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iProver---3.9.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : SWC108+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 : n016.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 03:07:55 PM UTC 2026

% Result   : Theorem 10.70s 12.42s
% Output   : CNFRefutation 10.70s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named f231ERROR: Could not build tree for root c_14044ERROR: MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
fof(f6,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( rearsegP(X0,X1)
          <=> ? [X2] :
                ( app(X2,X1) = X0
                & ssList(X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax6) ).

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

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

fof(f48,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( ( rearsegP(X1,X0)
              & rearsegP(X0,X1) )
           => X0 = X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax48) ).

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)
                 => ( ( ( ~ rearsegP(X3,X2)
                        | ~ neq(X2,nil) )
                      & ( nil != X2
                        | nil != X3 ) )
                    | ( ( ( segmentP(X1,X0)
                          & neq(X0,nil) )
                        | ~ neq(X1,nil) )
                      & ( nil = X0
                        | nil != X1 ) )
                    | 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)
                   => ( ( ( ~ rearsegP(X3,X2)
                          | ~ neq(X2,nil) )
                        & ( nil != X2
                          | nil != X3 ) )
                      | ( ( ( segmentP(X1,X0)
                            & neq(X0,nil) )
                          | ~ neq(X1,nil) )
                        & ( nil = X0
                          | nil != X1 ) )
                      | 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)
                  & ( ( rearsegP(X3,X2)
                      & neq(X2,nil) )
                    | ( nil = X2
                      & nil = X3 ) )
                  & ( ( ( ~ segmentP(X1,X0)
                        | ~ neq(X0,nil) )
                      & neq(X1,nil) )
                    | ( nil != X0
                      & nil = X1 ) )
                  & X0 = X2
                  & X1 = X3 ) ) ) ),
    inference(ennf_transformation,[],[f97]) ).

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

fof(f110,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ~ rearsegP(X1,X0)
          | ~ rearsegP(X0,X1)
          | X0 = X1 ) ),
    inference(ennf_transformation,[],[f48]) ).

fof(f111,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ~ rearsegP(X1,X0)
          | ~ rearsegP(X0,X1)
          | X0 = X1 ) ),
    inference(flattening,[],[f110]) ).

fof(f114,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ( rearsegP(X0,X1)
          <=> ? [X2] :
                ( app(X2,X1) = X0
                & ssList(X2) ) ) ) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f124,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(f131,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(X0,nil) = X0 ),
    inference(ennf_transformation,[],[f84]) ).

fof(f139,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ssList(app(X0,X1)) ) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f140,plain,
    ( ssList(sK0)
    & ssList(sK1)
    & ssList(sK2)
    & ssList(sK3)
    & ( ( rearsegP(sK3,sK2)
        & neq(sK2,nil) )
      | ( nil = sK2
        & nil = sK3 ) )
    & ( ( ( ~ segmentP(sK1,sK0)
          | ~ neq(sK0,nil) )
        & neq(sK1,nil) )
      | ( nil != sK0
        & nil = sK1 ) )
    & 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(f146,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ( ( ~ rearsegP(X0,X1)
              | ? [X2] :
                  ( app(X2,X1) = X0
                  & ssList(X2) ) )
            & ( ! [X2] :
                  ( app(X2,X1) != X0
                  | ~ ssList(X2) )
              | rearsegP(X0,X1) ) ) ) ),
    inference(nnf_transformation,[],[f114]) ).

fof(f147,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ( ( ~ rearsegP(X0,X1)
              | ? [X3] :
                  ( app(X3,X1) = X0
                  & ssList(X3) ) )
            & ( ! [X2] :
                  ( app(X2,X1) != X0
                  | ~ ssList(X2) )
              | rearsegP(X0,X1) ) ) ) ),
    inference(rectify,[],[f146]) ).

fof(f148,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ( ( ~ rearsegP(X0,X1)
              | ( app(sK8(X0,X1),X1) = X0
                & ssList(sK8(X0,X1)) ) )
            & ( ! [X2] :
                  ( app(X2,X1) != X0
                  | ~ ssList(X2) )
              | rearsegP(X0,X1) ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X3,sK8(X0,X1))],[f147]) ).

fof(f150,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,[],[f124]) ).

fof(f151,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,[],[f150]) ).

fof(f152,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))],[f151]) ).

fof(f155,plain,
    ssList(sK0),
    inference(cnf_transformation,[],[f140]) ).

fof(f156,plain,
    ssList(sK1),
    inference(cnf_transformation,[],[f140]) ).

fof(f159,plain,
    ( rearsegP(sK3,sK2)
    | nil = sK2 ),
    inference(cnf_transformation,[],[f140]) ).

fof(f160,plain,
    ( neq(sK2,nil)
    | nil = sK2 ),
    inference(cnf_transformation,[],[f140]) ).

fof(f161,plain,
    ( rearsegP(sK3,sK2)
    | nil = sK3 ),
    inference(cnf_transformation,[],[f140]) ).

fof(f162,plain,
    ( neq(sK2,nil)
    | nil = sK3 ),
    inference(cnf_transformation,[],[f140]) ).

fof(f164,plain,
    ( neq(sK1,nil)
    | nil != sK0 ),
    inference(cnf_transformation,[],[f140]) ).

fof(f165,plain,
    ( ~ segmentP(sK1,sK0)
    | ~ neq(sK0,nil)
    | nil = sK1 ),
    inference(cnf_transformation,[],[f140]) ).

fof(f167,plain,
    sK0 = sK2,
    inference(cnf_transformation,[],[f140]) ).

fof(f168,plain,
    sK1 = sK3,
    inference(cnf_transformation,[],[f140]) ).

fof(f180,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f186,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | ~ rearsegP(X1,X0)
      | ~ rearsegP(X0,X1)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f111]) ).

fof(f188,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | ~ rearsegP(X0,X1)
      | app(sK8(X0,X1),X1) = X0 ),
    inference(cnf_transformation,[],[f148]) ).

fof(f189,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | ~ rearsegP(X0,X1)
      | ssList(sK8(X0,X1)) ),
    inference(cnf_transformation,[],[f148]) ).

fof(f190,plain,
    ! [X2,X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | app(X2,X1) != X0
      | ~ ssList(X2)
      | rearsegP(X0,X1) ),
    inference(cnf_transformation,[],[f148]) ).

fof(f201,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,[],[f152]) ).

fof(f208,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(X0,nil) = X0 ),
    inference(cnf_transformation,[],[f131]) ).

fof(f216,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | ssList(app(X0,X1)) ),
    inference(cnf_transformation,[],[f139]) ).

fof(f218,plain,
    ( ~ segmentP(sK3,sK2)
    | ~ neq(sK2,nil)
    | nil = sK3 ),
    inference(definition_unfolding,[],[f165,f168,f167,f168,f167]) ).

fof(f219,plain,
    ( neq(sK3,nil)
    | nil != sK2 ),
    inference(definition_unfolding,[],[f164,f167,f168]) ).

fof(f221,plain,
    ssList(sK3),
    inference(definition_unfolding,[],[f156,f168]) ).

fof(f222,plain,
    ssList(sK2),
    inference(definition_unfolding,[],[f155,f167]) ).

fof(f226,plain,
    ! [X2,X1] :
      ( ~ ssList(app(X2,X1))
      | ~ ssList(X1)
      | ~ ssList(X2)
      | rearsegP(app(X2,X1),X1) ),
    inference(equality_resolution,[],[f190]) ).

fof(f228,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,[],[f201]) ).

tcf(c_50,negated_conjecture,
    ( ( nil = sK3 )
    | ~ segmentP(sK3,sK2)
    | ~ neq(sK2,nil) ),
    inference(cnf_transformation,[],[f218]) ).

tcf(c_51,negated_conjecture,
    ( neq(sK3,nil)
    | ( nil != sK2 ) ),
    inference(cnf_transformation,[],[f219]) ).

tcf(c_53,negated_conjecture,
    ( neq(sK2,nil)
    | ( nil = sK3 ) ),
    inference(cnf_transformation,[],[f162]) ).

tcf(c_54,negated_conjecture,
    ( rearsegP(sK3,sK2)
    | ( nil = sK3 ) ),
    inference(cnf_transformation,[],[f161]) ).

tcf(c_55,negated_conjecture,
    ( neq(sK2,nil)
    | ( nil = sK2 ) ),
    inference(cnf_transformation,[],[f160]) ).

tcf(c_56,negated_conjecture,
    ( rearsegP(sK3,sK2)
    | ( nil = sK2 ) ),
    inference(cnf_transformation,[],[f159]) ).

tcf(c_59,negated_conjecture,
    ssList(sK3),
    inference(cnf_transformation,[],[f221]) ).

tcf(c_60,negated_conjecture,
    ssList(sK2),
    inference(cnf_transformation,[],[f222]) ).

tcf(c_65,plain,
    ! [X0: $i] :
      ( ~ ssList(X0)
      | ~ neq(X0,X0) ),
    inference(cnf_transformation,[],[f231]) ).

tcf(c_72,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f180]) ).

tcf(c_78,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ rearsegP(X1,X0)
      | ~ rearsegP(X0,X1) ),
    inference(cnf_transformation,[],[f186]) ).

tcf(c_80,plain,
    ! [X0: $i,X1: $i] :
      ( rearsegP(app(X0,X1),X1)
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ ssList(app(X0,X1)) ),
    inference(cnf_transformation,[],[f226]) ).

tcf(c_81,plain,
    ! [X0: $i,X1: $i] :
      ( ssList(sK8(X0,X1))
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ rearsegP(X0,X1) ),
    inference(cnf_transformation,[],[f189]) ).

tcf(c_82,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(sK8(X0,X1),X1) = X0 )
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ rearsegP(X0,X1) ),
    inference(cnf_transformation,[],[f188]) ).

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,[],[f228]) ).

tcf(c_100,plain,
    ! [X0: $i] :
      ( ( app(X0,nil) = X0 )
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f208]) ).

tcf(c_108,plain,
    ! [X0: $i,X1: $i] :
      ( ssList(app(X0,X1))
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f216]) ).

tcf(c_147,plain,
    ! [X0: $i,X1: $i] :
      ( rearsegP(app(X0,X1),X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(global_subsumption_just,[status(thm)],[c_80,c_108,c_80]) ).

tcf(c_882,plain,
    ! [X0: $i] :
      ( ~ ssList(X0)
      | ( nil != sK2 )
      | ( X0 != sK3 )
      | ( X0 != nil ) ),
    inference(resolution_lifted,[status(thm)],[c_51,c_65]) ).

tcf(c_883,plain,
    ( ~ ssList(nil)
    | ( nil != sK2 )
    | ( nil != sK3 ) ),
    inference(unflattening,[status(thm)],[c_882]) ).

tcf(c_914,plain,
    ! [X0: $i] :
      ( ( nil = sK3 )
      | ~ ssList(X0)
      | ( X0 != sK2 )
      | ( X0 != nil ) ),
    inference(resolution_lifted,[status(thm)],[c_53,c_65]) ).

tcf(c_915,plain,
    ( ( nil = sK3 )
    | ~ ssList(nil)
    | ( nil != sK2 ) ),
    inference(unflattening,[status(thm)],[c_914]) ).

tcf(c_916,plain,
    nil != sK2,
    inference(global_subsumption_just,[status(thm)],[c_915,c_72,c_883,c_915]) ).

tcf(c_931,negated_conjecture,
    rearsegP(sK3,sK2),
    inference(global_subsumption_just,[status(thm)],[c_54,c_56,c_916]) ).

tcf(c_2135,plain,
    ! [X0: $i] : X0 = X0,
    theory(equality) ).

tcf(c_2139,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( rearsegP(X0,X2)
      | ~ rearsegP(X1,X3)
      | ( X2 != X3 )
      | ( X0 != X1 ) ),
    theory(equality) ).

tcf(c_2884,plain,
    app(sK3,nil) = sK3,
    inference(superposition,[status(thm)],[c_59,c_100]) ).

tcf(c_2885,plain,
    app(sK2,nil) = sK2,
    inference(superposition,[status(thm)],[c_60,c_100]) ).

tcf(c_2937,plain,
    ( rearsegP(sK2,nil)
    | ~ ssList(sK2)
    | ~ ssList(nil) ),
    inference(superposition,[status(thm)],[c_2885,c_147]) ).

tcf(c_2942,plain,
    rearsegP(sK2,nil),
    inference(forward_subsumption_resolution,[status(thm)],[c_2937,c_60,c_72]) ).

tcf(c_3403,plain,
    ( ( nil = sK2 )
    | ~ ssList(sK2)
    | ~ ssList(nil)
    | ~ rearsegP(sK2,nil)
    | ~ rearsegP(nil,sK2) ),
    inference(instantiation,[status(thm)],[c_78]) ).

tcf(c_3516,plain,
    ( ( app(sK8(sK3,sK2),sK2) = sK3 )
    | ~ ssList(sK2)
    | ~ ssList(sK3) ),
    inference(superposition,[status(thm)],[c_931,c_82]) ).

tcf(c_3538,plain,
    app(sK8(sK3,sK2),sK2) = sK3,
    inference(forward_subsumption_resolution,[status(thm)],[c_3516,c_60,c_59]) ).

tcf(c_3566,plain,
    ! [X0: $i,X1: $i] :
      ( rearsegP(nil,sK2)
      | ~ rearsegP(X0,X1)
      | ( sK2 != X1 )
      | ( nil != X0 ) ),
    inference(instantiation,[status(thm)],[c_2139]) ).

tcf(c_5016,plain,
    ! [X0: $i] :
      ( segmentP(app(sK3,X0),sK2)
      | ~ ssList(sK2)
      | ~ ssList(X0)
      | ~ ssList(sK8(sK3,sK2))
      | ~ ssList(app(app(sK8(sK3,sK2),sK2),X0)) ),
    inference(superposition,[status(thm)],[c_3538,c_90]) ).

tcf(c_5075,plain,
    ! [X0: $i] :
      ( segmentP(app(sK3,X0),sK2)
      | ~ ssList(sK2)
      | ~ ssList(X0)
      | ~ ssList(sK8(sK3,sK2))
      | ~ ssList(app(sK3,X0)) ),
    inference(light_normalisation,[status(thm)],[c_5016,c_3538]) ).

tcf(c_5076,plain,
    ! [X0: $i] :
      ( segmentP(app(sK3,X0),sK2)
      | ~ ssList(X0)
      | ~ ssList(sK8(sK3,sK2))
      | ~ ssList(app(sK3,X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5075,c_60]) ).

tcf(c_6358,plain,
    ! [X0: $i] :
      ( rearsegP(nil,sK2)
      | ~ rearsegP(X0,sK2)
      | ( sK2 != sK2 )
      | ( nil != X0 ) ),
    inference(instantiation,[status(thm)],[c_3566]) ).

tcf(c_6359,plain,
    sK2 = sK2,
    inference(instantiation,[status(thm)],[c_2135]) ).

tcf(c_12909,plain,
    ( rearsegP(nil,sK2)
    | ~ rearsegP(sK3,sK2)
    | ( sK2 != sK2 )
    | ( nil != sK3 ) ),
    inference(instantiation,[status(thm)],[c_6358]) ).

tcf(c_13668,plain,
    ( segmentP(sK3,sK2)
    | ~ ssList(nil)
    | ~ ssList(sK8(sK3,sK2))
    | ~ ssList(app(sK3,nil)) ),
    inference(superposition,[status(thm)],[c_2884,c_5076]) ).

tcf(c_13672,plain,
    ( segmentP(sK3,sK2)
    | ~ ssList(sK3)
    | ~ ssList(nil)
    | ~ ssList(sK8(sK3,sK2)) ),
    inference(light_normalisation,[status(thm)],[c_13668,c_2884]) ).

tcf(c_13673,plain,
    ( segmentP(sK3,sK2)
    | ~ ssList(sK8(sK3,sK2)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_13672,c_59,c_72]) ).

tcf(c_14041,plain,
    ~ ssList(sK8(sK3,sK2)),
    inference(global_subsumption_just,[status(thm)],[c_13673,c_60,c_72,c_56,c_55,c_50,c_916,c_2942,c_3403,c_6359,c_12909,c_13673]) ).

tcf(c_14043,plain,
    ( ~ ssList(sK2)
    | ~ ssList(sK3)
    | ~ rearsegP(sK3,sK2) ),
    inference(superposition,[status(thm)],[c_81,c_14041]) ).

tcf(c_14044,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_14043,c_60,c_59,c_931]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWC108+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05  % Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/10.42  % Computer : n016.cluster.edu
% 0.15/10.42  % Model    : x86_64 x86_64
% 0.15/10.42  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/10.42  % Memory   : 8046.5625MB
% 0.15/10.42  % OS       : Linux 6.8.0-71-generic
% 0.15/10.42  % CPULimit : 300
% 0.15/10.42  % WCLimit  : 300
% 0.15/10.42  % DateTime : Thu Sep 24 16:30:54 UTC 2026
% 0.15/10.43  % CPUTime  : 
% 0.15/10.43  Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/10.49  Running first-order theorem proving
% 0.15/10.49  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
% 0.18/10.50  
% 0.18/10.50  % ======== iProver multi-core TPTP/SMT =========
% 0.18/10.50  
% 0.18/10.50  % Detected problem language: tptp
% 0.18/10.52  % Proving...
% 10.70/12.42  % SZS status Started for theBenchmark.p
% 10.70/12.42  % SZS status Theorem for theBenchmark.p
% 10.70/12.42  
% 10.70/12.42  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.70/12.42  
% 10.70/12.42  % ------  iProver source info
% 10.70/12.42  
% 10.70/12.42  % git: date: 2026-07-19 20:42:38 +0200
% 10.70/12.42  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.70/12.42  % git: non_committed_changes: false
% 10.70/12.42  
% 10.70/12.42  % ------ Parsing...
% 10.70/12.42  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 10.70/12.42  
% 10.70/12.42  % ------ 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  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e % 
% 10.70/12.42  
% 10.70/12.42  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 10.70/12.42  
% 10.70/12.42  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 10.70/12.42  % ------ Proving...
% 10.70/12.42  % ------ Problem Properties 
% 10.70/12.42  
% 10.70/12.42  % 
% 10.70/12.42  % clauses                               49
% 10.70/12.42  % conjectures                           4
% 10.70/12.42  % EPR                                   21
% 10.70/12.42  % Horn                                  46
% 10.70/12.42  % unary                                 11
% 10.70/12.42  % binary                                7
% 10.70/12.42  % lits                                  154
% 10.70/12.42  % lits eq                               33
% 10.70/12.42  % fd_pure                               0
% 10.70/12.42  % fd_pseudo                             0
% 10.70/12.42  % fd_cond                               6
% 10.70/12.42  % fd_pseudo_cond                        6
% 10.70/12.42  % AC symbols                            0
% 10.70/12.42  
% 10.70/12.42  % ------ Schedule dynamic 5 is on 
% 10.70/12.42  
% 10.70/12.42  % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.70/12.42  
% 10.70/12.42  
% 10.70/12.42  % ------ 
% 10.70/12.42  % Current options:
% 10.70/12.42  % ------ 
% 10.70/12.42  
% 10.70/12.42  
% 10.70/12.42  % 
% 10.70/12.42  
% 10.70/12.42  % ------ Proving...
% 10.70/12.42  % 
% 10.70/12.42  
% 10.70/12.42  % SZS status Theorem for theBenchmark.p
% 10.70/12.42  
% 10.70/12.42  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.70/12.43  
% 10.70/12.43  
%------------------------------------------------------------------------------