/1.31  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 4.46/1.31  
% 4.46/1.31  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 4.46/1.31  % ------ Proving...
% 4.46/1.31  % ------ Problem Properties 
% 4.46/1.31  
% 4.46/1.31  % 
% 4.46/1.31  % clauses                               45
% 4.46/1.31  % conjectures                           4
% 4.46/1.31  % EPR                                   17
% 4.46/1.31  % Horn                                  29
% 4.46/1.31  % unary                                 5
% 4.46/1.31  % binary                                16
% 4.46/1.31  % lits                                  133
% 4.46/1.31  % lits eq                               12
% 4.46/1.31  % fd_pure                               0
% 4.46/1.31  % fd_pseudo                             0
% 4.46/1.31  % fd_cond                               0
% 4.46/1.31  % fd_pseudo_cond                        7
% 4.46/1.31  % AC symbols                            0
% 4.46/1.31  
% 4.46/1.31  % ------ Schedule dynamic 5 is on 
% 4.46/1.31  
% 4.46/1.31  % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.46/1.31  
% 4.46/1.31  
% 4.46/1.31  % ------ 
% 4.46/1.31  % Current options:
% 4.46/1.31  % ------ 
% 4.46/1.31  
% 4.46/1.31  
% 4.46/1.31  % 
% 4.46/1.31  
% 4.46/1.31  % ------ Proving...
% 4.46/1.31  % 
% 4.46/1.31  
% 4.46/1.31  % SZS status Theorem for theBenchmark.p
% 4.46/1.31  
% 4.46/1.31  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.46/1.32  
% 4.46/1.32  
%------------------------------------------------------------------------------