TSTP Solution File: SWC031+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SWC031+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n019.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 : Thu Aug 31 20:40:28 EDT 2023

% Result   : Theorem 9.61s 2.16s
% Output   : CNFRefutation 9.61s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named f597)

% Comments : 
%------------------------------------------------------------------------------
fof(f5,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( frontsegP(X0,X1)
          <=> ? [X2] :
                ( app(X1,X2) = X0
                & ssList(X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).

fof(f15,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( neq(X0,X1)
          <=> X0 != X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).

fof(f16,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ssList(cons(X1,X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).

fof(f21,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => nil != cons(X1,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).

fof(f22,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ssItem(hd(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).

fof(f26,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ssList(app(X0,X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).

fof(f28,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(nil,X0) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).

fof(f46,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( frontsegP(nil,X0)
      <=> nil = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax46) ).

fof(f57,axiom,
    ! [X0] :
      ( ssList(X0)
     => segmentP(X0,nil) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax57) ).

fof(f58,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( segmentP(nil,X0)
      <=> nil = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).

fof(f65,axiom,
    ! [X0] :
      ( ssItem(X0)
     => totalorderedP(cons(X0,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax65) ).

fof(f75,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ? [X1] :
            ( hd(X0) = X1
            & ssItem(X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax75) ).

fof(f76,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ? [X1] :
            ( tl(X0) = X1
            & ssList(X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax76) ).

fof(f78,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => cons(hd(X0),tl(X0)) = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax78) ).

fof(f81,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => cons(X1,X0) = app(cons(X1,nil),X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax81) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ( ( nil = X1
                        | nil != X0 )
                      & ( nil = X0
                        | nil != X1 ) )
                    | ? [X4] :
                        ( totalorderedP(X4)
                        & segmentP(X4,X2)
                        & frontsegP(X3,X4)
                        & neq(X2,X4)
                        & ssList(X4) )
                    | ~ totalorderedP(X2)
                    | ~ frontsegP(X3,X2)
                    | X0 != X2
                    | X1 != X3 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( ( nil = X1
                          | nil != X0 )
                        & ( nil = X0
                          | nil != X1 ) )
                      | ? [X4] :
                          ( totalorderedP(X4)
                          & segmentP(X4,X2)
                          & frontsegP(X3,X4)
                          & neq(X2,X4)
                          & ssList(X4) )
                      | ~ totalorderedP(X2)
                      | ~ frontsegP(X3,X2)
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f101,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( frontsegP(X0,X1)
          <=> ? [X2] :
                ( app(X1,X2) = X0
                & ssList(X2) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f118,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( neq(X0,X1)
          <=> X0 != X1 )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f119,plain,
    ! [X0] :
      ( ! [X1] :
          ( ssList(cons(X1,X0))
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f125,plain,
    ! [X0] :
      ( ! [X1] :
          ( nil != cons(X1,X0)
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f126,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f127,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f126]) ).

fof(f132,plain,
    ! [X0] :
      ( ! [X1] :
          ( ssList(app(X0,X1))
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f134,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f158,plain,
    ! [X0] :
      ( ( frontsegP(nil,X0)
      <=> nil = X0 )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f46]) ).

fof(f175,plain,
    ! [X0] :
      ( segmentP(X0,nil)
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f57]) ).

fof(f176,plain,
    ! [X0] :
      ( ( segmentP(nil,X0)
      <=> nil = X0 )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f58]) ).

fof(f180,plain,
    ! [X0] :
      ( totalorderedP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f65]) ).

fof(f186,plain,
    ! [X0] :
      ( ? [X1] :
          ( hd(X0) = X1
          & ssItem(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f75]) ).

fof(f187,plain,
    ! [X0] :
      ( ? [X1] :
          ( hd(X0) = X1
          & ssItem(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f186]) ).

fof(f188,plain,
    ! [X0] :
      ( ? [X1] :
          ( tl(X0) = X1
          & ssList(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f76]) ).

fof(f189,plain,
    ! [X0] :
      ( ? [X1] :
          ( tl(X0) = X1
          & ssList(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f188]) ).

fof(f192,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f78]) ).

fof(f193,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f192]) ).

fof(f198,plain,
    ! [X0] :
      ( ! [X1] :
          ( cons(X1,X0) = app(cons(X1,nil),X0)
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f81]) ).

fof(f221,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil != X1
                      & nil = X0 )
                    | ( nil != X0
                      & nil = X1 ) )
                  & ! [X4] :
                      ( ~ totalorderedP(X4)
                      | ~ segmentP(X4,X2)
                      | ~ frontsegP(X3,X4)
                      | ~ neq(X2,X4)
                      | ~ ssList(X4) )
                  & totalorderedP(X2)
                  & frontsegP(X3,X2)
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f97]) ).

fof(f222,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil != X1
                      & nil = X0 )
                    | ( nil != X0
                      & nil = X1 ) )
                  & ! [X4] :
                      ( ~ totalorderedP(X4)
                      | ~ segmentP(X4,X2)
                      | ~ frontsegP(X3,X4)
                      | ~ neq(X2,X4)
                      | ~ ssList(X4) )
                  & totalorderedP(X2)
                  & frontsegP(X3,X2)
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f221]) ).

fof(f245,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( frontsegP(X0,X1)
              | ! [X2] :
                  ( app(X1,X2) != X0
                  | ~ ssList(X2) ) )
            & ( ? [X2] :
                  ( app(X1,X2) = X0
                  & ssList(X2) )
              | ~ frontsegP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f101]) ).

fof(f246,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( frontsegP(X0,X1)
              | ! [X2] :
                  ( app(X1,X2) != X0
                  | ~ ssList(X2) ) )
            & ( ? [X3] :
                  ( app(X1,X3) = X0
                  & ssList(X3) )
              | ~ frontsegP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f245]) ).

fof(f247,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( app(X1,X3) = X0
          & ssList(X3) )
     => ( app(X1,sK11(X0,X1)) = X0
        & ssList(sK11(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f248,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( frontsegP(X0,X1)
              | ! [X2] :
                  ( app(X1,X2) != X0
                  | ~ ssList(X2) ) )
            & ( ( app(X1,sK11(X0,X1)) = X0
                & ssList(sK11(X0,X1)) )
              | ~ frontsegP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f246,f247]) ).

fof(f316,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( neq(X0,X1)
              | X0 = X1 )
            & ( X0 != X1
              | ~ neq(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f118]) ).

fof(f328,plain,
    ! [X0] :
      ( ( ( frontsegP(nil,X0)
          | nil != X0 )
        & ( nil = X0
          | ~ frontsegP(nil,X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f158]) ).

fof(f330,plain,
    ! [X0] :
      ( ( ( segmentP(nil,X0)
          | nil != X0 )
        & ( nil = X0
          | ~ segmentP(nil,X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f176]) ).

fof(f335,plain,
    ! [X0] :
      ( ? [X1] :
          ( hd(X0) = X1
          & ssItem(X1) )
     => ( hd(X0) = sK51(X0)
        & ssItem(sK51(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f336,plain,
    ! [X0] :
      ( ( hd(X0) = sK51(X0)
        & ssItem(sK51(X0)) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK51])],[f187,f335]) ).

fof(f337,plain,
    ! [X0] :
      ( ? [X1] :
          ( tl(X0) = X1
          & ssList(X1) )
     => ( tl(X0) = sK52(X0)
        & ssList(sK52(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f338,plain,
    ! [X0] :
      ( ( tl(X0) = sK52(X0)
        & ssList(sK52(X0)) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK52])],[f189,f337]) ).

fof(f343,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( nil != X1
                        & nil = X0 )
                      | ( nil != X0
                        & nil = X1 ) )
                    & ! [X4] :
                        ( ~ totalorderedP(X4)
                        | ~ segmentP(X4,X2)
                        | ~ frontsegP(X3,X4)
                        | ~ neq(X2,X4)
                        | ~ ssList(X4) )
                    & totalorderedP(X2)
                    & frontsegP(X3,X2)
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil != X1
                      & nil = sK53 )
                    | ( nil != sK53
                      & nil = X1 ) )
                  & ! [X4] :
                      ( ~ totalorderedP(X4)
                      | ~ segmentP(X4,X2)
                      | ~ frontsegP(X3,X4)
                      | ~ neq(X2,X4)
                      | ~ ssList(X4) )
                  & totalorderedP(X2)
                  & frontsegP(X3,X2)
                  & sK53 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK53) ) ),
    introduced(choice_axiom,[]) ).

fof(f344,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( nil != X1
                    & nil = sK53 )
                  | ( nil != sK53
                    & nil = X1 ) )
                & ! [X4] :
                    ( ~ totalorderedP(X4)
                    | ~ segmentP(X4,X2)
                    | ~ frontsegP(X3,X4)
                    | ~ neq(X2,X4)
                    | ~ ssList(X4) )
                & totalorderedP(X2)
                & frontsegP(X3,X2)
                & sK53 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( nil != sK54
                  & nil = sK53 )
                | ( nil != sK53
                  & nil = sK54 ) )
              & ! [X4] :
                  ( ~ totalorderedP(X4)
                  | ~ segmentP(X4,X2)
                  | ~ frontsegP(X3,X4)
                  | ~ neq(X2,X4)
                  | ~ ssList(X4) )
              & totalorderedP(X2)
              & frontsegP(X3,X2)
              & sK53 = X2
              & sK54 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK54) ) ),
    introduced(choice_axiom,[]) ).

fof(f345,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( nil != sK54
                & nil = sK53 )
              | ( nil != sK53
                & nil = sK54 ) )
            & ! [X4] :
                ( ~ totalorderedP(X4)
                | ~ segmentP(X4,X2)
                | ~ frontsegP(X3,X4)
                | ~ neq(X2,X4)
                | ~ ssList(X4) )
            & totalorderedP(X2)
            & frontsegP(X3,X2)
            & sK53 = X2
            & sK54 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( nil != sK54
              & nil = sK53 )
            | ( nil != sK53
              & nil = sK54 ) )
          & ! [X4] :
              ( ~ totalorderedP(X4)
              | ~ segmentP(X4,sK55)
              | ~ frontsegP(X3,X4)
              | ~ neq(sK55,X4)
              | ~ ssList(X4) )
          & totalorderedP(sK55)
          & frontsegP(X3,sK55)
          & sK53 = sK55
          & sK54 = X3
          & ssList(X3) )
      & ssList(sK55) ) ),
    introduced(choice_axiom,[]) ).

fof(f346,plain,
    ( ? [X3] :
        ( ( ( nil != sK54
            & nil = sK53 )
          | ( nil != sK53
            & nil = sK54 ) )
        & ! [X4] :
            ( ~ totalorderedP(X4)
            | ~ segmentP(X4,sK55)
            | ~ frontsegP(X3,X4)
            | ~ neq(sK55,X4)
            | ~ ssList(X4) )
        & totalorderedP(sK55)
        & frontsegP(X3,sK55)
        & sK53 = sK55
        & sK54 = X3
        & ssList(X3) )
   => ( ( ( nil != sK54
          & nil = sK53 )
        | ( nil != sK53
          & nil = sK54 ) )
      & ! [X4] :
          ( ~ totalorderedP(X4)
          | ~ segmentP(X4,sK55)
          | ~ frontsegP(sK56,X4)
          | ~ neq(sK55,X4)
          | ~ ssList(X4) )
      & totalorderedP(sK55)
      & frontsegP(sK56,sK55)
      & sK53 = sK55
      & sK54 = sK56
      & ssList(sK56) ) ),
    introduced(choice_axiom,[]) ).

fof(f347,plain,
    ( ( ( nil != sK54
        & nil = sK53 )
      | ( nil != sK53
        & nil = sK54 ) )
    & ! [X4] :
        ( ~ totalorderedP(X4)
        | ~ segmentP(X4,sK55)
        | ~ frontsegP(sK56,X4)
        | ~ neq(sK55,X4)
        | ~ ssList(X4) )
    & totalorderedP(sK55)
    & frontsegP(sK56,sK55)
    & sK53 = sK55
    & sK54 = sK56
    & ssList(sK56)
    & ssList(sK55)
    & ssList(sK54)
    & ssList(sK53) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56])],[f222,f346,f345,f344,f343]) ).

fof(f362,plain,
    ! [X2,X0,X1] :
      ( frontsegP(X0,X1)
      | app(X1,X2) != X0
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f248]) ).

fof(f438,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | X0 = X1
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f316]) ).

fof(f439,plain,
    ! [X0,X1] :
      ( ssList(cons(X1,X0))
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f119]) ).

fof(f440,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f447,plain,
    ! [X0,X1] :
      ( nil != cons(X1,X0)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f125]) ).

fof(f448,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f127]) ).

fof(f452,plain,
    ! [X0,X1] :
      ( ssList(app(X0,X1))
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f132]) ).

fof(f454,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f134]) ).

fof(f480,plain,
    ! [X0] :
      ( nil = X0
      | ~ frontsegP(nil,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f328]) ).

fof(f493,plain,
    ! [X0] :
      ( segmentP(X0,nil)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f175]) ).

fof(f494,plain,
    ! [X0] :
      ( nil = X0
      | ~ segmentP(nil,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f330]) ).

fof(f495,plain,
    ! [X0] :
      ( segmentP(nil,X0)
      | nil != X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f330]) ).

fof(f502,plain,
    ! [X0] :
      ( totalorderedP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f180]) ).

fof(f520,plain,
    ! [X0] :
      ( ssItem(sK51(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f336]) ).

fof(f521,plain,
    ! [X0] :
      ( hd(X0) = sK51(X0)
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f336]) ).

fof(f522,plain,
    ! [X0] :
      ( ssList(sK52(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f338]) ).

fof(f523,plain,
    ! [X0] :
      ( tl(X0) = sK52(X0)
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f338]) ).

fof(f525,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f193]) ).

fof(f528,plain,
    ! [X0,X1] :
      ( cons(X1,X0) = app(cons(X1,nil),X0)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f198]) ).

fof(f547,plain,
    ssList(sK53),
    inference(cnf_transformation,[],[f347]) ).

fof(f548,plain,
    ssList(sK54),
    inference(cnf_transformation,[],[f347]) ).

fof(f551,plain,
    sK54 = sK56,
    inference(cnf_transformation,[],[f347]) ).

fof(f552,plain,
    sK53 = sK55,
    inference(cnf_transformation,[],[f347]) ).

fof(f553,plain,
    frontsegP(sK56,sK55),
    inference(cnf_transformation,[],[f347]) ).

fof(f555,plain,
    ! [X4] :
      ( ~ totalorderedP(X4)
      | ~ segmentP(X4,sK55)
      | ~ frontsegP(sK56,X4)
      | ~ neq(sK55,X4)
      | ~ ssList(X4) ),
    inference(cnf_transformation,[],[f347]) ).

fof(f556,plain,
    ( nil = sK53
    | nil = sK54 ),
    inference(cnf_transformation,[],[f347]) ).

fof(f559,plain,
    ( nil != sK54
    | nil != sK53 ),
    inference(cnf_transformation,[],[f347]) ).

fof(f560,plain,
    ( nil != sK56
    | nil != sK55 ),
    inference(definition_unfolding,[],[f559,f551,f552]) ).

fof(f563,plain,
    ( nil = sK55
    | nil = sK56 ),
    inference(definition_unfolding,[],[f556,f552,f551]) ).

fof(f564,plain,
    ssList(sK56),
    inference(definition_unfolding,[],[f548,f551]) ).

fof(f565,plain,
    ssList(sK55),
    inference(definition_unfolding,[],[f547,f552]) ).

fof(f569,plain,
    ! [X2,X1] :
      ( frontsegP(app(X1,X2),X1)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(app(X1,X2)) ),
    inference(equality_resolution,[],[f362]) ).

fof(f585,plain,
    ( segmentP(nil,nil)
    | ~ ssList(nil) ),
    inference(equality_resolution,[],[f495]) ).

cnf(c_61,plain,
    ( ~ ssList(app(X0,X1))
    | ~ ssList(X0)
    | ~ ssList(X1)
    | frontsegP(app(X0,X1),X0) ),
    inference(cnf_transformation,[],[f569]) ).

cnf(c_138,plain,
    ( ~ ssList(X0)
    | ~ ssList(X1)
    | X0 = X1
    | neq(X0,X1) ),
    inference(cnf_transformation,[],[f438]) ).

cnf(c_140,plain,
    ( ~ ssItem(X0)
    | ~ ssList(X1)
    | ssList(cons(X0,X1)) ),
    inference(cnf_transformation,[],[f439]) ).

cnf(c_141,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f440]) ).

cnf(c_148,plain,
    ( cons(X0,X1) != nil
    | ~ ssItem(X0)
    | ~ ssList(X1) ),
    inference(cnf_transformation,[],[f447]) ).

cnf(c_149,plain,
    ( ~ ssList(X0)
    | X0 = nil
    | ssItem(hd(X0)) ),
    inference(cnf_transformation,[],[f448]) ).

cnf(c_153,plain,
    ( ~ ssList(X0)
    | ~ ssList(X1)
    | ssList(app(X0,X1)) ),
    inference(cnf_transformation,[],[f452]) ).

cnf(c_155,plain,
    ( ~ ssList(X0)
    | app(nil,X0) = X0 ),
    inference(cnf_transformation,[],[f454]) ).

cnf(c_177,plain,
    ( ~ frontsegP(X0,X1)
    | ~ ssItem(X2)
    | ~ ssList(X0)
    | ~ ssList(X1)
    | frontsegP(cons(X2,X0),cons(X2,X1)) ),
    inference(cnf_transformation,[],[f597]) ).

cnf(c_182,plain,
    ( ~ frontsegP(nil,X0)
    | ~ ssList(X0)
    | X0 = nil ),
    inference(cnf_transformation,[],[f480]) ).

cnf(c_194,plain,
    ( ~ ssList(X0)
    | segmentP(X0,nil) ),
    inference(cnf_transformation,[],[f493]) ).

cnf(c_195,plain,
    ( ~ ssList(nil)
    | segmentP(nil,nil) ),
    inference(cnf_transformation,[],[f585]) ).

cnf(c_196,plain,
    ( ~ segmentP(nil,X0)
    | ~ ssList(X0)
    | X0 = nil ),
    inference(cnf_transformation,[],[f494]) ).

cnf(c_203,plain,
    ( ~ ssItem(X0)
    | totalorderedP(cons(X0,nil)) ),
    inference(cnf_transformation,[],[f502]) ).

cnf(c_219,plain,
    ( ~ ssList(X0)
    | hd(X0) = sK51(X0)
    | X0 = nil ),
    inference(cnf_transformation,[],[f521]) ).

cnf(c_220,plain,
    ( ~ ssList(X0)
    | X0 = nil
    | ssItem(sK51(X0)) ),
    inference(cnf_transformation,[],[f520]) ).

cnf(c_221,plain,
    ( ~ ssList(X0)
    | tl(X0) = sK52(X0)
    | X0 = nil ),
    inference(cnf_transformation,[],[f523]) ).

cnf(c_222,plain,
    ( ~ ssList(X0)
    | X0 = nil
    | ssList(sK52(X0)) ),
    inference(cnf_transformation,[],[f522]) ).

cnf(c_224,plain,
    ( ~ ssList(X0)
    | cons(hd(X0),tl(X0)) = X0
    | X0 = nil ),
    inference(cnf_transformation,[],[f525]) ).

cnf(c_227,plain,
    ( ~ ssItem(X0)
    | ~ ssList(X1)
    | app(cons(X0,nil),X1) = cons(X0,X1) ),
    inference(cnf_transformation,[],[f528]) ).

cnf(c_246,negated_conjecture,
    ( nil != sK56
    | nil != sK55 ),
    inference(cnf_transformation,[],[f560]) ).

cnf(c_247,negated_conjecture,
    ( nil = sK56
    | nil = sK55 ),
    inference(cnf_transformation,[],[f563]) ).

cnf(c_248,negated_conjecture,
    ( ~ neq(sK55,X0)
    | ~ frontsegP(sK56,X0)
    | ~ segmentP(X0,sK55)
    | ~ ssList(X0)
    | ~ totalorderedP(X0) ),
    inference(cnf_transformation,[],[f555]) ).

cnf(c_250,negated_conjecture,
    frontsegP(sK56,sK55),
    inference(cnf_transformation,[],[f553]) ).

cnf(c_253,negated_conjecture,
    ssList(sK56),
    inference(cnf_transformation,[],[f564]) ).

cnf(c_254,negated_conjecture,
    ssList(sK55),
    inference(cnf_transformation,[],[f565]) ).

cnf(c_304,plain,
    ( ~ segmentP(nil,nil)
    | ~ ssList(nil)
    | nil = nil ),
    inference(instantiation,[status(thm)],[c_196]) ).

cnf(c_377,plain,
    ( ~ ssList(X0)
    | ~ ssList(X1)
    | frontsegP(app(X0,X1),X0) ),
    inference(global_subsumption_just,[status(thm)],[c_61,c_153,c_61]) ).

cnf(c_3698,plain,
    ( X0 != sK55
    | X1 != X2
    | ~ frontsegP(sK56,X2)
    | ~ segmentP(X2,sK55)
    | ~ ssList(X0)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ totalorderedP(X2)
    | X0 = X1 ),
    inference(resolution_lifted,[status(thm)],[c_138,c_248]) ).

cnf(c_3699,plain,
    ( ~ frontsegP(sK56,X0)
    | ~ segmentP(X0,sK55)
    | ~ ssList(X0)
    | ~ totalorderedP(X0)
    | ~ ssList(sK55)
    | sK55 = X0 ),
    inference(unflattening,[status(thm)],[c_3698]) ).

cnf(c_3701,plain,
    ( ~ totalorderedP(X0)
    | ~ ssList(X0)
    | ~ segmentP(X0,sK55)
    | ~ frontsegP(sK56,X0)
    | sK55 = X0 ),
    inference(global_subsumption_just,[status(thm)],[c_3699,c_254,c_3699]) ).

cnf(c_3702,plain,
    ( ~ frontsegP(sK56,X0)
    | ~ segmentP(X0,sK55)
    | ~ ssList(X0)
    | ~ totalorderedP(X0)
    | sK55 = X0 ),
    inference(renaming,[status(thm)],[c_3701]) ).

cnf(c_9760,plain,
    ( X0 != X1
    | X2 != X1
    | X2 = X0 ),
    theory(equality) ).

cnf(c_13474,plain,
    ( nil = sK55
    | frontsegP(nil,sK55) ),
    inference(superposition,[status(thm)],[c_247,c_250]) ).

cnf(c_14696,plain,
    ( ~ ssList(sK55)
    | nil = sK55 ),
    inference(superposition,[status(thm)],[c_13474,c_182]) ).

cnf(c_14697,plain,
    nil = sK55,
    inference(forward_subsumption_resolution,[status(thm)],[c_14696,c_254]) ).

cnf(c_14698,plain,
    nil != sK56,
    inference(backward_subsumption_resolution,[status(thm)],[c_246,c_14697]) ).

cnf(c_14704,plain,
    ( ~ frontsegP(sK56,X0)
    | ~ segmentP(X0,nil)
    | ~ ssList(X0)
    | ~ totalorderedP(X0)
    | X0 = nil ),
    inference(demodulation,[status(thm)],[c_3702,c_14697]) ).

cnf(c_14746,plain,
    ( ~ frontsegP(sK56,X0)
    | ~ ssList(X0)
    | ~ totalorderedP(X0)
    | X0 = nil ),
    inference(global_subsumption_just,[status(thm)],[c_14704,c_194,c_14704]) ).

cnf(c_15363,plain,
    ( nil != X0
    | sK56 != X0
    | nil = sK56 ),
    inference(instantiation,[status(thm)],[c_9760]) ).

cnf(c_15364,plain,
    ( nil != nil
    | sK56 != nil
    | nil = sK56 ),
    inference(instantiation,[status(thm)],[c_15363]) ).

cnf(c_16024,plain,
    ( hd(sK56) = sK51(sK56)
    | nil = sK56 ),
    inference(superposition,[status(thm)],[c_253,c_219]) ).

cnf(c_16025,plain,
    hd(sK56) = sK51(sK56),
    inference(forward_subsumption_resolution,[status(thm)],[c_16024,c_14698]) ).

cnf(c_16178,plain,
    ( ~ ssList(sK56)
    | sK56 = nil
    | ssItem(hd(sK56)) ),
    inference(instantiation,[status(thm)],[c_149]) ).

cnf(c_16219,plain,
    ( tl(sK56) = sK52(sK56)
    | nil = sK56 ),
    inference(superposition,[status(thm)],[c_253,c_221]) ).

cnf(c_16220,plain,
    tl(sK56) = sK52(sK56),
    inference(forward_subsumption_resolution,[status(thm)],[c_16219,c_14698]) ).

cnf(c_16313,plain,
    ( ~ ssList(sK56)
    | nil = sK56
    | ssItem(hd(sK56)) ),
    inference(superposition,[status(thm)],[c_16025,c_220]) ).

cnf(c_16314,plain,
    ssItem(hd(sK56)),
    inference(forward_subsumption_resolution,[status(thm)],[c_16313,c_14698,c_253]) ).

cnf(c_16323,plain,
    ( ~ ssList(sK56)
    | nil = sK56
    | ssList(tl(sK56)) ),
    inference(superposition,[status(thm)],[c_16220,c_222]) ).

cnf(c_16324,plain,
    ssList(tl(sK56)),
    inference(forward_subsumption_resolution,[status(thm)],[c_16323,c_14698,c_253]) ).

cnf(c_16338,plain,
    app(nil,tl(sK56)) = tl(sK56),
    inference(superposition,[status(thm)],[c_16324,c_155]) ).

cnf(c_16404,plain,
    ( ~ ssList(tl(sK56))
    | ~ ssList(nil)
    | frontsegP(tl(sK56),nil) ),
    inference(superposition,[status(thm)],[c_16338,c_377]) ).

cnf(c_16405,plain,
    frontsegP(tl(sK56),nil),
    inference(forward_subsumption_resolution,[status(thm)],[c_16404,c_141,c_16324]) ).

cnf(c_18543,plain,
    ( cons(hd(sK56),tl(sK56)) = sK56
    | nil = sK56 ),
    inference(superposition,[status(thm)],[c_253,c_224]) ).

cnf(c_18546,plain,
    cons(hd(sK56),tl(sK56)) = sK56,
    inference(forward_subsumption_resolution,[status(thm)],[c_18543,c_14698]) ).

cnf(c_18753,plain,
    ( ~ ssList(X0)
    | app(cons(hd(sK56),nil),X0) = cons(hd(sK56),X0) ),
    inference(superposition,[status(thm)],[c_16314,c_227]) ).

cnf(c_18930,plain,
    app(cons(hd(sK56),nil),tl(sK56)) = cons(hd(sK56),tl(sK56)),
    inference(superposition,[status(thm)],[c_16324,c_18753]) ).

cnf(c_18932,plain,
    app(cons(hd(sK56),nil),tl(sK56)) = sK56,
    inference(light_normalisation,[status(thm)],[c_18930,c_18546]) ).

cnf(c_22320,plain,
    ( ~ frontsegP(tl(sK56),X0)
    | ~ ssItem(hd(sK56))
    | ~ ssList(tl(sK56))
    | ~ ssList(X0)
    | frontsegP(sK56,cons(hd(sK56),X0)) ),
    inference(superposition,[status(thm)],[c_18546,c_177]) ).

cnf(c_22346,plain,
    ( ~ frontsegP(tl(sK56),X0)
    | ~ ssList(X0)
    | frontsegP(sK56,cons(hd(sK56),X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_22320,c_16324,c_16314]) ).

cnf(c_22404,plain,
    ( ~ frontsegP(tl(sK56),nil)
    | ~ ssList(nil)
    | frontsegP(sK56,cons(hd(sK56),nil)) ),
    inference(instantiation,[status(thm)],[c_22346]) ).

cnf(c_22426,plain,
    ( ~ ssList(cons(hd(sK56),nil))
    | ~ ssList(tl(sK56))
    | frontsegP(sK56,cons(hd(sK56),nil)) ),
    inference(superposition,[status(thm)],[c_18932,c_377]) ).

cnf(c_22434,plain,
    ( ~ ssList(cons(hd(sK56),nil))
    | frontsegP(sK56,cons(hd(sK56),nil)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_22426,c_16324]) ).

cnf(c_23147,plain,
    ( cons(hd(sK56),X0) != nil
    | ~ ssItem(hd(sK56))
    | ~ ssList(X0) ),
    inference(instantiation,[status(thm)],[c_148]) ).

cnf(c_23148,plain,
    ( ~ ssItem(hd(sK56))
    | ~ ssList(X0)
    | ssList(cons(hd(sK56),X0)) ),
    inference(instantiation,[status(thm)],[c_140]) ).

cnf(c_23156,plain,
    ( ~ ssItem(hd(sK56))
    | totalorderedP(cons(hd(sK56),nil)) ),
    inference(instantiation,[status(thm)],[c_203]) ).

cnf(c_23158,plain,
    ( ~ ssItem(hd(sK56))
    | ~ ssList(nil)
    | ssList(cons(hd(sK56),nil)) ),
    inference(instantiation,[status(thm)],[c_23148]) ).

cnf(c_23159,plain,
    ( cons(hd(sK56),nil) != nil
    | ~ ssItem(hd(sK56))
    | ~ ssList(nil) ),
    inference(instantiation,[status(thm)],[c_23147]) ).

cnf(c_38844,plain,
    frontsegP(sK56,cons(hd(sK56),nil)),
    inference(global_subsumption_just,[status(thm)],[c_22434,c_141,c_16405,c_22404]) ).

cnf(c_38849,plain,
    ( ~ ssList(cons(hd(sK56),nil))
    | ~ totalorderedP(cons(hd(sK56),nil))
    | cons(hd(sK56),nil) = nil ),
    inference(superposition,[status(thm)],[c_38844,c_14746]) ).

cnf(c_38861,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_38849,c_23159,c_23158,c_23156,c_16178,c_15364,c_14697,c_304,c_246,c_195,c_141,c_253]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWC031+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.12/0.35  % Computer : n019.cluster.edu
% 0.12/0.35  % Model    : x86_64 x86_64
% 0.12/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35  % Memory   : 8042.1875MB
% 0.12/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35  % CPULimit : 300
% 0.12/0.35  % WCLimit  : 300
% 0.12/0.35  % DateTime : Mon Aug 28 17:23:43 EDT 2023
% 0.12/0.35  % CPUTime  : 
% 0.21/0.49  Running first-order theorem proving
% 0.21/0.49  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 9.61/2.16  % SZS status Started for theBenchmark.p
% 9.61/2.16  % SZS status Theorem for theBenchmark.p
% 9.61/2.16  
% 9.61/2.16  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 9.61/2.16  
% 9.61/2.16  ------  iProver source info
% 9.61/2.16  
% 9.61/2.16  git: date: 2023-05-31 18:12:56 +0000
% 9.61/2.16  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 9.61/2.16  git: non_committed_changes: false
% 9.61/2.16  git: last_make_outside_of_git: false
% 9.61/2.16  
% 9.61/2.16  ------ Parsing...
% 9.61/2.16  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 9.61/2.16  
% 9.61/2.16  ------ 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 
% 9.61/2.16  
% 9.61/2.16  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 9.61/2.16  
% 9.61/2.16  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 9.61/2.16  ------ Proving...
% 9.61/2.16  ------ Problem Properties 
% 9.61/2.16  
% 9.61/2.16  
% 9.61/2.16  clauses                                 187
% 9.61/2.16  conjectures                             6
% 9.61/2.16  EPR                                     56
% 9.61/2.16  Horn                                    118
% 9.61/2.16  unary                                   20
% 9.61/2.16  binary                                  42
% 9.61/2.16  lits                                    631
% 9.61/2.16  lits eq                                 83
% 9.61/2.16  fd_pure                                 0
% 9.61/2.16  fd_pseudo                               0
% 9.61/2.16  fd_cond                                 22
% 9.61/2.16  fd_pseudo_cond                          14
% 9.61/2.16  AC symbols                              0
% 9.61/2.16  
% 9.61/2.16  ------ Schedule dynamic 5 is on 
% 9.61/2.16  
% 9.61/2.16  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 9.61/2.16  
% 9.61/2.16  
% 9.61/2.16  ------ 
% 9.61/2.16  Current options:
% 9.61/2.16  ------ 
% 9.61/2.16  
% 9.61/2.16  
% 9.61/2.16  
% 9.61/2.16  
% 9.61/2.16  ------ Proving...
% 9.61/2.16  
% 9.61/2.16  
% 9.61/2.16  % SZS status Theorem for theBenchmark.p
% 9.61/2.16  
% 9.61/2.16  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 9.61/2.16  
% 9.61/2.16  
%------------------------------------------------------------------------------