↑ Up

iProver---3.9.4.THM-CRf.s

View TPTP
Problem
Process solution in
SystemOnTSTP
Download .tgz
%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : SWC077+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM

% Computer : n011.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 03:07:47 PM UTC 2026

% Result   : Theorem 28.74s 4.71s
% Output   : CNFRefutation 28.74s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named f323ERROR: Could not build tree for root c_56800ERROR: MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
fof(f5,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( frontsegP(X0,X1)
          <=> ? [X2] :
                ( app(X1,X2) = X0
                & ssList(X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax5) ).

fof(f7,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( segmentP(X0,X1)
          <=> ? [X2] :
                ( ? [X3] :
                    ( app(app(X2,X1),X3) = X0
                    & ssList(X3) )
                & ssList(X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax7) ).

fof(f15,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( neq(X0,X1)
          <=> X0 != X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).

fof(f16,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ssList(cons(X1,X0)) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).

fof(f21,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => nil != cons(X1,X0) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).

fof(f26,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ssList(app(X0,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).

fof(f28,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(nil,X0) = X0 ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).

fof(f53,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ( ( segmentP(X1,X2)
                  & segmentP(X0,X1) )
               => segmentP(X0,X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax53) ).

fof(f55,axiom,
    ! [X0] :
      ( ssList(X0)
     => segmentP(X0,X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax55) ).

fof(f57,axiom,
    ! [X0] :
      ( ssList(X0)
     => segmentP(X0,nil) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax57) ).

fof(f68,axiom,
    ! [X0] :
      ( ssItem(X0)
     => strictorderedP(cons(X0,nil)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax68) ).

fof(f75,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ? [X1] :
            ( hd(X0) = X1
            & ssItem(X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax75) ).

fof(f76,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ? [X1] :
            ( tl(X0) = X1
            & ssList(X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax76) ).

fof(f78,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => cons(hd(X0),tl(X0)) = X0 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax78) ).

fof(f84,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(X0,nil) = X0 ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ( nil = X0
                      & nil = X1 )
                    | ? [X5] :
                        ( strictorderedP(X5)
                        & segmentP(X5,X2)
                        & frontsegP(X3,X5)
                        & neq(X2,X5)
                        & ssList(X5) )
                    | ? [X4] :
                        ( segmentP(X0,X4)
                        & segmentP(X1,X4)
                        & neq(X4,nil)
                        & ssList(X4) )
                    | ~ strictorderedP(X2)
                    | ~ frontsegP(X3,X2)
                    | X0 != X2
                    | X1 != X3 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( nil = X0
                        & nil = X1 )
                      | ? [X5] :
                          ( strictorderedP(X5)
                          & segmentP(X5,X2)
                          & frontsegP(X3,X5)
                          & neq(X2,X5)
                          & ssList(X5) )
                      | ? [X4] :
                          ( segmentP(X0,X4)
                          & segmentP(X1,X4)
                          & neq(X4,nil)
                          & ssList(X4) )
                      | ~ strictorderedP(X2)
                      | ~ frontsegP(X3,X2)
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(negated_conjecture,[status(cth)],[f96]) ).

fof(f98,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( ssList(X3)
                  & ( nil != X0
                    | nil != X1 )
                  & ! [X5] :
                      ( ~ strictorderedP(X5)
                      | ~ segmentP(X5,X2)
                      | ~ frontsegP(X3,X5)
                      | ~ neq(X2,X5)
                      | ~ ssList(X5) )
                  & ! [X4] :
                      ( ~ segmentP(X0,X4)
                      | ~ segmentP(X1,X4)
                      | ~ neq(X4,nil)
                      | ~ ssList(X4) )
                  & strictorderedP(X2)
                  & frontsegP(X3,X2)
                  & X0 = X2
                  & X1 = X3 ) ) ) ),
    inference(ennf_transformation,[],[f97]) ).

fof(f99,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( ssList(X3)
                  & ( nil != X0
                    | nil != X1 )
                  & ! [X5] :
                      ( ~ strictorderedP(X5)
                      | ~ segmentP(X5,X2)
                      | ~ frontsegP(X3,X5)
                      | ~ neq(X2,X5)
                      | ~ ssList(X5) )
                  & ! [X4] :
                      ( ~ segmentP(X0,X4)
                      | ~ segmentP(X1,X4)
                      | ~ neq(X4,nil)
                      | ~ ssList(X4) )
                  & strictorderedP(X2)
                  & frontsegP(X3,X2)
                  & X0 = X2
                  & X1 = X3 ) ) ) ),
    inference(flattening,[],[f98]) ).

fof(f100,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ( neq(X0,X1)
          <=> X0 != X1 ) ) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f102,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssItem(X1)
          | nil != cons(X1,X0) ) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f115,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ( frontsegP(X0,X1)
          <=> ? [X2] :
                ( app(X1,X2) = X0
                & ssList(X2) ) ) ) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f117,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | segmentP(X0,nil) ),
    inference(ennf_transformation,[],[f57]) ).

fof(f120,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | segmentP(X0,X0) ),
    inference(ennf_transformation,[],[f55]) ).

fof(f123,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ! [X2] :
              ( ~ ssList(X2)
              | ~ segmentP(X1,X2)
              | ~ segmentP(X0,X1)
              | segmentP(X0,X2) ) ) ),
    inference(ennf_transformation,[],[f53]) ).

fof(f124,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ! [X2] :
              ( ~ ssList(X2)
              | ~ segmentP(X1,X2)
              | ~ segmentP(X0,X1)
              | segmentP(X0,X2) ) ) ),
    inference(flattening,[],[f123]) ).

fof(f125,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ( segmentP(X0,X1)
          <=> ? [X2] :
                ( ? [X3] :
                    ( app(app(X2,X1),X3) = X0
                    & ssList(X3) )
                & ssList(X2) ) ) ) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f127,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | strictorderedP(cons(X0,nil)) ),
    inference(ennf_transformation,[],[f68]) ).

fof(f135,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssItem(X1)
          | ssList(cons(X1,X0)) ) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f136,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(X0,nil) = X0 ),
    inference(ennf_transformation,[],[f84]) ).

fof(f143,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(nil,X0) = X0 ),
    inference(ennf_transformation,[],[f28]) ).

fof(f144,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ssList(app(X0,X1)) ) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f147,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | nil = X0
      | cons(hd(X0),tl(X0)) = X0 ),
    inference(ennf_transformation,[],[f78]) ).

fof(f148,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | nil = X0
      | cons(hd(X0),tl(X0)) = X0 ),
    inference(flattening,[],[f147]) ).

fof(f151,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | nil = X0
      | ? [X1] :
          ( hd(X0) = X1
          & ssItem(X1) ) ),
    inference(ennf_transformation,[],[f75]) ).

fof(f152,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | nil = X0
      | ? [X1] :
          ( hd(X0) = X1
          & ssItem(X1) ) ),
    inference(flattening,[],[f151]) ).

fof(f168,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | nil = X0
      | ? [X1] :
          ( tl(X0) = X1
          & ssList(X1) ) ),
    inference(ennf_transformation,[],[f76]) ).

fof(f169,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | nil = X0
      | ? [X1] :
          ( tl(X0) = X1
          & ssList(X1) ) ),
    inference(flattening,[],[f168]) ).

fof(f178,plain,
    ( ssList(sK0)
    & ssList(sK1)
    & ssList(sK2)
    & ssList(sK3)
    & ( nil != sK0
      | nil != sK1 )
    & ! [X5] :
        ( ~ strictorderedP(X5)
        | ~ segmentP(X5,sK2)
        | ~ frontsegP(sK3,X5)
        | ~ neq(sK2,X5)
        | ~ ssList(X5) )
    & ! [X4] :
        ( ~ segmentP(sK0,X4)
        | ~ segmentP(sK1,X4)
        | ~ neq(X4,nil)
        | ~ ssList(X4) )
    & strictorderedP(sK2)
    & frontsegP(sK3,sK2)
    & sK0 = sK2
    & sK1 = sK3 ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f99]) ).

fof(f180,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ( ( ~ neq(X0,X1)
              | X0 != X1 )
            & ( X0 = X1
              | neq(X0,X1) ) ) ) ),
    inference(nnf_transformation,[],[f100]) ).

fof(f186,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ( ( ~ frontsegP(X0,X1)
              | ? [X2] :
                  ( app(X1,X2) = X0
                  & ssList(X2) ) )
            & ( ! [X2] :
                  ( app(X1,X2) != X0
                  | ~ ssList(X2) )
              | frontsegP(X0,X1) ) ) ) ),
    inference(nnf_transformation,[],[f115]) ).

fof(f187,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ( ( ~ frontsegP(X0,X1)
              | ? [X3] :
                  ( app(X1,X3) = X0
                  & ssList(X3) ) )
            & ( ! [X2] :
                  ( app(X1,X2) != X0
                  | ~ ssList(X2) )
              | frontsegP(X0,X1) ) ) ) ),
    inference(rectify,[],[f186]) ).

fof(f188,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ( ( ~ frontsegP(X0,X1)
              | ( app(X1,sK8(X0,X1)) = X0
                & ssList(sK8(X0,X1)) ) )
            & ( ! [X2] :
                  ( app(X1,X2) != X0
                  | ~ ssList(X2) )
              | frontsegP(X0,X1) ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X3,sK8(X0,X1))],[f187]) ).

fof(f190,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ( ( ~ segmentP(X0,X1)
              | ? [X2] :
                  ( ? [X3] :
                      ( app(app(X2,X1),X3) = X0
                      & ssList(X3) )
                  & ssList(X2) ) )
            & ( ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) )
              | segmentP(X0,X1) ) ) ) ),
    inference(nnf_transformation,[],[f125]) ).

fof(f191,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ( ( ~ segmentP(X0,X1)
              | ? [X4] :
                  ( ? [X5] :
                      ( app(app(X4,X1),X5) = X0
                      & ssList(X5) )
                  & ssList(X4) ) )
            & ( ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) )
              | segmentP(X0,X1) ) ) ) ),
    inference(rectify,[],[f190]) ).

fof(f192,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ( ( ~ segmentP(X0,X1)
              | ( app(app(sK9(X0,X1),X1),sK10(X0,X1)) = X0
                & ssList(sK10(X0,X1))
                & ssList(sK9(X0,X1)) ) )
            & ( ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) )
              | segmentP(X0,X1) ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X4,sK9(X0,X1)),skolemize(X5,sK10(X0,X1))],[f191]) ).

fof(f200,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | nil = X0
      | ( hd(X0) = sK16(X0)
        & ssItem(sK16(X0)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X1,sK16(X0))],[f152]) ).

fof(f203,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | nil = X0
      | ( tl(X0) = sK17(X0)
        & ssList(sK17(X0)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(X1,sK17(X0))],[f169]) ).

fof(f204,plain,
    ssList(sK0),
    inference(cnf_transformation,[],[f178]) ).

fof(f205,plain,
    ssList(sK1),
    inference(cnf_transformation,[],[f178]) ).

fof(f208,plain,
    ( nil != sK0
    | nil != sK1 ),
    inference(cnf_transformation,[],[f178]) ).

fof(f209,plain,
    ! [X5] :
      ( ~ strictorderedP(X5)
      | ~ segmentP(X5,sK2)
      | ~ frontsegP(sK3,X5)
      | ~ neq(sK2,X5)
      | ~ ssList(X5) ),
    inference(cnf_transformation,[],[f178]) ).

fof(f210,plain,
    ! [X4] :
      ( ~ segmentP(sK0,X4)
      | ~ segmentP(sK1,X4)
      | ~ neq(X4,nil)
      | ~ ssList(X4) ),
    inference(cnf_transformation,[],[f178]) ).

fof(f212,plain,
    frontsegP(sK3,sK2),
    inference(cnf_transformation,[],[f178]) ).

fof(f213,plain,
    sK0 = sK2,
    inference(cnf_transformation,[],[f178]) ).

fof(f214,plain,
    sK1 = sK3,
    inference(cnf_transformation,[],[f178]) ).

fof(f219,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | X0 = X1
      | neq(X0,X1) ),
    inference(cnf_transformation,[],[f180]) ).

fof(f222,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssItem(X1)
      | nil != cons(X1,X0) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f226,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f237,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | ~ frontsegP(X0,X1)
      | app(X1,sK8(X0,X1)) = X0 ),
    inference(cnf_transformation,[],[f188]) ).

fof(f238,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | ~ frontsegP(X0,X1)
      | ssList(sK8(X0,X1)) ),
    inference(cnf_transformation,[],[f188]) ).

fof(f239,plain,
    ! [X2,X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | app(X1,X2) != X0
      | ~ ssList(X2)
      | frontsegP(X0,X1) ),
    inference(cnf_transformation,[],[f188]) ).

fof(f242,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | segmentP(X0,nil) ),
    inference(cnf_transformation,[],[f117]) ).

fof(f244,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | segmentP(X0,X0) ),
    inference(cnf_transformation,[],[f120]) ).

fof(f246,plain,
    ! [X2,X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | ~ ssList(X2)
      | ~ segmentP(X1,X2)
      | ~ segmentP(X0,X1)
      | segmentP(X0,X2) ),
    inference(cnf_transformation,[],[f124]) ).

fof(f250,plain,
    ! [X2,X3,X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | app(app(X2,X1),X3) != X0
      | ~ ssList(X3)
      | ~ ssList(X2)
      | segmentP(X0,X1) ),
    inference(cnf_transformation,[],[f192]) ).

fof(f257,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | strictorderedP(cons(X0,nil)) ),
    inference(cnf_transformation,[],[f127]) ).

fof(f271,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssItem(X1)
      | ssList(cons(X1,X0)) ),
    inference(cnf_transformation,[],[f135]) ).

fof(f272,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(X0,nil) = X0 ),
    inference(cnf_transformation,[],[f136]) ).

fof(f279,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(nil,X0) = X0 ),
    inference(cnf_transformation,[],[f143]) ).

fof(f280,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | ssList(app(X0,X1)) ),
    inference(cnf_transformation,[],[f144]) ).

fof(f282,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | nil = X0
      | cons(hd(X0),tl(X0)) = X0 ),
    inference(cnf_transformation,[],[f148]) ).

fof(f284,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | nil = X0
      | hd(X0) = sK16(X0) ),
    inference(cnf_transformation,[],[f200]) ).

fof(f285,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | nil = X0
      | ssItem(sK16(X0)) ),
    inference(cnf_transformation,[],[f200]) ).

fof(f297,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | nil = X0
      | tl(X0) = sK17(X0) ),
    inference(cnf_transformation,[],[f203]) ).

fof(f298,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | nil = X0
      | ssList(sK17(X0)) ),
    inference(cnf_transformation,[],[f203]) ).

fof(f304,plain,
    ! [X4] :
      ( ~ segmentP(sK2,X4)
      | ~ segmentP(sK3,X4)
      | ~ neq(X4,nil)
      | ~ ssList(X4) ),
    inference(definition_unfolding,[],[f210,f214,f213]) ).

fof(f305,plain,
    ( nil != sK2
    | nil != sK3 ),
    inference(definition_unfolding,[],[f208,f214,f213]) ).

fof(f306,plain,
    ssList(sK3),
    inference(definition_unfolding,[],[f205,f214]) ).

fof(f307,plain,
    ssList(sK2),
    inference(definition_unfolding,[],[f204,f213]) ).

fof(f312,plain,
    ! [X2,X1] :
      ( ~ ssList(app(X1,X2))
      | ~ ssList(X1)
      | ~ ssList(X2)
      | frontsegP(app(X1,X2),X1) ),
    inference(equality_resolution,[],[f239]) ).

fof(f314,plain,
    ! [X2,X3,X1] :
      ( ~ ssList(app(app(X2,X1),X3))
      | ~ ssList(X1)
      | ~ ssList(X3)
      | ~ ssList(X2)
      | segmentP(app(app(X2,X1),X3),X1) ),
    inference(equality_resolution,[],[f250]) ).

tcf(c_49,negated_conjecture,
    frontsegP(sK3,sK2),
    inference(cnf_transformation,[],[f212]) ).

tcf(c_51,negated_conjecture,
    ! [X0: $i] :
      ( ~ ssList(X0)
      | ~ segmentP(sK2,X0)
      | ~ segmentP(sK3,X0)
      | ~ neq(X0,nil) ),
    inference(cnf_transformation,[],[f304]) ).

tcf(c_52,negated_conjecture,
    ! [X0: $i] :
      ( ~ ssList(X0)
      | ~ strictorderedP(X0)
      | ~ segmentP(X0,sK2)
      | ~ neq(sK2,X0)
      | ~ frontsegP(sK3,X0) ),
    inference(cnf_transformation,[],[f209]) ).

tcf(c_53,negated_conjecture,
    ( ( sK2 != nil )
    | ( sK3 != nil ) ),
    inference(cnf_transformation,[],[f305]) ).

tcf(c_56,negated_conjecture,
    ssList(sK3),
    inference(cnf_transformation,[],[f306]) ).

tcf(c_57,negated_conjecture,
    ssList(sK2),
    inference(cnf_transformation,[],[f307]) ).

tcf(c_61,plain,
    ! [X0: $i,X1: $i] :
      ( neq(X0,X1)
      | ( X0 = X1 )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f219]) ).

tcf(c_65,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | ( cons(X0,X1) != nil ) ),
    inference(cnf_transformation,[],[f222]) ).

tcf(c_69,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f226]) ).

tcf(c_73,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( frontsegP(cons(X2,X0),cons(X2,X1))
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ frontsegP(X0,X1) ),
    inference(cnf_transformation,[],[f323]) ).

tcf(c_80,plain,
    ! [X0: $i,X1: $i] :
      ( frontsegP(app(X0,X1),X0)
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ ssList(app(X0,X1)) ),
    inference(cnf_transformation,[],[f312]) ).

tcf(c_81,plain,
    ! [X0: $i,X1: $i] :
      ( ssList(sK8(X0,X1))
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ frontsegP(X0,X1) ),
    inference(cnf_transformation,[],[f238]) ).

tcf(c_82,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(X1,sK8(X0,X1)) = X0 )
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ frontsegP(X0,X1) ),
    inference(cnf_transformation,[],[f237]) ).

tcf(c_85,plain,
    ! [X0: $i] :
      ( segmentP(X0,nil)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f242]) ).

tcf(c_87,plain,
    ! [X0: $i] :
      ( segmentP(X0,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f244]) ).

tcf(c_89,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( segmentP(X0,X2)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ segmentP(X1,X2)
      | ~ segmentP(X0,X1) ),
    inference(cnf_transformation,[],[f246]) ).

tcf(c_90,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( segmentP(app(app(X0,X1),X2),X1)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ ssList(app(app(X0,X1),X2)) ),
    inference(cnf_transformation,[],[f314]) ).

tcf(c_99,plain,
    ! [X0: $i] :
      ( strictorderedP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f257]) ).

tcf(c_113,plain,
    ! [X0: $i,X1: $i] :
      ( ssList(cons(X1,X0))
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f271]) ).

tcf(c_114,plain,
    ! [X0: $i] :
      ( ( app(X0,nil) = X0 )
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f272]) ).

tcf(c_121,plain,
    ! [X0: $i] :
      ( ( app(nil,X0) = X0 )
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f279]) ).

tcf(c_122,plain,
    ! [X0: $i,X1: $i] :
      ( ssList(app(X0,X1))
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f280]) ).

tcf(c_124,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( cons(hd(X0),tl(X0)) = X0 )
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f282]) ).

tcf(c_126,plain,
    ! [X0: $i] :
      ( ssItem(sK16(X0))
      | ( X0 = nil )
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f285]) ).

tcf(c_127,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( hd(X0) = sK16(X0) )
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f284]) ).

tcf(c_139,plain,
    ! [X0: $i] :
      ( ssList(sK17(X0))
      | ( X0 = nil )
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f298]) ).

tcf(c_140,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ( tl(X0) = sK17(X0) )
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f297]) ).

tcf(c_206,plain,
    ! [X0: $i,X1: $i] :
      ( frontsegP(app(X0,X1),X0)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(global_subsumption_just,[status(thm)],[c_80,c_122,c_80]) ).

tcf(c_1506,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = X2 )
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ segmentP(sK2,X0)
      | ~ segmentP(sK3,X0)
      | ( X2 != nil )
      | ( X0 != X1 ) ),
    inference(resolution_lifted,[status(thm)],[c_51,c_61]) ).

tcf(c_1507,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ segmentP(sK2,X0)
      | ~ segmentP(sK3,X0) ),
    inference(unflattening,[status(thm)],[c_1506]) ).

tcf(c_1509,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ segmentP(sK3,X0)
      | ~ segmentP(sK2,X0)
      | ~ ssList(X0) ),
    inference(global_subsumption_just,[status(thm)],[c_1507,c_69,c_1507]) ).

tcf(c_1510,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ segmentP(sK2,X0)
      | ~ segmentP(sK3,X0) ),
    inference(renaming,[status(thm)],[c_1509]) ).

tcf(c_1547,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = X2 )
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ strictorderedP(X0)
      | ~ segmentP(X0,sK2)
      | ~ frontsegP(sK3,X0)
      | ( X2 != sK2 )
      | ( X0 != X1 ) ),
    inference(resolution_lifted,[status(thm)],[c_52,c_61]) ).

tcf(c_1548,plain,
    ! [X0: $i] :
      ( ( X0 = sK2 )
      | ~ ssList(sK2)
      | ~ ssList(X0)
      | ~ strictorderedP(X0)
      | ~ segmentP(X0,sK2)
      | ~ frontsegP(sK3,X0) ),
    inference(unflattening,[status(thm)],[c_1547]) ).

tcf(c_1550,plain,
    ! [X0: $i] :
      ( ( X0 = sK2 )
      | ~ frontsegP(sK3,X0)
      | ~ segmentP(X0,sK2)
      | ~ strictorderedP(X0)
      | ~ ssList(X0) ),
    inference(global_subsumption_just,[status(thm)],[c_1548,c_57,c_1548]) ).

tcf(c_1551,plain,
    ! [X0: $i] :
      ( ( X0 = sK2 )
      | ~ ssList(X0)
      | ~ strictorderedP(X0)
      | ~ segmentP(X0,sK2)
      | ~ frontsegP(sK3,X0) ),
    inference(renaming,[status(thm)],[c_1550]) ).

tcf(c_4313,plain,
    app(sK2,nil) = sK2,
    inference(superposition,[status(thm)],[c_57,c_114]) ).

tcf(c_4336,plain,
    app(nil,sK2) = sK2,
    inference(superposition,[status(thm)],[c_57,c_121]) ).

tcf(c_4548,plain,
    ( ( sK3 = nil )
    | ( hd(sK3) = sK16(sK3) ) ),
    inference(superposition,[status(thm)],[c_56,c_127]) ).

tcf(c_4600,plain,
    ( ssItem(hd(sK3))
    | ( sK3 = nil )
    | ~ ssList(sK3) ),
    inference(superposition,[status(thm)],[c_4548,c_126]) ).

tcf(c_4601,plain,
    ( ssItem(hd(sK3))
    | ( sK3 = nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_4600,c_56]) ).

tcf(c_4746,plain,
    ( ( sK3 = nil )
    | ( tl(sK3) = sK17(sK3) ) ),
    inference(superposition,[status(thm)],[c_56,c_140]) ).

tcf(c_4854,plain,
    ( ( sK2 = nil )
    | ~ ssList(sK2)
    | ~ segmentP(sK2,sK2)
    | ~ segmentP(sK3,sK2) ),
    inference(instantiation,[status(thm)],[c_1510]) ).

tcf(c_4895,plain,
    ( segmentP(sK2,sK2)
    | ~ ssList(sK2) ),
    inference(instantiation,[status(thm)],[c_87]) ).

tcf(c_4945,plain,
    ( ssList(tl(sK3))
    | ( sK3 = nil )
    | ~ ssList(sK3) ),
    inference(superposition,[status(thm)],[c_4746,c_139]) ).

tcf(c_4946,plain,
    ( ssList(tl(sK3))
    | ( sK3 = nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_4945,c_56]) ).

tcf(c_4959,plain,
    ( ( sK3 = nil )
    | ( app(nil,tl(sK3)) = tl(sK3) ) ),
    inference(superposition,[status(thm)],[c_4946,c_121]) ).

tcf(c_5366,plain,
    ( frontsegP(tl(sK3),nil)
    | ( sK3 = nil )
    | ~ ssList(nil)
    | ~ ssList(tl(sK3)) ),
    inference(superposition,[status(thm)],[c_4959,c_206]) ).

tcf(c_5367,plain,
    ( frontsegP(tl(sK3),nil)
    | ( sK3 = nil )
    | ~ ssList(tl(sK3)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5366,c_69]) ).

tcf(c_6509,plain,
    ( ( app(sK2,sK8(sK3,sK2)) = sK3 )
    | ~ ssList(sK2)
    | ~ ssList(sK3) ),
    inference(superposition,[status(thm)],[c_49,c_82]) ).

tcf(c_6530,plain,
    app(sK2,sK8(sK3,sK2)) = sK3,
    inference(forward_subsumption_resolution,[status(thm)],[c_6509,c_57,c_56]) ).

tcf(c_8792,plain,
    ( ( sK2 = nil )
    | ( tl(sK2) = sK17(sK2) ) ),
    inference(superposition,[status(thm)],[c_57,c_140]) ).

tcf(c_10299,plain,
    ! [X0: $i] :
      ( segmentP(app(sK2,X0),sK2)
      | ~ ssList(nil)
      | ~ ssList(sK2)
      | ~ ssList(X0)
      | ~ ssList(app(app(nil,sK2),X0)) ),
    inference(superposition,[status(thm)],[c_4336,c_90]) ).

tcf(c_10327,plain,
    ! [X0: $i] :
      ( segmentP(app(sK2,X0),sK2)
      | ~ ssList(nil)
      | ~ ssList(sK2)
      | ~ ssList(X0)
      | ~ ssList(app(sK2,X0)) ),
    inference(light_normalisation,[status(thm)],[c_10299,c_4336]) ).

tcf(c_10328,plain,
    ! [X0: $i] :
      ( segmentP(app(sK2,X0),sK2)
      | ~ ssList(X0)
      | ~ ssList(app(sK2,X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_10327,c_69,c_57]) ).

tcf(c_10543,plain,
    ! [X0: $i] :
      ( ~ ssList(X0)
      | ~ ssItem(hd(sK3))
      | ( cons(hd(sK3),X0) != nil ) ),
    inference(instantiation,[status(thm)],[c_65]) ).

tcf(c_10544,plain,
    ( strictorderedP(cons(hd(sK3),nil))
    | ~ ssItem(hd(sK3)) ),
    inference(instantiation,[status(thm)],[c_99]) ).

tcf(c_10545,plain,
    ( ~ ssList(nil)
    | ~ ssItem(hd(sK3))
    | ( cons(hd(sK3),nil) != nil ) ),
    inference(instantiation,[status(thm)],[c_10543]) ).

tcf(c_10560,plain,
    ! [X0: $i] :
      ( ssList(cons(hd(sK3),X0))
      | ~ ssList(X0)
      | ~ ssItem(hd(sK3)) ),
    inference(instantiation,[status(thm)],[c_113]) ).

tcf(c_10561,plain,
    ( ssList(cons(hd(sK3),nil))
    | ~ ssList(nil)
    | ~ ssItem(hd(sK3)) ),
    inference(instantiation,[status(thm)],[c_10560]) ).

tcf(c_10702,plain,
    ( ssList(tl(sK2))
    | ( sK2 = nil )
    | ~ ssList(sK2) ),
    inference(superposition,[status(thm)],[c_8792,c_139]) ).

tcf(c_10703,plain,
    ( ssList(tl(sK2))
    | ( sK2 = nil ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_10702,c_57]) ).

tcf(c_10716,plain,
    ( ( sK2 = nil )
    | ( app(nil,tl(sK2)) = tl(sK2) ) ),
    inference(superposition,[status(thm)],[c_10703,c_121]) ).

tcf(c_10752,plain,
    ( segmentP(sK2,sK2)
    | ~ ssList(nil)
    | ~ ssList(app(sK2,nil)) ),
    inference(superposition,[status(thm)],[c_4313,c_10328]) ).

tcf(c_10753,plain,
    ( segmentP(sK3,sK2)
    | ~ ssList(sK8(sK3,sK2))
    | ~ ssList(app(sK2,sK8(sK3,sK2))) ),
    inference(superposition,[status(thm)],[c_6530,c_10328]) ).

tcf(c_10759,plain,
    ( segmentP(sK2,sK2)
    | ~ ssList(nil)
    | ~ ssList(sK2) ),
    inference(light_normalisation,[status(thm)],[c_10752,c_4313]) ).

tcf(c_10760,plain,
    segmentP(sK2,sK2),
    inference(forward_subsumption_resolution,[status(thm)],[c_10759,c_69,c_57]) ).

tcf(c_10761,plain,
    ( segmentP(sK3,sK2)
    | ~ ssList(sK3)
    | ~ ssList(sK8(sK3,sK2)) ),
    inference(light_normalisation,[status(thm)],[c_10753,c_6530]) ).

tcf(c_10762,plain,
    ( segmentP(sK3,sK2)
    | ~ ssList(sK8(sK3,sK2)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_10761,c_56]) ).

tcf(c_10795,plain,
    ( segmentP(sK3,sK2)
    | ~ ssList(sK2)
    | ~ ssList(sK3)
    | ~ frontsegP(sK3,sK2) ),
    inference(superposition,[status(thm)],[c_81,c_10762]) ).

tcf(c_10796,plain,
    segmentP(sK3,sK2),
    inference(forward_subsumption_resolution,[status(thm)],[c_10795,c_57,c_56,c_49]) ).

tcf(c_10797,plain,
    ( ( sK2 = nil )
    | ~ ssList(sK2)
    | ~ segmentP(sK2,sK2) ),
    inference(superposition,[status(thm)],[c_10796,c_1510]) ).

tcf(c_10800,plain,
    ! [X0: $i] :
      ( segmentP(sK3,X0)
      | ~ ssList(sK2)
      | ~ ssList(sK3)
      | ~ ssList(X0)
      | ~ segmentP(sK2,X0) ),
    inference(superposition,[status(thm)],[c_10796,c_89]) ).

tcf(c_10802,plain,
    sK2 = nil,
    inference(forward_subsumption_resolution,[status(thm)],[c_10797,c_57,c_10760]) ).

tcf(c_10809,plain,
    ! [X0: $i] :
      ( segmentP(sK3,X0)
      | ~ ssList(X0)
      | ~ segmentP(sK2,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_10800,c_57,c_56]) ).

tcf(c_10859,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ strictorderedP(X0)
      | ~ segmentP(X0,nil)
      | ~ frontsegP(sK3,X0) ),
    inference(demodulation,[status(thm)],[c_1551,c_10802]) ).

tcf(c_13219,plain,
    sK2 = nil,
    inference(global_subsumption_just,[status(thm)],[c_10716,c_57,c_4854,c_4895,c_10796]) ).

tcf(c_13236,plain,
    ( ( nil != nil )
    | ( sK3 != nil ) ),
    inference(demodulation,[status(thm)],[c_53,c_13219]) ).

tcf(c_13242,plain,
    sK3 != nil,
    inference(equality_resolution_simp,[status(thm)],[c_13236]) ).

tcf(c_43280,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ segmentP(sK2,X0) ),
    inference(global_subsumption_just,[status(thm)],[c_1510,c_69,c_1507,c_10809]) ).

tcf(c_43330,plain,
    ( ( sK2 = nil )
    | ~ ssList(sK2) ),
    inference(superposition,[status(thm)],[c_87,c_43280]) ).

tcf(c_43332,plain,
    sK2 = nil,
    inference(forward_subsumption_resolution,[status(thm)],[c_43330,c_57]) ).

tcf(c_43333,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ strictorderedP(X0)
      | ~ segmentP(X0,nil)
      | ~ frontsegP(sK3,X0) ),
    inference(demodulation,[status(thm)],[c_1551,c_43332]) ).

tcf(c_43343,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ strictorderedP(X0)
      | ~ frontsegP(sK3,X0) ),
    inference(global_subsumption_just,[status(thm)],[c_43333,c_85,c_10859]) ).

tcf(c_44161,plain,
    ( ( sK3 = nil )
    | ( hd(sK3) = sK16(sK3) ) ),
    inference(superposition,[status(thm)],[c_56,c_127]) ).

tcf(c_44171,plain,
    hd(sK3) = sK16(sK3),
    inference(forward_subsumption_resolution,[status(thm)],[c_44161,c_13242]) ).

tcf(c_44262,plain,
    ( ( sK3 = nil )
    | ( tl(sK3) = sK17(sK3) ) ),
    inference(superposition,[status(thm)],[c_56,c_140]) ).

tcf(c_44272,plain,
    tl(sK3) = sK17(sK3),
    inference(forward_subsumption_resolution,[status(thm)],[c_44262,c_13242]) ).

tcf(c_44592,plain,
    ( ssItem(hd(sK3))
    | ( sK3 = nil )
    | ~ ssList(sK3) ),
    inference(superposition,[status(thm)],[c_44171,c_126]) ).

tcf(c_44593,plain,
    ssItem(hd(sK3)),
    inference(forward_subsumption_resolution,[status(thm)],[c_44592,c_13242,c_56]) ).

tcf(c_44597,plain,
    ( ssList(tl(sK3))
    | ( sK3 = nil )
    | ~ ssList(sK3) ),
    inference(superposition,[status(thm)],[c_44272,c_139]) ).

tcf(c_44598,plain,
    ssList(tl(sK3)),
    inference(forward_subsumption_resolution,[status(thm)],[c_44597,c_13242,c_56]) ).

tcf(c_45325,plain,
    ( ( sK3 = nil )
    | ( cons(hd(sK3),tl(sK3)) = sK3 ) ),
    inference(superposition,[status(thm)],[c_56,c_124]) ).

tcf(c_45339,plain,
    cons(hd(sK3),tl(sK3)) = sK3,
    inference(forward_subsumption_resolution,[status(thm)],[c_45325,c_13242]) ).

tcf(c_46661,plain,
    ! [X0: $i] :
      ( frontsegP(sK3,cons(hd(sK3),X0))
      | ~ ssList(X0)
      | ~ ssItem(hd(sK3))
      | ~ ssList(tl(sK3))
      | ~ frontsegP(tl(sK3),X0) ),
    inference(superposition,[status(thm)],[c_45339,c_73]) ).

tcf(c_46678,plain,
    ! [X0: $i] :
      ( frontsegP(sK3,cons(hd(sK3),X0))
      | ~ ssList(X0)
      | ~ frontsegP(tl(sK3),X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_46661,c_44593,c_44598]) ).

tcf(c_56769,plain,
    ! [X0: $i] :
      ( ( cons(hd(sK3),X0) = nil )
      | ~ ssList(X0)
      | ~ frontsegP(tl(sK3),X0)
      | ~ ssList(cons(hd(sK3),X0))
      | ~ strictorderedP(cons(hd(sK3),X0)) ),
    inference(superposition,[status(thm)],[c_46678,c_43343]) ).

tcf(c_56799,plain,
    ( ( cons(hd(sK3),nil) = nil )
    | ~ ssList(nil)
    | ~ frontsegP(tl(sK3),nil)
    | ~ ssList(cons(hd(sK3),nil))
    | ~ strictorderedP(cons(hd(sK3),nil)) ),
    inference(instantiation,[status(thm)],[c_56769]) ).

tcf(c_56800,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_56799,c_10796,c_10561,c_10545,c_10544,c_5367,c_4946,c_4895,c_4854,c_4601,c_53,c_69,c_57]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWC077+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37  % Computer : n011.cluster.edu
% 0.09/0.37  % Model    : x86_64 x86_64
% 0.09/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37  % Memory   : 8046.5625MB
% 0.09/0.37  % OS       : Linux 6.8.0-71-generic
% 0.09/0.38  % CPULimit : 300
% 0.09/0.38  % WCLimit  : 300
% 0.09/0.38  % DateTime : Thu Sep 24 16:15:43 UTC 2026
% 0.09/0.38  % CPUTime  : 
% 0.09/0.38  Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.42  Running first-order theorem proving
% 0.09/0.42  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
% 0.09/0.43  
% 0.09/0.43  % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.43  
% 0.09/0.43  % Detected problem language: tptp
% 0.09/0.44  % Proving...
% 28.74/4.71  % SZS status Started for theBenchmark.p
% 28.74/4.71  % SZS status Theorem for theBenchmark.p
% 28.74/4.71  
% 28.74/4.71  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 28.74/4.71  
% 28.74/4.71  % ------  iProver source info
% 28.74/4.71  
% 28.74/4.71  % git: date: 2026-07-19 20:42:38 +0200
% 28.74/4.71  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 28.74/4.71  % git: non_committed_changes: false
% 28.74/4.71  
% 28.74/4.71  % ------ Parsing...
% 28.74/4.71  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 28.74/4.71  
% 28.74/4.71  % ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e % 
% 28.74/4.71  
% 28.74/4.71  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 28.74/4.71  
% 28.74/4.71  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 28.74/4.71  % ------ Proving...
% 28.74/4.71  % ------ Problem Properties 
% 28.74/4.71  
% 28.74/4.71  % 
% 28.74/4.71  % clauses                               88
% 28.74/4.71  % conjectures                           5
% 28.74/4.71  % EPR                                   33
% 28.74/4.71  % Horn                                  65
% 28.74/4.71  % unary                                 12
% 28.74/4.71  % binary                                10
% 28.74/4.71  % lits                                  310
% 28.74/4.71  % lits eq                               63
% 28.74/4.71  % fd_pure                               0
% 28.74/4.71  % fd_pseudo                             0
% 28.74/4.71  % fd_cond                               19
% 28.74/4.71  % fd_pseudo_cond                        10
% 28.74/4.71  % AC symbols                            0
% 28.74/4.71  
% 28.74/4.71  % ------ Schedule dynamic 5 is on 
% 28.74/4.71  
% 28.74/4.71  % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 28.74/4.71  
% 28.74/4.71  
% 28.74/4.71  % ------ 
% 28.74/4.71  % Current options:
% 28.74/4.71  % ------ 
% 28.74/4.71  
% 28.74/4.71  
% 28.74/4.71  % 
% 28.74/4.71  
% 28.74/4.71  % ------ Proving...
% 28.74/4.71  % 
% 28.74/4.71  
% 28.74/4.71  % SZS status Theorem for theBenchmark.p
% 28.74/4.71  
% 28.74/4.71  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 28.74/4.71  
% 28.74/4.71  
%------------------------------------------------------------------------------