↑ Up

iProver---3.9.4.THM-CRf.s

View TPTP
Problem
Process solution in
SystemOnTSTP
Download .tgz
%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : COM023+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM

% Computer : n013.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 01:04:21 PM UTC 2026

% Result   : Theorem 1.21s 1.29s
% Output   : CNFRefutation 1.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   71 (  13 unt;   2 def)
%            Number of atoms       :  297 (   1 equ)
%            Maximal formula atoms :   18 (   4 avg)
%            Number of connectives :  388 ( 162   ~; 169   |;  49   &)
%                                         (   5 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   1 con; 0-3 aty)
%            Number of variables   :  107 (   0 sgn  92   !;  15   ?;  28   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f10,axiom,
    ! [X0] :
      ( aRewritingSystem0(X0)
     => ( isConfluent0(X0)
      <=> ! [X1,X2,X3] :
            ( ( sdtmndtasgtdt0(X1,X0,X3)
              & sdtmndtasgtdt0(X1,X0,X2)
              & aElement0(X3)
              & aElement0(X2)
              & aElement0(X1) )
           => ? [X4] :
                ( sdtmndtasgtdt0(X3,X0,X4)
                & sdtmndtasgtdt0(X2,X0,X4)
                & aElement0(X4) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCRDef) ).

fof(f15,axiom,
    aRewritingSystem0(xR),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656) ).

fof(f17,axiom,
    ! [X0,X1,X2] :
      ( ( sdtmndtasgtdt0(X0,xR,X2)
        & sdtmndtasgtdt0(X0,xR,X1)
        & aElement0(X2)
        & aElement0(X1)
        & aElement0(X0) )
     => ? [X3] :
          ( sdtmndtasgtdt0(X2,xR,X3)
          & sdtmndtasgtdt0(X1,xR,X3)
          & aElement0(X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__715) ).

fof(f18,conjecture,
    isConfluent0(xR),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(f19,negated_conjecture,
    ~ isConfluent0(xR),
    inference(negated_conjecture,[status(cth)],[f18]) ).

fof(f24,plain,
    ~ isConfluent0(xR),
    inference(flattening,[],[f19]) ).

fof(f35,plain,
    ! [X0] :
      ( ~ aRewritingSystem0(X0)
      | ( isConfluent0(X0)
      <=> ! [X1,X2,X3] :
            ( ~ sdtmndtasgtdt0(X1,X0,X3)
            | ~ sdtmndtasgtdt0(X1,X0,X2)
            | ~ aElement0(X3)
            | ~ aElement0(X2)
            | ~ aElement0(X1)
            | ? [X4] :
                ( sdtmndtasgtdt0(X3,X0,X4)
                & sdtmndtasgtdt0(X2,X0,X4)
                & aElement0(X4) ) ) ) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f36,plain,
    ! [X0] :
      ( ~ aRewritingSystem0(X0)
      | ( isConfluent0(X0)
      <=> ! [X1,X2,X3] :
            ( ~ sdtmndtasgtdt0(X1,X0,X3)
            | ~ sdtmndtasgtdt0(X1,X0,X2)
            | ~ aElement0(X3)
            | ~ aElement0(X2)
            | ~ aElement0(X1)
            | ? [X4] :
                ( sdtmndtasgtdt0(X3,X0,X4)
                & sdtmndtasgtdt0(X2,X0,X4)
                & aElement0(X4) ) ) ) ),
    inference(flattening,[],[f35]) ).

fof(f45,plain,
    ! [X0,X1,X2] :
      ( ~ sdtmndtasgtdt0(X0,xR,X2)
      | ~ sdtmndtasgtdt0(X0,xR,X1)
      | ~ aElement0(X2)
      | ~ aElement0(X1)
      | ~ aElement0(X0)
      | ? [X3] :
          ( sdtmndtasgtdt0(X2,xR,X3)
          & sdtmndtasgtdt0(X1,xR,X3)
          & aElement0(X3) ) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f46,plain,
    ! [X0,X1,X2] :
      ( ~ sdtmndtasgtdt0(X0,xR,X2)
      | ~ sdtmndtasgtdt0(X0,xR,X1)
      | ~ aElement0(X2)
      | ~ aElement0(X1)
      | ~ aElement0(X0)
      | ? [X3] :
          ( sdtmndtasgtdt0(X2,xR,X3)
          & sdtmndtasgtdt0(X1,xR,X3)
          & aElement0(X3) ) ),
    inference(flattening,[],[f45]) ).

fof(f59,plain,
    ! [X0] :
      ( ~ sP1(X0)
      | ( ( ~ isConfluent0(X0)
          | sP0(X0) )
        & ( ~ sP0(X0)
          | isConfluent0(X0) ) ) ),
    inference(nnf_transformation,[],[f48]) ).

fof(f75,plain,
    ! [X0,X1,X2] :
      ( ~ sdtmndtasgtdt0(X0,xR,X2)
      | ~ sdtmndtasgtdt0(X0,xR,X1)
      | ~ aElement0(X2)
      | ~ aElement0(X1)
      | ~ aElement0(X0)
      | ( sdtmndtasgtdt0(X2,xR,sK17(X1,X2))
        & sdtmndtasgtdt0(X1,xR,sK17(X1,X2))
        & aElement0(sK17(X1,X2)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(X3,sK17(X1,X2))],[f46]) ).

fof(f88,plain,
    ! [X0] :
      ( ~ sP1(X0)
      | ~ sP0(X0)
      | isConfluent0(X0) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f98,plain,
    ! [X0] :
      ( ~ aRewritingSystem0(X0)
      | sP1(X0) ),
    inference(cnf_transformation,[],[f49]) ).

fof(f121,plain,
    aRewritingSystem0(xR),
    inference(cnf_transformation,[],[f15]) ).

fof(f124,plain,
    ! [X2,X0,X1] :
      ( ~ sdtmndtasgtdt0(X0,xR,X2)
      | ~ sdtmndtasgtdt0(X0,xR,X1)
      | ~ aElement0(X2)
      | ~ aElement0(X1)
      | ~ aElement0(X0)
      | sdtmndtasgtdt0(X2,xR,sK17(X1,X2)) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f125,plain,
    ! [X2,X0,X1] :
      ( ~ sdtmndtasgtdt0(X0,xR,X2)
      | ~ sdtmndtasgtdt0(X0,xR,X1)
      | ~ aElement0(X2)
      | ~ aElement0(X1)
      | ~ aElement0(X0)
      | sdtmndtasgtdt0(X1,xR,sK17(X1,X2)) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f126,plain,
    ! [X2,X0,X1] :
      ( ~ sdtmndtasgtdt0(X0,xR,X2)
      | ~ sdtmndtasgtdt0(X0,xR,X1)
      | ~ aElement0(X2)
      | ~ aElement0(X1)
      | ~ aElement0(X0)
      | aElement0(sK17(X1,X2)) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f127,plain,
    ~ isConfluent0(xR),
    inference(cnf_transformation,[],[f24]) ).

tcf(c_60,plain,
    ! [X0: $i] :
      ( isConfluent0(X0)
      | ~ sP1(X0)
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f88]) ).

tcf(c_71,plain,
    ! [X0: $i] :
      ( sP1(X0)
      | ~ aRewritingSystem0(X0) ),
    inference(cnf_transformation,[],[f98]) ).

tcf(c_94,plain,
    aRewritingSystem0(xR),
    inference(cnf_transformation,[],[f121]) ).

tcf(c_97,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( aElement0(sK17(X2,X1))
      | ~ aElement0(X2)
      | ~ aElement0(X1)
      | ~ aElement0(X0)
      | ~ sdtmndtasgtdt0(X0,xR,X2)
      | ~ sdtmndtasgtdt0(X0,xR,X1) ),
    inference(cnf_transformation,[],[f126]) ).

tcf(c_98,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sdtmndtasgtdt0(X2,xR,sK17(X2,X1))
      | ~ aElement0(X2)
      | ~ aElement0(X1)
      | ~ aElement0(X0)
      | ~ sdtmndtasgtdt0(X0,xR,X2)
      | ~ sdtmndtasgtdt0(X0,xR,X1) ),
    inference(cnf_transformation,[],[f125]) ).

tcf(c_99,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sdtmndtasgtdt0(X1,xR,sK17(X2,X1))
      | ~ aElement0(X2)
      | ~ aElement0(X1)
      | ~ aElement0(X0)
      | ~ sdtmndtasgtdt0(X0,xR,X2)
      | ~ sdtmndtasgtdt0(X0,xR,X1) ),
    inference(cnf_transformation,[],[f124]) ).

tcf(c_100,negated_conjecture,
    ~ isConfluent0(xR),
    inference(cnf_transformation,[],[f127]) ).

tcf(c_105,plain,
    ( sP1(xR)
    | ~ aRewritingSystem0(xR) ),
    inference(instantiation,[status(thm)],[c_71]) ).

tcf(c_114,plain,
    ( isConfluent0(xR)
    | ~ sP1(xR)
    | ~ sP0(xR) ),
    inference(instantiation,[status(thm)],[c_60]) ).

tcf(c_974,plain,
    ! [X0: $i] :
      ( ~ sP1(X0)
      | ~ sP0(X0)
      | ( X0 != xR ) ),
    inference(resolution_lifted,[status(thm)],[c_60,c_100]) ).

tcf(c_975,plain,
    ( ~ sP1(xR)
    | ~ sP0(xR) ),
    inference(unflattening,[status(thm)],[c_974]) ).

tcf(c_976,plain,
    ~ sP0(xR),
    inference(global_subsumption_just,[status(thm)],[c_975,c_94,c_100,c_105,c_114]) ).

tcf(c_4368,plain,
    ~ sP0(xR),
    inference(demodulation,[status(thm)],[c_976]) ).

fof(f47,definition,
    ! [X0] :
      ( sP0(X0)
    <=> ! [X1,X2,X3] :
          ( ~ sdtmndtasgtdt0(X1,X0,X3)
          | ~ sdtmndtasgtdt0(X1,X0,X2)
          | ~ aElement0(X3)
          | ~ aElement0(X2)
          | ~ aElement0(X1)
          | ? [X4] :
              ( sdtmndtasgtdt0(X3,X0,X4)
              & sdtmndtasgtdt0(X2,X0,X4)
              & aElement0(X4) ) ) ),
    introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).

fof(f48,definition,
    ! [X0] :
      ( ~ sP1(X0)
      | ( isConfluent0(X0)
      <=> sP0(X0) ) ),
    introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).

fof(f49,plain,
    ! [X0] :
      ( ~ aRewritingSystem0(X0)
      | sP1(X0) ),
    inference(definition_folding,[],[f36,f48,f47]) ).

fof(f60,plain,
    ! [X0] :
      ( ( ~ sP0(X0)
        | ! [X1,X2,X3] :
            ( ~ sdtmndtasgtdt0(X1,X0,X3)
            | ~ sdtmndtasgtdt0(X1,X0,X2)
            | ~ aElement0(X3)
            | ~ aElement0(X2)
            | ~ aElement0(X1)
            | ? [X4] :
                ( sdtmndtasgtdt0(X3,X0,X4)
                & sdtmndtasgtdt0(X2,X0,X4)
                & aElement0(X4) ) ) )
      & ( ? [X1,X2,X3] :
            ( sdtmndtasgtdt0(X1,X0,X3)
            & sdtmndtasgtdt0(X1,X0,X2)
            & aElement0(X3)
            & aElement0(X2)
            & aElement0(X1)
            & ! [X4] :
                ( ~ sdtmndtasgtdt0(X3,X0,X4)
                | ~ sdtmndtasgtdt0(X2,X0,X4)
                | ~ aElement0(X4) ) )
        | sP0(X0) ) ),
    inference(nnf_transformation,[],[f47]) ).

fof(f61,plain,
    ! [X0] :
      ( ( ~ sP0(X0)
        | ! [X5,X6,X7] :
            ( ~ sdtmndtasgtdt0(X5,X0,X7)
            | ~ sdtmndtasgtdt0(X5,X0,X6)
            | ~ aElement0(X7)
            | ~ aElement0(X6)
            | ~ aElement0(X5)
            | ? [X8] :
                ( sdtmndtasgtdt0(X7,X0,X8)
                & sdtmndtasgtdt0(X6,X0,X8)
                & aElement0(X8) ) ) )
      & ( ? [X1,X2,X3] :
            ( sdtmndtasgtdt0(X1,X0,X3)
            & sdtmndtasgtdt0(X1,X0,X2)
            & aElement0(X3)
            & aElement0(X2)
            & aElement0(X1)
            & ! [X4] :
                ( ~ sdtmndtasgtdt0(X3,X0,X4)
                | ~ sdtmndtasgtdt0(X2,X0,X4)
                | ~ aElement0(X4) ) )
        | sP0(X0) ) ),
    inference(rectify,[],[f60]) ).

fof(f62,plain,
    ! [X0] :
      ( ( ~ sP0(X0)
        | ! [X5,X6,X7] :
            ( ~ sdtmndtasgtdt0(X5,X0,X7)
            | ~ sdtmndtasgtdt0(X5,X0,X6)
            | ~ aElement0(X7)
            | ~ aElement0(X6)
            | ~ aElement0(X5)
            | ( sdtmndtasgtdt0(X7,X0,sK8(X0,X6,X7))
              & sdtmndtasgtdt0(X6,X0,sK8(X0,X6,X7))
              & aElement0(sK8(X0,X6,X7)) ) ) )
      & ( ( sdtmndtasgtdt0(sK5(X0),X0,sK7(X0))
          & sdtmndtasgtdt0(sK5(X0),X0,sK6(X0))
          & aElement0(sK7(X0))
          & aElement0(sK6(X0))
          & aElement0(sK5(X0))
          & ! [X4] :
              ( ~ sdtmndtasgtdt0(sK7(X0),X0,X4)
              | ~ sdtmndtasgtdt0(sK6(X0),X0,X4)
              | ~ aElement0(X4) ) )
        | sP0(X0) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8]),skolemize(X1,sK5(X0)),skolemize(X2,sK6(X0)),skolemize(X3,sK7(X0)),skolemize(X8,sK8(X0,X6,X7))],[f61]) ).

fof(f92,plain,
    ! [X0] :
      ( sdtmndtasgtdt0(sK5(X0),X0,sK7(X0))
      | sP0(X0) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f93,plain,
    ! [X0] :
      ( sdtmndtasgtdt0(sK5(X0),X0,sK6(X0))
      | sP0(X0) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f94,plain,
    ! [X0] :
      ( aElement0(sK7(X0))
      | sP0(X0) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f95,plain,
    ! [X0] :
      ( aElement0(sK6(X0))
      | sP0(X0) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f96,plain,
    ! [X0] :
      ( aElement0(sK5(X0))
      | sP0(X0) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f97,plain,
    ! [X0,X4] :
      ( ~ sdtmndtasgtdt0(sK7(X0),X0,X4)
      | ~ sdtmndtasgtdt0(sK6(X0),X0,X4)
      | ~ aElement0(X4)
      | sP0(X0) ),
    inference(cnf_transformation,[],[f62]) ).

tcf(c_62,plain,
    ! [X0: $i,X1: $i] :
      ( sP0(X0)
      | ~ aElement0(X1)
      | ~ sdtmndtasgtdt0(sK7(X0),X0,X1)
      | ~ sdtmndtasgtdt0(sK6(X0),X0,X1) ),
    inference(cnf_transformation,[],[f97]) ).

tcf(c_63,plain,
    ! [X0: $i] :
      ( sP0(X0)
      | aElement0(sK5(X0)) ),
    inference(cnf_transformation,[],[f96]) ).

tcf(c_64,plain,
    ! [X0: $i] :
      ( sP0(X0)
      | aElement0(sK6(X0)) ),
    inference(cnf_transformation,[],[f95]) ).

tcf(c_65,plain,
    ! [X0: $i] :
      ( sP0(X0)
      | aElement0(sK7(X0)) ),
    inference(cnf_transformation,[],[f94]) ).

tcf(c_66,plain,
    ! [X0: $i] :
      ( sP0(X0)
      | sdtmndtasgtdt0(sK5(X0),X0,sK6(X0)) ),
    inference(cnf_transformation,[],[f93]) ).

tcf(c_67,plain,
    ! [X0: $i] :
      ( sP0(X0)
      | sdtmndtasgtdt0(sK5(X0),X0,sK7(X0)) ),
    inference(cnf_transformation,[],[f92]) ).

tcf(c_106,plain,
    ( sP0(xR)
    | aElement0(sK7(xR)) ),
    inference(instantiation,[status(thm)],[c_65]) ).

tcf(c_107,plain,
    ( sP0(xR)
    | aElement0(sK6(xR)) ),
    inference(instantiation,[status(thm)],[c_64]) ).

tcf(c_108,plain,
    ( sP0(xR)
    | aElement0(sK5(xR)) ),
    inference(instantiation,[status(thm)],[c_63]) ).

tcf(c_113,plain,
    ( sP0(xR)
    | sdtmndtasgtdt0(sK5(xR),xR,sK6(xR)) ),
    inference(instantiation,[status(thm)],[c_66]) ).

tcf(c_5298,plain,
    ! [X0: $i] :
      ( sP0(xR)
      | aElement0(sK17(X0,sK7(xR)))
      | ~ aElement0(X0)
      | ~ aElement0(sK5(xR))
      | ~ aElement0(sK7(xR))
      | ~ sdtmndtasgtdt0(sK5(xR),xR,X0) ),
    inference(superposition,[status(thm)],[c_67,c_97]) ).

tcf(c_5299,plain,
    ! [X0: $i] :
      ( aElement0(sK17(X0,sK7(xR)))
      | ~ aElement0(X0)
      | ~ aElement0(sK5(xR))
      | ~ aElement0(sK7(xR))
      | ~ sdtmndtasgtdt0(sK5(xR),xR,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5298,c_4368]) ).

tcf(c_5347,plain,
    ! [X0: $i] :
      ( aElement0(sK17(X0,sK7(xR)))
      | ~ aElement0(X0)
      | ~ sdtmndtasgtdt0(sK5(xR),xR,X0) ),
    inference(global_subsumption_just,[status(thm)],[c_5299,c_94,c_100,c_105,c_106,c_108,c_114,c_5299]) ).

tcf(c_5356,plain,
    ( sP0(xR)
    | aElement0(sK17(sK6(xR),sK7(xR)))
    | ~ aElement0(sK6(xR)) ),
    inference(superposition,[status(thm)],[c_66,c_5347]) ).

tcf(c_5361,plain,
    ( aElement0(sK17(sK6(xR),sK7(xR)))
    | ~ aElement0(sK6(xR)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5356,c_4368]) ).

tcf(c_5366,plain,
    aElement0(sK17(sK6(xR),sK7(xR))),
    inference(global_subsumption_just,[status(thm)],[c_5361,c_94,c_100,c_105,c_107,c_114,c_5361]) ).

tcf(c_5404,plain,
    ! [X0: $i] :
      ( sP0(xR)
      | sdtmndtasgtdt0(X0,xR,sK17(X0,sK7(xR)))
      | ~ aElement0(X0)
      | ~ aElement0(sK5(xR))
      | ~ aElement0(sK7(xR))
      | ~ sdtmndtasgtdt0(sK5(xR),xR,X0) ),
    inference(superposition,[status(thm)],[c_67,c_98]) ).

tcf(c_5410,plain,
    ! [X0: $i] :
      ( sdtmndtasgtdt0(X0,xR,sK17(X0,sK7(xR)))
      | ~ aElement0(X0)
      | ~ aElement0(sK5(xR))
      | ~ aElement0(sK7(xR))
      | ~ sdtmndtasgtdt0(sK5(xR),xR,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5404,c_4368]) ).

tcf(c_5557,plain,
    ! [X0: $i] :
      ( sdtmndtasgtdt0(X0,xR,sK17(X0,sK7(xR)))
      | ~ aElement0(X0)
      | ~ sdtmndtasgtdt0(sK5(xR),xR,X0) ),
    inference(global_subsumption_just,[status(thm)],[c_5410,c_94,c_100,c_105,c_106,c_108,c_114,c_5410]) ).

tcf(c_5566,plain,
    ( sP0(xR)
    | ~ aElement0(sK6(xR))
    | ~ sdtmndtasgtdt0(sK5(xR),xR,sK6(xR))
    | ~ aElement0(sK17(sK6(xR),sK7(xR)))
    | ~ sdtmndtasgtdt0(sK7(xR),xR,sK17(sK6(xR),sK7(xR))) ),
    inference(superposition,[status(thm)],[c_5557,c_62]) ).

tcf(c_5590,plain,
    ( ~ aElement0(sK6(xR))
    | ~ sdtmndtasgtdt0(sK5(xR),xR,sK6(xR))
    | ~ sdtmndtasgtdt0(sK7(xR),xR,sK17(sK6(xR),sK7(xR))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5566,c_4368,c_5366]) ).

tcf(c_5603,plain,
    ~ sdtmndtasgtdt0(sK7(xR),xR,sK17(sK6(xR),sK7(xR))),
    inference(global_subsumption_just,[status(thm)],[c_5590,c_94,c_100,c_105,c_107,c_113,c_114,c_5590]) ).

tcf(c_5691,plain,
    ! [X0: $i] :
      ( sP0(xR)
      | sdtmndtasgtdt0(sK7(xR),xR,sK17(X0,sK7(xR)))
      | ~ aElement0(X0)
      | ~ aElement0(sK5(xR))
      | ~ aElement0(sK7(xR))
      | ~ sdtmndtasgtdt0(sK5(xR),xR,X0) ),
    inference(superposition,[status(thm)],[c_67,c_99]) ).

tcf(c_5700,plain,
    ! [X0: $i] :
      ( sdtmndtasgtdt0(sK7(xR),xR,sK17(X0,sK7(xR)))
      | ~ aElement0(X0)
      | ~ aElement0(sK5(xR))
      | ~ aElement0(sK7(xR))
      | ~ sdtmndtasgtdt0(sK5(xR),xR,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5691,c_4368]) ).

tcf(c_5900,plain,
    ! [X0: $i] :
      ( sdtmndtasgtdt0(sK7(xR),xR,sK17(X0,sK7(xR)))
      | ~ aElement0(X0)
      | ~ sdtmndtasgtdt0(sK5(xR),xR,X0) ),
    inference(global_subsumption_just,[status(thm)],[c_5700,c_94,c_100,c_105,c_106,c_108,c_114,c_5700]) ).

tcf(c_5914,plain,
    ( ~ aElement0(sK6(xR))
    | ~ sdtmndtasgtdt0(sK5(xR),xR,sK6(xR)) ),
    inference(superposition,[status(thm)],[c_5900,c_5603]) ).

tcf(c_5950,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_5914,c_114,c_113,c_107,c_105,c_100,c_94]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : COM023+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37  % Computer : n013.cluster.edu
% 0.11/0.37  % Model    : x86_64 x86_64
% 0.11/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37  % Memory   : 8046.5625MB
% 0.11/0.37  % OS       : Linux 6.8.0-71-generic
% 0.11/0.38  % CPULimit : 300
% 0.11/0.38  % WCLimit  : 300
% 0.11/0.38  % DateTime : Fri Sep 25 07:48:51 UTC 2026
% 0.11/0.38  % CPUTime  : 
% 0.11/0.38  Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41  Running first-order theorem proving
% 0.11/0.41  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
% 0.11/0.42  
% 0.11/0.42  % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42  
% 0.11/0.42  % Detected problem language: tptp
% 0.11/0.43  % Proving...
% 1.21/1.29  % SZS status Started for theBenchmark.p
% 1.21/1.29  % SZS status Theorem for theBenchmark.p
% 1.21/1.29  
% 1.21/1.29  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.21/1.29  
% 1.21/1.29  % ------  iProver source info
% 1.21/1.29  
% 1.21/1.29  % git: date: 2026-07-19 20:42:38 +0200
% 1.21/1.29  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.21/1.29  % git: non_committed_changes: false
% 1.21/1.29  
% 1.21/1.29  % ------ Parsing...
% 1.21/1.29  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 1.21/1.29  
% 1.21/1.29  % ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe_e  sup_sim: 0  sf_s  rm: 5 0s  sf_e  pe_s  pe_e % 
% 1.21/1.29  
% 1.21/1.29  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 1.21/1.29  
% 1.21/1.29  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 1.21/1.29  % ------ Proving...
% 1.21/1.29  % ------ Problem Properties 
% 1.21/1.29  
% 1.21/1.29  % 
% 1.21/1.29  % clauses                               44
% 1.21/1.29  % conjectures                           0
% 1.21/1.29  % EPR                                   12
% 1.21/1.29  % Horn                                  27
% 1.21/1.29  % unary                                 4
% 1.21/1.29  % binary                                10
% 1.21/1.29  % lits                                  184
% 1.21/1.29  % lits eq                               1
% 1.21/1.29  % fd_pure                               0
% 1.21/1.29  % fd_pseudo                             0
% 1.21/1.29  % fd_cond                               0
% 1.21/1.29  % fd_pseudo_cond                        1
% 1.21/1.29  % AC symbols                            0
% 1.21/1.29  
% 1.21/1.29  % ------ Schedule dynamic 5 is on 
% 1.21/1.29  
% 1.21/1.29  % ------ no conjectures: strip conj schedule 
% 1.21/1.29  
% 1.21/1.29  % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 1.21/1.29  
% 1.21/1.29  
% 1.21/1.29  % ------ 
% 1.21/1.29  % Current options:
% 1.21/1.29  % ------ 
% 1.21/1.29  
% 1.21/1.29  
% 1.21/1.29  % 
% 1.21/1.29  
% 1.21/1.29  % ------ Proving...
% 1.21/1.29  % 
% 1.21/1.29  
% 1.21/1.29  % SZS status Theorem for theBenchmark.p
% 1.21/1.29  
% 1.21/1.29  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.21/1.30  
% 1.21/1.30  
%------------------------------------------------------------------------------