↑ Up

Drodi---4.1.1.THM-CRf.s

View TPTP
Problem
Process solution in
SystemOnTSTP
Download .tgz
%------------------------------------------------------------------------------
% File     : Drodi---4.1.1
% Problem  : GEO084+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p

% 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 : Thu Sep 24 12:24:01 PM UTC 2026

% Result   : Theorem 17.52s 2.67s
% Output   : CNFRefutation 17.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   71 (  10 unt;   0 def)
%            Number of atoms       :  247 (  62 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  245 (  69   ~; 135   |;  34   &)
%                                         (   4 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-3 aty)
%            Number of variables   :  159 ( 147   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [C,C1] :
      ( part_of(C1,C)
    <=> ! [P] :
          ( incident_c(P,C1)
         => incident_c(P,C) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [C,C1,C2] :
      ( C = sum(C1,C2)
    <=> ! [Q] :
          ( incident_c(Q,C)
        <=> ( incident_c(Q,C2)
            | incident_c(Q,C1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f17,conjecture,
    ! [C1,C2,C3,P] :
      ( ( meet(P,C1,C2)
        & part_of(C2,C3)
        & part_of(C1,C3) )
     => part_of(sum(C1,C2),C3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f18,negated_conjecture,
    ~ ! [C1,C2,C3,P] :
        ( ( meet(P,C1,C2)
          & part_of(C2,C3)
          & part_of(C1,C3) )
       => part_of(sum(C1,C2),C3) ),
    inference(negated_conjecture,[status(cth)],[f17]) ).

fof(f19,plain,
    ! [C,C1] :
      ( part_of(C1,C)
    <=> ! [P] :
          ( incident_c(P,C)
          | ~ incident_c(P,C1) ) ),
    inference(pre_NNF_transformation,[status(thm)],[f1]) ).

fof(f20,plain,
    ! [C,C1] :
      ( ( ? [P] :
            ( ~ incident_c(P,C)
            & incident_c(P,C1) )
        | part_of(C1,C) )
      & ( ! [P] :
            ( incident_c(P,C)
            | ~ incident_c(P,C1) )
        | ~ part_of(C1,C) ) ),
    inference(NNF_transformation,[status(thm)],[f19]) ).

fof(f21,plain,
    ( ! [C,C1] :
        ( ? [P] :
            ( ~ incident_c(P,C)
            & incident_c(P,C1) )
        | part_of(C1,C) )
    & ! [C,C1] :
        ( ! [P] :
            ( incident_c(P,C)
            | ~ incident_c(P,C1) )
        | ~ part_of(C1,C) ) ),
    inference(miniscoping,[status(thm)],[f20]) ).

fof(f22,plain,
    ( ! [C,C1] :
        ( ( ~ incident_c(sK0_skl(C1,C),C)
          & incident_c(sK0_skl(C1,C),C1) )
        | part_of(C1,C) )
    & ! [C,C1] :
        ( ! [P] :
            ( incident_c(P,C)
            | ~ incident_c(P,C1) )
        | ~ part_of(C1,C) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(P,sK0_skl(C1,C))],[f21]) ).

fof(f23,plain,
    ! [X0,X1,X2] :
      ( incident_c(X2,X1)
      | ~ incident_c(X2,X0)
      | ~ part_of(X0,X1) ),
    inference(cnf_transformation,[status(thm)],[f22]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( incident_c(sK0_skl(X0,X1),X0)
      | part_of(X0,X1) ),
    inference(cnf_transformation,[status(thm)],[f22]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ~ incident_c(sK0_skl(X0,X1),X1)
      | part_of(X0,X1) ),
    inference(cnf_transformation,[status(thm)],[f22]) ).

fof(f26,plain,
    ! [C,C1,C2] :
      ( ( ? [Q] :
            ( ( incident_c(Q,C2)
              | incident_c(Q,C1)
              | incident_c(Q,C) )
            & ( ( ~ incident_c(Q,C2)
                & ~ incident_c(Q,C1) )
              | ~ incident_c(Q,C) ) )
        | C = sum(C1,C2) )
      & ( ! [Q] :
            ( ( ( ~ incident_c(Q,C2)
                & ~ incident_c(Q,C1) )
              | incident_c(Q,C) )
            & ( incident_c(Q,C2)
              | incident_c(Q,C1)
              | ~ incident_c(Q,C) ) )
        | C != sum(C1,C2) ) ),
    inference(NNF_transformation,[status(thm)],[f2]) ).

fof(f27,plain,
    ( ! [C,C1,C2] :
        ( ? [Q] :
            ( ( incident_c(Q,C2)
              | incident_c(Q,C1)
              | incident_c(Q,C) )
            & ( ( ~ incident_c(Q,C2)
                & ~ incident_c(Q,C1) )
              | ~ incident_c(Q,C) ) )
        | C = sum(C1,C2) )
    & ! [C,C1,C2] :
        ( ( ! [Q] :
              ( ( ~ incident_c(Q,C2)
                & ~ incident_c(Q,C1) )
              | incident_c(Q,C) )
          & ! [Q] :
              ( incident_c(Q,C2)
              | incident_c(Q,C1)
              | ~ incident_c(Q,C) ) )
        | C != sum(C1,C2) ) ),
    inference(miniscoping,[status(thm)],[f26]) ).

fof(f28,plain,
    ( ! [C,C1,C2] :
        ( ( ( incident_c(sK1_skl(C2,C1,C),C2)
            | incident_c(sK1_skl(C2,C1,C),C1)
            | incident_c(sK1_skl(C2,C1,C),C) )
          & ( ( ~ incident_c(sK1_skl(C2,C1,C),C2)
              & ~ incident_c(sK1_skl(C2,C1,C),C1) )
            | ~ incident_c(sK1_skl(C2,C1,C),C) ) )
        | C = sum(C1,C2) )
    & ! [C,C1,C2] :
        ( ( ! [Q] :
              ( ( ~ incident_c(Q,C2)
                & ~ incident_c(Q,C1) )
              | incident_c(Q,C) )
          & ! [Q] :
              ( incident_c(Q,C2)
              | incident_c(Q,C1)
              | ~ incident_c(Q,C) ) )
        | C != sum(C1,C2) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(Q,sK1_skl(C2,C1,C))],[f27]) ).

fof(f29,plain,
    ! [X0,X1,X2,X3] :
      ( incident_c(X3,X2)
      | incident_c(X3,X1)
      | ~ incident_c(X3,X0)
      | X0 != sum(X1,X2) ),
    inference(cnf_transformation,[status(thm)],[f28]) ).

fof(f30,plain,
    ! [X0,X1,X2,X3] :
      ( ~ incident_c(X3,X1)
      | incident_c(X3,X0)
      | X0 != sum(X1,X2) ),
    inference(cnf_transformation,[status(thm)],[f28]) ).

fof(f31,plain,
    ! [X0,X1,X2,X3] :
      ( ~ incident_c(X3,X2)
      | incident_c(X3,X0)
      | X0 != sum(X1,X2) ),
    inference(cnf_transformation,[status(thm)],[f28]) ).

fof(f32,plain,
    ! [X0,X1,X2] :
      ( ~ incident_c(sK1_skl(X2,X1,X0),X1)
      | ~ incident_c(sK1_skl(X2,X1,X0),X0)
      | X0 = sum(X1,X2) ),
    inference(cnf_transformation,[status(thm)],[f28]) ).

fof(f33,plain,
    ! [X0,X1,X2] :
      ( ~ incident_c(sK1_skl(X2,X1,X0),X2)
      | ~ incident_c(sK1_skl(X2,X1,X0),X0)
      | X0 = sum(X1,X2) ),
    inference(cnf_transformation,[status(thm)],[f28]) ).

fof(f34,plain,
    ! [X0,X1,X2] :
      ( incident_c(sK1_skl(X2,X1,X0),X2)
      | incident_c(sK1_skl(X2,X1,X0),X1)
      | incident_c(sK1_skl(X2,X1,X0),X0)
      | X0 = sum(X1,X2) ),
    inference(cnf_transformation,[status(thm)],[f28]) ).

fof(f104,plain,
    ? [C1,C2,C3,P] :
      ( ~ part_of(sum(C1,C2),C3)
      & meet(P,C1,C2)
      & part_of(C2,C3)
      & part_of(C1,C3) ),
    inference(pre_NNF_transformation,[status(thm)],[f18]) ).

fof(f105,plain,
    ? [C1,C2,C3] :
      ( ~ part_of(sum(C1,C2),C3)
      & ? [P] : meet(P,C1,C2)
      & part_of(C2,C3)
      & part_of(C1,C3) ),
    inference(miniscoping,[status(thm)],[f104]) ).

fof(f106,plain,
    ( ~ part_of(sum(sK13_skl,sK14_skl),sK15_skl)
    & meet(sK16_skl,sK13_skl,sK14_skl)
    & part_of(sK14_skl,sK15_skl)
    & part_of(sK13_skl,sK15_skl) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl,sK15_skl,sK16_skl]),skolemize(C1,sK13_skl),skolemize(C2,sK14_skl),skolemize(C3,sK15_skl),skolemize(P,sK16_skl)],[f105]) ).

fof(f107,plain,
    part_of(sK13_skl,sK15_skl),
    inference(cnf_transformation,[status(thm)],[f106]) ).

fof(f108,plain,
    part_of(sK14_skl,sK15_skl),
    inference(cnf_transformation,[status(thm)],[f106]) ).

fof(f110,plain,
    ~ part_of(sum(sK13_skl,sK14_skl),sK15_skl),
    inference(cnf_transformation,[status(thm)],[f106]) ).

fof(f111,plain,
    ! [X0,X1,X2] :
      ( incident_c(X0,X2)
      | incident_c(X0,X1)
      | ~ incident_c(X0,sum(X1,X2)) ),
    inference(destructive_equality_resolution,[status(thm)],[f29]) ).

fof(f112,plain,
    ! [X0,X1,X2] :
      ( ~ incident_c(X0,X1)
      | incident_c(X0,sum(X1,X2)) ),
    inference(destructive_equality_resolution,[status(thm)],[f30]) ).

fof(f113,plain,
    ! [X0,X1,X2] :
      ( ~ incident_c(X0,X2)
      | incident_c(X0,sum(X1,X2)) ),
    inference(destructive_equality_resolution,[status(thm)],[f31]) ).

fof(f125,plain,
    ! [X0,X1,X2] :
      ( incident_c(sK0_skl(sum(X0,X1),X2),X1)
      | incident_c(sK0_skl(sum(X0,X1),X2),X0)
      | part_of(sum(X0,X1),X2) ),
    inference(resolution,[status(thm)],[f24,f111]) ).

fof(f127,plain,
    ! [X0,X1,X2] :
      ( ~ incident_c(sK0_skl(X0,sum(X1,X2)),X2)
      | part_of(X0,sum(X1,X2)) ),
    inference(resolution,[status(thm)],[f25,f113]) ).

fof(f128,plain,
    ! [X0,X1,X2] :
      ( ~ incident_c(sK0_skl(X0,sum(X1,X2)),X1)
      | part_of(X0,sum(X1,X2)) ),
    inference(resolution,[status(thm)],[f25,f112]) ).

fof(f177,plain,
    ! [X0] :
      ( ~ incident_c(sK1_skl(X0,X0,X0),X0)
      | X0 = sum(X0,X0)
      | X0 = sum(X0,X0) ),
    inference(resolution,[status(thm)],[f34,f33]) ).

fof(f182,plain,
    ! [X0,X1,X2,X3] :
      ( incident_c(sK1_skl(X3,X2,sum(X0,X1)),X1)
      | incident_c(sK1_skl(X3,X2,sum(X0,X1)),X0)
      | incident_c(sK1_skl(X3,X2,sum(X0,X1)),X3)
      | incident_c(sK1_skl(X3,X2,sum(X0,X1)),X2)
      | sum(X0,X1) = sum(X2,X3) ),
    inference(resolution,[status(thm)],[f34,f111]) ).

fof(f188,plain,
    ! [X0,X1,X2,X3] :
      ( incident_c(sK1_skl(X3,sum(X1,X2),X0),X2)
      | incident_c(sK1_skl(X3,sum(X1,X2),X0),X1)
      | incident_c(sK1_skl(X3,sum(X1,X2),X0),X3)
      | incident_c(sK1_skl(X3,sum(X1,X2),X0),X0)
      | X0 = sum(sum(X1,X2),X3) ),
    inference(resolution,[status(thm)],[f34,f111]) ).

fof(f193,plain,
    ! [X0] :
      ( ~ incident_c(sK1_skl(X0,X0,X0),X0)
      | X0 = sum(X0,X0) ),
    inference(duplicate_literals_removal,[status(thm)],[f177]) ).

fof(f305,plain,
    ! [X0,X1,X2,X3] :
      ( ~ incident_c(sK0_skl(X0,sum(X1,sum(X2,X3))),X2)
      | part_of(X0,sum(X1,sum(X2,X3))) ),
    inference(resolution,[status(thm)],[f127,f112]) ).

fof(f353,plain,
    ! [X0,X1,X2] :
      ( incident_c(sK0_skl(sum(X0,X1),sum(X1,X2)),X0)
      | part_of(sum(X0,X1),sum(X1,X2))
      | part_of(sum(X0,X1),sum(X1,X2)) ),
    inference(resolution,[status(thm)],[f128,f125]) ).

fof(f361,plain,
    ! [X0,X1,X2] :
      ( incident_c(sK0_skl(sum(X0,X1),sum(X1,X2)),X0)
      | part_of(sum(X0,X1),sum(X1,X2)) ),
    inference(duplicate_literals_removal,[status(thm)],[f353]) ).

fof(f496,plain,
    ! [X0] :
      ( X0 = sum(X0,X0)
      | X0 = sum(X0,X0) ),
    inference(resolution,[status(thm)],[f193,f34]) ).

fof(f505,plain,
    ! [X0] : X0 = sum(X0,X0),
    inference(duplicate_literals_removal,[status(thm)],[f496]) ).

fof(f1033,plain,
    ! [X0,X1] :
      ( ~ incident_c(sK1_skl(X0,X1,sum(X0,X0)),sum(X0,X0))
      | sum(X0,X0) = sum(X1,X0)
      | incident_c(sK1_skl(X0,X1,sum(X0,X0)),X1)
      | sum(X0,X0) = sum(X1,X0) ),
    inference(resolution,[status(thm)],[f182,f33]) ).

fof(f1125,plain,
    ! [X0,X1] :
      ( ~ incident_c(sK1_skl(X0,X1,sum(X0,X0)),sum(X0,X0))
      | sum(X0,X0) = sum(X1,X0)
      | incident_c(sK1_skl(X0,X1,sum(X0,X0)),X1)
      | X0 = sum(X1,X0) ),
    inference(forward_demodulation,[status(thm)],[f505,f1033]) ).

fof(f1126,plain,
    ! [X0,X1] :
      ( ~ incident_c(sK1_skl(X0,X1,sum(X0,X0)),sum(X0,X0))
      | sum(X0,X0) = sum(X1,X0)
      | incident_c(sK1_skl(X0,X1,X0),X1)
      | X0 = sum(X1,X0) ),
    inference(forward_demodulation,[status(thm)],[f505,f1125]) ).

fof(f1127,plain,
    ! [X0,X1] :
      ( ~ incident_c(sK1_skl(X0,X1,sum(X0,X0)),sum(X0,X0))
      | X0 = sum(X1,X0)
      | incident_c(sK1_skl(X0,X1,X0),X1)
      | X0 = sum(X1,X0) ),
    inference(forward_demodulation,[status(thm)],[f505,f1126]) ).

fof(f1128,plain,
    ! [X0,X1] :
      ( ~ incident_c(sK1_skl(X0,X1,X0),sum(X0,X0))
      | X0 = sum(X1,X0)
      | incident_c(sK1_skl(X0,X1,X0),X1)
      | X0 = sum(X1,X0) ),
    inference(forward_demodulation,[status(thm)],[f505,f1127]) ).

fof(f1129,plain,
    ! [X0,X1] :
      ( ~ incident_c(sK1_skl(X0,X1,X0),X0)
      | X0 = sum(X1,X0)
      | incident_c(sK1_skl(X0,X1,X0),X1)
      | X0 = sum(X1,X0) ),
    inference(forward_demodulation,[status(thm)],[f505,f1128]) ).

fof(f1130,plain,
    ! [X0,X1] :
      ( ~ incident_c(sK1_skl(X0,X1,X0),X0)
      | incident_c(sK1_skl(X0,X1,X0),X1)
      | X0 = sum(X1,X0) ),
    inference(duplicate_literals_removal,[status(thm)],[f1129]) ).

fof(f1131,plain,
    ! [X0,X1] :
      ( ~ incident_c(sK1_skl(X0,X1,X0),X0)
      | X0 = sum(X1,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f1130,f32]) ).

fof(f1792,plain,
    ! [X0,X1,X2] :
      ( ~ incident_c(sK1_skl(X0,X1,X0),X2)
      | ~ part_of(X2,X0)
      | X0 = sum(X1,X0) ),
    inference(resolution,[status(thm)],[f1131,f23]) ).

fof(f2122,plain,
    ! [X0] :
      ( ~ incident_c(sK1_skl(sK15_skl,X0,sK15_skl),sK14_skl)
      | sK15_skl = sum(X0,sK15_skl) ),
    inference(resolution,[status(thm)],[f1792,f108]) ).

fof(f2123,plain,
    ! [X0] :
      ( ~ incident_c(sK1_skl(sK15_skl,X0,sK15_skl),sK13_skl)
      | sK15_skl = sum(X0,sK15_skl) ),
    inference(resolution,[status(thm)],[f1792,f107]) ).

fof(f3501,plain,
    ( incident_c(sK1_skl(sK15_skl,sum(sK14_skl,sK14_skl),sK15_skl),sK15_skl)
    | incident_c(sK1_skl(sK15_skl,sum(sK14_skl,sK14_skl),sK15_skl),sK15_skl)
    | sK15_skl = sum(sum(sK14_skl,sK14_skl),sK15_skl)
    | sK15_skl = sum(sum(sK14_skl,sK14_skl),sK15_skl) ),
    inference(resolution,[status(thm)],[f2122,f188]) ).

fof(f3508,plain,
    ( incident_c(sK1_skl(sK15_skl,sum(sK14_skl,sK14_skl),sK15_skl),sK15_skl)
    | incident_c(sK1_skl(sK15_skl,sum(sK14_skl,sK14_skl),sK15_skl),sK15_skl)
    | sK15_skl = sum(sum(sK14_skl,sK14_skl),sK15_skl)
    | sK15_skl = sum(sK14_skl,sK15_skl) ),
    inference(forward_demodulation,[status(thm)],[f505,f3501]) ).

fof(f3509,plain,
    ( incident_c(sK1_skl(sK15_skl,sum(sK14_skl,sK14_skl),sK15_skl),sK15_skl)
    | incident_c(sK1_skl(sK15_skl,sum(sK14_skl,sK14_skl),sK15_skl),sK15_skl)
    | sK15_skl = sum(sK14_skl,sK15_skl)
    | sK15_skl = sum(sK14_skl,sK15_skl) ),
    inference(forward_demodulation,[status(thm)],[f505,f3508]) ).

fof(f3510,plain,
    ( incident_c(sK1_skl(sK15_skl,sum(sK14_skl,sK14_skl),sK15_skl),sK15_skl)
    | incident_c(sK1_skl(sK15_skl,sK14_skl,sK15_skl),sK15_skl)
    | sK15_skl = sum(sK14_skl,sK15_skl)
    | sK15_skl = sum(sK14_skl,sK15_skl) ),
    inference(forward_demodulation,[status(thm)],[f505,f3509]) ).

fof(f3511,plain,
    ( incident_c(sK1_skl(sK15_skl,sK14_skl,sK15_skl),sK15_skl)
    | incident_c(sK1_skl(sK15_skl,sK14_skl,sK15_skl),sK15_skl)
    | sK15_skl = sum(sK14_skl,sK15_skl)
    | sK15_skl = sum(sK14_skl,sK15_skl) ),
    inference(forward_demodulation,[status(thm)],[f505,f3510]) ).

fof(f3512,plain,
    ( incident_c(sK1_skl(sK15_skl,sK14_skl,sK15_skl),sK15_skl)
    | sK15_skl = sum(sK14_skl,sK15_skl) ),
    inference(duplicate_literals_removal,[status(thm)],[f3511]) ).

fof(f3513,plain,
    sK15_skl = sum(sK14_skl,sK15_skl),
    inference(forward_subsumption_resolution,[status(thm)],[f3512,f1131]) ).

fof(f5031,plain,
    ( incident_c(sK1_skl(sK15_skl,sum(sK13_skl,sK13_skl),sK15_skl),sK15_skl)
    | incident_c(sK1_skl(sK15_skl,sum(sK13_skl,sK13_skl),sK15_skl),sK15_skl)
    | sK15_skl = sum(sum(sK13_skl,sK13_skl),sK15_skl)
    | sK15_skl = sum(sum(sK13_skl,sK13_skl),sK15_skl) ),
    inference(resolution,[status(thm)],[f2123,f188]) ).

fof(f5038,plain,
    ( incident_c(sK1_skl(sK15_skl,sum(sK13_skl,sK13_skl),sK15_skl),sK15_skl)
    | incident_c(sK1_skl(sK15_skl,sum(sK13_skl,sK13_skl),sK15_skl),sK15_skl)
    | sK15_skl = sum(sum(sK13_skl,sK13_skl),sK15_skl)
    | sK15_skl = sum(sK13_skl,sK15_skl) ),
    inference(forward_demodulation,[status(thm)],[f505,f5031]) ).

fof(f5039,plain,
    ( incident_c(sK1_skl(sK15_skl,sum(sK13_skl,sK13_skl),sK15_skl),sK15_skl)
    | incident_c(sK1_skl(sK15_skl,sum(sK13_skl,sK13_skl),sK15_skl),sK15_skl)
    | sK15_skl = sum(sK13_skl,sK15_skl)
    | sK15_skl = sum(sK13_skl,sK15_skl) ),
    inference(forward_demodulation,[status(thm)],[f505,f5038]) ).

fof(f5040,plain,
    ( incident_c(sK1_skl(sK15_skl,sum(sK13_skl,sK13_skl),sK15_skl),sK15_skl)
    | incident_c(sK1_skl(sK15_skl,sK13_skl,sK15_skl),sK15_skl)
    | sK15_skl = sum(sK13_skl,sK15_skl)
    | sK15_skl = sum(sK13_skl,sK15_skl) ),
    inference(forward_demodulation,[status(thm)],[f505,f5039]) ).

fof(f5041,plain,
    ( incident_c(sK1_skl(sK15_skl,sK13_skl,sK15_skl),sK15_skl)
    | incident_c(sK1_skl(sK15_skl,sK13_skl,sK15_skl),sK15_skl)
    | sK15_skl = sum(sK13_skl,sK15_skl)
    | sK15_skl = sum(sK13_skl,sK15_skl) ),
    inference(forward_demodulation,[status(thm)],[f505,f5040]) ).

fof(f5042,plain,
    ( incident_c(sK1_skl(sK15_skl,sK13_skl,sK15_skl),sK15_skl)
    | sK15_skl = sum(sK13_skl,sK15_skl) ),
    inference(duplicate_literals_removal,[status(thm)],[f5041]) ).

fof(f5043,plain,
    sK15_skl = sum(sK13_skl,sK15_skl),
    inference(forward_subsumption_resolution,[status(thm)],[f5042,f1131]) ).

fof(f6870,plain,
    ! [X0,X1,X2] :
      ( part_of(sum(X0,X1),sum(X1,sum(X0,X2)))
      | part_of(sum(X0,X1),sum(X1,sum(X0,X2))) ),
    inference(resolution,[status(thm)],[f361,f305]) ).

fof(f6905,plain,
    ! [X0,X1,X2] : part_of(sum(X0,X1),sum(X1,sum(X0,X2))),
    inference(duplicate_literals_removal,[status(thm)],[f6870]) ).

fof(f8669,plain,
    ! [X0] : part_of(sum(sK13_skl,X0),sum(X0,sK15_skl)),
    inference(paramodulation,[status(thm)],[f5043,f6905]) ).

fof(f8691,plain,
    part_of(sum(sK13_skl,sK14_skl),sK15_skl),
    inference(paramodulation,[status(thm)],[f3513,f8669]) ).

fof(f8699,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f8691,f110]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : GEO084+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03  % Command  : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35  % Computer : n020.cluster.edu
% 0.09/0.35  % Model    : x86_64 x86_64
% 0.09/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35  % Memory   : 8046.5625MB
% 0.09/0.35  % OS       : Linux 6.8.0-71-generic
% 0.09/0.35  % CPULimit : 300
% 0.09/0.35  % WCLimit  : 300
% 0.09/0.35  % DateTime : Sun Sep 20 10:16:31 UTC 2026
% 0.09/0.35  % CPUTime  : 
% 0.12/0.36  % Drodi V4.1.1
% 17.52/2.67  % Refutation found
% 17.52/2.67  % SZS status Theorem for theBenchmark: Theorem is valid
% 17.52/2.67  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.14/2.71  % Elapsed time: 2.347224 seconds
% 1.14/2.71  % CPU time: 18.349492 seconds
% 1.14/2.71  % Total memory used: 186.576 MB
% 1.14/2.71  % Net memory used: 172.122 MB
%------------------------------------------------------------------------------