TSTP Solution File: COM022+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : COM022+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n004.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May  3 02:10:29 EDT 2024

% Result   : Theorem 3.93s 1.18s
% Output   : CNFRefutation 3.93s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named f170)

% Comments : 
%------------------------------------------------------------------------------
fof(f8,axiom,
    ! [X0,X1,X2] :
      ( ( aElement0(X2)
        & aRewritingSystem0(X1)
        & aElement0(X0) )
     => ( sdtmndtasgtdt0(X0,X1,X2)
      <=> ( sdtmndtplgtdt0(X0,X1,X2)
          | X0 = X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTCRDef) ).

fof(f13,axiom,
    ! [X0,X1] :
      ( ( aRewritingSystem0(X1)
        & aElement0(X0) )
     => ! [X2] :
          ( aNormalFormOfIn0(X2,X0,X1)
        <=> ( ~ ? [X3] : aReductOfIn0(X3,X2,X1)
            & sdtmndtasgtdt0(X0,X1,X2)
            & aElement0(X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNFRDef) ).

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

fof(f17,axiom,
    ( aElement0(xc)
    & aElement0(xb)
    & aElement0(xa) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__731) ).

fof(f19,conjecture,
    ( ( ( sdtmndtplgtdt0(xa,xR,xc)
        & sdtmndtplgtdt0(xa,xR,xb) )
     => ? [X0] :
          ( ? [X1] :
              ( ? [X2] :
                  ( ? [X3] :
                      ( sdtmndtasgtdt0(xc,xR,X3)
                      & sdtmndtasgtdt0(xb,xR,X3)
                      & aNormalFormOfIn0(X3,X2,xR) )
                  & sdtmndtasgtdt0(X1,xR,X2)
                  & sdtmndtasgtdt0(X0,xR,X2)
                  & aElement0(X2) )
              & sdtmndtasgtdt0(X1,xR,xc)
              & aReductOfIn0(X1,xa,xR)
              & aElement0(X1) )
          & sdtmndtasgtdt0(X0,xR,xb)
          & aReductOfIn0(X0,xa,xR)
          & aElement0(X0) ) )
   => ( ( sdtmndtasgtdt0(xa,xR,xc)
        & sdtmndtasgtdt0(xa,xR,xb) )
     => ? [X0] :
          ( sdtmndtasgtdt0(xc,xR,X0)
          & sdtmndtasgtdt0(xb,xR,X0)
          & aElement0(X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(f20,negated_conjecture,
    ~ ( ( ( sdtmndtplgtdt0(xa,xR,xc)
          & sdtmndtplgtdt0(xa,xR,xb) )
       => ? [X0] :
            ( ? [X1] :
                ( ? [X2] :
                    ( ? [X3] :
                        ( sdtmndtasgtdt0(xc,xR,X3)
                        & sdtmndtasgtdt0(xb,xR,X3)
                        & aNormalFormOfIn0(X3,X2,xR) )
                    & sdtmndtasgtdt0(X1,xR,X2)
                    & sdtmndtasgtdt0(X0,xR,X2)
                    & aElement0(X2) )
                & sdtmndtasgtdt0(X1,xR,xc)
                & aReductOfIn0(X1,xa,xR)
                & aElement0(X1) )
            & sdtmndtasgtdt0(X0,xR,xb)
            & aReductOfIn0(X0,xa,xR)
            & aElement0(X0) ) )
     => ( ( sdtmndtasgtdt0(xa,xR,xc)
          & sdtmndtasgtdt0(xa,xR,xb) )
       => ? [X0] :
            ( sdtmndtasgtdt0(xc,xR,X0)
            & sdtmndtasgtdt0(xb,xR,X0)
            & aElement0(X0) ) ) ),
    inference(negated_conjecture,[],[f19]) ).

fof(f25,plain,
    ~ ( ( ( sdtmndtplgtdt0(xa,xR,xc)
          & sdtmndtplgtdt0(xa,xR,xb) )
       => ? [X0] :
            ( ? [X1] :
                ( ? [X2] :
                    ( ? [X3] :
                        ( sdtmndtasgtdt0(xc,xR,X3)
                        & sdtmndtasgtdt0(xb,xR,X3)
                        & aNormalFormOfIn0(X3,X2,xR) )
                    & sdtmndtasgtdt0(X1,xR,X2)
                    & sdtmndtasgtdt0(X0,xR,X2)
                    & aElement0(X2) )
                & sdtmndtasgtdt0(X1,xR,xc)
                & aReductOfIn0(X1,xa,xR)
                & aElement0(X1) )
            & sdtmndtasgtdt0(X0,xR,xb)
            & aReductOfIn0(X0,xa,xR)
            & aElement0(X0) ) )
     => ( ( sdtmndtasgtdt0(xa,xR,xc)
          & sdtmndtasgtdt0(xa,xR,xb) )
       => ? [X4] :
            ( sdtmndtasgtdt0(xc,xR,X4)
            & sdtmndtasgtdt0(xb,xR,X4)
            & aElement0(X4) ) ) ),
    inference(rectify,[],[f20]) ).

fof(f32,plain,
    ! [X0,X1,X2] :
      ( ( sdtmndtasgtdt0(X0,X1,X2)
      <=> ( sdtmndtplgtdt0(X0,X1,X2)
          | X0 = X2 ) )
      | ~ aElement0(X2)
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f33,plain,
    ! [X0,X1,X2] :
      ( ( sdtmndtasgtdt0(X0,X1,X2)
      <=> ( sdtmndtplgtdt0(X0,X1,X2)
          | X0 = X2 ) )
      | ~ aElement0(X2)
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(flattening,[],[f32]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( aNormalFormOfIn0(X2,X0,X1)
        <=> ( ! [X3] : ~ aReductOfIn0(X3,X2,X1)
            & sdtmndtasgtdt0(X0,X1,X2)
            & aElement0(X2) ) )
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( aNormalFormOfIn0(X2,X0,X1)
        <=> ( ! [X3] : ~ aReductOfIn0(X3,X2,X1)
            & sdtmndtasgtdt0(X0,X1,X2)
            & aElement0(X2) ) )
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(flattening,[],[f42]) ).

fof(f48,plain,
    ( ! [X4] :
        ( ~ sdtmndtasgtdt0(xc,xR,X4)
        | ~ sdtmndtasgtdt0(xb,xR,X4)
        | ~ aElement0(X4) )
    & sdtmndtasgtdt0(xa,xR,xc)
    & sdtmndtasgtdt0(xa,xR,xb)
    & ( ? [X0] :
          ( ? [X1] :
              ( ? [X2] :
                  ( ? [X3] :
                      ( sdtmndtasgtdt0(xc,xR,X3)
                      & sdtmndtasgtdt0(xb,xR,X3)
                      & aNormalFormOfIn0(X3,X2,xR) )
                  & sdtmndtasgtdt0(X1,xR,X2)
                  & sdtmndtasgtdt0(X0,xR,X2)
                  & aElement0(X2) )
              & sdtmndtasgtdt0(X1,xR,xc)
              & aReductOfIn0(X1,xa,xR)
              & aElement0(X1) )
          & sdtmndtasgtdt0(X0,xR,xb)
          & aReductOfIn0(X0,xa,xR)
          & aElement0(X0) )
      | ~ sdtmndtplgtdt0(xa,xR,xc)
      | ~ sdtmndtplgtdt0(xa,xR,xb) ) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f49,plain,
    ( ! [X4] :
        ( ~ sdtmndtasgtdt0(xc,xR,X4)
        | ~ sdtmndtasgtdt0(xb,xR,X4)
        | ~ aElement0(X4) )
    & sdtmndtasgtdt0(xa,xR,xc)
    & sdtmndtasgtdt0(xa,xR,xb)
    & ( ? [X0] :
          ( ? [X1] :
              ( ? [X2] :
                  ( ? [X3] :
                      ( sdtmndtasgtdt0(xc,xR,X3)
                      & sdtmndtasgtdt0(xb,xR,X3)
                      & aNormalFormOfIn0(X3,X2,xR) )
                  & sdtmndtasgtdt0(X1,xR,X2)
                  & sdtmndtasgtdt0(X0,xR,X2)
                  & aElement0(X2) )
              & sdtmndtasgtdt0(X1,xR,xc)
              & aReductOfIn0(X1,xa,xR)
              & aElement0(X1) )
          & sdtmndtasgtdt0(X0,xR,xb)
          & aReductOfIn0(X0,xa,xR)
          & aElement0(X0) )
      | ~ sdtmndtplgtdt0(xa,xR,xc)
      | ~ sdtmndtplgtdt0(xa,xR,xb) ) ),
    inference(flattening,[],[f48]) ).

fof(f56,plain,
    ! [X1,X0] :
      ( ? [X2] :
          ( ? [X3] :
              ( sdtmndtasgtdt0(xc,xR,X3)
              & sdtmndtasgtdt0(xb,xR,X3)
              & aNormalFormOfIn0(X3,X2,xR) )
          & sdtmndtasgtdt0(X1,xR,X2)
          & sdtmndtasgtdt0(X0,xR,X2)
          & aElement0(X2) )
      | ~ sP4(X1,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).

fof(f57,plain,
    ( ! [X4] :
        ( ~ sdtmndtasgtdt0(xc,xR,X4)
        | ~ sdtmndtasgtdt0(xb,xR,X4)
        | ~ aElement0(X4) )
    & sdtmndtasgtdt0(xa,xR,xc)
    & sdtmndtasgtdt0(xa,xR,xb)
    & ( ? [X0] :
          ( ? [X1] :
              ( sP4(X1,X0)
              & sdtmndtasgtdt0(X1,xR,xc)
              & aReductOfIn0(X1,xa,xR)
              & aElement0(X1) )
          & sdtmndtasgtdt0(X0,xR,xb)
          & aReductOfIn0(X0,xa,xR)
          & aElement0(X0) )
      | ~ sdtmndtplgtdt0(xa,xR,xc)
      | ~ sdtmndtplgtdt0(xa,xR,xb) ) ),
    inference(definition_folding,[],[f49,f56]) ).

fof(f63,plain,
    ! [X0,X1,X2] :
      ( ( ( sdtmndtasgtdt0(X0,X1,X2)
          | ( ~ sdtmndtplgtdt0(X0,X1,X2)
            & X0 != X2 ) )
        & ( sdtmndtplgtdt0(X0,X1,X2)
          | X0 = X2
          | ~ sdtmndtasgtdt0(X0,X1,X2) ) )
      | ~ aElement0(X2)
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(nnf_transformation,[],[f33]) ).

fof(f64,plain,
    ! [X0,X1,X2] :
      ( ( ( sdtmndtasgtdt0(X0,X1,X2)
          | ( ~ sdtmndtplgtdt0(X0,X1,X2)
            & X0 != X2 ) )
        & ( sdtmndtplgtdt0(X0,X1,X2)
          | X0 = X2
          | ~ sdtmndtasgtdt0(X0,X1,X2) ) )
      | ~ aElement0(X2)
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(flattening,[],[f63]) ).

fof(f81,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( aNormalFormOfIn0(X2,X0,X1)
            | ? [X3] : aReductOfIn0(X3,X2,X1)
            | ~ sdtmndtasgtdt0(X0,X1,X2)
            | ~ aElement0(X2) )
          & ( ( ! [X3] : ~ aReductOfIn0(X3,X2,X1)
              & sdtmndtasgtdt0(X0,X1,X2)
              & aElement0(X2) )
            | ~ aNormalFormOfIn0(X2,X0,X1) ) )
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(nnf_transformation,[],[f43]) ).

fof(f82,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( aNormalFormOfIn0(X2,X0,X1)
            | ? [X3] : aReductOfIn0(X3,X2,X1)
            | ~ sdtmndtasgtdt0(X0,X1,X2)
            | ~ aElement0(X2) )
          & ( ( ! [X3] : ~ aReductOfIn0(X3,X2,X1)
              & sdtmndtasgtdt0(X0,X1,X2)
              & aElement0(X2) )
            | ~ aNormalFormOfIn0(X2,X0,X1) ) )
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(flattening,[],[f81]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( aNormalFormOfIn0(X2,X0,X1)
            | ? [X3] : aReductOfIn0(X3,X2,X1)
            | ~ sdtmndtasgtdt0(X0,X1,X2)
            | ~ aElement0(X2) )
          & ( ( ! [X4] : ~ aReductOfIn0(X4,X2,X1)
              & sdtmndtasgtdt0(X0,X1,X2)
              & aElement0(X2) )
            | ~ aNormalFormOfIn0(X2,X0,X1) ) )
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(rectify,[],[f82]) ).

fof(f84,plain,
    ! [X1,X2] :
      ( ? [X3] : aReductOfIn0(X3,X2,X1)
     => aReductOfIn0(sK16(X1,X2),X2,X1) ),
    introduced(choice_axiom,[]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( aNormalFormOfIn0(X2,X0,X1)
            | aReductOfIn0(sK16(X1,X2),X2,X1)
            | ~ sdtmndtasgtdt0(X0,X1,X2)
            | ~ aElement0(X2) )
          & ( ( ! [X4] : ~ aReductOfIn0(X4,X2,X1)
              & sdtmndtasgtdt0(X0,X1,X2)
              & aElement0(X2) )
            | ~ aNormalFormOfIn0(X2,X0,X1) ) )
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f83,f84]) ).

fof(f90,plain,
    ! [X1,X0] :
      ( ? [X2] :
          ( ? [X3] :
              ( sdtmndtasgtdt0(xc,xR,X3)
              & sdtmndtasgtdt0(xb,xR,X3)
              & aNormalFormOfIn0(X3,X2,xR) )
          & sdtmndtasgtdt0(X1,xR,X2)
          & sdtmndtasgtdt0(X0,xR,X2)
          & aElement0(X2) )
      | ~ sP4(X1,X0) ),
    inference(nnf_transformation,[],[f56]) ).

fof(f91,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( sdtmndtasgtdt0(xc,xR,X3)
              & sdtmndtasgtdt0(xb,xR,X3)
              & aNormalFormOfIn0(X3,X2,xR) )
          & sdtmndtasgtdt0(X0,xR,X2)
          & sdtmndtasgtdt0(X1,xR,X2)
          & aElement0(X2) )
      | ~ sP4(X0,X1) ),
    inference(rectify,[],[f90]) ).

fof(f92,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( sdtmndtasgtdt0(xc,xR,X3)
              & sdtmndtasgtdt0(xb,xR,X3)
              & aNormalFormOfIn0(X3,X2,xR) )
          & sdtmndtasgtdt0(X0,xR,X2)
          & sdtmndtasgtdt0(X1,xR,X2)
          & aElement0(X2) )
     => ( ? [X3] :
            ( sdtmndtasgtdt0(xc,xR,X3)
            & sdtmndtasgtdt0(xb,xR,X3)
            & aNormalFormOfIn0(X3,sK19(X0,X1),xR) )
        & sdtmndtasgtdt0(X0,xR,sK19(X0,X1))
        & sdtmndtasgtdt0(X1,xR,sK19(X0,X1))
        & aElement0(sK19(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f93,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( sdtmndtasgtdt0(xc,xR,X3)
          & sdtmndtasgtdt0(xb,xR,X3)
          & aNormalFormOfIn0(X3,sK19(X0,X1),xR) )
     => ( sdtmndtasgtdt0(xc,xR,sK20(X0,X1))
        & sdtmndtasgtdt0(xb,xR,sK20(X0,X1))
        & aNormalFormOfIn0(sK20(X0,X1),sK19(X0,X1),xR) ) ),
    introduced(choice_axiom,[]) ).

fof(f94,plain,
    ! [X0,X1] :
      ( ( sdtmndtasgtdt0(xc,xR,sK20(X0,X1))
        & sdtmndtasgtdt0(xb,xR,sK20(X0,X1))
        & aNormalFormOfIn0(sK20(X0,X1),sK19(X0,X1),xR)
        & sdtmndtasgtdt0(X0,xR,sK19(X0,X1))
        & sdtmndtasgtdt0(X1,xR,sK19(X0,X1))
        & aElement0(sK19(X0,X1)) )
      | ~ sP4(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK19,sK20])],[f91,f93,f92]) ).

fof(f95,plain,
    ( ! [X0] :
        ( ~ sdtmndtasgtdt0(xc,xR,X0)
        | ~ sdtmndtasgtdt0(xb,xR,X0)
        | ~ aElement0(X0) )
    & sdtmndtasgtdt0(xa,xR,xc)
    & sdtmndtasgtdt0(xa,xR,xb)
    & ( ? [X1] :
          ( ? [X2] :
              ( sP4(X2,X1)
              & sdtmndtasgtdt0(X2,xR,xc)
              & aReductOfIn0(X2,xa,xR)
              & aElement0(X2) )
          & sdtmndtasgtdt0(X1,xR,xb)
          & aReductOfIn0(X1,xa,xR)
          & aElement0(X1) )
      | ~ sdtmndtplgtdt0(xa,xR,xc)
      | ~ sdtmndtplgtdt0(xa,xR,xb) ) ),
    inference(rectify,[],[f57]) ).

fof(f96,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( sP4(X2,X1)
            & sdtmndtasgtdt0(X2,xR,xc)
            & aReductOfIn0(X2,xa,xR)
            & aElement0(X2) )
        & sdtmndtasgtdt0(X1,xR,xb)
        & aReductOfIn0(X1,xa,xR)
        & aElement0(X1) )
   => ( ? [X2] :
          ( sP4(X2,sK21)
          & sdtmndtasgtdt0(X2,xR,xc)
          & aReductOfIn0(X2,xa,xR)
          & aElement0(X2) )
      & sdtmndtasgtdt0(sK21,xR,xb)
      & aReductOfIn0(sK21,xa,xR)
      & aElement0(sK21) ) ),
    introduced(choice_axiom,[]) ).

fof(f97,plain,
    ( ? [X2] :
        ( sP4(X2,sK21)
        & sdtmndtasgtdt0(X2,xR,xc)
        & aReductOfIn0(X2,xa,xR)
        & aElement0(X2) )
   => ( sP4(sK22,sK21)
      & sdtmndtasgtdt0(sK22,xR,xc)
      & aReductOfIn0(sK22,xa,xR)
      & aElement0(sK22) ) ),
    introduced(choice_axiom,[]) ).

fof(f98,plain,
    ( ! [X0] :
        ( ~ sdtmndtasgtdt0(xc,xR,X0)
        | ~ sdtmndtasgtdt0(xb,xR,X0)
        | ~ aElement0(X0) )
    & sdtmndtasgtdt0(xa,xR,xc)
    & sdtmndtasgtdt0(xa,xR,xb)
    & ( ( sP4(sK22,sK21)
        & sdtmndtasgtdt0(sK22,xR,xc)
        & aReductOfIn0(sK22,xa,xR)
        & aElement0(sK22)
        & sdtmndtasgtdt0(sK21,xR,xb)
        & aReductOfIn0(sK21,xa,xR)
        & aElement0(sK21) )
      | ~ sdtmndtplgtdt0(xa,xR,xc)
      | ~ sdtmndtplgtdt0(xa,xR,xb) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK21,sK22])],[f95,f97,f96]) ).

fof(f106,plain,
    ! [X2,X0,X1] :
      ( sdtmndtplgtdt0(X0,X1,X2)
      | X0 = X2
      | ~ sdtmndtasgtdt0(X0,X1,X2)
      | ~ aElement0(X2)
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f64]) ).

fof(f139,plain,
    ! [X2,X0,X1] :
      ( aElement0(X2)
      | ~ aNormalFormOfIn0(X2,X0,X1)
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f85]) ).

fof(f144,plain,
    aRewritingSystem0(xR),
    inference(cnf_transformation,[],[f15]) ).

fof(f147,plain,
    aElement0(xa),
    inference(cnf_transformation,[],[f17]) ).

fof(f148,plain,
    aElement0(xb),
    inference(cnf_transformation,[],[f17]) ).

fof(f149,plain,
    aElement0(xc),
    inference(cnf_transformation,[],[f17]) ).

fof(f153,plain,
    ! [X0,X1] :
      ( aElement0(sK19(X0,X1))
      | ~ sP4(X0,X1) ),
    inference(cnf_transformation,[],[f94]) ).

fof(f156,plain,
    ! [X0,X1] :
      ( aNormalFormOfIn0(sK20(X0,X1),sK19(X0,X1),xR)
      | ~ sP4(X0,X1) ),
    inference(cnf_transformation,[],[f94]) ).

fof(f157,plain,
    ! [X0,X1] :
      ( sdtmndtasgtdt0(xb,xR,sK20(X0,X1))
      | ~ sP4(X0,X1) ),
    inference(cnf_transformation,[],[f94]) ).

fof(f158,plain,
    ! [X0,X1] :
      ( sdtmndtasgtdt0(xc,xR,sK20(X0,X1))
      | ~ sP4(X0,X1) ),
    inference(cnf_transformation,[],[f94]) ).

fof(f165,plain,
    ( sP4(sK22,sK21)
    | ~ sdtmndtplgtdt0(xa,xR,xc)
    | ~ sdtmndtplgtdt0(xa,xR,xb) ),
    inference(cnf_transformation,[],[f98]) ).

fof(f166,plain,
    sdtmndtasgtdt0(xa,xR,xb),
    inference(cnf_transformation,[],[f98]) ).

fof(f167,plain,
    sdtmndtasgtdt0(xa,xR,xc),
    inference(cnf_transformation,[],[f98]) ).

fof(f168,plain,
    ! [X0] :
      ( ~ sdtmndtasgtdt0(xc,xR,X0)
      | ~ sdtmndtasgtdt0(xb,xR,X0)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f98]) ).

cnf(c_57,plain,
    ( ~ aElement0(X0)
    | ~ aRewritingSystem0(X1)
    | sdtmndtasgtdt0(X0,X1,X0) ),
    inference(cnf_transformation,[],[f170]) ).

cnf(c_58,plain,
    ( ~ sdtmndtasgtdt0(X0,X1,X2)
    | ~ aElement0(X0)
    | ~ aElement0(X2)
    | ~ aRewritingSystem0(X1)
    | X0 = X2
    | sdtmndtplgtdt0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f106]) ).

cnf(c_92,plain,
    ( ~ aNormalFormOfIn0(X0,X1,X2)
    | ~ aElement0(X1)
    | ~ aRewritingSystem0(X2)
    | aElement0(X0) ),
    inference(cnf_transformation,[],[f139]) ).

cnf(c_94,plain,
    aRewritingSystem0(xR),
    inference(cnf_transformation,[],[f144]) ).

cnf(c_97,plain,
    aElement0(xc),
    inference(cnf_transformation,[],[f149]) ).

cnf(c_98,plain,
    aElement0(xb),
    inference(cnf_transformation,[],[f148]) ).

cnf(c_99,plain,
    aElement0(xa),
    inference(cnf_transformation,[],[f147]) ).

cnf(c_103,plain,
    ( ~ sP4(X0,X1)
    | sdtmndtasgtdt0(xc,xR,sK20(X0,X1)) ),
    inference(cnf_transformation,[],[f158]) ).

cnf(c_104,plain,
    ( ~ sP4(X0,X1)
    | sdtmndtasgtdt0(xb,xR,sK20(X0,X1)) ),
    inference(cnf_transformation,[],[f157]) ).

cnf(c_105,plain,
    ( ~ sP4(X0,X1)
    | aNormalFormOfIn0(sK20(X0,X1),sK19(X0,X1),xR) ),
    inference(cnf_transformation,[],[f156]) ).

cnf(c_108,plain,
    ( ~ sP4(X0,X1)
    | aElement0(sK19(X0,X1)) ),
    inference(cnf_transformation,[],[f153]) ).

cnf(c_109,negated_conjecture,
    ( ~ sdtmndtasgtdt0(xc,xR,X0)
    | ~ sdtmndtasgtdt0(xb,xR,X0)
    | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f168]) ).

cnf(c_110,negated_conjecture,
    sdtmndtasgtdt0(xa,xR,xc),
    inference(cnf_transformation,[],[f167]) ).

cnf(c_111,negated_conjecture,
    sdtmndtasgtdt0(xa,xR,xb),
    inference(cnf_transformation,[],[f166]) ).

cnf(c_112,negated_conjecture,
    ( ~ sdtmndtplgtdt0(xa,xR,xc)
    | ~ sdtmndtplgtdt0(xa,xR,xb)
    | sP4(sK22,sK21) ),
    inference(cnf_transformation,[],[f165]) ).

cnf(c_1173,plain,
    ( X0 != sK22
    | X1 != sK21
    | ~ sdtmndtplgtdt0(xa,xR,xc)
    | ~ sdtmndtplgtdt0(xa,xR,xb)
    | aElement0(sK19(X0,X1)) ),
    inference(resolution_lifted,[status(thm)],[c_108,c_112]) ).

cnf(c_1174,plain,
    ( ~ sdtmndtplgtdt0(xa,xR,xc)
    | ~ sdtmndtplgtdt0(xa,xR,xb)
    | aElement0(sK19(sK22,sK21)) ),
    inference(unflattening,[status(thm)],[c_1173]) ).

cnf(c_1206,plain,
    ( X0 != sK22
    | X1 != sK21
    | ~ sdtmndtplgtdt0(xa,xR,xc)
    | ~ sdtmndtplgtdt0(xa,xR,xb)
    | aNormalFormOfIn0(sK20(X0,X1),sK19(X0,X1),xR) ),
    inference(resolution_lifted,[status(thm)],[c_105,c_112]) ).

cnf(c_1207,plain,
    ( ~ sdtmndtplgtdt0(xa,xR,xc)
    | ~ sdtmndtplgtdt0(xa,xR,xb)
    | aNormalFormOfIn0(sK20(sK22,sK21),sK19(sK22,sK21),xR) ),
    inference(unflattening,[status(thm)],[c_1206]) ).

cnf(c_1217,plain,
    ( X0 != sK22
    | X1 != sK21
    | ~ sdtmndtplgtdt0(xa,xR,xc)
    | ~ sdtmndtplgtdt0(xa,xR,xb)
    | sdtmndtasgtdt0(xb,xR,sK20(X0,X1)) ),
    inference(resolution_lifted,[status(thm)],[c_104,c_112]) ).

cnf(c_1218,plain,
    ( ~ sdtmndtplgtdt0(xa,xR,xc)
    | ~ sdtmndtplgtdt0(xa,xR,xb)
    | sdtmndtasgtdt0(xb,xR,sK20(sK22,sK21)) ),
    inference(unflattening,[status(thm)],[c_1217]) ).

cnf(c_1228,plain,
    ( X0 != sK22
    | X1 != sK21
    | ~ sdtmndtplgtdt0(xa,xR,xc)
    | ~ sdtmndtplgtdt0(xa,xR,xb)
    | sdtmndtasgtdt0(xc,xR,sK20(X0,X1)) ),
    inference(resolution_lifted,[status(thm)],[c_103,c_112]) ).

cnf(c_1229,plain,
    ( ~ sdtmndtplgtdt0(xa,xR,xc)
    | ~ sdtmndtplgtdt0(xa,xR,xb)
    | sdtmndtasgtdt0(xc,xR,sK20(sK22,sK21)) ),
    inference(unflattening,[status(thm)],[c_1228]) ).

cnf(c_1659,plain,
    ( sK20(sK22,sK21) != X0
    | sK19(sK22,sK21) != X1
    | X2 != xR
    | ~ sdtmndtplgtdt0(xa,xR,xc)
    | ~ sdtmndtplgtdt0(xa,xR,xb)
    | ~ aElement0(X1)
    | ~ aRewritingSystem0(X2)
    | aElement0(X0) ),
    inference(resolution_lifted,[status(thm)],[c_92,c_1207]) ).

cnf(c_1660,plain,
    ( ~ aElement0(sK19(sK22,sK21))
    | ~ sdtmndtplgtdt0(xa,xR,xc)
    | ~ sdtmndtplgtdt0(xa,xR,xb)
    | ~ aRewritingSystem0(xR)
    | aElement0(sK20(sK22,sK21)) ),
    inference(unflattening,[status(thm)],[c_1659]) ).

cnf(c_1661,plain,
    ( ~ sdtmndtplgtdt0(xa,xR,xb)
    | ~ sdtmndtplgtdt0(xa,xR,xc)
    | aElement0(sK20(sK22,sK21)) ),
    inference(global_subsumption_just,[status(thm)],[c_1660,c_94,c_1174,c_1660]) ).

cnf(c_1662,plain,
    ( ~ sdtmndtplgtdt0(xa,xR,xc)
    | ~ sdtmndtplgtdt0(xa,xR,xb)
    | aElement0(sK20(sK22,sK21)) ),
    inference(renaming,[status(thm)],[c_1661]) ).

cnf(c_1893,plain,
    ( X0 != xR
    | ~ sdtmndtasgtdt0(X1,X0,X2)
    | ~ aElement0(X1)
    | ~ aElement0(X2)
    | X1 = X2
    | sdtmndtplgtdt0(X1,X0,X2) ),
    inference(resolution_lifted,[status(thm)],[c_58,c_94]) ).

cnf(c_1894,plain,
    ( ~ sdtmndtasgtdt0(X0,xR,X1)
    | ~ aElement0(X0)
    | ~ aElement0(X1)
    | X0 = X1
    | sdtmndtplgtdt0(X0,xR,X1) ),
    inference(unflattening,[status(thm)],[c_1893]) ).

cnf(c_1911,plain,
    ( X0 != xR
    | ~ aElement0(X1)
    | sdtmndtasgtdt0(X1,X0,X1) ),
    inference(resolution_lifted,[status(thm)],[c_57,c_94]) ).

cnf(c_1912,plain,
    ( ~ aElement0(X0)
    | sdtmndtasgtdt0(X0,xR,X0) ),
    inference(unflattening,[status(thm)],[c_1911]) ).

cnf(c_5406,negated_conjecture,
    sdtmndtasgtdt0(xa,xR,xb),
    inference(demodulation,[status(thm)],[c_111]) ).

cnf(c_5407,negated_conjecture,
    sdtmndtasgtdt0(xa,xR,xc),
    inference(demodulation,[status(thm)],[c_110]) ).

cnf(c_5408,negated_conjecture,
    ( ~ sdtmndtasgtdt0(xc,xR,X0)
    | ~ sdtmndtasgtdt0(xb,xR,X0)
    | ~ aElement0(X0) ),
    inference(demodulation,[status(thm)],[c_109]) ).

cnf(c_6481,plain,
    ( ~ sdtmndtasgtdt0(xb,xR,sK20(sK22,sK21))
    | ~ aElement0(sK20(sK22,sK21))
    | ~ sdtmndtplgtdt0(xa,xR,xc)
    | ~ sdtmndtplgtdt0(xa,xR,xb) ),
    inference(superposition,[status(thm)],[c_1229,c_5408]) ).

cnf(c_6486,plain,
    ( ~ sdtmndtplgtdt0(xa,xR,xc)
    | ~ sdtmndtplgtdt0(xa,xR,xb) ),
    inference(global_subsumption_just,[status(thm)],[c_6481,c_1218,c_1662,c_6481]) ).

cnf(c_6520,plain,
    ( ~ sdtmndtasgtdt0(xb,xR,xc)
    | ~ aElement0(xc) ),
    inference(superposition,[status(thm)],[c_1912,c_5408]) ).

cnf(c_6521,plain,
    ~ sdtmndtasgtdt0(xb,xR,xc),
    inference(forward_subsumption_resolution,[status(thm)],[c_6520,c_97]) ).

cnf(c_6703,plain,
    ( ~ aElement0(xc)
    | ~ aElement0(xa)
    | xc = xa
    | sdtmndtplgtdt0(xa,xR,xc) ),
    inference(superposition,[status(thm)],[c_5407,c_1894]) ).

cnf(c_6704,plain,
    ( ~ aElement0(xb)
    | ~ aElement0(xa)
    | xb = xa
    | sdtmndtplgtdt0(xa,xR,xb) ),
    inference(superposition,[status(thm)],[c_5406,c_1894]) ).

cnf(c_6707,plain,
    ( xb = xa
    | sdtmndtplgtdt0(xa,xR,xb) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_6704,c_99,c_98]) ).

cnf(c_6710,plain,
    ( xc = xa
    | sdtmndtplgtdt0(xa,xR,xc) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_6703,c_99,c_97]) ).

cnf(c_6737,plain,
    ( ~ sdtmndtplgtdt0(xa,xR,xb)
    | xc = xa ),
    inference(superposition,[status(thm)],[c_6710,c_6486]) ).

cnf(c_6745,plain,
    ( xc = xa
    | xb = xa ),
    inference(superposition,[status(thm)],[c_6707,c_6737]) ).

cnf(c_6756,plain,
    ( ~ sdtmndtasgtdt0(xa,xR,xc)
    | xc = xa ),
    inference(superposition,[status(thm)],[c_6745,c_6521]) ).

cnf(c_6761,plain,
    xc = xa,
    inference(forward_subsumption_resolution,[status(thm)],[c_6756,c_5407]) ).

cnf(c_6767,plain,
    ( ~ sdtmndtasgtdt0(xb,xR,X0)
    | ~ sdtmndtasgtdt0(xa,xR,X0)
    | ~ aElement0(X0) ),
    inference(demodulation,[status(thm)],[c_5408,c_6761]) ).

cnf(c_6792,plain,
    ( ~ sdtmndtasgtdt0(xa,xR,xb)
    | ~ aElement0(xb) ),
    inference(superposition,[status(thm)],[c_1912,c_6767]) ).

cnf(c_6793,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_6792,c_98,c_5406]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : COM022+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13  % Command  : run_iprover %s %d THM
% 0.14/0.35  % Computer : n004.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Fri May  3 00:36:03 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.93/1.18  % SZS status Started for theBenchmark.p
% 3.93/1.18  % SZS status Theorem for theBenchmark.p
% 3.93/1.18  
% 3.93/1.18  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.93/1.18  
% 3.93/1.18  ------  iProver source info
% 3.93/1.18  
% 3.93/1.18  git: date: 2024-05-02 19:28:25 +0000
% 3.93/1.18  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.93/1.18  git: non_committed_changes: false
% 3.93/1.18  
% 3.93/1.18  ------ Parsing...
% 3.93/1.18  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.93/1.18  
% 3.93/1.18  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e  sup_sim: 0  sf_s  rm: 7 0s  sf_e  pe_s  pe_e 
% 3.93/1.18  
% 3.93/1.18  ------ Preprocessing... gs_s  sp: 1 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.93/1.18  
% 3.93/1.18  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.93/1.18  ------ Proving...
% 3.93/1.18  ------ Problem Properties 
% 3.93/1.18  
% 3.93/1.18  
% 3.93/1.18  clauses                                 58
% 3.93/1.18  conjectures                             9
% 3.93/1.18  EPR                                     22
% 3.93/1.18  Horn                                    44
% 3.93/1.18  unary                                   6
% 3.93/1.18  binary                                  15
% 3.93/1.18  lits                                    204
% 3.93/1.18  lits eq                                 1
% 3.93/1.18  fd_pure                                 0
% 3.93/1.18  fd_pseudo                               0
% 3.93/1.18  fd_cond                                 0
% 3.93/1.18  fd_pseudo_cond                          1
% 3.93/1.18  AC symbols                              0
% 3.93/1.18  
% 3.93/1.18  ------ Schedule dynamic 5 is on 
% 3.93/1.18  
% 3.93/1.18  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.93/1.18  
% 3.93/1.18  
% 3.93/1.18  ------ 
% 3.93/1.18  Current options:
% 3.93/1.18  ------ 
% 3.93/1.18  
% 3.93/1.18  
% 3.93/1.18  
% 3.93/1.18  
% 3.93/1.18  ------ Proving...
% 3.93/1.18  
% 3.93/1.18  
% 3.93/1.18  % SZS status Theorem for theBenchmark.p
% 3.93/1.18  
% 3.93/1.18  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.93/1.18  
% 3.93/1.18  
%------------------------------------------------------------------------------